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.
Spherical harmonics, invariant theory and Maxwell's poles
Dowker, J S
2008-01-01
I discuss the relation between harmonic polynomials and invariant theory and show that homogeneous, harmonic polynomials correspond to ternary forms that are apolar to a base conic (the absolute). The calculation of Schlesinger that replaces such a form by a polarised binary form is reviewed. It is suggested that Sylvester's theorem on the uniqueness of Maxwell's pole expression for harmonics is renamed the Clebsch-Sylvester theorem. The relation between certain constructs in invariant theory and angular momentum theory is enlarged upon and I resurrect the Joos--Weinberg matrices. Hilbert's projection operators are considered and their generalisations by Story and Elliott are related to similar, more recent constructions in group theory and quantum mechanics, the ternary case being equivalent to SU(3).
Harmonic analysis and the theory of probability
Bochner, Salomon
2005-01-01
Nineteenth-century studies of harmonic analysis were closely linked with the work of Joseph Fourier on the theory of heat and with that of P. S. Laplace on probability. During the 1920s, the Fourier transform developed into one of the most effective tools of modern probabilistic research; conversely, the demands of the probability theory stimulated further research into harmonic analysis.Mathematician Salomon Bochner wrote a pair of landmark books on the subject in the 1930s and 40s. In this volume, originally published in 1955, he adopts a more probabilistic view and emphasizes stochastic pro
Killing vector fields and harmonic superfield theories
Groeger, Josua, E-mail: groegerj@mathematik.hu-berlin.de [Humboldt-Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, 12489 Berlin (Germany)
2014-09-15
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Theory of harmonic dissipation in disordered solids
Damart, T.; Tanguy, A.; Rodney, D.
2017-02-01
Mechanical spectroscopy, i.e., cyclic deformations at varying frequencies, is used theoretically and numerically to compute dissipation in model glasses. From a normal mode analysis, we show that in the high-frequency terahertz regime where dissipation is harmonic, the quality factor (or loss angle) can be expressed analytically. This expression is validated through nonequilibrium molecular dynamics simulations applied to a model of amorphous silica (SiO2). Dissipation is shown to arise from nonaffine relaxations triggered by the applied strain through the excitation of vibrational eigenmodes that act as damped harmonic oscillators. We discuss an asymmetry vector field, which encodes the information about the structural origin of dissipation computed by mechanical spectroscopy. In the particular case of silica, we find that the motion of oxygen atoms, which induce a deformation of the Si-O-Si bonds, is the main contributor to harmonic energy dissipation.
Theory of high gain harmonic generation an analytical estimate
Yu Li Hua
2002-01-01
We discuss the theory of the High Gain Harmonic Generation (HGHG). First, we describe an analytical estimate using the HGHG parameters in the DUVFEL project at BNL as an example. We show that the effective energy spread in a chicane dispersion section is found to be very small, and the effect of finite emittance can be neglected during the calculation of coherent harmonic generation. Then we discuss some issues such as the intensity stability, and how to use HGHG to obtain information about local energy spread. We compare these issues with recent experimental results in the infrared. We discuss some of the key issues in the cascading HGHG scheme and its possible limitations.
Imaging theory of nonlinear second harmonic and third harmonic generations in confocal microscopy
TANG; Zhilie; XING; Da; LIU; Songhao
2004-01-01
The imaging theory of nonlinear second harmonic generation (SHG) and third harmonic generation (THG) in confocal microscopy is presented in this paper. The nonlinear effect of SHG and THG on the imaging properties of confocal microscopy has been analyzed in detail by the imaging theory. It is proved that the imaging process of SHG and THG in confocal microscopy, which is different from conventional coherent imaging or incoherent imaging, can be divided into two different processes of coherent imaging. The three-dimensional point spread functions (3D-PSF) of SHG and THG confocal microscopy are derived based on the nonlinear principles of SHG and THG. The imaging properties of SHG and THG confocal microscopy are discussed in detail according to its 3D-PSF. It is shown that the resolution of SHG and THG confocal microscopy is higher than that of single-and two-photon confocal microscopy.
Dynamical mean field theory of optical third harmonic generation
Jafari, S. A.; Tohyama, T.; Maekawa, S.
2006-01-01
We formulate the third harmonic generation (THG) within the dynamical mean field theory (DMFT) approximation of the Hubbard model. In the limit of large dimensions, where DMFT becomes exact, the vertex corrections to current vertices are identically zero, and hence the calculation of the THG spectrum reduces to a time-ordered convolution, followd by appropriate analytic continuuation. We present the typical THG spectrum of the Hubbard model obtained by this method. Within our DMFT calculation...
Harmonic Oscillators as Bridges between Theories: Einstein, Dirac, and Feynman
Kim, Y S; Noz, Marilyn E.
2004-01-01
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement, decoherence, and Feynman's rest of the universe. In addition, it is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called $SL(2,c)$...
Effective field theory in the harmonic-oscillator basis
Binder, S; Hagen, G; Papenbrock, T; Wendt, K A
2015-01-01
We develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. We derive useful analytical expressions for an exact and efficient calculation of matrix elements. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Many-body coupled-cluster calculations of nuclei up to 132Sn exhibit a fast convergence of ground-state energies and radii in feasible model spaces.
Harmonic Chain with Velocity Flips: Thermalization and Kinetic Theory
Lukkarinen, Jani; Marcozzi, Matteo; Nota, Alessia
2016-12-01
We consider the detailed structure of correlations in harmonic chains with pinning and a bulk velocity flip noise during the heat relaxation phase which occurs on diffusive time scales, for t=O(L^2) where L is the chain length. It has been shown earlier that for non-degenerate harmonic interactions these systems thermalize, and the dominant part of the correlations is given by local thermal equilibrium determined by a temperature profile which satisfies a linear heat equation. Here we are concerned with two new aspects about the thermalization process: the first order corrections in 1 / L to the local equilibrium correlations and the applicability of kinetic theory to study the relaxation process. Employing previously derived explicit uniform estimates for the temperature profile, we first derive an explicit form for the first order corrections to the particle position-momentum correlations. By suitably revising the definition of the Wigner transform and the kinetic scaling limit we derive a phonon Boltzmann equation whose predictions agree with the explicit computation. Comparing the two results, the corrections can be understood as arising from two different sources: a current-related term and a correction to the position-position correlations related to spatial changes in the phonon eigenbasis.
Effective field theory in the harmonic oscillator basis
Binder, S.; Ekström, A.; Hagen, G.; Papenbrock, T.; Wendt, K. A.
2016-04-01
We develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.
Squeezed light from second-harmonic generation: experiment versus theory.
Ralph, T C; Taubman, M S; White, A G; McClelland, D E; Bachor, H A
1995-06-01
We report excellent quantitative agreement between theoretical predictions and experimental observation of squeezing from a singly resonant second-harmonic-generating crystal. Limitations in the noise suppression imposed by the pump laser are explicitly modeled and confirmed by our measurements.
Loghmani, Nick Mehrdad
2011-01-01
Harmonic theory provides a mathematical framework to describe the structure, behavior, evolution and emergence of harmonic systems. A harmonic system is context aware, contains elements that manifest characteristics either collaboratively or independently according to system's expression and can interact with its environment. This theory provides a fresh way to analyze emergence and collaboration of "ad-hoc" and complex systems.
Atomic harmonic generation in time-dependent R-matrix theory
Brown, A. C.; Robinson, D. J.; van der Hart, H. W.
2012-11-01
We have developed the capability to determine accurate harmonic spectra for multielectron atoms within time-dependent R-matrix (TDRM) theory. Harmonic spectra can be calculated using the expectation value of the dipole length, velocity, or acceleration operator. We assess the calculation of the harmonic spectrum from He irradiated by 390-nm laser light with intensities up to 4×1014 W cm-2 using each form, including the influence of the multielectron basis used in the TDRM code. The spectra are consistent between the different forms, although the dipole acceleration calculation breaks down at lower harmonics. The results obtained from TDRM theory are compared with results from the helium code, finding good quantitative agreement between the methods. We find that bases which include pseudostates give the best comparison with the helium code, but models comprising only physical orbitals also produce accurate results.
Atomic harmonic generation in time-dependent R-matrix theory
Brown, A C; van der Hart, H W
2012-01-01
We have developed the capability to determine accurate harmonic spectra for multielectron atoms within time-dependent R-matrix (TDRM) theory. Harmonic spectra can be calculated using the expectation value of the dipole length, velocity or acceleration operator. We assess the calculation of the harmonic spectrum from He irradiated by 390 nm laser light with intensities up to 4 x 10(14) W cm(-2) using each form, including the influence of the multielectron basis used in the TDRM code. The spectra are consistent between the different forms, although the dipole acceleration calculation breaks down at lower harmonics. The results obtained from TDRM theory are compared with results from the HELIUM code finding good quantitative agreement between the methods. We find that bases which include pseudostates give the best comparison with the HELIUM code, but models comprising only physical orbitals also produce accurate results.
Harmonic Maps to Buildings and Singular Perturbation Theory
Katzarkov, Ludmil; Pandit, Pranav; Simpson, Carlos
2013-01-01
The notion of a universal building associated with a point in the Hitchin base is introduced. This is a building equipped with a harmonic map from a Riemann surface that is initial among harmonic maps which induce the given cameral cover of the Riemann surface. In the rank one case, the universal building is the leaf space of the quadratic differential defining the point in the Hitchin base. The main conjectures of this paper are: (1) the universal building always exists; (2) the harmonic map to the universal building controls the asymptotics of the Riemann-Hilbert correspondence and the non-abelian Hodge correspondence; (3) the singularities of the universal building give rise to Spectral Networks; and (4) the universal building encodes the data of a 3d Calabi-Yau category whose space of stability conditions has a connected component that contains the Hitchin base. The main theorem establishes the existence of the universal building, conjecture (3), as well as the Riemann-Hilbert part of conjecture (2), in t...
NEWTONIAN EQUATIONS OF MOTION AND HARMONIC CONDITIONS IN THE THEORY OF GRAVITATION,
The relation between Newtonian equations of motion and harmonic conditions in Einstein’s theory of gravitation is examined. Assuming that a metric...tensor can be represented in the form of a power series, it is proved that in order to obtain Newtonian equations of motion, it is necessary to use...harmonic coordinate conditions of zero order. It is also proved that in Infeld’s method for deriving Newtonian equations of motion from the equations
Resonance energy transfer: The unified theory via vector spherical harmonics.
Grinter, Roger; Jones, Garth A
2016-08-21
In this work, we derive the well-established expression for the quantum amplitude associated with the resonance energy transfer (RET) process between a pair of molecules that are beyond wavefunction overlap. The novelty of this work is that the field of the mediating photon is described in terms of a spherical wave rather than a plane wave. The angular components of the field are constructed in terms of vector spherical harmonics while Hankel functions are used to define the radial component. This approach alleviates the problem of having to select physically correct solution from non-physical solutions, which seems to be inherent in plane wave derivations. The spherical coordinate system allows one to easily decompose the photon's fields into longitudinal and transverse components and offers a natural way to analyse near-, intermediate-, and far-zone RET within the context of the relative orientation of the transition dipole moments for the two molecules.
Off- and on-shell harmonic superspaces for 6D SYM theories
Ivanov, Evgeny
2016-01-01
It is a brief account of the harmonic superspace formulations of {\\cal N}=(1,0) and {\\cal N}=(1,1) SYM theories in six dimensions. The on-shell {\\cal N}=(1,1) harmonic superspace is argued to provide an efficient tool of constructing candidate counterterms and other invariants of {\\cal N}=(1,1) SYM. It allows one, e.g., to find out an essential difference between the single- and double-trace dimension d=10 invariants, which could be capable to explain the absence of the three-loop double-trace (non-planar) counterterms in this theory. The defining superspace constraints of {\\cal N}=(1,1) SYM are solved in terms of {\\cal N}=(1,0) harmonic superfields.
Models of soft rotators and the theory of a harmonic rotator
Zakir, Zahid
2012-01-01
The states of a planar oscillator are separated to a vibrational mode, containing a zero-point energy, and a rotational mode without the zero-point energy, but having a conserved angular momentum. On the basis of the analysis of properties of models of rigid and semirigid rotators, the theory of soft rotators is formulated where the harmonic attractive force is balanced only by the centrifugal force. As examples a Coulomb rotator (the Bohr model) and a magneto-harmonic rotator (the Fock-Landau levels) are considered. Disappearance of the radial speed in the model of a magneto-harmonic rotator is taken as a defining property of a pure rotational motion in the harmonic potential. After the exception of energies of the magnetic and spin decompositions, specific to magnetic fields, one turns to a simple and general model of a planar harmonic rotator (circular oscillator without radial speed) where kinetic energy is reduced to the purely rotational energy. Energy levels of the harmonic rotator have the same freque...
Quantum Electrodynamics Basis of Classical-Field High-Harmonic Generation Theory
王兵兵; 高靓辉; 傅盘铭; 郭东升; R. R. Freeman
2001-01-01
From the nonperturbative quantum electrodynamics theory, we derive the Landau-Dykhne formula which represents the quantum-mechanical formulation of the three-step model. These studies provide a basis for the classical-field approaches to high-order harmonic generation and justify some assumptions used in classical-field modelling.
Müller, H W; Wagner, C; Albers, J; Knorr, K
1996-01-01
We present an analytical stability theory for the onset of the Faraday instability, applying over a wide frequency range between shallow water gravity and deep water capillary waves. For sufficiently thin fluid layers the surface is predicted to occur in harmonic rather than subharmonic resonance with the forcing. An experimental confirmation of this result is given. PACS: 47.20.Ma, 47.20.Gv, 47.15.Cb
Theory of backward second-harmonic localization in nonlinear left-handed media
Centeno, Emmanuel; Ciracì, Cristian
2008-12-01
Recent research on photonic crystals possessing a quadratic nonlinear response has revealed a second-harmonic light localization phenomenon that originates from an all-angle phase matching between counterpropagating Bloch modes at the fundamental and double frequencies [E. Centeno , Phys. Rev. Lett. 98, 263903 (2007)]. In this paper, we develop an electromagnetic theory describing the nature of this parametric light localization, which appears in properly design metamaterials or photonic crystals exhibiting nonlinear left-handed behaviors. We demonstrate that interferences between converging phase-matched and diverging anti-phase-matched waves create a localized second-harmonic wave focused on the pump emitter on the scale of half the wavelength. This light trapping is accompanied by the enhancement of the second-harmonic intensity, which linearly increases with the size of the two-dimensional domain. We finally show that the second-harmonic localization effect previously proposed for GaN photonic crystals can also be obtained with LiNbO3 material.
Analysis IV integration and spectral theory, harmonic analysis, the garden of modular delights
Godement, Roger
2015-01-01
Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2). As in volumes I to III, the inimitable style of the author is recognizable here too, not only because of his refusal to write in the compact style used nowadays in many textbooks. The first part (Integration), a wise combination of mathematics said to be modern and classical, is universally useful whereas the second part leads the reader towards a very active and specialized field of research, with possibly broad generalizations.
Deformed Harmonic Oscillators for Metal Clusters and Balian-Bloch Theory
Bonatsos, D; Raychev, P P; Terziev, P A; Bonatsos, Dennis
2003-01-01
The predictions for the shell structure of metal clusters of the three-dimensional q-deformed harmonic oscillator (3D q-HO), utilizing techniques of quantum groups and having the symmetry Uq(3)$\\supset$SOq(3), are compared to the restrictions imposed by the periodic orbit theory of Balian and Bloch, of electrons moving in a spherical cavity. It is shown that agreement between the predictions of the two models is established through the introduction of an additional term to the Hamiltonian of the 3D q-HO, which does not influence the predictions for supershells. This term preserves the Uq(3)$\\supset$SOq(3) symmetry, while in addition it can be derived through a variational procedure, analogous to the one leading from the usual harmonic oscillator to the Morse oscillator by introducing the concept of the Variable Frequency Oscillator (VFO).
Strong-field-approximation theory of high-order harmonic generation by polyatomic molecules
Odžak, S.; Hasović, E.; Milošević, D. B.
2016-04-01
A theory of high-order harmonic generation by arbitrary polyatomic molecules is introduced. A polyatomic molecule is modeled by an (N +1 ) -particle system, which consists of N heavy atomic (ionic) centers and an electron. After the separation of the center-of-mass coordinate, the dynamics of this system is reduced to the relative electronic and nuclear coordinates. Various versions (with or without the dressing of the initial and/or final molecular state) of the molecular strong-field approximation are introduced. For neutral polyatomic molecules the derived expression for the T -matrix element takes a simple form. The interference minima in the harmonic spectrum are explained as a multiple-slit type of interference. This is illustrated by numerical examples for the ozone (O3) and carbon dioxide (CO2) molecules.
Gorbach, Andrey V
2016-01-01
We present perturbation theory for analysis of generic third-order nonlinear processes in graphene integrated photonic structures. Optical response of graphene is treated as the nonlinear boundary condition in Maxwell equations. The derived models are applied for analysis of third harmonic generation in a graphene coated dielectric micro-fibre. The efficiency of up to few percent is predicted when using sub-picosecond pump pulses with energies of the order of $0.1$nJ in a sub-millimeter long fibre, when operating near the resonance of the graphene nonlinear conductivity $\\hbar\\omega=(2/3)E_F$.
Deformed Relativistic Hartree Theory in Coordinate Space and in Harmonic Oscillator Basis
ZHOU Shan-Gui; MENG Jie; Shuhei YAMAJI; YANG Si-Chun
2000-01-01
The deformed relativistic Hartree theory (DRH) is solved both in coordinate space (DRH-c) and in harmonic oscillator basis (DRH-o). Results obtained from these two methods are compared in details. The DRH-c and DRH-o calculations give similar total binding energies, deformation, level structures and radii for nitrogen iso topes, while their descriptions on the density distributions for drip-line nuclei are very different. The large spatiai istributions of nucleon densities, which is crucial to understand a weakly bound system, can only be obtained by DRH-c calculations. This implies that the DRH theory should be solved in coordinate space in order to describe uclei close to the drip line.
Peng, Fang Zheng [Tennessee Univ., Knoxville, TN (United States); Lai, Jih-Sheng [Oak Ridge National Lab., TN (United States)
1996-10-01
A generalized theory of instantaneous reactive power for three-phase power systems is proposed in this paper. This theory gives a generalized definition of instantaneous reactive power, which is valid for sinusoidal or nonsinusoidal, balanced or unbalanced, three- phase power systems with or without zero-sequence currents and/or voltages. The properties and physical meanings of the newly defined instantaneous reactive power are discussed in detail. With this new reactive power theory, it is very easy to calculate and decompose all components, such as fundamental active/reactive power and current, harmonic current, etc. Reactive power and/or harmonic compensation systems for a three-phase distorted power system with and without zero-sequence components in the source voltage and/or load current are then used as examples to demonstrate the measurement, decomposition, and compensation of reactive power and harmonics.
Purity and decoherence in the theory of a damped harmonic oscillator
Isar, A.; Sandulescu, A.; Scheid, W.
1999-12-01
For the generalized master equations derived by Karrlein and Grabert for the microscopic model of a damped harmonic oscillator, the conditions for purity of states are written, in particular for different initial conditions and different types of damping, including Ohmic, Drude, and weak coupling cases, and the Agarwal and Weidlich-Haake models. It is shown that the states which remain pure are the squeezed states with variances that are constant in time. For pure states, generalized nonlinear Schrödinger-type equations corresponding to these master equations are also obtained. Then the condition for purity of states of a damped harmonic oscillator is considered in the framework of Lindblad theory for open quantum systems. For a special choice of the environment coefficients, correlated coherent states with constant variances and covariance are shown to be the only states which remain pure all the time during the evolution of the considered system. In Karrlein-Grabert and Lindblad models, as well as in the particular models considered, expressions for the rate of entropy production are written, and it is shown that state which preserve their purity in time are also states which minimize entropy production and, therefore, are the most stable state under evolution in the presence of the environment, and play an important role in the description of decoherence phenomenon.
Chan, Kitty S; Gross, Alden L; Pezzin, Liliana E; Brandt, Jason; Kasper, Judith D
2015-12-01
To harmonize measures of cognitive performance using item response theory (IRT) across two international aging studies. Data for persons ≥65 years from the Health and Retirement Study (HRS, N = 9,471) and the English Longitudinal Study of Aging (ELSA, N = 5,444). Cognitive performance measures varied (HRS fielded 25, ELSA 13); 9 were in common. Measurement precision was examined for IRT scores based on (a) common items, (b) common items adjusted for differential item functioning (DIF), and (c) DIF-adjusted all items. Three common items (day of date, immediate word recall, and delayed word recall) demonstrated DIF by survey. Adding survey-specific items improved precision but mainly for HRS respondents at lower cognitive levels. IRT offers a feasible strategy for harmonizing cognitive performance measures across other surveys and for other multi-item constructs of interest in studies of aging. Practical implications depend on sample distribution and the difficulty mix of in-common and survey-specific items. © The Author(s) 2015.
Wang, Yi-Ze; Li, Feng-Ming
2016-08-01
Structures under parametric load can be induced to the parametric instability in which the excitation frequency is located the instability region. In the present work, the parametric instability of double-walled carbon nanotubes is studied. The axial harmonic excitation is considered and the nonlocal continuum theory is applied. The critical equation is derived as the Mathieu form by the Galerkin's theory and the instability condition is presented with the Bolotin's method. Numerical calculations are performed and it can be seen that the van der Waals interaction can enhance the stability of double-walled nanotubes under the parametric excitation. The parametric instability becomes more obvious with the matrix stiffness decreasing and small scale coefficient increasing. The parametric instability is going to be more significant for higher mode numbers. For the nanosystem with the soft matrix and higher mode number, the small scale coefficient and the ratio of the length to the diameter have obvious influences on the starting point of the instability region.
Density-functional theory of strongly correlated Fermi gases in elongated harmonic traps
Xianlong, Gao; Polini, Marco; Asgari, Reza; Tosi, M. P.
2006-03-01
Two-component Fermi gases with tunable repulsive or attractive interactions inside quasi-one-dimensional (Q1D) harmonic wells may soon become the cleanest laboratory realizations of strongly correlated Luttiger and Luther-Emery liquids under confinement. We present a microscopic Kohn-Sham density-functional theory of these systems, with specific attention to a gas on the approach to a confinement-induced Feshbach resonance. The theory employs the one-dimensional Gaudin-Yang model as the reference system and transfers the appropriate Q1D ground-state correlations to the confined inhomogeneous gas via a suitable local-density approximation to the exchange and correlation energy functional. Quantitative understanding of the role of the interactions in the bulk shell structure of the axial density profile is thereby achieved. While repulsive intercomponent interactions depress the amplitude of the shell structure of the noninteracting gas, attractive interactions stabilize atomic-density waves through spin pairing. These should be clearly observable in atomic clouds containing of the order of up to 100 atoms.
Theory of nonlinear harmonic generation in free-electron lasers with helical wigglers
Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.
2007-05-15
CoherentHarmonicGeneration (CHG), and in particularNonlinearHarmonicGeneration (NHG), is of importance for both short wavelength Free-Electron Lasers (FELs), in relation with the achievement of shorter wavelengths with a fixed electron-beam energy, and high-average power FEL resonators, in relation with destructive effects of higher harmonics radiation on mirrors. In this paper we present a treatment of NHG from helical wigglers with particular emphasis on the second harmonic. Our study is based on an exact analytical solution of Maxwell's equations, derived with the help of a Green's function method. In particular, we demonstrate that nonlinear harmonic generation (NHG) fromhelicalwigglers vanishes on axis. Our conclusion is in open contrast with results in literature, that include a kinematical mistake in the description of the electron motion. (orig.)
Arfaoui, [No Value; Bermudez, [No Value; Bottari, G; De Nadai, C; Jalkanen, JP; Kajzar, F; Leigh, DA; Lubomska, M; Mendoza, SM; Niziol, J; Rudolf, P; Zerbetto, F; Arfaoui, Imad; Bermúdez, Verónica; Jalkanen, Jukka-Pekka
2006-01-01
Surface enhanced second harmonic generation (SE SHG) experiments on molecular structures, macrocycles, catenanes, and rotaxanes, deposited as monolayers and multilayers by vacuum sublimation on silver, are reported. The measurements show that the molecules form ordered thin films, where the highest
Optimum Design of Passive Harmonic Filter by Using Game Theory Concepts
Ali Dastfan
2014-03-01
Passive harmonic Filters (PHF are the simplest, cheapest, and the most effective way to reduce harmonics of the voltage and current waveforms. In designing the PHF, the main goals are to minimize the cost of the filters and reduce the total harmonic distortion of currents and voltages at the Point of Common Coupling (PCC to the acceptable range which are defined by standards. In this paper, an important multiobjective optimization approaches namely Strength Pareto Evolutionary Algorithm (SPEA has been used for tuning the PHF parameters. This approach is applied to IEEE 13 node test system with a six-pulse converter as a harmonic source. Another approach, called Nash GA, is based on non-cooperative game gives an optimal point known as Nash equilibrium. This approach is also simulated on IEEE test system. The result of optimization shows lower THD and cost for optimal PHFs in comparison with the conventionally designed one. To make comparison, some results of these methods are compared and discussed.
Isar, Aurelian
1995-01-01
The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.
High-order harmonic generation driven by metal nanotip photoemission: theory and simulations
Ciappina, M F; Lewenstein, M; Krüger, M; Hommelhoff, P
2014-01-01
We present theoretical predictions of high-order harmonic generation (HHG) resulting from the interaction of short femtosecond laser pulses with metal nanotips. It has been demonstrated that high energy electrons can be generated using nanotips as sources; furthermore the recollision mechanism has been proven to be the physical mechanism behind this photoemission. If recollision exists, it should be possible to convert the laser-gained energy by the electron in the continuum in a high energy photon. Consequently the emission of harmonic radiation appears to be viable, although it has not been experimentally demonstrated hitherto. We employ a quantum mechanical time dependent approach to model the electron dipole moment including both the laser experimental conditions and the bulk matter properties. The use of metal tips shall pave a new way of generating coherent XUV light with a femtosecond laser field.
Hassouneh, O.; Brown, A. C.; van der Hart, H. W.
2014-10-01
We demonstrate the capability of ab initio time-dependent R -matrix theory to obtain accurate harmonic generation spectra of noble-gas atoms at near-IR wavelengths between 1200 and 1800 nm and peak intensities up to 1.8 × 10 14 W /cm 2. To accommodate the excursion length of the ejected electron, we use an angular-momentum expansion up to Lmax=279 . The harmonic spectra show evidence of atomic structure through the presence of a Cooper minimum in harmonic generation for Kr, and of multielectron interaction through the giant resonance for Xe. The theoretical spectra agree well with those obtained experimentally.
Hassouneh, O; van der Hart, H W
2014-01-01
We demonstrate the capability of ab-initio time-dependent R-matrix theory to obtain accurate harmonic generation spectra of noble-gas atoms at Near-IR wavelengths between 1200 and 1800 nm and peak intensities up to 1.8 X 10(14) W/cm(2) . To accommodate the excursion length of the ejected electron, we use an angular-momentum expansion up to Lmax = 279. The harmonic spectra show evidence of atomic structure through the presence of a Cooper minimum in harmonic generation for Kr, and of multielectron interaction through the giant resonance for Xe. The theoretical spectra agree well with those obtained experimentally.
Lee, J. J.
2016-01-01
Full Text Available Here we provide a description of the IRT estimation method known as Normal Ogive Harmonic Analysis Robust Method (NOHARM. Although in some ways this method has been superseded by new computer programs that also adopt a specifically factor-analytic approach, its fundamental principles remain useful in certain applications, which include calculating the residual covariance matrix and rescaling the distribution of the common factor (latent trait. These principles can be applied to parameter estimates obtained by any method.
Harmonic Gauss maps and self-dual equations in string theory
Parthasarathy, R; Parthasarathy, R; Viswanathan, K S
1994-01-01
The string world sheet, regarded as Riemann surface, in background R^3 and R^4 is described by the generalised Gauss map. When the Gauss map is harmonic or equivalently for surfaces of constant mean scalar curvature, we obtain an Abelian self-dual system, using SO(3) and SO(4) gauge fields constructed in our earlier studies. This compliments our earlier result that h\\surd g\\ =\\ 1 surfaces exhibit Virasaro symmetry. The self-dual system so obtained is compared with self-dual Chern-Simons system and a generalized Liouville equation involving extrinsic geometry is obtained. \\vspace{0.2cm} The world sheet in background R^n, \\ n>4 is described by the generalized Gauss map. It is first shown that when the Gauss map is harmonic, the scalar mean curvature is constant. SO(n) gauge fields are constructed from the geometry of the surface and expressed in terms of the Gauss map. It is shown that the harmonic map satisfies a non-Abelian self-dual system of equations for the gauge group SO(2)\\times SO(n-2).
Sly, Krystal L; Conboy, John C
2017-06-01
A novel application of second harmonic correlation spectroscopy (SHCS) for the direct determination of molecular adsorption and desorption kinetics to a surface is discussed in detail. The surface-specific nature of second harmonic generation (SHG) provides an efficient means to determine the kinetic rates of adsorption and desorption of molecular species to an interface without interference from bulk diffusion, which is a significant limitation of fluorescence correlation spectroscopy (FCS). The underlying principles of SHCS for the determination of surface binding kinetics are presented, including the role of optical coherence and optical heterodyne mixing. These properties of SHCS are extremely advantageous and lead to an increase in the signal-to-noise (S/N) of the correlation data, increasing the sensitivity of the technique. The influence of experimental parameters, including the uniformity of the TEM00 laser beam, the overall photon flux, and collection time are also discussed, and are shown to significantly affect the S/N of the correlation data. Second harmonic correlation spectroscopy is a powerful, surface-specific, and label-free alternative to other correlation spectroscopic methods for examining surface binding kinetics.
The Effects of Ambient Conditions on Helicopter Harmonic Noise Radiation: Theory and Experiment
Greenwood, Eric; Sim, Ben W.; Boyd, D. Douglas, Jr.
2016-01-01
The effects of ambient atmospheric conditions, air temperature and density, on rotor harmonic noise radiation are characterized using theoretical models and experimental measurements of helicopter noise collected at three different test sites at elevations ranging from sea level to 7000 ft above sea level. Significant changes in the thickness, loading, and blade-vortex interaction noise levels and radiation directions are observed across the different test sites for an AS350 helicopter flying at the same indicated airspeed and gross weight. However, the radiated noise is shown to scale with ambient pressure when the flight condition of the helicopter is defined in nondimensional terms. Although the effective tip Mach number is identified as the primary governing parameter for thickness noise, the nondimensional weight coefficient also impacts lower harmonic loading noise levels, which contribute strongly to low frequency harmonic noise radiation both in and out of the plane of the horizon. Strategies for maintaining the same nondimensional rotor operating condition under different ambient conditions are developed using an analytical model of single main rotor helicopter trim and confirmed using a CAMRAD II model of the AS350 helicopter. The ability of the Fundamental Rotorcraft Acoustics Modeling from Experiments (FRAME) technique to generalize noise measurements made under one set of ambient conditions to make accurate noise predictions under other ambient conditions is also validated.
Li, Yuhui; Zhang, Shancai
2004-01-01
The high-gain harmonic generation (HGHG) free-electron laser (FEL) is an important candidate for a fourth-generation light source. Lots of theoretical work has been performed. Recently a further 1D theory about HGHG FEL has been developed. It considers the effects of different parameters for the whole process. An initial program based on this theory has been made. In this paper, a brief comparison of the results from this 1D program and from TDA (3D code) is discussed. It also analyses the parameters for Shanghai deep ultra violate free-electron laser source (SDUV-FEL), including electron beam energy spread, seed laser power, strength of dispersion section etc.
Theory of anomalous backscattering in second harmonic X-mode ECRH experiments
Gusakov, E. Z.; Popov, A. Yu. [Ioffe Institute, 26 Polytekhnicheskaya st., St. Petersburg 194021 (Russian Federation)
2016-08-15
A quantitative model explaining generation of the anomalous backscattering signal in the second harmonic X-mode electron cyclotron resonance heating (ECRH) experiments at TEXTOR tokamak as a secondary nonlinear process which accompanies a primary low-threshold parametric decay instability (PDI) leading to excitation of two—upper hybrid (UH)—plasmons trapped in plasma is developed. The primary absolute PDI enhancing the UH wave fluctuations from the thermal noise level is supposed to be saturated due to a cascade of secondary low-threshold decays of the daughter UH wave leading to excitation of the secondary UH waves down-shifted in frequency and the ion Bernstein wave. A set of equations describing the cascade is derived and solved numerically. The results of numerical modelling are shown to be in agreement with the analytical estimations of the growth rate of the initial and secondary parametric decays and the saturation level. The generation of backscattering signal is explained by coupling of the daughter UH waves. The fine details of the frequency spectrum of the anomalously reflected extraordinary wave and the absolute value of the observed backscattering signal in the second harmonic X-mode ECRH experiments at TEXTOR are reproduced.
Theory of anomalous backscattering in second harmonic X-mode ECRH experiments
Gusakov, E. Z.; Popov, A. Yu.
2016-08-01
A quantitative model explaining generation of the anomalous backscattering signal in the second harmonic X-mode electron cyclotron resonance heating (ECRH) experiments at TEXTOR tokamak as a secondary nonlinear process which accompanies a primary low-threshold parametric decay instability (PDI) leading to excitation of two—upper hybrid (UH)—plasmons trapped in plasma is developed. The primary absolute PDI enhancing the UH wave fluctuations from the thermal noise level is supposed to be saturated due to a cascade of secondary low-threshold decays of the daughter UH wave leading to excitation of the secondary UH waves down-shifted in frequency and the ion Bernstein wave. A set of equations describing the cascade is derived and solved numerically. The results of numerical modelling are shown to be in agreement with the analytical estimations of the growth rate of the initial and secondary parametric decays and the saturation level. The generation of backscattering signal is explained by coupling of the daughter UH waves. The fine details of the frequency spectrum of the anomalously reflected extraordinary wave and the absolute value of the observed backscattering signal in the second harmonic X-mode ECRH experiments at TEXTOR are reproduced.
An Application of the Harmonic Oscillator Model to Verify Dunning’s Theory of the Economic Growth
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.
Reaction-diffusion theory in the presence of an attractive harmonic potential
Spendier, K.; Sugaya, S.; Kenkre, V. M.
2013-12-01
Problems involving the capture of a moving entity by a trap occur in a variety of physical situations, the moving entity being an electron, an excitation, an atom, a molecule, a biological object such as a receptor cluster, a cell, or even an animal such as a mouse carrying an epidemic. Theoretical considerations have almost always assumed that the particle motion is translationally invariant. We study here the case when that assumption is relaxed, in that the particle is additionally subjected to a harmonic potential. This tethering to a center modifies the reaction-diffusion phenomenon. Using a Smoluchowski equation to describe the system, we carry out a study which is explicit in one dimension but can be easily extended for arbitrary dimensions. Interesting features emerge depending on the relative location of the trap, the attractive center, and the initial placement of the diffusing particle.
Conformal mapping of some non-harmonic functions in transport theory
Bazant, M Z
2003-01-01
Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace's equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection-diffusion equations for potential flows, and the Nernst-Planck equations for electrochemical transport in quasi-neutral or supporting electrolytes. Exact solutions for complicated geometries are obtained by conformal mapping to simple geometries in the usual way. Novel examples include nonlinear advection-diffusion layers around absorbing objects and concentration polarizations in electrochemical cells. Although some of these results could be obtained by other methods (e.g. Boussinesq's streamline coordinates), the present approach is based on a simple unifying principle with more general applicability. It reveals a basic geometrical equivalence of similarity sol...
Theory of enhanced second-harmonic generation in some artificial materials
HUANG Ji-ping
2007-01-01
We review the recent theoretical investigation on enhanced second-harmonic generation (SHG) in soft nonlinear optical materials based on ferrofluids, graded metallic films, and graded metal-dielectric films of anisotropic particles. The SHG of soft ferrofluid-based nonlinear optical materials possess magnetic-field controllabilities, i.e., magnetic-field-controllable anisotropy, red-shift and enhancement, which are caused to appear by the shift of a resonant plasmon frequency due to the formation of the chains of the coated nanoparticles. Both graded metallic films and graded metal-dielectric films of anisotropic particles can serve as a novel optical material for producing a broad structure in both the linear and SHG response and an enhancement in the SHG signal, due to the local field effects.
Accurate high-harmonic spectra from time-dependent two-particle reduced density matrix theory
Lackner, Fabian; Sato, Takeshi; Ishikawa, Kenichi L; Burgdörfer, Joachim
2016-01-01
The accurate description of the non-linear response of many-electron systems to strong-laser fields remains a major challenge. Methods that bypass the unfavorable exponential scaling with particle number are required to address larger systems. In this paper we present a fully three-dimensional implementation of the time-dependent two-particle reduced density matrix (TD-2RDM) method for many-electron atoms. We benchmark this approach by a comparison with multi-configurational time-dependent Hartree-Fock (MCTDHF) results for the harmonic spectra of beryllium and neon. We show that the TD-2RDM is very well-suited to describe the non-linear atomic response and to reveal the influence of electron-correlation effects.
周振功; 王彪
2001-01-01
The scattering of harmonic waves by two collinear symmetric cracks is studied using the non-local theory. A one-dimensional non-local kernel was used to replace a twodimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform was applied and a mixed boundary value problem was formulated. Then a set of triple integral equations was solved by using Schmidt's method. This method is more exact and more reasonable than Eringen' s for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non- local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of incident wave.
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
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Schröder, Markus; Schreiber, Michael; Kleinekathöfer, Ulrich
2007-03-21
Several techniques to solve a hierarchical set of equations of motion for propagating a reduced density matrix coupled to a thermal bath have been developed in recent years. This is either done using the path integral technique as in the original proposal by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1998)] or by the use of stochastic fields as done by Yan et al. [Chem. Phys. Lett. 395, 216 (2004)]. Based on the latter ansatz a compact derivation of the hierarchy using a decomposition of the spectral density function is given in the present contribution. The method is applied to calculate the time evolution of the reduced density matrix describing the motion in a harmonic, an anharmonic, and two coupled oscillators where each system is coupled to a thermal bath. Calculations to several orders in the system-bath coupling with two different truncations of the hierarchy are performed. The respective density matrices are used to calculate the time evolution of various system properties and the results are compared and discussed with a special focus on the convergence with respect to the truncation scheme applied.
Codis, Sandrine; Gavazzi, Raphaël; Pichon, Christophe; Gouin, Céline
2017-09-01
Aims: Gravitational lensing allows us to quantify the angular distribution of the convergence field around clusters of galaxies to constrain their connectivity to the cosmic web. We describe the corresponding theory in Lagrangian space in which analytical results can be obtained by identifying clusters to peaks in the initial field. Methods: We derived the three-point Gaussian statistics of a two-dimensional (2D) field and its first and second derivatives. The formalism allowed us to study the statistics of the field in a shell around a central peak, in particular its multipolar decomposition. Results: The peak condition is shown to significantly remove power from the dipolar contribution and to modify the monopole and quadrupole. As expected, higher order multipoles are not significantly modified by the constraint. Analytical predictions are successfully checked against measurements in Gaussian random fields. The effect of substructures and radial weighting is shown to be small and does not change the qualitative picture.The non-linear evolution is shown to induce a non-linear bias of all multipoles proportional to the cluster mass. Conclusions: We predict the Gaussian and weakly non-Gaussian statistics of multipolar moments of a 2D field around a peak as a proxy for the azimuthal distribution of the convergence field around a cluster of galaxies. A quantitative estimate of this multipolar decomposition of the convergence field around clusters in numerical simulations of structure formation and in observations will be presented in two forthcoming papers.
Eliazar, Iddo
2017-05-01
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.
Howard, I A
2003-01-01
There is ongoing interest in the kinetic energy functional T sub s [rho] in density functional theory. The present study lies in this area and concerns the Pauli potential V sub P [rho]. A differential equation is obtained here for V sub P (x) in one dimension for a general two-level system. Also, as a specific example, such a functional of rho(x), the ground-state Fermion density, is given for the case of N Fermions which are harmonically confined. (letter to the editor)
2014-09-01
nonlinearly loaded, perfectly conducting scatterer) is assumed to be excited by infinitesimal electric dipoles at ’r transmitting time-harmonic fields at...that for the half-space problem, for the calculation of the dyadic and scalar Green’s functions within the integral equation solver, exact...and located at the center of the array—is a vertical infinitesimal electric dipole operating over the frequency band [300 MHz, 1.5 GHz] in 401P
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.
Gluck, P.; Krakower, Zeev
2010-01-01
We present a unit comprising theory, simulation and experiment for a body oscillating on a vertical spring, in which the simultaneous use of a force probe and an ultrasonic range finder enables one to explore quantitatively and understand many aspects of simple and damped harmonic motions. (Contains 14 figures.)
Introduction to abstract harmonic analysis
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.
Morrey spaces in harmonic analysis
David R. Adams; Xiao, Jie
2012-01-01
Through a geometric capacitary analysis based on space dualities, this paper addresses several fundamental aspects of functional analysis and potential theory for the Morrey spaces in harmonic analysis over the Euclidean spaces.
Morrey spaces in harmonic analysis
Adams, David R.; Xiao, Jie
2012-10-01
Through a geometric capacitary analysis based on space dualities, this paper addresses several fundamental aspects of functional analysis and potential theory for the Morrey spaces in harmonic analysis over the Euclidean spaces.
van den Berg, Stéphanie M; de Moor, Marleen H M; McGue, Matt; Pettersson, Erik; Terracciano, Antonio; Verweij, Karin J H; Amin, Najaf; Derringer, Jaime; Esko, Tõnu; van Grootheest, Gerard; Hansell, Narelle K; Huffman, Jennifer; Konte, Bettina; Lahti, Jari; Luciano, Michelle; Matteson, Lindsay K; Viktorin, Alexander; Wouda, Jasper; Agrawal, Arpana; Allik, Jüri; Bierut, Laura; Broms, Ulla; Campbell, Harry; Smith, George Davey; Eriksson, Johan G; Ferrucci, Luigi; Franke, Barbera; Fox, Jean-Paul; de Geus, Eco J C; Giegling, Ina; Gow, Alan J; Grucza, Richard; Hartmann, Annette M; Heath, Andrew C; Heikkilä, Kauko; Iacono, William G; Janzing, Joost; Jokela, Markus; Kiemeney, Lambertus; Lehtimäki, Terho; Madden, Pamela A F; Magnusson, Patrik K E; Northstone, Kate; Nutile, Teresa; Ouwens, Klaasjan G; Palotie, Aarno; Pattie, Alison; Pesonen, Anu-Katriina; Polasek, Ozren; Pulkkinen, Lea; Pulkki-Råback, Laura; Raitakari, Olli T; Realo, Anu; Rose, Richard J; Ruggiero, Daniela; Seppälä, Ilkka; Slutske, Wendy S; Smyth, David C; Sorice, Rossella; Starr, John M; Sutin, Angelina R; Tanaka, Toshiko; Verhagen, Josine; Vermeulen, Sita; Vuoksimaa, Eero; Widen, Elisabeth; Willemsen, Gonneke; Wright, Margaret J; Zgaga, Lina; Rujescu, Dan; Metspalu, Andres; Wilson, James F; Ciullo, Marina; Hayward, Caroline; Rudan, Igor; Deary, Ian J; Räikkönen, Katri; Arias Vasquez, Alejandro; Costa, Paul T; Keltikangas-Järvinen, Liisa; van Duijn, Cornelia M; Penninx, Brenda W J H; Krueger, Robert F; Evans, David M; Kaprio, Jaakko; Pedersen, Nancy L; Martin, Nicholas G; Boomsma, Dorret I
2014-07-01
Mega- or meta-analytic studies (e.g. genome-wide association studies) are increasingly used in behavior genetics. An issue in such studies is that phenotypes are often measured by different instruments across study cohorts, requiring harmonization of measures so that more powerful fixed effect meta-analyses can be employed. Within the Genetics of Personality Consortium, we demonstrate for two clinically relevant personality traits, Neuroticism and Extraversion, how Item-Response Theory (IRT) can be applied to map item data from different inventories to the same underlying constructs. Personality item data were analyzed in >160,000 individuals from 23 cohorts across Europe, USA and Australia in which Neuroticism and Extraversion were assessed by nine different personality inventories. Results showed that harmonization was very successful for most personality inventories and moderately successful for some. Neuroticism and Extraversion inventories were largely measurement invariant across cohorts, in particular when comparing cohorts from countries where the same language is spoken. The IRT-based scores for Neuroticism and Extraversion were heritable (48 and 49 %, respectively, based on a meta-analysis of six twin cohorts, total N = 29,496 and 29,501 twin pairs, respectively) with a significant part of the heritability due to non-additive genetic factors. For Extraversion, these genetic factors qualitatively differ across sexes. We showed that our IRT method can lead to a large increase in sample size and therefore statistical power. The IRT approach may be applied to any mega- or meta-analytic study in which item-based behavioral measures need to be harmonized.
van den Berg, S. M.; de Moor, M. H. M.; McGue, Matt
2014-01-01
-analyses can be employed. Within the Genetics of Personality Consortium, we demonstrate for two clinically relevant personality traits, Neuroticism and Extraversion, how Item-Response Theory (IRT) can be applied to map item data from different inventories to the same underlying constructs. Personality item...... data were analyzed in > 160,000 individuals from 23 cohorts across Europe, USA and Australia in which Neuroticism and Extraversion were assessed by nine different personality inventories. Results showed that harmonization was very successful for most personality inventories and moderately successful...... for some. Neuroticism and Extraversion inventories were largely measurement invariant across cohorts, in particular when comparing cohorts from countries where the same language is spoken. The IRT-based scores for Neuroticism and Extraversion were heritable (48 and 49 %, respectively, based on a meta...
Piquette, Jean C; McLaughlin, Elizabeth A
2007-06-01
A complex material-constant theory of lossy piezoelectrics is fully solved for crystal class 3m for harmonic time dependence of the fields and stresses. A new demonstration that the theory's eigen coupling factor equation applies to the lossy alternating current (AC) case also is given. The solution presented for crystal class 3m provides a complete orthonormal set of eigenvectors and eigenvalues for the eigen coupling factor problem, and it also provides a complete orthonormal set of eigenvectors and eigenvalues for the eigen loss tangent problem, for this crystal class. It is shown that two positive coupling factors are sufficient to express an arbitrary 3m crystal state. Despite the complex nature of the material constants, the Holland-EerNisse theory produces fully real expressions for the coupling factors. The loss tangent eigenvalues also are fully real and positive. The loss eigenstates are important because driving a crystal in a loss eigenstate tends to minimize the impact of material losses. Given also is a set of loss inequalities for crystal class 3m. The loss inequalities of crystal class 6mm are recovered from these when d22 and s(E)14 both vanish.
Bozkaya, Uğur; Sherrill, C David
2013-08-07
Orbital-optimized coupled-electron pair theory [or simply "optimized CEPA(0)," OCEPA(0), for short] and its analytic energy gradients are presented. For variational optimization of the molecular orbitals for the OCEPA(0) method, a Lagrangian-based approach is used along with an orbital direct inversion of the iterative subspace algorithm. The cost of the method is comparable to that of CCSD [O(N(6)) scaling] for energy computations. However, for analytic gradient computations the OCEPA(0) method is only half as expensive as CCSD since there is no need to solve the λ2-amplitude equation for OCEPA(0). The performance of the OCEPA(0) method is compared with that of the canonical MP2, CEPA(0), CCSD, and CCSD(T) methods, for equilibrium geometries, harmonic vibrational frequencies, and hydrogen transfer reactions between radicals. For bond lengths of both closed and open-shell molecules, the OCEPA(0) method improves upon CEPA(0) and CCSD by 25%-43% and 38%-53%, respectively, with Dunning's cc-pCVQZ basis set. Especially for the open-shell test set, the performance of OCEPA(0) is comparable with that of CCSD(T) (ΔR is 0.0003 Å on average). For harmonic vibrational frequencies of closed-shell molecules, the OCEPA(0) method again outperforms CEPA(0) and CCSD by 33%-79% and 53%-79%, respectively. For harmonic vibrational frequencies of open-shell molecules, the mean absolute error (MAE) of the OCEPA(0) method (39 cm(-1)) is fortuitously even better than that of CCSD(T) (50 cm(-1)), while the MAEs of CEPA(0) (184 cm(-1)) and CCSD (84 cm(-1)) are considerably higher. For complete basis set estimates of hydrogen transfer reaction energies, the OCEPA(0) method again exhibits a substantially better performance than CEPA(0), providing a mean absolute error of 0.7 kcal mol(-1), which is more than 6 times lower than that of CEPA(0) (4.6 kcal mol(-1)), and comparing to MP2 (7.7 kcal mol(-1)) there is a more than 10-fold reduction in errors. Whereas the MAE for the CCSD method is
Wang, Fa-Qiang; Zhang, Hao; Ma, Xi-Kui
2012-02-01
In this paper, period-doubling bifurcation in a two-stage power factor correction converter is analyzed by using the method of incremental harmonic balance (IHB) and Floquet theory. A two-stage power factor correction converter typically employs a cascade configuration of a pre-regulator boost power factor correction converter with average current mode control to achieve a near unity power factor and a tightly regulated post-regulator DC—DC Buck converter with voltage feedback control to regulate the output voltage. Based on the assumption that the tightly regulated post-regulator DC—DC Buck converter is represented as a constant power sink and some other assumptions, the simplified model of the two-stage power factor correction converter is derived and its approximate periodic solution is calculated by the method of IHB. And then, the stability of the system is investigated by using Floquet theory and the stable boundaries are presented on the selected parameter spaces. Finally, some experimental results are given to confirm the effectiveness of the theoretical analysis.
2007-01-01
In this paper, the dynamic stress field near crack tips in the functionally graded materials subjected to the harmonic anti-plane shear stress waves was investi- gated by means of the non-local theory. The traditional concepts of the non-local theory were extended to solve the fracture problem of functionally graded materials. To make the analysis tractable, it was assumed that the material properties vary exponentially with coordinate parallel to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable was the displacement on the crack surfaces. To solve the dual integral equations, the displacement on the crack surfaces was expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solutions yield a finite hoop stress at crack tips, thus allowing us to use the maximum stress as a fracture criterion. The magnitude of the finite dynamic stress field depends on the crack length, the parameter describing the functionally graded materials, the circular frequency of the incident waves and the lattice parameter of materials.
ZHANG PeiWei; ZHOU ZhenGong; WU LinZhi
2007-01-01
In this paper, the dynamic stress field near crack tips in the functionally graded materials subjected to the harmonic anti-plane shear stress waves was investigated by means of the non-local theory. The traditional concepts of the non-local theory were extended to solve the fracture problem of functionally graded materials.To make the analysis tractable, it was assumed that the material properties vary exponentially with coordinate parallel to the crack. By use of the Fourier transform,the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable was the displacement on the crack surfaces. To solve the dual integral equations, the displacement on the crack surfaces was expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solutions yield a finite hoop stress at crack tips, thus allowing us to use the maximum stress as a fracture criterion. The magnitude of the finite dynamic stress field depends on the crack length, the parameter describing the functionally graded materials, the circular frequency of the incident waves and the lattice parameter of materials.
Wang Fa-Qiang; Zhang Hao; Ma Xi-Kui
2012-01-01
In this paper,period-doubling bifurcation in a two-stage power factor correction converter is analyzed by using the method of incremental harmonic balance (IHB) and Floquet theory.A two-stage power factor correction converter typically employs a cascade configuration of a pre-regulator boost power factor correction converter with average current mode control to achieve a near unity power factor and a tightly regulated post-regulator DC-DC Buck converter with voltage feedback control to regulate the output voltage. Based on the assumption that the tightly regulated postregulator DC-DC Buck converter is represented as a constant power sink and some other assumptions,the simplified model of the two-stage power factor correction converter is derived and its approximate periodic solution is calculated by the method of IHB.And then,the stability of the system is investigated by using Floquet theory and the stable boundaries are presented on the selected parameter spaces.Finally,some experimental results are given to confirm the effectiveness of the theoretical analysis.
Explaining the harmonic sequence paradox.
Schmidt, Ulrich; Zimper, Alexander
2012-05-01
According to the harmonic sequence paradox, an expected utility decision maker's willingness to pay for a gamble whose expected payoffs evolve according to the harmonic series is finite if and only if his marginal utility of additional income becomes zero for rather low payoff levels. Since the assumption of zero marginal utility is implausible for finite payoff levels, expected utility theory - as well as its standard generalizations such as cumulative prospect theory - are apparently unable to explain a finite willingness to pay. This paper presents first an experimental study of the harmonic sequence paradox. Additionally, it demonstrates that the theoretical argument of the harmonic sequence paradox only applies to time-patient decision makers, whereas the paradox is easily avoided if time-impatience is introduced.
Harmonic and geometric analysis
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...
Bennett, Charles L.
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.
The harmonics detection method based on neural network applied ...
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Keywords: Artificial Neural Networks (ANN), p-q theory, (SAPF), Harmonics, Total Harmonic Distortion. 1. ... Recently, some methods based on artificial intelligence have been applied In order to improve ..... The effect is the reduction of.
Phononic High Harmonic Generation
Ganesan, Adarsh; 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. Subsequently, the down-conversion of second harmonic phonons into first harmonic phonons and conversion of first and second harmonic phonons into third harmonic phonons occur. On the similar lines, an eventual conversion of third harmonic phonons to high orders is also observed to commence. This surprising physical pathway for phononic low-order to high-order harmonic conversion may find general relevance to other physical systems.
Harmonic functions on groups and Fourier algebras
Chu, Cho-Ho
2002-01-01
This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.
Tubaldi, Eleonora; Amabili, Marco; Païdoussis, Michael P.
2017-05-01
In deformable shells conveying pulsatile flow, oscillatory pressure changes cause local movements of the fluid and deformation of the shell wall, which propagate downstream in the form of a wave. In biomechanics, it is the propagation of the pulse that determines the pressure gradient during the flow at every location of the arterial tree. In this study, a woven Dacron aortic prosthesis is modelled as an orthotropic circular cylindrical shell described by means of the Novozhilov nonlinear shell theory. Flexible boundary conditions are considered to simulate connection with the remaining tissue. Nonlinear vibrations of the shell conveying pulsatile flow and subjected to pulsatile pressure are investigated taking into account the effects of the pulse-wave propagation. For the first time in literature, coupled fluid-structure Lagrange equations of motion for a non-material volume with wave propagation in case of pulsatile flow are developed. The fluid is modeled as a Newtonian inviscid pulsatile flow and it is formulated using a hybrid model based on the linear potential flow theory and considering the unsteady viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. Contributions of pressure and velocity propagation are also considered in the pressure drop along the shell and in the pulsatile frictional traction on the internal wall in the axial direction. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior of a pressurized Dacron aortic graft conveying blood flow. A pulsatile time-dependent blood flow model is considered by applying the first harmonic of the physiological waveforms of velocity and pressure during the heart beating period. Geometrically nonlinear vibration response to pulsatile flow and transmural pulsatile pressure, considering the propagation of pressure and velocity changes inside the shell, is here presented via frequency-response curves, time histories, bifurcation
Harmonic Theory and Machine Learning
Nanclares, Jorge; Rapallini, Ulises Mario Alberto
2007-01-01
A natural inference mechanism is presented : the Black Box problem is transformed into a Dirichlet's problem on the closed cube. Then it is solved in closed polynomial form, together with a Mean-Value theorem and a Maximum Principle.A generalization to Polytopes and a reduction of any Dirichlet problem on compacta is mapp ed into a unit cub e in more dimensions.An algorithm for calculating the solution is suggested. Facultad de Informática
Stepinski, T.; Lingvall, F.; Ping Wu [Uppsala Univ. (Sweden). Dept. of Materials Science
2001-07-01
presented. The calculated results show how the harmonics evolve as the plane wave propagates. It should be noted that the work presented here is at its preliminary stage, the goal of the present and future work is to build a simulating tool for material harmonic imaging technology. The theory of phase conjugation is presented and different methods of wave phase conjugation (WPC) are reviewed and characterized in the third chapter. The ability of WPC to self-adaptive focus ultrasonic waves in inhomogeneous media makes it interesting in the application to the inspection of as EB welds. The WPC can be performed either in time or frequency domain. Time domain method, known as time reversal mirrors is reviewed in some detail with focus on its applications to NDT. Frequency domain techniques use nonlinear piezoelectric or magnetic materials. The choice of magneto-acoustic phase conjugation, performed in nonlinear magnetic ceramics as a candidate for the feasibility demonstration is motivated. Details of the preliminary experiment with high frequency NDE application (10 MHz) are presented. NDE methods suitable for the characterization of cast iron are reviewed in the fourth chapter. Two groups of methods that could be used in an industrial environment, those based on ultrasound and on eddy current measurement are presented in some detail. The review is focused on sensing the interaction of elastic waves with the microstructure of cast iron. It is explained how three different features of ultrasound, the sound velocity, the attenuation and the backscattering, can be used for the characterization.
Elements of abstract harmonic analysis
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
Harmonic functions with varying coefficients
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.
Artificial Neural Network in Harmonic Reduction of STATCOM
Li Hongmei; Li Zhenran; Zheng Peiying
2005-01-01
To eliminate harmonic pollution incurred from the static synchronous compensator(STATCOM), a method of applying artificial neural network is presented. When PWM wave is formed based on the harmonic suppression theory, a concave is set on certain angle of the square wave to suppress unnecessary harmonics, by timely and on-line determining the chopping angle corresponding to respective harmonics through artificial neural network, i.e. by setting the position of concave to eliminate corresponding harmonics, the harmonic component on output voltage of the inverter can be improved. To conclude through computer simulation test, the perfect control effect has been proved.
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.
Exact propagators in harmonic superspace
Kuzenko, Sergei M.
2004-10-01
Within the background field formulation in harmonic superspace for quantum N = 2 super-Yang-Mills theories, the propagators of the matter, gauge and ghost superfields possess a complicated dependence on the SU(2) harmonic variables via the background vector multiplet. This dependence is shown to simplify drastically in the case of an on-shell vector multiplet. For a covariantly constant background vector multiplet, we exactly compute all the propagators. In conjunction with the covariant multi-loop scheme developed in arxiv:hep-th/0302205, these results provide an efficient (manifestly N = 2 supersymmetric) technical setup for computing multi-loop quantum corrections to effective actions in N = 2 supersymmetric gauge theories, including the N = 4 super-Yang-Mills theory.
Exact propagators in harmonic superspace
Kuzenko, S M
2004-01-01
Within the background field formulation in harmonic superspace for quantum N = 2 super Yang-Mills theories, the propagators of the matter, gauge and ghost superfields possess a complicated dependence on the SU(2) harmonic variables via the background vector multiplet. This dependence is shown to simplify drastically in the case of an on-shell vector multiplet. For a covariantly constant background vector multiplet, we exactly compute all the propagators. In conjunction with the covariant multi-loop scheme developed in hep-th/0302205, these results provide an efficient (manifestly N = 2 supersymmetric) technical setup for computing multi-loop quantum corrections to effective actions in N = 2 supersymmetric gauge theories, including the N = 4 super Yang-Mills theory.
van den Berg, Stéphanie Martine; Moor, Marleen H.M.; McGue, Matt; Petterson, Erik; Terracciano, Antonio; Verweij, Karin J.H.; Amin, Najaf; Derringer, Jaime; Esko, Tonu; van Grootheest, Gerard; Hansell, Narelle K.; Huffman, Jennifer; Konte, Bettina; Lahti, Jari; Luciano, Michelle; Matteson, Lindsay K.; Viktorin, Alexander; Wouda, Jasper; Agrawal, Arpana; Allik, Jüri; Beirut, Laura; Broms, Ulla; Campbell, Harry; Smith, George Davey; Eriksson, Johan G.; Ferrucci, Luigi; Franke, Barbera; Fox, Gerardus J.A.; de Geus, Eco J.C.; Giegling, Ina; Gow, Alan J.; Grucza, Richard; Hartmann, Annette M.; Heath, Andrew C.; Heikkilä, Kauko; Iacono, William G.; Janzing, Joost; Jokela, Markus; Kiemeney, Lambertus; Lehtimäki, Terho; Madden, Pamela A.F.; Magnusson, Patrik K.E.; Northstone, Kate; Nutile, Teresa; Ouwens, Klaasjan G.; Palotie, Aarno; Pattie, Alison; Pesonen, Anu-Katriina; Polasek, Ozren; Pulkkinen, Lea; Pulkki-Raback, Laura; Raitakari, Olli T.; Realo, Anu; Rose, Richard J.; Ruggiero, Daniela; Seppälä, Ilkka; Slutske, Wendy S.; Smyth, David C.; Sorice, Rossella; Starr, John M.; Sutin, Angelina R.; Tanaka, Toshiko; Verhagen, Josine; Vermeulen, Sita; Vuoksimaa, Eero; Widen, Elisabeth; Willemsen, Gonneke; Wright, Margaret J.; Zgaga, Lina; Rujescu, Dan; Metspalu, Andres; Wilson, James F.; Ciullo, Marina; Hayward, Caroline; Rudan, Igor; Deary, Ian J.; Räikkönen, Katri; Vasquez, Alejandro Arias; Costa, Paul T.; Keltikangas-Järvinen, Liisa; van Duijn, Cornelia M.; Penninx, Brenda W.J.H.; Krueger, Robert F.; Evans, David M.; Kaprio, Jaakko; Pedersen, Nancy L.; Martin, Nicolas G.; Boomsma, Dorret I.
2014-01-01
Mega- or meta-analytic studies (e.g. genome-wide association studies) are increasingly used in behavior genetics. An issue in such studies is that phenotypes are often measured by different instruments across study cohorts, requiring harmonization of measures so that more powerful fixed effect
S.M. van den Berg (Stéphanie); M.H.M. de Moor; M. McGue (Matt); E. Pettersson (Erik); A. Terracciano; K.J.H. Verweij (Karin J.); N. Amin (Najaf); J. Derringer; T. Esko (Tõnu); G. van Grootheest (Gerard); N.K. Hansell (Narelle); J.E. Huffman (Jennifer); B. Konte; J. Lahti (Jari); M. Luciano (Michelle); L.K. Matteson (Lindsay); A. Viktorin (Alexander); J. Wouda (Jasper); A. Agrawal (Arpana); J. Allik; L.J. Bierut (Laura); U. Broms (Ulla); H. Campbell (Harry); G.D. Smith (George Davey); K. Hagen (Knut); L. Ferrucci (Luigi); B. Franke (Barbara); J.P. Fox (Jean-Paul); E.J.C. de Geus (Eco); I. Giegling (Ina); A.J. Gow (Alan J.); R. Grucza; A.M. Hartmann (Annette M); A.C. Heath (Andrew); K. Heikkilä (Kauko); W.G. Iacono (William); J.G.E. Janzing (Joost); M. Jokela (Markus); L.A.L.M. Kiemeney (Bart); T. Lehtimäki (Terho); P.A.F. Madden (Pamela); P.K. Magnusson (Patrik); K. Northstone (Kate); T. Nutile; K.G. Ouwens (Klaasjan); A. Palotie (Aarno); A. Pattie (Alison); A.-K. Pesonen (Anu-Katriina); O. Polasek (Ozren); L. Pulkkinen (Lea); L. Pulkki-Råback (Laura); O. Raitakari (Olli); A. Realo; R.J. Rose (Richard); D. Ruggiero; I. Seppälä (Ilkka); W.S. Slutske (Wendy); D.C. Smyth (David); R. Sorice; J.M. Starr (John); A.R. Sutin; T. Tanaka (Toshiko); J. Verhagen (Josine); S.H.H.M. Vermeulen (Sita); E. Vuoksimaa (Eero); E. Widen (Elisabeth); G.A.H.M. Willemsen (Gonneke); M.J. Wright (Margaret); L. Zgaga (Lina); D. Rujescu (Dan); A. Metspalu (Andres); J.F. Wilson (James F); M. Ciullo; C. Hayward (Caroline); I. Rudan (Igor); I.J. Deary (Ian); K. Räikkönen (Katri); A. Arias-Vásquez (Alejandro); P.T. Costa (Paul); L. Keltikangas-Järvinen (Liisa); C.M. van Duijn (Cock); B.W.J.H. Penninx (Brenda); R.F. Krueger; D.M. Evans (David); J. Kaprio (Jaakko); N.L. Pedersen (Nancy); N.G. Martin (Nicholas); D.I. Boomsma (Dorret)
2014-01-01
textabstractMega- or meta-analytic studies (e.g. genome-wide association studies) are increasingly used in behavior genetics. An issue in such studies is that phenotypes are often measured by different instruments across study cohorts, requiring harmonization of measures so that more powerful fixed
Berg, S.M. van den; Moor, M.H. de; McGue, M.; Pettersson, E.; Terracciano, A.; Verweij, K.J.H.; Amin, N.; Derringer, J.; Esko, T.; Grootheest, G. van; Hansell, N.K.; Huffman, J.; Konte, B.; Lahti, J.; Luciano, M.; Matteson, L.K.; Viktorin, A.; Wouda, J.; Agrawal, A.; Allik, J.; Bierut, L.; Broms, U.; Campbell, H.; Smith, G.D.; Eriksson, J.G.; Ferrucci, L.; Franke, B.; Fox, J.P.; Geus, E.J. de; Giegling, I.; Gow, A.J.; Grucza, R.; Hartmann, A.M.; Heath, A.C.; Heikkila, K.; Iacono, W.G.; Janzing, J.; Jokela, M.; Kiemeney, B.; Lehtimaki, T.; Madden, P.A.F.; Magnusson, P.K.; Northstone, K.; Nutile, T.; Ouwens, K.G.; Palotie, A.; Pattie, A.; Pesonen, A.K.; Polasek, O.; Pulkkinen, L.; Pulkki-Raback, L.; Raitakari, O.T.; Realo, A.; Rose, R.J.; Ruggiero, D.; Seppala, I.; Slutske, W.S.; Smyth, D.C.; Sorice, R.; Starr, J.M.; Sutin, A.R.; Tanaka, T.; Verhagen, J.; Vermeulen, S.; Vuoksimaa, E.; Widen, E.; Willemsen, G.; Wright, M.J.; Zgaga, L.; Rujescu, D.; Metspalu, A.; Wilson, J.F.; Ciullo, M.; Hayward, C.; Rudan, I.; Deary, I.J.; Raikkonen, K.; Arias Vasquez, A.; Costa, P.T.; Keltikangas-Jarvinen, L.; Duijn, C.M. van; Penninx, B.W.J.H.; Krueger, R.F.; Evans, D.M.; Kaprio, J.; Pedersen, N.L.; Martin, N.G.; Boomsma, D.I.
2014-01-01
Mega- or meta-analytic studies (e.g. genome-wide association studies) are increasingly used in behavior genetics. An issue in such studies is that phenotypes are often measured by different instruments across study cohorts, requiring harmonization of measures so that more powerful fixed effect
Berg, S.M. van den; Moor, M.H.M. de; McGue, M.; Pettersson, E.; Terracciano, A.; Verweij, K.J.H.; Amin, N.; Derringer, J.; Esko, T.; Grootheest, G. van; Hansell, N.K.; Huffman, J.E.; Konte, B.; Lahti, J.; Luciano, M.; Matteson, L.K.; Viktorin, A.; Wouda, J.; Agrawal, A.; Allik, J.; Bierut, L.J.; Broms, U.; Campbell, H.; Smith, G.D.; Eriksson, J.G.; Ferrucci, L.; Franke, B.; Fox, J.P.; Geus, E.J.C. de; Giegling, I.; Gow, A.J.; Grucza, R.; Hartmann, A.M.; Heath, A.C.; Heikkilä, K.; Iacono, W.G.; Janzing, J.G.E.; Jokela, M.; Kiemeney, L.; Lehtimäki, T.; Madden, P.A.F.; Magnusson, P.K.E.; Northstone, K.; Nutile, T.; Ouwens, K.G.; Palotie, A.; Pattie, A.; Pesonen, A.K.; Polasek, O.; Pulkkinen, L.; Pulkki-Raback, L.; Raitakari, O.T.; Realo, A.; Rose, R.J.; Ruggiero, D.; Seppälä, I.; Slutske, W.S.; Smyth, D.C.; Sorice, R.; Starr, J.M.; Sutin, A.R.; Tanaka, T.; Verhagen, J.; Vermeulen, H.H.M.; Vuoksimaa, E.; Widen, E.; Willemsen, G.; Wright, M.J.; Zgaga, L.; Rujescu, D.; Metspalu, A.; Wilson, J.F.; Ciullo, M.; Hayward, C.; Rudan, I.; Deary, I.J.; Raikkonen, K.; Vasquez, A.A.; Costa, P.T.; Keltikangas-Jarvinen, L.; Duijn, C.M. van; Penninx, B.W.J.H.; Krueger, R.F.; Evans, D.M.; Kaprio, J.; Pedersen, N.L.; Martin, N.G.; Boomsma, D.I.
2014-01-01
Mega- or meta-analytic studies (e.g. genome-wide association studies) are increasingly used in behavior genetics. An issue in such studies is that phenotypes are often measured by different instruments across study cohorts, requiring harmonization of measures so that more powerful fixed effect
High order harmonic generation in rare gases
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 ~10^{13}-10^{14} W/cm^{2}) is focused into a dense (~10^{17} particles/cm^{3}) 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.
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.
High Orbital Angular Momentum Harmonic Generation
Vieira, J.; Trines, R. M. G. M.; Alves, E. P.; Fonseca, R. A.; Mendonça, J. T.; Bingham, R.; Norreys, P.; Silva, L. O.
2016-12-01
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 realized in any nonlinear optical Kerr media supporting three-wave interactions.
High orbital angular momentum harmonic generation
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.
General -Harmonic Blaschke Bodies
Yibin Feng; Weidong Wang
2014-02-01
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. In particular, we obtain the extreme values concerning the volume and the -dual geominimal surface area of this new notion.
基于谐波小波包理论的轴承故障诊断%Fault diagnosis of rolling bearings based on harmonic wavelet packet theory
吴逍; 纪国宜
2011-01-01
The application of practical wavelet analysis in fault diagnosis is growing rapidly. There are many different wavelets to use but no accepted procedure for choosing among them,the results of them have great difference. The investigation of harmonic wavelet and harmonic wavelet packet analysis revealed good characteristics in vibration signal analysis on partial frequency domain. A simulating example and several experimental examples illustrate how the harmonic wavelet packets method is applied to fault diagnosis of rolling bearings. The favorable results are obtained through the analysis of those signals on a test rig. It is shown that harmonic wavelet packet has many advantages over other wavelets and has the broad application prospect in the domain of fault diagnosis.%小波分析在故障诊断中得到较广泛的应用,但采用不同的小波,分析结果往往会有很大差异.通过对谐波小波和谐波小波包的分析研究,指出了谐波小波包对振动信号局部频段分析的优良特性.结合仿真信号与故障实验进行分析,提出将谐波小波包方法用于诊断轴承故障.实验验证取得了满意结果,表明谐波小波包方法是一种有效的故障诊断工具.
Harmonic Damping in DG-Penetrated Distribution Network
Lu, Jinghang; Savaghebi, Mehdi; Guerrero, Josep M.
2016-01-01
Grid background harmonics may be amplified, propagate through a long distribution feeder and even lead to power system instability. In this paper, harmonic propagation issue is investigated and mitigation of the harmonics is analyzed by using transmission line theory which has already been applied...... in power systems. It is demonstrated that a specific harmonic will not be amplified if the feeder’s length is less than one quarter of the harmonic wavelength meanwhile the terminal impedance is less than characteristic impedance. Besides, three scenarios will be considered in accordance...... with the relationship between the feeder’s length and harmonic wavelength. Harmonic suppression control strategies will be respectively designed considering 5th and 7th harmonics coexisting in the distribution line. Finally, a simulation study has been performed to verify the theoretical analysis and demonstrate...
Harmonic Lattice Dynamics of Germanium
Nelin, G.
1974-07-01
The phonon dispersion relations of the DELTA-, LAMBDA-, and SIGMA-directions of germanium at 80 K are analysed in terms of current harmonic lattice dynamical models. On the basis of this experience, a new model is proposed which gives a unified account of the strong points of the previous models. The principal elements of the presented theory are quasiparticle bond charges combined with a valence force field.
Miliordos, Evangelos; Aprà, Edoardo; Xantheas, Sotiris S
2013-09-21
We report the first optimum geometries and harmonic vibrational frequencies for the ring pentamer and several water hexamer (prism, cage, cyclic and two book) at the coupled-cluster including single, double, and full perturbative triple excitations (CCSD(T))/aug-cc-pVDZ level of theory. All five examined hexamer isomer minima previously reported by Møller-Plesset perturbation theory (MP2) are also minima on the CCSD(T) potential energy surface (PES). In addition, all CCSD(T) minimum energy structures for the n = 2-6 cluster isomers are quite close to the ones previously obtained by MP2 on the respective PESs, as confirmed by a modified Procrustes analysis that quantifies the difference between any two cluster geometries. The CCSD(T) results confirm the cooperative effect of the homodromic ring networks (systematic contraction of the nearest-neighbor (nn) intermolecular separations with cluster size) previously reported by MP2, albeit with O-O distances shorter by ~0.02 Å, indicating that MP2 overcorrects this effect. The harmonic frequencies at the minimum geometries were obtained by the double differentiation of the CCSD(T) energy using an efficient scheme based on internal coordinates that reduces the number of required single point energy evaluations by ~15% when compared to the corresponding double differentiation using Cartesian coordinates. Negligible differences between MP2 and CCSD(T) frequencies are found for the librational modes, while uniform increases of ~15 and ~25 cm(-1) are observed for the bending and "free" OH harmonic frequencies. The largest differences between CCSD(T) and MP2 are observed for the harmonic hydrogen bonded frequencies, for which the former produces larger absolute values than the latter. Their CCSD(T) redshifts from the monomer values (Δω) are smaller than the MP2 ones, due to the fact that CCSD(T) produces shorter elongations (ΔR) of the respective hydrogen bonded OH lengths from the monomer value with respect to MP2. Both
Structural relations between nested harmonic sums
Bluemlein, J.
2008-07-15
We describe the structural relations between nested harmonic sums emerging in the description of physical single scale quantities up to the 3-loop level in renormalizable gauge field theories. These are weight w=6 harmonic sums. We identify universal basic functions which allow to describe a large class of physical quantities and derive their complex analysis. For the 3-loop QCD Wilson coefficients 35 basic functions are required, whereas a subset of 15 describes the 3-loop anomalous dimensions. (orig.)
Index calculation by means of harmonic expansion
Imamura, Yosuke
2015-01-01
We review derivation of superconformal indices by means of supersymmetric localization and spherical harmonic expansion for 3d N=2, 4d N=1, and 6d N=(1,0) supersymmetric gauge theories. We demonstrate calculation of indices for vector multiplets in each dimensions by analysing energy eigenmodes in S^pxR. For the 6d index we consider the perturbative contribution only. We put focus on technical details of harmonic expansion rather than physical applications.
Stevenson, Gareth P; Baker, Ruth E; Kennedy, Gareth F; Bond, Alan M; Gavaghan, David J; Gillow, Kathryn
2013-02-14
The potential-dependences of the rate constants associated with heterogeneous electron transfer predicted by the empirically based Butler-Volmer and fundamentally based Marcus-Hush formalisms are well documented for dc cyclic voltammetry. However, differences are often subtle, so, presumably on the basis of simplicity, the Butler-Volmer method is generally employed in theoretical-experimental comparisons. In this study, the ability of Large Amplitude Fourier Transform AC Cyclic Voltammetry to distinguish the difference in behaviour predicted by the two formalisms has been investigated. The focus of this investigation is on the difference in the profiles of the first to sixth harmonics, which are readily accessible when a large amplitude of the applied ac potential is employed. In particular, it is demonstrated that systematic analysis of the higher order harmonic responses in suitable kinetic regimes provides predicted deviations of Marcus-Hush from Butler-Volmer behaviour to be established from a single experiment under conditions where the background charging current is minimal.
Nonlinear harmonics in the high-gain harmonic generation (HGHG) experiment
Biedron, S G; Milton, S V; Yu, L H; Wang, X J
2001-01-01
We have previously performed rigorous analyses of the nonlinear harmonics in self-amplified spontaneous emission (SASE) free-electron lasers (FELs) using a 3D simulation code. To date, we have presented only preliminary results of these higher harmonics resulting in the high-gain harmonic generation (HGHG) process. A single-pass, high-gain FEL experiment based on the HGHG theory is underway at the Accelerator Test Facility (ATF) at Brookhaven National Laboratory (BNL) in collaboration with the Advanced Photon Source (APS) at Argonne National Laboratory (ANL). Using the above experiment's design parameters, the specific case of the harmonic output from the HGHG experiment will be examined using a 3D simulation code. The sensitivity of nonlinear harmonic output for this HGHG experiment as functions of emittance, energy spread, and peak current in both cases, and for the dispersive section strength and input seed power in the HGHG case, will be presented.
Frediani, Luca; Ågren, Hans; Ferrighi, Lara; Ruud, Kenneth
2005-10-01
We present the first implementation of the quadratic response function for multiconfigurational self-consistent-field wave functions of solvated molecules described by a polarizable continuum model employing a molecule-shaped cavity. We apply the methodology to the first hyperpolarizability β and, in particular, the second-harmonic generation process for a series of conjugated push-pull oligomers, as well as for para-nitroaniline. The effect of solvation on the dispersion of the hyperpolarizability and the change in the hyperpolarizability for increasing chain length of the oligomers in vacuum and in solution is considered. The effect of a correlated description is analyzed by comparing the Hartree-Fock hyperpolarizabilities to the multiconfigurational self-consistent-field hyperpolarizabilities. The effect of geometry relaxation in the solvent on the properties of the solvated molecules are also investigated.
Frediani, Luca; Agren, Hans; Ferrighi, Lara; Ruud, Kenneth
2005-10-08
We present the first implementation of the quadratic response function for multiconfigurational self-consistent-field wave functions of solvated molecules described by a polarizable continuum model employing a molecule-shaped cavity. We apply the methodology to the first hyperpolarizability beta and, in particular, the second-harmonic generation process for a series of conjugated push-pull oligomers, as well as for para-nitroaniline. The effect of solvation on the dispersion of the hyperpolarizability and the change in the hyperpolarizability for increasing chain length of the oligomers in vacuum and in solution is considered. The effect of a correlated description is analyzed by comparing the Hartree-Fock hyperpolarizabilities to the multiconfigurational self-consistent-field hyperpolarizabilities. The effect of geometry relaxation in the solvent on the properties of the solvated molecules are also investigated.
Illuminating Molecular Symmetries with Bicircular High-Order-Harmonic Generation
Reich, Daniel M
2016-01-01
We present a complete theory of bicircular high-order-harmonic emission from N-fold rotationally symmetric molecules. Using a rotating frame of reference we predict the complete structure of the high-order-harmonic spectra for arbitrary driving frequency ratios and show how molecular symmetries can be directly identified from the harmonic signal. Our findings reveal that a characteristic fingerprint of rotational molecular symmetries can be universally observed in the ultrafast response of molecules to strong bicircular fields.
High-Order Harmonic Generation in the Ionization Process
CHEN Jing; CHEN Shi-Gang; LIU Jie
2000-01-01
Based on the nonperturbative quantum electrodynamics scattering theory for multiphoton ionization developed recently, high-order harmonic generated in the ionization process is discussed. The influence of the Coulomb potential is treated as a perturbation in the expansion of the transition matrix. It is deduced that the harmonic photons are emitted in the resonant process during ionization and the width of the harmonic peaks is just the ionization rate of the atom.
Covariant harmonic oscillators and coupled harmonic oscillators
Han, Daesoo; Kim, Young S.; Noz, Marilyn E.
1995-01-01
It is shown that the system of two coupled harmonic oscillators shares the basic symmetry properties with the covariant harmonic oscillator formalism which provides a concise description of the basic features of relativistic hadronic features observed in high-energy laboratories. It is shown also that the coupled oscillator system has the SL(4,r) symmetry in classical mechanics, while the present formulation of quantum mechanics can accommodate only the Sp(4,r) portion of the SL(4,r) symmetry. The possible role of the SL(4,r) symmetry in quantum mechanics is discussed.
DFIG Harmonic Current Controlling with the Grid Low Harmonic Voltage
Huan Wang
2014-01-01
Full Text Available This study presents a vector control strategy based on stator harmonic current closed-loop, it adds individually the control loop about of each stator harmonic current to restrain the stator harmonic current, in order to meet the THD criteria. The control strategy of restraining the harmonic current presents the design of the stator harmonic current restrains the current controller. It influences the rotor voltage of the stator harmonic current restraining strategies.
The harmonic oscillator and nuclear physics
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.
ON HARMONIC MAPS INTO SYMPLECTIC GROUPS Sp(N)
无
2001-01-01
By means of the theory of harmonic maps into the unitary group U(N), the authors study harmonic maps into the symplectic group Sp(N). The symplectic uniton and symplectic ex- tended uniton are introduced. The method of the symplectic Backlund transformation and the Darboux transformation is used to construct new symplectic unitons from a known one.
Harmonic moment dynamics in Laplacian growth.
Leshchiner, Alexander; Thrasher, Matthew; Mineev-Weinstein, Mark B; Swinney, Harry L
2010-01-01
Harmonic moments are integrals of integer powers of z=x+iy over a domain. Here, the domain is an exterior of a bubble of air growing in an oil layer between two horizontal closely spaced plates. Harmonic moments are a natural basis for such Laplacian growth phenomena because, unlike other representations, these moments linearize the zero surface tension problem [S. Richardson, J. Fluid Mech. 56, 609 (1972)], so that all moments except the lowest one (the area of the bubble) are conserved in time. In our experiments, we directly determine the harmonic moments and show that for nonzero surface tension, all moments (except the lowest one) decay in time rather than exhibiting the divergences of other representations. Further, we derive an expression that relates the derivative of the k(th) harmonic moment M(k) to measurable quantities (surface tension, viscosity, the distance between the plates, and a line integral over the contour encompassing the growing bubble). The laboratory observations are in good accord with the expression we derive for dM(k)/dt , which is proportional to the surface tension; thus in the zero surface tension limit, the moments (above k=0) are all conserved, in accord with Richardson's theory. In addition, from the measurements of the time evolution of the harmonic moments we obtain a value for the surface tension that is within 20% of the accepted value. In conclusion, our analysis and laboratory observations demonstrate that an interface dynamics description in terms of harmonic moments is physically realizable and robust.
Glassman, R B
2000-02-01
1. The capacity of working memory (WM) for about 7+/-2 ("the magical number") serially organized simple verbal items may represent a fundamental constant of cognition. Indeed, there is the same capacity for sense of familiarity of a number of recently encountered places, observed in radial maze performance both of lab rats and of humans. 2. Moreover, both species show a peculiar capacity for retaining WM of place over delays. The literature also describes paradoxes of extended time duration in certain human verbal recall tasks. Certain bird species have comparable capacity for delayed recall of about 4 to 8 food caches in a laboratory room. 3. In addition to these paradoxes of the time dimension with WM (still sometimes called "short-term" memory) there are another set of paradoxes of dimensionality for human judgment of magnitudes, noted by Miller in his classic 1956 paper on "the magical number." We are able to reliably refer magnitudes to a rating scale of up to about seven divisions. Remarkably, that finding is largely independent of perceptual modality or even of the extent of a linear interval selected within any given modality. 4. These paradoxes suggest that "the magical number 7+/2" depends on fundamental properties of mammalian brains. 5. This paper theorizes that WM numerosity is conserved as a fundamental constant, by means of elasticity of cognitive dimensionality, including the temporal pace of arrival of significant items of cognitive information. 6. A conjectural neural code for WM item-capacity is proposed here, which extends the hypothetical principle of binding-by-synchrony. The hypothesis is that several coactive frequencies of brain electrical rhythms each mark a WM item. 7. If, indeed, WM does involve a brain wave frequency code (perhaps within the gamma frequency range that has often been suggested with the binding hypothesis) mathematical considerations suggest additional relevance of harmonic relationships. That is, if copresent sinusoids
Large- quantum chromodynamics and harmonic sums
Eduardo De Rafael
2012-06-01
In the large- limit of QCD, two-point functions of local operators become harmonic sums. I review some properties which follow from this fact and which are relevant for phenomenological applications. This has led us to consider a class of analytic number theory functions as toy models of large- QCD which also is discussed.
Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)
2016-07-01
Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.
Perturbative Semiclassical Trace Formulae for Harmonic Oscillators
Møller-Andersen, Jakob; Ögren, Magnus
2015-01-01
In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even monomial perturbation, which we use to study the resulting...... 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...
Music of the heavens Kepler's harmonic astronomy
Stephenson, Bruce
2014-01-01
Valued today for its development of the third law of planetary motion, Harmonice mundi (1619) was intended by Kepler to expand on ancient efforts to discern a Creator's plan for the planetary system--an arrangement thought to be based on harmonic relationships. Challenging critics who characterize Kepler's theories of harmonic astronomy as ""mystical,"" Bruce Stephenson offers the first thorough technical analysis of the music the astronomer thought the heavens made, and the logic that led him to find musical patterns in his data. In so doing, Stephenson illuminates crucial aspects of Kepler'
A Novel PWM Generator Based on the Theory of Harmonic Elimination%基于谐波消去原理的新型PWM发生器
朱其新; 张培建; 迟磊
2000-01-01
A novel PWM generator based on the theory of harmonicelimination is proposed in this paper, which has the following ad-vantages such as sheer digitizing, not occupying the time of the mi-croproessor and simpler circuit.%介绍了一种基于谐波消去原理的新型PWM发生器，该系统具有全数字控制、电路简单、不占用微机资源等优点。
Quantum dynamics of the damped harmonic oscillator
Philbin, T G
2012-01-01
The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of additional harmonic oscillators as a reservoir. But a discrete reservoir cannot directly yield dynamics such as Ohmic damping (proportional to velocity) of the oscillator of interest. By using a continuum of oscillators as a reservoir, we canonically quantize the harmonic oscillator with Ohmic damping and also with general damping behaviour. The dynamics of a damped oscillator is determined by an arbitrary effective susceptibility that obeys Kramers-Kronig relations. This approach offers an alternative description of nano-mechanical oscillators and opto-mechanical systems.
Fifth-Order Harmonic Generation using a Coherent Controlled Two-Pulsed Optical Field
刘婷婷; 王大威; 陆伟新; 孙泉; 杨宏; 蒋红兵; 龚旗煌
2002-01-01
We have experimentally studied the characteristics of fifth-order harmonic radiation produced by two coherent femtosecond laser pulses with a changeable relative phase. The intensities of harmonic generation are found to increase vith the coherent degree. In one optical period, the temporal variation of harmonics exhibits an asymmetric characteristic, vhich is interpreted in terms of ionization theory and the deformation of the wave packets of fundamental field contribution to harmonic generation.
Andrea Alparone
2014-05-01
Structural, energetic, spectroscopic, linear and nonlinear optical (NLO) properties of the environmental mutagens 1- and 3-nitro-6-azabenzo[]pyrene -oxides were characterized by means of Hartree-Fock as well as B3LYP and CAM-B3LYP density functional theory computations. The NLO investigations were performed for the second harmonic generation (SHG) and electro-optical Pockels effect (EOPE) at the incident wavelength of 1064 nm. The results show that, the predicted structures, vibrational spectra, nucleus independent chemical shifts, ionization energy, electron affinity as well as electronic polarizabilities are little influenced by the position of the nitro substituent. Differently, the dipole moment () and the first-order hyperpolarizabilities () are significantly dependent on the isomerization. The rather different mutagenic activity of the investigated isomers could be related to their diverse polarity. At the CAM-B3LYP level, when passing from the 1- to the 3-nitro-6-azabenzo[a]pyrene -oxide isomer, the datum increases by about 5 D (a factor of three), whereas the static and dynamic values decrease by ca. 50%. Dipole moment measurement and SHG and EOPE NLO techniques are potentially useful to distinguish these important environmental mutagens.
Second harmonic generation imaging
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...
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.
Booster Double Harmonic Setup Notes
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.
Optical klystron and harmonic generation free electron laser
Qika Jia
2005-06-01
Full Text Available The optical field evolution of an optical klystron free electron laser is analytically described for both low gain and high gain cases. The harmonic optical klystron (HOK in which the second undulator is resonant on the higher harmonic of the first undulator is analyzed as a harmonic amplifier. The optical field evolution equation of the HOK is derived analytically for both the CHG mode (coherent harmonic generation, the quadratic gain regime and the HGHG mode (high gain harmonic generation, the exponential gain regime, the effects of energy spread, energy modulation, and dispersion in the whole process are taken into account. The linear theory is given and discussed for the HGHG mode. The analytical formula is given for the CHG mode.
Harmonic Intravascular Ultrasound
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 arte
Harmonic Intravascular Ultrasound
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 arte
Harmonization versus Mutual Recognition
Jørgensen, Jan Guldager; Schröder, Philipp
with the opportunity to start export sales. In contrast, harmonization, in particular the prospect that one’s own national (but not the foreign) standard becomes the only globally accepted standard, opens the foreign market without balancing entry at home. We study these scenarios in a reduced form lobby game with two...
ZHAOZhen-gang
2005-01-01
We have constructed the positive definite metric matrixes for the bounded domains of Rn and proved an inequality which is about the Jacobi matrix of a harmonic mapping on a bounded domain of Rn and the metric matrix of the same bounded domain.
Harmonics in transmission power systems
Wiechowski, Wojciech Tomasz
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....... It is concluded that since some background harmonic distortion is practically always present in the network, a method based on variation of harmonic values must be used. The incremental values of harmonic distortion will allow to verify the harmonic model, despite the existence of background harmonic distortion...... GPS-synchronized OMICRON CMC256 units. Two such units are installed at 400 kV substations at both ends of the disconnected line and a third unit is located at a substation in a distance of 80 km. Time domain "snap-shot" measurements of three-phase voltages and currents are synchronously taken for some...
Young children's harmonic perception.
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.
Second harmonic optical coherence tomography
Jiang,Yi; Tomov, Ivan; Wang, Yimin; Chen, Zhongping
2004-01-01
Second harmonic optical coherence tomography, which uses coherence gating of second-order nonlinear optical response of biological tissues for imaging, is described and demonstrated. Femtosecond laser pulses were used to excite second harmonic waves from collagen harvested from rat tail tendon and a reference nonlinear crystal. Second harmonic interference fringe signals were detected and used for image construction. Because of the strong dependence of second harmonic generation on molecular ...
Considering the Harmonic Sequence “Paradox”
Robert Vivian
2011-06-01
Full Text Available Blavatskyy (2006 formulated a game of chance based on the harmonic series which, he suggests, leads to a St Petersburg type of paradox. In view of the importance of the St Petersburg game in decision theory, any game which leads to a St Petersburg game type paradox is of interest. Blavatskyy’s game is re-examined in this article to conclude that it does not lead to a St Petersburg type paradox.
Unitary representations and harmonic analysis an introduction
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.
Use of dominant harmonic active filters in high power applications
Cheng, Po-Tai
The application of power electronics equipment is increasing rapidly. It is estimated that 60% of electrical power will be processed by power electronics equipment by year 2000. These equipments typically require rectifiers for AC-DC power conversion. Due to their nonlinear nature, most rectifiers draw harmonic current from the utility grid. The harmonic current causes higher energy losses, and may excite resonance conditions in the utility grid. Harmonic standards such as IEEE 519 and IEC 1000-3-2 have been proposed to regulate the harmonic current and voltage levels. This work is to develop a dominant harmonic active filter (DHAF) to realize a cost-effective active filtering solution for nonlinear loads in the range of megawatt and above. The DHAF system achieves harmonic isolation at dominant harmonic frequencies, e.g. the 5th and 7th. This approach allows use of low switching frequency and small rating active filter inverters (1%--2% of the load MVA rating) for implementation. Review of conventional passive filters and various active filters based on high bandwidth PWM inverters is provided. The control theory of the DHAF system is presented. Comparison of the DHAF system and other dominant harmonic filtering approach is provided. Simulation results and laboratory prototype test results are presented to validate the effectiveness of the proposed DHAF system.
Harmonic sums and polylogarithms generated by cyclotomic polynomials
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.)
Soft X-ray harmonic comb from relativistic electron spikes
Pirozhkov, A S; 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
2012-01-01
We demonstrate a new high-order harmonic generation mechanism reaching the `water window' spectral region in experiments with multi-terawatt femtosecond lasers irradiating gas jets. A few hundred harmonic orders are resolved, giving uJ/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.
Deformed quantum harmonic oscillator with diffusion and dissipation
Isar, A
2002-01-01
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master equation and of equations of motion for observables depend on the deformation function. The steady state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation.
Deformed quantum harmonic oscillator with diffusion and dissipation
Isar, A.; Scheid, W.
2002-07-01
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master equation and of equations of motion for observables depend on the deformation function. The steady-state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation.
SOME BOUNDARY INCREASING PROPERTIES OF HARMONIC FUNCTIONS IN LIPSCHITZ DOMAIN
ZHANGYIPING
1996-01-01
The object of this paper is to study the non-tangential increasing properties of positive harmonic function u in Lipschitz domain by means of Martin representation theory, A necessary and sufficient condition of the control of growth of u near any fixed boundary point is obtained. It is shown that the non-tangential increasing degree of u near a boundary point is exactly the local degree of its representation measure with respect to the harmonic measure. Some exanlples are given.
Principles of harmonic analysis
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.
Harmonization versus Mutual Recognition
Jørgensen, Jan Guldager; Schröder, Philipp
The present paper examines trade liberalization driven by the coordination of product standards. For oligopolistic firms situated in separate markets that are initially sheltered by national standards, mutual recognition of standards implies entry and reduced profits at home paired......, harmonized standards may fail to harvest the full pro-competitive effects from trade liberalization compared to mutual recognition; moreover, the issue is most pronounced in markets featuring price competition....
Static third-harmonic lines in widely variable fiber continuum generation
Tu, Haohua; Zhao, Youbo; Liu, Yuan; Boppart, Stephen A.
2014-01-01
An intriguing phenomenon of third-harmonic generation under fiber continuum generation is the emission of an anharmonic signal. One popular interpretation of this effect has developed into a general theory of fiber third-harmonic generation. Here we produce "static" third-harmonic lines dictated fully by fiber properties independent of pump parameters, in contrast to the signals of all known phase-matched nonlinear optical processes that vary dynamically with these parameters. We argue that the anharmonic signal is an illusion of the continuum generation, that it is in fact harmonic, and that this theory should be reevaluated.
Towards automated biomedical ontology harmonization.
Uribe, Gustavo A; Lopez, Diego M; Blobel, Bernd
2014-01-01
The use of biomedical ontologies is increasing, especially in the context of health systems interoperability. Ontologies are key pieces to understand the semantics of information exchanged. However, given the diversity of biomedical ontologies, it is essential to develop tools that support harmonization processes amongst them. Several algorithms and tools are proposed by computer scientist for partially supporting ontology harmonization. However, these tools face several problems, especially in the biomedical domain where ontologies are large and complex. In the harmonization process, matching is a basic task. This paper explains the different ontology harmonization processes, analyzes existing matching tools, and proposes a prototype of an ontology harmonization service. The results demonstrate that there are many open issues in the field of biomedical ontology harmonization, such as: overcoming structural discrepancies between ontologies; the lack of semantic algorithms to automate the process; the low matching efficiency of existing algorithms; and the use of domain and top level ontologies in the matching process.
Harmonic space and quaternionic manifolds
Galperin, A; Ogievetsky, O V
1994-01-01
We find a principle of harmonic analyticity underlying the quaternionic (quaternion-K\\"ahler) geometry and solve the differential constraints which define this geometry. To this end the original $4n$-dimensional quaternionic manifold is extended to a bi-harmonic space. The latter includes additional harmonic coordinates associated with both the tangent local $Sp(1)$ group and an extra rigid $SU(2)$ group rotating the complex structures. Then the constraints can be rewritten as integrability conditions for the existence of an analytic subspace in the bi-harmonic space and solved in terms of two unconstrained potentials on the analytic subspace. Geometrically, the potentials have the meaning of vielbeins associated with the harmonic coordinates. We also establish a one-to-one correspondence between the quaternionic spaces and off-shell $N=2$ supersymmetric sigma-models coupled to $N=2$ supergravity. The general $N=2$ sigma-model Lagrangian when written in the harmonic superspace is composed of the quaternionic ...
Coulomb time delays in high harmonic generation
Smirnova, Olga
2016-01-01
Measuring the time it takes to remove an electron from an atom or molecule during photoionization using newly developed attosecond spectroscopies has been a focus of many recent experiments. However, the outcome of such measurement depends on measurement protocols and specific observables available in each particular experiment. One of such protocols relies on high harmonic generation. First, we derive rigorous and general expressions for ionization and recombination times in high harmonic generation experiments. We show that these times are different from, but related to ionization times measured in photo-electron spectroscopy, i.e. using attosecond streak camera, RABBITT and atto-clock methods. Second, we use the Analytical R-Matrix theory (ARM) to calculate these times and compare them with experimental values.
Coulomb time delays in high harmonic generation
Torlina, Lisa; Smirnova, Olga
2017-02-01
Measuring the time it takes to remove an electron from an atom or molecule during photoionization has been the focus of a number of recent experiments using newly developed attosecond spectroscopies. The interpretation of such measurements, however, depends critically on the measurement protocol and the specific observables available in each experiment. One such protocol relies on high harmonic generation. In this paper, we derive rigorous and general expressions for ionisation and recombination times in high harmonic generation experiments. We show that these times are different from, but related to, ionisation times measured in photoelectron spectroscopy: that is, those obtained using the attosecond streak camera, RABBITT and attoclock methods. We then proceed to use the analytical R-matrix theory to calculate these times and compare them with experimental values.
Next generation data harmonization
Armstrong, Chandler; Brown, Ryan M.; Chaves, Jillian; Czerniejewski, Adam; Del Vecchio, Justin; Perkins, Timothy K.; Rudnicki, Ron; Tauer, Greg
2015-05-01
Analysts are presented with a never ending stream of data sources. Often, subsets of data sources to solve problems are easily identified but the process to align data sets is time consuming. However, many semantic technologies do allow for fast harmonization of data to overcome these problems. These include ontologies that serve as alignment targets, visual tools and natural language processing that generate semantic graphs in terms of the ontologies, and analytics that leverage these graphs. This research reviews a developed prototype that employs all these approaches to perform analysis across disparate data sources documenting violent, extremist events.
Second harmonic generation microscopy
Brüggemann, Dagmar Adeline; Brewer, Jonathan R.; Risbo, Jens
2010-01-01
Myofibers and collagen show non-linear optical properties enabling imaging using second harmonic generation (SHG) microscopy. The technique is evaluated for use as a tool for real-time studies of thermally induced changes in thin samples of unfixed and unstained pork. The forward and the backward......-temperature endotherm peak observable in the differential scanning calorimetry (DSC) thermograms. DSC analysis of epimysium, the connective tissue layer that enfold skeletal muscles, produces one large endotherm starting at 57 °C and peaking at 59.5 °C. SHG microscopy of collagen fibers reveals a variability of thermal...
Computing with Harmonic Functions
Axler, Sheldon
2015-01-01
This document is the manual for a free Mathematica package for computing with harmonic functions. This package allows the user to make calculations that would take a prohibitive amount of time if done without a computer. For example, the Poisson integral of any polynomial can be computed exactly. This software can find exact solutions to Dirichlet, Neumann, and biDirichlet problems in R^n with polynomial data on balls, ellipsoids, and annular regions. It can also find bases for spaces of sphe...
M. A. Navascués
2013-01-01
Full Text Available This paper tackles the construction of fractal maps on the unit sphere. The functions defined are a generalization of the classical spherical harmonics. The methodology used involves an iterated function system and a linear and bounded operator of functions on the sphere. For a suitable choice of the coefficients of the system, one obtains classical maps on the sphere. The different values of the system parameters provide Bessel sequences, frames, and Riesz fractal bases for the Lebesgue space of the square integrable functions on the sphere. The Laplace series expansion is generalized to a sum in terms of the new fractal mappings.
Harmonic Generation in a Traveling-Wave Tube
Wong, Patrick; Zhang, Peng; Lau, Y. Y.; Greening, Geoffrey; Gilgenbach, Ronald; Chernin, David; Simon, David; Hoff, Brad
2016-10-01
Crowding of electron orbits in a traveling-wave tube (TWT) may lead to significant harmonic contents in the beam current, even in the linear regime. Here, we consider a wideband TWT that exhibits gain at the second harmonic. We analytically formulate equations governing the evolution of the generation of second harmonic, including axial variations of the Pierce parameters. The second harmonic output is phase-controlled by the input signal which consists only of a fundamental frequency. Several test cases are performed and compared with simulation using the CHRISTINE code. Reasonable agreement between theory and simulation is found. Work supported by AFOSR FA9550-15-1-0097, ONR N00014-16-1-2353, and L-3 Communications Electron Device Division.
Harmonics radiation of graphene surface plasmon polaritons in terahertz regime
Li, D., E-mail: dazhi_li@hotmail.com [Institute for Laser Technology, Suita, Osaka 565-0871 (Japan); Wang, Y. [School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054 (China); Nakajima, M. [Institute of Laser Engineering, Osaka University, Suita, Osaka 565-0871 (Japan); Hashida, M. [Advanced Research Center for Beam Science, ICR, Kyoto University, Gokasho, Uji, Kyoto 611-0011 (Japan); Wei, Y. [School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054 (China); Miyamoto, S. [Laboratory of Advanced Science and Technology for Industry, University of Hyogo, Ako, Hyogo 678-1205 (Japan)
2016-06-03
This letter presents an approach to extract terahertz radiation from surface plasmon polaritons excited in the surface of a uniform graphene structure by an electron beam. A sidewall configuration is proposed to lift the surface plasmon mode to be close to the light line, so that some of its harmonics have chances to go above the light line and become radiative. The harmonics are considered to be excited by a train of periodic electron bunches. The physical mechanism in this scheme is analyzed with three-dimensional theory, and the harmonics excitation and radiation are demonstrated through numerical calculations. The results show that this technique could be an alternative to transform the surface plasmon polaritons into radiation. - Highlights: • An approach to extract terahertz radiation from graphene surface plasmon polaritons is presented. • A sidewall configuration is proposed to lift the surface plasmon mode. • Harmonics of surface plasmon polaritons are possible to radiate.
On The Harmonic Oscillator Group
Lopez, Raquel M; Vega-Guzman, Jose M
2011-01-01
We discuss the maximum kinematical invariance group of the quantum harmonic oscillator from a view point of the Ermakov-type system. The invariance group of generalized driven harmonic oscillator is shown to be isomorphic to the corresponding Schroedinger group of the free particle.
EXTENSIONS OF EULER HARMONIC SUMS
Djurdje Cvijović
2012-10-01
Full Text Available Three new closed-form summation formulae involving harmonic numbers are established using simple arguments and they are very general extensions of Euler’s famous harmonic sum identity. Some illustrative special cases as well as immediate consequences of the main results are also considered.
Harmonic Series Meets Fibonacci Sequence
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?
Tissue Harmonic Synthetic Aperture Imaging
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...... harmonic techniques have been made, but none of these methods have so far been applicable for in-vivo imaging. The basis of this project is a synthetic aperture technique known as synthetic aperture sequential beamforming (SASB). The technique utilizes a two step beamforming approach to drastically reduce...
Automatic Functional Harmonic Analysis
de Haas, W.B.; Magalhães, J.P.; Wiering, F.; Veltkamp, R.C.
2013-01-01
Music scholars have been studying tonal harmony intensively for centuries, yielding numerous theories and models. Unfortunately, a large number of these theories are formulated in a rather informal fashion and lack mathematical precision. In this article we present HarmTrace, a functional model of W
Factorization and uniton numbers for harmonic maps into the unitary group U(N)
东瑜昕; 沈一兵
1996-01-01
The factorization of harmonic maps from a simply-connected domain to the unitary group is studied, showing that the theory of isotropic harmonic maps is equivalent to that of 2-unitons. Furthermore, a positive answer is given to the Uhlenbeck’s conjecture on the upper bound of minimal uniton numbers.
Contributions of Determining the Forces Distribution in the Harmonic Drive
Sava Ianici
2006-10-01
Full Text Available The paper presents an original method for determining the forces distributions on the portant elements of the harmonic drives. This method is based on the thin wall shells theory anal on the rotating character of the distributed forces that work upon the flexible toothed wheel.
Optimal Selective Harmonic Control for Power Harmonics Mitigation
Zhou, Keliang; Yang, Yongheng; Blaabjerg, Frede
2015-01-01
the cost, the complexity and the performance: high accuracy, fast transient response, easy-implementation, cost-effective, and also easy-to-design. The analysis and synthesis of the optimal SHC system are addressed. The proposed SHC offers power convert-ers a tailor-made optimal control solution......This paper proposes an Internal Model Principle (IMP) based optimal Selective Harmonic Controller (SHC) for power converters to mitigate power harmonics. According to the harmonics distribution caused by power converters, a universal recursive SHC module is developed to deal with a featured group...... 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...
FROM THE HARMONIZATION NEED TO THE SPONTANEOUS ACCOUNTING HARMONIZATION
2009-01-01
The issue of international accounting harmonization has achieved, mainly within the last decade, a significant dimension in the field of international accounting research. The main determinant factor for this state of the art is the process aiming at redu
Power quality issues current harmonics
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
Lattice harmonics expansion revisited
Kontrym-Sznajd, G.; Holas, A.
2017-04-01
The main subject of the work is to provide the most effective way of determining the expansion of some quantities into orthogonal polynomials, when these quantities are known only along some limited number of sampling directions. By comparing the commonly used Houston method with the method based on the orthogonality relation, some relationships, which define the applicability and correctness of these methods, are demonstrated. They are verified for various sets of sampling directions applicable for expanding quantities having the full symmetry of the Brillouin zone of cubic and non-cubic lattices. All results clearly show that the Houston method is always better than the orthogonality-relation one. For the cubic symmetry we present a few sets of special directions (SDs) showing how their construction and, next, a proper application depend on the choice of various sets of lattice harmonics. SDs are important mainly for experimentalists who want to reconstruct anisotropic quantities from their measurements, performed at a limited number of sampling directions.
Crane, Edward; Volkov, Stanislav; Wade, Andrew; Waters, Robert
2009-01-01
We study a generalized Polya urn model with two types of ball. If the drawn ball is red it is replaced together with a black ball, but if the drawn ball is black it is replaced and a red ball is thrown out of the urn. When only black balls remain, the roles of the colours are swapped and the process restarts. We prove that the resulting Markov chain is transient but that if we throw out a ball every time the colours swap, the process is positive-recurrent. We show that the embedded process obtained by observing the number of balls in the urn at the swapping times has a scaling limit that is essentially the square of a Bessel diffusion. We consider an oriented percolation model naturally associated with the urn process, and obtain detailed information about its structure, showing that the open subgraph is an infinite tree with a single end. We also study a natural continuous-time embedding of the urn process that demonstrates the relation to the simple harmonic oscillator; in this setting our transience result...
LI Chao-Hong; DUAN Yi-Wu; Wing-Ki Liu; Jian-Min Yuan
2001-01-01
Within Born-Oppenheimer approximation, by using the classical trajectory theory, a description for the high order harmonic generation of the hydrogen molecular ion interacting with ultrashort laser pulses has been pre sented. The Coulomb singularities have been remedied by the regularization. The action-angle variables have been used to generate the initial inversion symmetry microcanonical distribution. Within a proper intensity range, a harmonic plateau with only odd harmonics appears. For a larger intensity, because of the existence of chaos, the harmonic spectra become noisier. For a large enough intensity, the ionization takes place and the harmonics disappear. So the chaos causes the noises, the ionization suppresses the harmonic generation, and the onset of the ionization follows the onset of chaos.
Pythagorean Triples from Harmonic Sequences.
DiDomenico, Angelo S.; Tanner, Randy J.
2001-01-01
Shows how all primitive Pythagorean triples can be generated from harmonic sequences. Use inductive and deductive reasoning to explore how Pythagorean triples are connected with another area of mathematics. (KHR)
Echo-Enabled Harmonic Generation
Stupakov, Gennady; /SLAC
2012-06-28
A recently proposed concept of the Echo-Enabled Harmonic Generation (EEHG) FEL uses two laser modulators in combination with two dispersion sections to generate a high-harmonic density modulation in a relativistic beam. This seeding technique holds promise of a one-stage soft x-ray FEL that radiates not only transversely but also longitudinally coherent pulses. Currently, an experimental verification of the concept is being conducted at the SLAC National Accelerator Laboratory aimed at the demonstration of the EEHG.
Echo-Enabled Harmonic Generation
Stupakov, Gennady; /SLAC
2012-06-28
A recently proposed concept of the Echo-Enabled Harmonic Generation (EEHG) FEL uses two laser modulators in combination with two dispersion sections to generate a high-harmonic density modulation in a relativistic beam. This seeding technique holds promise of a one-stage soft x-ray FEL that radiates not only transversely but also longitudinally coherent pulses. Currently, an experimental verification of the concept is being conducted at the SLAC National Accelerator Laboratory aimed at the demonstration of the EEHG.
Foliated stochastic calculus: Harmonic measures
Catuogno, Pedro J; Ruffino, Paulo R
2010-01-01
In this article we present an intrinsec construction of foliated Brownian motion via stochastic calculus adapted to foliation. The stochastic approach together with a proposed foliated vector calculus provide a natural method to work on harmonic measures. Other results include a decomposition of the Laplacian in terms of the foliated and basic Laplacians, a characterization of totally invariant measures and a differential equation for the density of harmonic measures.
Harmonic structures and intrinsic torsion
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....
Harmonic analysis on exponential solvable Lie groups
Fujiwara, Hidenori
2015-01-01
This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated alge...
Harmonic Current Predictors for Wind Turbines
Shun-Yu Chan
2013-03-01
Full Text Available The harmonic impact caused by wind turbines should be carefully investigated before wind turbines are interconnected. However, the harmonic currents of wind turbines are not easily predicted due to the variations of wind speed. If the harmonic current outputs can be predicted accurately, the harmonic impact of wind turbines and wind farms for power grids can be analyzed efficiently. Therefore, this paper analyzes the harmonic current characteristics of wind turbines and investigates the feasibility of developing harmonic current predictors. Field measurement, data sorting, and analysis are conducted for wind turbines. Two harmonic current predictors are proposed based on the measured harmonic data. One is the Auto-Regressive and Moving Average (ARMA-based harmonic current predictor, which can be used for real-time prediction. The other is the stochastic harmonic current predictor considering the probability density distributions of harmonic currents. It uses the measured harmonic data to establish the probability density distributions of harmonic currents at different wind speeds, and then uses them to implement a long-term harmonic current prediction. Test results use the measured data to validate the forecast ability of these two harmonic current predictors. The ARMA-based predictor obtains poor performance on some harmonic orders due to the stochastic characteristics of harmonic current caused by the variations of wind speed. Relatively, the prediction results of stochastic harmonic current predictor show that the harmonic currents of a wind turbine in long-term operation can be effectively analyzed by the established probability density distributions. Therefore, the proposed stochastic harmonic current predictor is helpful in predicting and analyzing the possible harmonic problems during the operation of wind turbines and wind farms.
Spherical harmonics in texture analysis
Schaeben, Helmut; van den Boogaart, K. Gerald
2003-07-01
The objective of this contribution is to emphasize the fundamental role of spherical harmonics in constructive approximation on the sphere in general and in texture analysis in particular. The specific purpose is to present some methods of texture analysis and pole-to-orientation probability density inversion in a unifying approach, i.e. to show that the classic harmonic method, the pole density component fit method initially introduced as a distinct alternative, and the spherical wavelet method for high-resolution texture analysis share a common mathematical basis provided by spherical harmonics. Since pole probability density functions and orientation probability density functions are probability density functions defined on the sphere Ω3⊂ R3 or hypersphere Ω4⊂ R4, respectively, they belong at least to the space of measurable and integrable functions L1( Ωd), d=3, 4, respectively. Therefore, first a basic and simplified method to derive real symmetrized spherical harmonics with the mathematical property of providing a representation of rotations or orientations, respectively, is presented. Then, standard orientation or pole probability density functions, respectively, are introduced by summation processes of harmonic series expansions of L1( Ωd) functions, thus avoiding resorting to intuition and heuristics. Eventually, it is shown how a rearrangement of the harmonics leads quite canonically to spherical wavelets, which provide a method for high-resolution texture analysis. This unified point of view clarifies how these methods, e.g. standard functions, apply to texture analysis of EBSD orientation measurements.
Prony Analysis for Power System Transient Harmonics
Qi Li
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.
Validation of phantom-based harmonization for patient harmonization.
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
Bohá\\{v}cik, J; August\\'\\{i}n, P
2013-01-01
We find the possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator. We evaluate the conditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. We discuss the case, when the starting point of the propagator is zero. We present the results in analytical form for positive and negative frequency.
Harmonics radiation of graphene surface plasmon polaritons in terahertz regime
Li, D.; Wang, Y.; Nakajima, M.; Hashida, M.; Wei, Y.; Miyamoto, S.
2016-06-01
This letter presents an approach to extract terahertz radiation from surface plasmon polaritons excited in the surface of a uniform graphene structure by an electron beam. A sidewall configuration is proposed to lift the surface plasmon mode to be close to the light line, so that some of its harmonics have chances to go above the light line and become radiative. The harmonics are considered to be excited by a train of periodic electron bunches. The physical mechanism in this scheme is analyzed with three-dimensional theory, and the harmonics excitation and radiation are demonstrated through numerical calculations. The results show that this technique could be an alternative to transform the surface plasmon polaritons into radiation.
Harmonic morphisms and subharmonic functions
Gabjin Yun
2005-03-01
Full Text Available Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let ÃÂ•:MÃ¢Â†Â’N be a surjective harmonic morphism. We prove that if N admits a subharmonic function with finite Dirichlet integral which is not harmonic, and ÃÂ• has finite energy, then ÃÂ• is a constant map. Similarly, if f is a subharmonic function on N which is not harmonic and such that |df| is bounded, and if Ã¢ÂˆÂ«M|dÃÂ•|<Ã¢ÂˆÂž, then ÃÂ• is a constant map. We also show that if Nm(mÃ¢Â‰Â¥3 has at least two ends of infinite volume satisfying the Sobolev inequality or positivity of the first eigenvalue of the Laplacian, then there are no nonconstant surjective harmonic morphisms with finite energy. For p-harmonic morphisms, similar results hold.
TAX HARMONIZATION VERSUS FISCAL COMPETITION
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.
Harmonic structures and intrinsic torsion
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.......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...
Second Harmonic Light Scattering from Macromolecules: Collagen.
Roth, Shmuel
In this work we present the theory and practice of optical second harmonic generation (SHG) as applied to rat-tail tendon collagen. Our work is the first quantitative application of SHG to biological systems. The angular dependence of SHG is found to display a sharp, intense, forward peak superimposed on a broad background. The sharp peak is shown to imply long-range polar order, while the broad background corresponds to that predicted for the random "up"/"down" array of collagen fibrils seen with the electron microscope. The dependence of fibril diameter distribution on age and state of hydration is measured. Our experiments also reveal information concerning the structure of the fibrils and their arrangement in the tendon. The degree of polar order, the coherence length of tendon for harmonic generation and the absolute magnitude of the nonlinear susceptibility of the collagen fibril are also determined. The biological significance of these findings and the many advantages of SHG for the structural study of biological macromolecules and tissues are discussed.
Harmonic morphisms and bicomplex numbers
Baird, Paul
2009-01-01
We use functions of a bicomplex variable to unify the existing constructions of harmonic morphisms from a 3-dimensional Euclidean or pseudo-Euclidean space to a Riemannian or Lorentzian surface. This is done by using the notion of complex-harmonic morphism between complex Riemannian manifolds and showing how these are given by bicomplex-holomorphic functions when the codomain is one-bicomplex dimensional. Interesting compactifications involving bicomplex manifolds are given. By taking real slices, we recover well-known compactifications for the three possible real cases.
The Obstacle Problem for the -Harmonic Equation
Bao Gejun
2010-01-01
Full Text Available Firstly, we define an order for differential forms. Secondly, we also define the supersolution and subsolution of the -harmonic equation and the obstacle problems for differential forms which satisfy the -harmonic equation, and we obtain the relations between the solutions to -harmonic equation and the solution to the obstacle problem of the -harmonic equation. Finally, as an application of the obstacle problem, we prove the existence and uniqueness of the solution to the -harmonic equation on a bounded domain with a smooth boundary , where the -harmonic equation satisfies where is any given differential form which belongs to .
Third Harmonic Imaging using a Pulse Inversion
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 harmonic component for imaging on any ultrasound system capable of PI. PI was used to perform 3rd harmonic Bmode scans of a water-filled wire phantom on an experimental ultrasound system. The 3rd harmonic...
FROM THE HARMONIZATION NEED TO THE SPONTANEOUS ACCOUNTING HARMONIZATION
Matis Dumitru
2009-05-01
Full Text Available The issue of international accounting harmonization has achieved, mainly within the last decade, a significant dimension in the field of international accounting research. The main determinant factor for this state of the art is the process aiming at redu
High-Efficiency Harmonically Terminated Diode and Transistor Rectifiers
Roberg, M; Reveyrand, T; Ramos, I; Falkenstein, EA; Popovic, Z
2012-12-01
This paper presents a theoretical analysis of harmonically terminated high-efficiency power rectifiers and experimental validation on a class-C single Schottky-diode rectifier and a class-F-1 GaN transistor rectifier. The theory is based on a Fourier analysis of current and voltage waveforms, which arise across the rectifying element when different harmonic terminations are presented at its terminals. An analogy to harmonically terminated power amplifier (PA) theory is discussed. From the analysis, one can obtain an optimal value for the dc load given the RF circuit design. An upper limit on rectifier efficiency is derived for each case as a function of the device on-resistance. Measured results from fundamental frequency source-pull measurement of a Schottky diode rectifier with short-circuit terminations at the second and third harmonics are presented. A maximal device rectification efficiency of 72.8% at 2.45 GHz matches the theoretical prediction. A 2.14-GHz GaN HEMT rectifier is designed based on a class-F-1 PA. The gate of the transistor is terminated in an optimal impedance for self-synchronous rectification. Measurements of conversion efficiency and output dc voltage for varying gate RF impedance, dc load, and gate bias are shown with varying input RF power at the drain. The rectifier demonstrates an efficiency of 85% for a 10-W input RF power at the transistor drain with a dc voltage of 30 V across a 98-Omega resistor.
Multi-photon resonance enhanced super high-order harmonic generation
Lin Zheng-Zhe; Zhuang Jun; Ning Xi-Jing
2010-01-01
This paper proposes highly charged ions pumped by intense laser to produce very high order harmonics.Numerical simulations and full quantum theory of Ne9+ ions driven by laser pulses at 1064 nm in the power range of 109 W/cm2 ～ 1015 W/cm2 show that the emission spectrum corresponds to the electronic transitions from the excited states to the ground state,which is very different from the spectrum of general high-order harmonic generation.In such situation,harmonic order as high as 1000 can be obtained without producing lower order harmonics and the energy conversion efficiency is close to general high order harmonic generation of hydrogen atom in the same laser field.
Demonstration of harmonic interaction in an undulator up to the 15th order
D. Xiang
2013-11-01
Full Text Available We report on experimental studies on the harmonic interaction between an optical laser and a relativistic electron beam in an undulator up to the 15th order. In this experiment, a significant energy modulation is imprinted on the beam longitudinal phase space through the electron-laser interaction when the laser frequency is the 3rd, 5th, 7th, 9th or 15th harmonic of the fundamental resonant frequency of the undulator. The experimental results are in good agreement with theory, and indicate that high harmonic interactions in undulators with large K values and small phase errors can be quite efficient. The results confirm the basic physics of harmonic interaction with a goal toward ushering forward the development of many high harmonic based applications in free-electron lasers.
Image composition with color harmonization
Congde Wang; Rong Zhang; Fan Deng
2009-01-01
Image matting and color transfer are combined to achieve image composition.Firstly,digital matting is used to pull out the region of interest.Secondly,taking color harmonization into account,color transfer techniques are introduced in pasting the region onto the target image.Experimental results show that the proposed approach generates visually plea.sing composite images.
Tides and tidal harmonics at Umbharat, Gujarat
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...
Tectonics of the terrestrial litosphere in spherical harmonics
Mokhnatkin, A. V.; Petrov, S. D.; Gorshkov, V. L.; Shcherbakova, N. V.; Smirnov, S. S.; Trofimov, D. A.
2016-11-01
According to the classical tectonics theory, lithosphere is divided into more than twenty plates that are considered as absolutely rigid. However, modern astronomical and geodetic observations reveal disagreements with the standard theory. First of all, there are already more than two hundreds plates and newer ones are still being discovered. Then, it was found out that lithospheric plates cannot be regarded as absolutely rigid, since they are evidently subject to deformations. This work is aimed at expansion of velocities of the global geodetic network stations into vector spherical harmonic series on the assumption of division of the velocity field into toroidal and poloidal components. Spherical harmonics up to fourth degree are obtained for corresponding components and a preliminary attempt of their geophysical interpretation is submitted.
Harmonic and applied analysis from groups to signals
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 ...
The Computation of Potential Harmonic Coefficients Using Global Crustal Information
Tsoulis, D.
Topographic/isostatic potential harmonic coefficients can be computed from a global elevation model, when one accounts for the compensation of the upper crust according to a certain model of isostasy. The theory is based on a series expansion of the inverse distance function, which enables an efficient computation of the dimensionless poten- tial coefficients on the sphere. The availability of global crustal models permits the application of the same theory, with the exception that here the theoretically defined boundary between upper crust and mantle is replaced with crustal thickness informa- tion derived mainly from processing repeated seismic observations. The present paper deals with the spherical harmonic analysis of such a model, namely the CRUST 2.0 global crustal model, and compares the derived spectrum with the respective coeffi- cient sets delivered by the application of idealized isostatic models such as those of Airy/Heiskanen or Pratt/Hayford.
Third harmonic measurement in printed electronics
Samano, A; Xu, Y.; Harrison, D.; Hunt, C; Wickham, M; Thomas, O.
2014-01-01
The purpose of this research paper is to investigate the defects detecting technique in printed electronics by the third harmonic measurements. Various types of defects were introduced on the samples and the third harmonic signal was measured using a component linearity tester (Radiometer CLT1). The relationship between the defects in the printed samples and the third harmonic signal and the third harmonic ratio was identified.
Third Harmonic Imaging using a Pulse Inversion
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...
Harmonic functions of superprocesses and conditioned superprocesses’
赵学雷
1996-01-01
The harmonic functions for superprocesses are defined by applying the martingale property. Under a general condition, a classification theorem of harmonic functions for homogeneous superprocesses is obtained in terms of the solutions to a measure functional equation. The conditioned superdiffusions in a regular domain by Doob’s harmonic transform are defined and investigated.
Harmonic oscillator: an analysis via Fourier series
de Castro, A S
2013-01-01
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple harmonic oscillator. It is also shown that the damped harmonic oscillator is susceptible to the analysis.
Influence of circular aperture on high-order harmonic generation
Tingting Liu(刘婷婷); Weixin Lu(陆伟新); Dawei Wang(王大威); Hong Yang(杨宏); Qihuang Gong(龚旗煌)
2003-01-01
The influence of circular aperture on the intensity of high-order harmonic generation (HHG) with intense femtosecond laser pulse was studied both experimentally and theoretically. The intensity variety of HHG with the diameter of circular aperture was observed in pulsed Ar gas. The result was discussed and interpreted in terms of the theory of Hankel transform. It is found that using the Gaussian beam truncated by an aperture could enhance the conversion efficiency of HHG at certain conditions.
Bose gases in one-dimensional harmonic trap
JI-XUAN HOU; JING YANG
2016-10-01
Thermodynamic quantities, occupation numbers and their fluctuations of a one-dimensional Bose gas confined by a harmonic potential are studied using different ensemble approaches. Combining number theory methods, a new approach is presented to calculate the occupation numbers of different energy levels in microcanonical ensemble. The visible difference of the ground state occupation number in grand-canonical ensemble and microcanonical ensemble is found to decrease by power law as the number of particles increases.
Thermal state of the general time-dependent harmonic oscillator
Jeong-Ryeol Choi
2003-07-01
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 satisfying Leouville–von Neumann equation to calculate various expectation values in the thermal state. We applied our theory to a special case which is the forced Caldirola–Kanai oscillator.
Schauder estimates for parabolic equation of bi-harmonic type
无
2007-01-01
Global Schauder estimates for the initial-value parabolic problem of the bi-harmonic type are proved, and the existence and uniqueness of the solutions in the suitable space are obtained. Similarly to the second-order case, first a formal expression of solutions by the Fourier transform is obtained, and then the regularity, uniqueness and existence of solutions using the potential theory and approximation argument are got.out approach is simple and straightforward.
Harmonic analysis with respect to heat kernel measure
Hall, B C
2000-01-01
I review certain results in harmonic analysis for systems whose configuration space is a compact Lie group. The results described involve a heat kernel measure, which plays the same role as a Gaussian measure on Euclidean space. The main constructions are group analogs of the Hermite expansion, the Segal-Bargmann transform, and the Taylor expansion. The results are related to geometric quantization, to stochastic analysis, and to the quantization of 1+1-dimensional Yang-Mills theory.
Input Harmonic Analysis on the Slim DC-Link Drive Using Harmonic State Space Model
Yang, Feng; Kwon, Jun Bum; Wang, Xiongfei
2017-01-01
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...... 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...
Second-Harmonic and Third-Harmonic Generations in the Thue-Morse Dielectric Superlattice
蔡祥宝
2002-01-01
Theoretical work on the optical properties of the one-dimensional dielectric superlattice is extended. 3Byv means of a transfer matrix method, the second-harmonic and third-harmonic generations in a one-dimensional tinite Thue Morse dielectric superlattice are analysed. The electric field amplitude variables of the second-harmonic and third-harmonic can be expressed by the formula of matrices. Taking advantage of numerical procedure, we discuss the dependence of the second-harmonic and third-harmonic on the fundamental wavelength and the field amplitude variables of the fundamental wave. High conversion efficiency of the third-harmonic can be obtained at some special fundamental wavelength.
Harmonics elimination algorithm for operational modal analysis using random decrement technique
Modak, S. V.; Rawal, Chetan; Kundra, T. K.
2010-05-01
Operational modal analysis (OMA) extracts modal parameters of a structure using their output response, during operation in general. OMA, when applied to mechanical engineering structures is often faced with the problem of harmonics present in the output response, and can cause erroneous modal extraction. This paper demonstrates for the first time that the random decrement (RD) method can be efficiently employed to eliminate the harmonics from the randomdec signatures. Further, the research work shows effective elimination of large amplitude harmonics also by proposing inclusion of additional random excitation. This obviously need not be recorded for analysis, as is the case with any other OMA method. The free decays obtained from RD have been used for system modal identification using eigen-system realization algorithm (ERA). The proposed harmonic elimination method has an advantage over previous methods in that it does not require the harmonic frequencies to be known and can be used for multiple harmonics, including periodic signals. The theory behind harmonic elimination is first developed and validated. The effectiveness of the method is demonstrated through a simulated study and then by experimental studies on a beam and a more complex F-shape structure, which resembles in shape to the skeleton of a drilling or milling machine tool. Cases with presence of single and multiple harmonics in the response are considered.
Lorentz Harmonics, Squeeze Harmonics and Their Physical Applications
Marilyn E. Noz
2011-02-01
Full Text Available Among the symmetries in physics, the rotation symmetry is most familiar to us. It is known that the spherical harmonics serve useful purposes when the world is rotated. Squeeze transformations are also becoming more prominent in physics, particularly in optical sciences and in high-energy physics. As can be seen from Dirac’s light-cone coordinate system, Lorentz boosts are squeeze transformations. Thus the squeeze transformation is one of the fundamental transformations in Einstein’s Lorentz-covariant world. It is possible to define a complete set of orthonormal functions defined for one Lorentz frame. It is shown that the same set can be used for other Lorentz frames. Transformation properties are discussed. Physical applications are discussed in both optics and high-energy physics. It is shown that the Lorentz harmonics provide the mathematical basis for squeezed states of light. It is shown also that the same set of harmonics can be used for understanding Lorentz-boosted hadrons in high-energy physics. It is thus possible to transmit physics from one branch of physics to the other branch using the mathematical basis common to them.
Boundary behavior of Gleason's problem in hyperbolic harmonic Bergman spaces
REN; Guangbin
2005-01-01
［1］Choe, B. R., Koo, H., Yi, H., Gleason's problem for harmonic functions on Half-spaces, Integr. Equ. Oper.Theory., 2000, 36(3): 269-287.［2］Ren, G. B., Shi, J. H., Gleason's problem in weighted Bergman space on egg domains, Science in China, Ser. A,1998, 41(3): 225-231.［3］Zhu, K. H., The Bergman spaces, the Bloch spaces and Gleason's problem, Trans. Amer. Math. Soc., 1988,309(1): 253-268.［4］Rudin, W., Function Theory in the Unit Ball of Cn, New York: Springer, 1980, 1-436.［5］Krantz, S., Function Theory in Several Complex Variables, New York: John Wiley & Sons Inc, 1992, 1-437.［6］Geller, D., Some results in Hp-theory for the Heisenberg group, Duke Math. J., 1980, 47(2): 365-390.［7］Leutwiler, H., On a distance invariant under Mobius transformations in Rn, Ann. Acad. Sci. Fennice Series A I Mathematica, 1987, 12(1): 3-17.［8］Ahlfors, L. V., Mobius, Transformations in Several Dimensions, Minneapolis: University of Minnesota, 1981,1-150.［9］Axler, S., Bourdon, P., Ramey, W., Harmonic Function Theory, New York: Springer, 1992, 1-231.［10］Coifman, R. R., Rochberg, R., Representation Theorems for Holomorphic and Harmonic Functions in Lp, Paris:Soc. Math. France, 1980, 11-66.［11］Miao, J., Reproducing kernels for harmonic Bergman spaces of the unit ball, Mh. Math., 1998, 125(1): 25-35.［12］Stroethoff, K., Harmonic Bergman spaces, in Holomorphic Spaces (eds. Axler, S., McCarthy, J. E., Sarason,D.), Cambridge: Cambridge University Press, 1998, 51-63.［13］Djrbashian, A. E., Shamoian, F. A., Topics in the Theory of Apα Spaces, Leipzig: Teubner, 1988, 1-199.［14］Erdely, A., Magnus, W., Oberhettinger, F. et al., Higher Transcendental Functions I, New York: McGraw-Hill,1953, 1-302.［15］Rainville, E. D., Special Functions, New York: Chelsea Publishing Co., 1971, 1-365.
Cascading Enhancement of Reflected Optical Third-Harmonic Imaging in Bio-Tissues
Yao; Duan-zheng; Xiong; Gui-guang
2003-01-01
A new nonlinear optical third-harmonic imaging technology in reflected fashion in bio-tissues by using cascading effect, a process whereby the second-order effects combine to contribute to a third-order nonlinear process, hs been analyzed. The performance of the reflected optical third harmonic imaging enhanced by cascading effect in bio-tissues is analyzed with the semi-classical theory. The microscopic understanding of the enhancement of cascaded optical third-harmonic imaging the reflected manner in bio-tissues has been discussed. Some ideas for further enhancement is given.
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.
Harmonic Detection at Initialization With Kalman Filter
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......Most power electronic equipment these days generate harmonic disturbances, these devices hold nonlinear voltage/current characteristic. The harmonics generated can potentially be harmful to the consumer supply. Typically, filters are integrated at the power source or utility location to filter out...
A Fulling-Kuchment theorem for the 1D harmonic oscillator
Guillemin, Victor
2011-01-01
We prove that there exists a pair of "non-isospectral" 1D semiclassical Schr\\"odinger operators whose spectra agree modulo h^\\infty. In particular, all their semiclassical trace invariants are the same. Our proof is based on an idea of Fulling-Kuchment and Hadamard's variational formula applied to suitable perturbations of the harmonic oscillator. Keywords: Inverse spectral problems, semiclassical Schr\\"odinger operators, trace invariants, Hadamard's variational formula, harmonic oscillator, Penrose mushroom, Sturm-Liouville theory.
Efficient Dual-LBO Second-Harmonic Generation by Using a Polarization Modulation Configuration
毕勇; 孙志培; 李瑞宁; 张瑛; 姚爱云; 林学春; 许祖彦; 王舫
2003-01-01
We analyse the relationship of conversion efficiency with the inter-crystal phase shift by the heuristic theory and propose a novel configuration of two cascaded nonlinear crystals for the second-harmonic generation with the polarization modulation. With this configuration, 70% external doubling efffciency is obtained, which is, to the best of our knowledge, the highest conversion efficiency with LBO crystal external frequency doubling. This configuration provides a simple and effective method to improve the second harmonic conversion efficiency.
Analysis on h-harmonics and Dunkl transforms
2015-01-01
As a unique case in this Advanced Courses book series, the authors have jointly written this introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replaced by a reflection-invariant weighted measure. The theory, originally introduced by C. Dunkl, has been expanded on by many authors over the last 20 years. These notes provide an overview of what has been developed so far. The first chapter gives a brief recount of the basics of ordinary spherical harmonics and the Fourier transform. The Dunkl operators, the intertwining operators between partial derivatives and the Dunkl operators are introduced and discussed in the second chapter. The next three chapters are devoted to analysis on the sphere, and the final two chapters to the Dunkl transform. The authors’ focus is on the analysis side of both h-harmonics and Dunkl transforms. The need for background knowledge on reflection groups is kept to a...
Odd Harmonics in Exoplanet Photometry: Weather or Artifact?
Cowan, Nicolas B; Bouffard, Elie; Meynig, Max; Haggard, Hal M
2016-01-01
Photometry of short-period planetary systems allows astronomers to monitor exoplanets, their host stars, and their mutual interactions. In addition to the transits of a planet in front of its star and the eclipses of the planet by its star, researchers have reported flux variations at the orbital frequency and its harmonics: planetary reflection and/or emission and Doppler beaming of starlight produce one peak per orbit, while ellipsoidal variations of a tidally distorted star and/or planet produce two maxima per orbit. Researchers have also reported significant photometric variability at three times the orbital frequency, sometimes much greater than the predictions of tidal theory. The reflected phase variations of a homogeneous planet contains power at even orbital harmonics-important for studies of ellipsoidal variations-but cannot contain odd orbital harmonics. We show that odd harmonics can, however, be produced by an edge-on planet with a time-variable map, or an inclined planet with a North-South (N-S)...
Detection of Harmonic Occurring using Kalman Filtering
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......./current characteristic. These harmonics are not to be allowed to grow beyond a certain limit to avoid any grave consequence to the customer’s main supply. Filters can be implemented at the power source or utility location to eliminate these harmonics. In this paper we detect the instance at which these harmonics occur...
Harmonic vibrations of multispan beams
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....
Harmonic ratcheting for fast acceleration
Cook, N.; Brennan, J. M.; Peggs, S.
2014-04-01
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 are taken into consideration.
Representation Discovery using Harmonic Analysis
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
Properties of Fermion Spherical Harmonics
Hunter, G; Hunter, Geoffrey; Emami-Razavi, Mohsen
2005-01-01
The Fermion Spherical harmonics [$Y_\\ell^{m}(\\theta,\\phi)$ for half-odd-integer $\\ell$ and $m$ - presented in a previous paper] are shown to have the same eigenfunction properties as the well-known Boson Spherical Harmonics [$Y_\\ell^{m}(\\theta,\\phi)$ for integer $\\ell$ and $m$]. The Fermion functions are shown to differ from the Boson functions in so far as the ladder operators $M_+$ ($M_-$) that ascend (descend) the sequence of harmonics over the values of $m$ for a given value of $\\ell$, do not produce the expected result {\\em in just one case}: when the value of $m$ changes from $\\pm{1/2}$ to $\\mp{1/2}$; i.e. when $m$ changes sign; in all other cases the ladder operators produce the usually expected result including anihilation when a ladder operator attempts to take $m$ outside the range: $-\\ell\\le m\\le +\\ell$. The unexpected result in the one case does not invalidate this scalar coordinate representation of spin angular momentum, because the eigenfunction property is essential for a valid quantum mechani...
Molecular Simulations using Spherical Harmonics
CAI, Wen-Sheng; XU, Jia-Wei; SHAO, Xue-Guang; MAIGRET, Bernard
2003-01-01
Computer-aided drug design is to develop a chemical that binds to a target macromolecule known to play a key role in a disease state. In recognition of ligands by their protein receptors,molecular surfaces are often used because they represent the interacting part of molecules and they should reflex the complementarity between ligand and receptor. However, assessing the surface complementarity by searching all relative position of two surfaces is often computationally expensive. The complementarity of lobe-hole is very important in protein-ligand interactions. Spherical harmonic models based on expansions of spherical harmonic functions were used as a fingerprint to approximate the binding cavity and the ligand, respectively. This defines a new way to identify the complementarity between lobes and holes. The advantage of this method is that two spherical harmonic surfaces to be compared can be defined separately. This method can be used as a filter to eliminate candidates among a large number of conformations, and it will speed up the docking procedure. Therefore, it is possible to select complementary ligands or complementary conformations of a ligand and the macromoleeules, by comparing their fingerprints previously stored in a database.
McBee, Kerry D.
resonance producing configurations based upon a required compensation level also provides a utility company with a means to determine if voltage support shall be purchased from an outside source. Documentation within this dissertation describes the engineering and mathematical theories that support the MINLP dependent harmonic resonance identification algorithm.
A generalized harmonic map equation for micromagnetics (abstract)
Kotiuga, P. R.
1991-04-01
Static micromagnetic configurations are determined by minimizing the sum of anisotropy, demagnetization, exchange, and external interaction energies subject to the constraint that the magnitude of the magnetization vector is constant throughout a sample. If this constraint is not explicitly imposed in a numerical or analytical investigation, a Lagrange multiplier type of term must be appended to the energy functional. In a region R, two candidates are λ∫R(1 - ‖m(r)‖2)2 dV and ∫Rλ(r)(1 - ‖m(r)‖2)dV. The first expression is a Higgs or penalty term in the terminology of physicists and numerical analysts. The penalty parameter λ is given a physical meaning through the Ginsburg-Landau theory.1 The second expression is avoided by physicists and numerical analysts since the scalar Lagrange multiplier λ(r) represents an unwelcomed proliferation of variables. Following the theory of harmonic maps, the scalar Lagrange multiplier field is eliminated in this paper and a generalized harmonic map equation for micromagnetics is obtained. This equation has no extraneous phenomenological constants and enables one to ignore the original constraint in numerical solutions. It also provides a means for tying together results concerning singularities of harmonic maps2 with Block point phenomena believed to exist in VBL memories. This, in turn, enables one to make general inferences about the energetics of Bloch points which are not possible through purely topological investigations or simulations involving specific geometries.
Measurement and Analysis Harmonics Using DSP
Lee, Sang Ik; Yoo, Jae Geun; Jeon, Jonog Chay [Korea Electrical Safety Corporation (Korea)
2002-07-01
Limitation countermeasure on harmonics occurred by power conversion installation. motor speed control equipment, and so on of power system is very important problem, and first of all, accuracy harmonics analysis in system is required for appropriate limitation counterplan. Analysis and judgement on power system harmonic by measurement are needed because analysis by mathematical model generally used for these harmonic analysis, if nonlinear ingredient is included in system, is not relatively correct. So, in this paper, system to measure and analyze harmonic by installing it in a power system, using DSP(Digital Signal Processor), is designed and developed, Also, it's performance is verified by installing it in the system that harmonics occurred. (author). 5 refs., 10 figs.
High-harmonic spectroscopy of aligned molecules
Yun, Hyeok; Yun, Sang Jae; Lee, Gae Hwang; Nam, Chang Hee
2017-01-01
High harmonics emitted from aligned molecules driven by intense femtosecond laser pulses provide the opportunity to explore the structural information of molecules. The field-free molecular alignment technique is an expedient tool for investigating the structural characteristics of linear molecules. The underlying physics of field-free alignment, showing the characteristic revival structure specific to molecular species, is clearly explained from the quantum-phase analysis of molecular rotational states. The anisotropic nature of molecules is shown from the harmonic polarization measurement performed with spatial interferometry. The multi-orbital characteristics of molecules are investigated using high-harmonic spectroscopy, applied to molecules of N2 and CO2. In the latter case the two-dimensional high-harmonic spectroscopy, implemented using a two-color laser field, is applied to distinguish harmonics from different orbitals. Molecular high-harmonic spectroscopy will open a new route to investigate ultrafast dynamics of molecules.
Improved Continuous-Time Higher Harmonic Control Using Hinfinity Methods
Fan, Frank H.
The helicopter is a versatile aircraft that can take-off and land vertically, hover efficiently, and maneuver in confined space. This versatility is enabled by the main rotor, which also causes undesired harmonic vibration during operation. This unwanted vibration has a negative impact on the practicality of the helicopter and also increases its operational cost. Passive control techniques have been applied to helicopter vibration suppression, but these methods are generally heavy and are not robust to changes in operating conditions. Feedback control offers the advantages of robustness and potentially higher performance over passive control techniques, and amongst the various feedback schemes, Shaw's higher harmonic control algorithm has been shown to be an effective method for attenuating harmonic disturbance in helicopters. In this thesis, the higher harmonic disturbance algorithm is further developed to achieve improved performance. One goal in this thesis is to determine the importance of periodicity in the helicopter rotor dynamics for control synthesis. Based on the analysis of wind tunnel data and simulation results, we conclude the helicopter rotor can be modeled reasonably well as linear and time-invariant for control design purposes. Modeling the helicopter rotor as linear time-invariant allows us to apply linear control theory concepts to the higher harmonic control problem. Another goal in this thesis is to find the limits of performance in harmonic disturbance rejection. To achieve this goal, we first define the metrics to measure the performance of the controller in terms of response speed and robustness to changes in the plant dynamics. The performance metrics are incorporated into an Hinfinity control problem. For a given plant, the resulting Hinfinity controller achieves the maximum performance, thus allowing us to identify the performance limitation in harmonic disturbance rejection. However, the Hinfinity controllers are of high order, and may
Anomalous Dissipative Quantum Harmonic Oscillator
CHEN Dian-Yong; BAI Zhan-Wu; DONG Yu-Bing
2008-01-01
We investigate the low-temperature statistical properties of a harmonic oscillator coupled to a heat bath, where the low-frequency spectrum vanishes. We obtain the exact result of the zero point energy. Due to the low frequency shortage of environmental oscillators' spectral density, the coordinate and momentum correlation functions decay as r-4and r-6 respectively at zero temperature, where T is the correlation time. The low-temperature behavior of the mean energy does not violate the third law of thermodynamics, but differs largely from the Ohmic spectrum case.
Excited Sessile Drops Perform Harmonically
Chang, Chun-Ti; Steen, Paul H
2013-01-01
In our fluid dynamics video, we demonstrate our method of visualizing and identifying various mode shapes of mechanically oscillated sessile drops. By placing metal mesh under an oscillating drop and projecting light from below, the drop's shape is visualized by the visually deformed mesh pattern seen in the top view. The observed modes are subsequently identified by their number of layers and sectors. An alternative identification associates them with spherical harmonics, as demonstrated in the tutorial. Clips of various observed modes are presented, followed by a 10-second quiz of mode identification.
Making space for harmonic oscillators
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.
Quantizing the damped harmonic oscillator
Latimer, D C [Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235 (United States)
2005-03-04
We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that the unitary dilation of the contraction semigroup governing the dynamics of the system is a logical extension of the doubling procedure, and it allows one to avoid the mathematical difficulties encountered with the previous method.
Studies in Above- and Below-Threshold Harmonics in Argon with an Infrared Femtosecond Laser
Chew, Andrew; Yin, Yanchun; Li, Jie; Ren, Xiaoming; Cunningham, Eric; Wu, Yi; Chang, Zenghu
2016-05-01
We investigate and compare the above- and below-threshold harmonics in Argon gas using our recently-developed 1 kHz, two-cycle (11.4 fs), 3mJ, and carrier-envelope-phase(CEP)-stable laser at 1.6 μm. Such ultraviolet pulses can serve as pump or probe for studying dynamics in atoms and molecules. Unlike high harmonics with photon energy well above the ionization potential, the mechanism for generating harmonics near the ionization threshold is still under intense investigation. Previous work by Chini et al. on below-threshold harmonics was done using a 0.8 μm few-cycle Ti:Sapphire spectrally-broadened source with energy up to 300 μJ. It has been predicted by theory that free-free transitions dominate the below threshold harmonic generation as the laser wavelength increase from near infrared to mid-infrared. We are therefore interested in investigating how using a longer wavelength laser might lead to changes to the behavior of below-threshold harmonics when we vary various parameters. We report the π-periodity CEP dependence and ellipticity dependence of the above- and below-threshold harmonics. This material was based on work supported by National Science Foundation (1068604), Army Research Office (W911NF-14-1-0383), Air Force Office of Scientific Research (FA9550-15-1-0037) and the DARPA PULSE program by a Grant from AMRDEC (W31P4Q1310017).
Polarization-fan high-order harmonics
Fleischer, Avner; Bordo, Eliyahu; Kfir, Ofer; Sidorenko, Pavel; Cohen, Oren
2017-02-01
We predict high-order harmonics in which the polarization within the spectral bandwidth of each harmonic varies with frequency continuously and significantly. For example, the interaction of counter-rotating circularly-polarized bichromatic drivers having close central frequencies with isotropic gas leads to the emission of polarization-fan harmonics where each harmonic in the spectrum has the following property: it is nearly circularly-polarized in one tail of the harmonic peak, linear in the center of the peak and nearly circular with the opposite helicity in the opposite tail. Also, we show that polarization-fan high harmonics with modulated ellipticity are obtained when elliptical drivers are used. Polarization-fan harmonics are obtained as a result of multiple (at least two) head-on recollisions of electrons with their parent ions occurring from different angles in a two-dimensional plane. The use of bichromatic drivers with close central frequencies largely preserves the single-cycle, single-atom and macroscopic physics of ‘ordinary’ high harmonic generation, where both the driver and high harmonics are linearly polarized. Thus, it should offer several attracting features, including (i) a direct route for extending the maximal photon energy of observed helical high harmonics to keV by using bichromatic drivers only in the mid-IR region and (ii) utilizing phase matching methods that were developed for ‘ordinary’ high harmonic generation driven by quasi-monochromatic pulses (e.g. pressure tuning phase matching). These polarization-fan harmonics may be utilized for exploring non-repetitive ultrafast chiral phenomena, e.g. dynamics of magnetic domains, in a single shot.
Introduction to classical and quantum harmonic oscillators
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
Second-harmonic optical coherence tomography
Jiang, Yi; Tomov, Ivan; Wang, Yimin; Chen, Zhongping
2004-05-01
Second-harmonic optical coherence tomography, which uses coherence gating of second-order nonlinear optical responses of biological tissues for imaging, is described and demonstrated. Femtosecond laser pulses were used to excite second-harmonic waves from collagen harvested from rat tail tendon and a reference nonlinear crystal. Second-harmonic interference fringe signals were detected and used for image construction. Because of the strong dependence of second-harmonic generation on molecular and tissue structures, this technique imparts contrast and resolution enhancement to conventional optical coherence tomography.
Harmonic Retrieval in Colored ARMA Noise
无
2000-01-01
We propose a new approach to harmonic retrieval in colored ARMA noise. A suitable filter is first used to remove all the sharp power spectrum peaks of the noisy observed process, then some kinds of cross correlation is employed to identify the noise characteristics. After filtering the noisy observed process with the identified noise characteristics again, SVD-TLS method can be applied to retrieve the harmonics. The proposed approach can be used to retrieve real-valued harmonic signals in colored ARMA noise with no restrictions on the phase coupling of harmonics and the distribution of the noise. Simulation examples show its effectiveness.
Effects of harmonic roving on pitch discrimination
Santurette, Sébastien; de Kérangal, Mathilde le Gal; Joshi, Suyash Narendra
2015-01-01
Performance in pitch discrimination tasks is limited by variability intrinsic to listeners which may arise from peripheral auditory coding limitations or more central noise sources. The present study aimed at quantifying such “internal noise” by estimating the amount of harmonic roving required...... 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...
Harmonization of European track quality
Popović Zdenka
2014-01-01
Full Text Available This paper deals with characterisation of track geometry, track measuring and recording system, as well as geometric quality levels. The legal framework and state of the art in the field of harmonization of track geometry technical regulation in the Republic of Serbia were presented. In particular, the paper discusses the European standard EN 13848 Series (Parts 1-6. Principal track geometric parameters were analyzed according to EN 13848-1. Track geometric quality levels were examined according to EN 13848-5. The evaluation of track geometry quality according to prEN 13848-6 was analyzed as well. The objective of creation of the European standard EN 13848 Series (Parts 1-6 was defining a unique approach for the evaluation of track geometry quality of various European railway infrastructures. The Institute for Standardization of Serbia has adopted and published five of six parts of this standard. This paper is a part of an effort to harmonize the Serbian railway technical regulations with those of the European Union. .
Bansal, Dipanshu; Aref, Amjad; Dargush, Gary; Delaire, Olivier
2016-09-01
Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally-derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. We illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound \\text{FeSi} over a wide range of temperature. Results agree well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.
Optical second-harmonic generation in lossy media: Application to GaSe and InSe
Bringuier, E.; Bourdon, A.; Piccioli, N.; Chevy, A.
1994-06-01
The paper deals with optical second-harmonic generation in a medium absorbing the second-harmonic radiation, and where phase matching between the fundamental and second-harmonic radiation is not necessarily achieved. We first take the waves to be in the form of traveling waves, and describe the damping of the fundamental beam due to harmonic creation. It is found that both second-harmonic absorption and phase mismatch enhance the depletion length of the pump wave. Before depletion, the second-harmonic output power is independent of the traversed thickness if it exceeds the second-harmonic attenuation length. When depletion occurs, the second-harmonic output power is constant, instead of quadratic, in the input power. Next, second-harmonic generation in a plane-parallel plate of lossy material is envisaged in the case of normal incidence, including the multiple reflections expected in high-reflectance materials. The expressions of the harmonic output intensity, transmitted or reflected, of this paper and from the conventional treatment, are compared. The deviation is noticeable in the case of the transmitted harmonic power, and may be considerable in the case of the reflected power. Last, measurements of the second-harmonic output intensity in GaSe and InSe are reported at a fundamental wavelength of 1.06 μm. The sample dependence is in good agreement with our theory, which in turn is applied to derive new values of the nonlinear optical susceptibilities in the layered-structured III-VI materials. The treatment is fully analytical and may be applied to a wealth of materials.
Reduction of multiple harmonic sums and harmonic polylogarithms
Bluemlein, J. [DESY, Deutsches Elektronen Synchrotron, DESY, Platanenallee 6, D-15735 Zeuthen (Germany)]. E-mail: johannes.blumlein@desy.de
2004-11-21
The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index class rather than on their value. We show how to find a basis of the associated algebra. The length of the basis l is found to be =<1/d, where d is the depth of the sums considered and is given by the 2nd Witt formula. It can be also determined by counting the Lyndon words of the respective index set. The relations derived can be used to simplify results of higher-order calculations in QED and QCD.
Reduction of multiple harmonic sums and harmonic polylogarithms
Blümlein, J.
2004-11-01
The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index class rather than on their value. We show how to find a basis of the associated algebra. The length of the basis l is found to be ⩽1/d, where d is the depth of the sums considered and is given by the 2nd Witt formula. It can be also determined by counting the Lyndon words of the respective index set. The relations derived can be used to simplify results of higher-order calculations in QED and QCD.
Farkas, G.; Toth, C. (Research Institute for Solid-State Physics, P.O. Box 49, H-1525 Budapest (Hungary)); Moustaizis, S.D.; Papadogiannis, N.A.; Fotakis, C. (Foundation for Research and Technology, Hellas, P.O. Box 1527, Heraklion 711 10, Crete (Greece))
1992-10-01
Illuminating a gold surface by strong (5 GW/cm{sup 2}) picosecond neodymium-doped yttrium aluminum garnet laser pulses at grazing incidence, we observed a generation of coherent beams of both even and odd harmonics up to fifth order in the reflected direction with efficiencies 10{sup {minus}10--}10{sup {minus}13}. The observed decrease of the harmonic efficiencies with increasing harmonic order is much weaker than predicted by perturbative theories.
Bounded relative motion under zonal harmonics perturbations
Baresi, Nicola; Scheeres, Daniel J.
2017-04-01
The problem of finding natural bounded relative trajectories between the different units of a distributed space system is of great interest to the astrodynamics community. This is because most popular initialization methods still fail to establish long-term bounded relative motion when gravitational perturbations are involved. Recent numerical searches based on dynamical systems theory and ergodic maps have demonstrated that bounded relative trajectories not only exist but may extend up to hundreds of kilometers, i.e., well beyond the reach of currently available techniques. To remedy this, we introduce a novel approach that relies on neither linearized equations nor mean-to-osculating orbit element mappings. The proposed algorithm applies to rotationally symmetric bodies and is based on a numerical method for computing quasi-periodic invariant tori via stroboscopic maps, including extra constraints to fix the average of the nodal period and RAAN drift between two consecutive equatorial plane crossings of the quasi-periodic solutions. In this way, bounded relative trajectories of arbitrary size can be found with great accuracy as long as these are allowed by the natural dynamics and the physical constraints of the system (e.g., the surface of the gravitational attractor). This holds under any number of zonal harmonics perturbations and for arbitrary time intervals as demonstrated by numerical simulations about an Earth-like planet and the highly oblate primary of the binary asteroid (66391) 1999 KW4.
The harmonized INFOGEST in vitro digestion method
Egger, Lotti; Ménard, Olivia; Delgado-Andrade, Cristina; Alvito, Paula; Assunção, Ricardo; Balance, Simon; Barberá, Reyes; Brodkorb, Andre; Cattenoz, Thomas; Clemente, Alfonso; Comi, Irene; Dupont, Didier; Garcia-Llatas, Guadalupe; Lagarda, María Jesús; Feunteun, Le Steven; Janssen Duijghuijsen, Lonneke; Karakaya, Sibel; Lesmes, Uri; Mackie, Alan R.; Martins, Carla; Meynier, Anne; Miralles, Beatriz; Murray, B.S.; Pihlanto, Anne; Picariello, Gianluca; Santos, C.N.; Simsek, Sebnem; Recio, Isidra; Rigby, Neil; Rioux, Laurie Eve; Stoffers, Helena; Tavares, Ana; Tavares, Lucelia; Turgeon, Sylvie; Ulleberg, E.K.; Vegarud, G.E.; Vergères, Guy; Portmann, Reto
2016-01-01
Within the active field of in vitro digestion in food research, the COST Action INFOGEST aimed to harmonize in vitro protocols simulating human digestion on the basis of physiologically inferred conditions. A harmonized static in vitro digestion (IVD) method was recently published as a primary
Sunspots and Their Simple Harmonic Motion
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.
The Harmonic Organization of Auditory Cortex
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.
Pairwise harmonics for shape analysis
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.
Libsharp - spherical harmonic transforms revisited
Reinecke, Martin
2013-01-01
We present libsharp, a code library for spherical harmonic transforms (SHTs), which evolved from the libpsht library, addressing several of its shortcomings, such as adding MPI support for distributed memory systems and SHTs of fields with arbitrary spin, but also supporting new developments in CPU instruction sets like the Advanced Vector Extensions (AVX) or fused multiply-accumulate (FMA) instructions. The library is implemented in portable C99 and provides an interface that can be easily accessed from other programming languages such as C++, Fortran, Python etc. Generally, libsharp's performance is at least on par with that of its predecessor; however, significant improvements were made to the algorithms for scalar SHTs, which are roughly twice as fast when using the same CPU capabilities. The library is available at http://sourceforge.net/projects/libsharp/ under the terms of the GNU General Public License.
Tang, Xiaoli [Physics Department, Auburn University, Auburn, Alabama (United States); Dong, Jianjun [Physics Department, Auburn University, Auburn, Alabama (United States)
2009-06-01
We report a recent first-principles calculation of harmonic and anharmonic lattice dynamics of MgO. The 2nd order harmonic and 3rd order anharmonic interatomic interaction terms are computed explicitly, and their pressure dependences are discussed. The phonon mode Grueneisen parameters derived based on our calculated 3rd order lattice anharmonicity are in good agreement with those estimated using the finite difference method. The implications for lattice thermal conductivity at high pressure are discussed based on a simple kinetic transport theory.
Harmonics Monitoring Survey on LED Lamps
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.
Power Factor Correction to Mitigate Harmonic Distortion
Kochetkov, Gary
Many direct current (DC) devices must receive their power from the alternating current (AC) grid. Rectifiers use diodes to create DC for these devices. Due to diodes' non-linear nature however, harmonics are created and these travel back into the grid. A significant presence of harmonics causes component heating and possible malfunction. A harmonic mitigation procedure is needed. With the correct usage of transistors, the current drawn by a rectifier can be manipulated to remove almost all harmonics. This process is called power factor correction (PFC), and formally acts to reduce the total harmonic distortion (THD) of the current. To investigate this, a three phase active rectifier was computer simulated and a controller was designed to provide switching signals for the transistors. Finally, the device was constructed in the laboratory to drive a DC motor, verifying its operating principle outside of the idealities of simulation.
Bates, David Robert
1962-01-01
Quantum Theory: A Treatise in Three Volumes, I: Elements focuses on the principles, methodologies, and approaches involved in quantum theory, including quantum mechanics, linear combinations, collisions, and transitions. The selection first elaborates on the fundamental principles of quantum mechanics, exactly soluble bound state problems, and continuum. Discussions focus on delta function normalization, spherically symmetric potentials, rectangular potential wells, harmonic oscillators, spherically symmetrical potentials, Coulomb potential, axiomatic basis, consequences of first three postula
ZHANG Jingtao
2015-08-01
Full Text Available High-order harmonics generated from aligned molecules are studied by a nonperturbative QED theory and the effect of the multiple molecular orbits is included.The harmonic spectra generated from single molecular orbit exhibit an interference minimum which is induced by the molecular structure.The location of the spectral minimum shifts with the laser intensity in long laser pulses,but is fixed in ultrashort laser pulses.This difference is owed to the quiver motion of the electron in the laser pulses.The maximal shift of the spectral minimum equals to the increment of the ponderomotive energy and depends linearly on the laser intensity.The interference between the harmonics generated from multiple molecular orbits has two principal effects:one is obscuring the deep minima in the overall harmonic spectrum,the other is manifesting the phase jump in the harmonics generated from single molecular orbit.
Harmonics mitigation on industrial loads using series and parallel ...
This work compared the use of series and parallel resonant harmonic filters in suppressing harmonics using Simulink ... From the analysis, series resonant filter mitigated the total harmonic distortion from 30.080% to 3.460%. ... Article Metrics.
Teaching from a Microgravity Environment: Harmonic Oscillator and Pendulum
Benge, Raymond; Young, Charlotte; Davis, Shirley; Worley, Alan; Smith, Linda; Gell, Amber
2009-04-01
This presentation reports on an educational experiment flown in January 2009 as part of NASA's Microgravity University program. The experiment flown was an investigation into the properties of harmonic oscillators in reduced gravity. Harmonic oscillators are studied in every introductory physics class. The equation for the period of a harmonic oscillator does not include the acceleration due to gravity, so the period should be independent of gravity. However, the equation for the period of a pendulum does include the acceleration due to gravity, so the period of a pendulum should appear longer under reduced gravity (such as lunar or Martian gravity) and shorter under hyper-gravity. These environments can be simulated aboard an aircraft. Video of the experiments being performed aboard the aircraft is to be used in introductory physics classes. Students will be able to record information from watching the experiment performed aboard the aircraft in a similar manner to how they collect data in the laboratory. They can then determine if the experiment matches theory. Video and an experimental procedure are being prepared based upon this flight, and these materials will be available for download by faculty anywhere with access to the internet who wish to use the experiment in their own classrooms.
Resonance widths in open microwave cavities studied by harmonic inversion.
Kuhl, U; Höhmann, R; Main, J; Stöckmann, H-J
2008-06-27
From the measurement of a reflection spectrum of an open microwave cavity, the poles of the scattering matrix in the complex plane have been determined. The resonances have been extracted by means of the harmonic inversion method. By this, it became possible to resolve the resonances in a regime where the linewidths exceed the mean level spacing up to a factor of 10, a value inaccessible in experiments up to now. The obtained experimental distributions of linewidths were found to be in perfect agreement with predictions from random matrix theory when wall absorption and fluctuations caused by couplings to additional channels are considered.
M2-Branes in N = 3 Harmonic Superspace
E. Ivanov
2010-01-01
Full Text Available We give a brief account of the recently proposed N = 3 superfield formulation of the N = 6, 3D superconformal theory of Aharony et al (ABJM describing a low-energy limit of the system of multiple M2-branes on the AdS4×S7/Zk background. This formulation is given in harmonic N = 3 superspace and reveals a number of surprising new features. In particular, the sextic scalar potential of ABJM arises at the on-shell component level as the result of eliminating appropriate auxiliary fields, while there is no explicit superpotential at the off-shell superfield level.
Time-Harmonic Optical Chirality in Inhomogeneous Space
Gutsche, Philipp; Hammerschmidt, Martin; Burger, Sven; Schmidt, Frank
2016-01-01
Optical chirality has been recently suggested to complement the physically relevant conserved quantities of the well-known Maxwell's equations. This time-even pseudoscalar is expected to provide further insight in polarization phenomena of electrodynamics such as spectroscopy of chiral molecules. Previously, the corresponding continuity equation was stated for homogeneous lossless media only. We extend the underlying theory to arbitrary setups and analyse piecewise-constant material distributions in particular. Our implementation in a Finite Element Method framework is applied to illustrative examples in order to introduce this novel tool for the analysis of time-harmonic simulations of nano-optical devices.
Non-Markovian quantum Brownian motion of a harmonic oscillator
Tang, J.
1994-02-01
We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.
Dynamics and ergodicity of the infinite harmonic crystal
van Hemmen, J. L.
1980-10-01
This is a comprehensive, relatively formal study of the a priori infinite harmonic crystal. A phase space is introduced and the equations of motion of a harmonic crystal, which need not be a primitive one, are explicitly solved by several methods. The crystal is taken infinite right at the beginni ng. Exploiting the fact that the dynamics is known we derive the thermal equilibrium state of the infinite system. In so doing we use the classical Kubo-Martin-Schwinger (KMS) condition. The thermal equilibrium state is a, so-called, gaussian measure on the phase space. The traditional procedure of the thermodynamic limit is considered as well. In both cases we exploit the advantages of the technique of Fourier transforms of measures. This technique is elucidated in a separate section, where the many connections with Euclidean quantum field theory are also indicated. Finally we settle the problem of the existence of a crystalline state in its appropriate setting: the infinite system. The system is a “crystal” only if it is three-dimensional. The three essential ingredients of the ergodic analysis are a phase space, a dynamics, and an invariant state, here the thermal equilibrium state. A system is ergodic when the time average of any observable equals its phase average. There are, however, stronger notions of ergodicity which are classified in an “ergodic hierarchy”. When a system is Bernoulli it is at the top of this hierarchy. A finite harmonic system is never ergodic. Here it is shown that, generally speaking, a perfect, infinite harmonic crystal in thermal equilibrium has to be Bernoulli. A detailed discussion of the physical relevance of this result has been included.
Achieser, N I
2004-01-01
A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of pr
Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth;
2015-01-01
be difficult in terms of complex multi-parallel connected systems, especially in the case of renewable energy, where possibilities for intermittent operation due to the weather conditions exist. Hence, it can bring many different operating points to the power converter, and the impedance characteristics can...... change compared to the conventional operation. In this paper, a Harmonic State Space modeling method, which is based on the Linear Time varying theory, is used to analyze different operating points of the parallel connected converters. The analyzed results show that the HSS modeling approach explicitly...
Ali Ajami
2013-01-01
Full Text Available Eliminating the specific harmonics especially low-order harmonics of the output voltage of 9-level inverter using SHE-PWM control scheme is investigated. Harmonic minimization is the intricate optimization problems because the nonlinear transcendental equations have multiple local optima. Increasing the degrees of freedom in the suggested method means that the number of switching angles increases. The suggested method is able to eliminate high number of undesired harmonics. As the number of switching angles increases, using either traditional iterative techniques or resultant theory method gets useless. In this paper to overcome this problem the imperialist competitive algorithm (ICA is used. Also a DC-DC converter is used to enhance the SHE performance in the range for which the conventional SHE methods do not have any solution. Experimental and simulation results of a 9-level inverter show that the proposed method effectively minimizes a large number of particular harmonics so the total harmonics distortion of output voltage will be lower.
Field measurement and analysis of harmonic levels
Karunakara, K.; Muthu Kumar, E.; Rajesh Kumar, O.; Nambudiri, P.V.V.; Srinivasan, K.N. [Central Power Research Institute, Bangalore (India)
1999-07-01
The level of harmonics on the transmission and distribution network is rising over the years, due to the rapid development and usage of electronic and semiconductor devices in the industries, as these devices produce harmonic currents. As the harmonic currents produced by these devices are unproductive and affect the ideal sinusoidal waveshapes, these have to be limited to a tolerable limit at the Point of Common Coupling (PCC). Before setting a tolerable limit on harmonics it is necessary to know the level of harmonics already present in the system, so that the limits suggested are comprehensive and practicable. To have a fair idea about the current and voltage harmonics on the Indian system, Central Power Research Institute (CPRI) has carried out a lot of measurements both on the distribution network and transmission network over the past 13 years. This paper discusses the harmonic measurements carried out by CPRI on different loads and voltage levels on the Indian network. The methodology adopted for measurement and results are also discussed in this paper. (author)
Intravascular ultrasound tissue harmonic imaging in vivo.
Frijlink, Martijn E; Goertz, David E; van Damme, Luc C A; Krams, Rob; van der Steen, Antonius F W
2006-10-01
Tissue harmonic imaging (THI) has been shown to increase image quality of medical ultrasound in the frequency range from 2 to 10 MHz and might, therefore, also be used to improve image quality in intravascular ultrasound (IVUS). In this study we constructed a prototype IVUS system that could operate in both fundamental frequency and second harmonic imaging modes. This system uses a conventional, continuously rotating, single-element IVUS catheter and was operated in fundamental 20 MHz, fundamental 40 MHz, and harmonic 40 MHz modes (transmit 20 MHz, receive 40 MHz). Hydrophone beam characterization measurements demonstrated the build-up of a second harmonic signal as a function of increasing pressure. Imaging experiments were conducted in both a tissue-mimicking phantom and in an atherosclerotic animal model in vivo. Acquisitions of fundamental 20 and 40 MHz and second harmonic acquisitions resulted in cross sections of the phantom and a rabbit aorta. The harmonic results of the imaging experiments showed the feasibility of intravascular THI with a conventional IVUS catheter both in a phantom and in vivo. The harmonic acquisitions also showed the potential of THI to reduce image artifacts compared to fundamental imaging.
Schneidmiller, E A
2012-01-01
Harmonic lasing in a free electron laser with a planar undulator (under the condition that the fundamental frequency is suppressed) might be a cheap and efficient way of extension of wavelength ranges of existing and planned X-ray FEL facilities. Contrary to nonlinear harmonic generation, harmonic lasing can provide much more intense, stable, and narrow-band FEL beam which is easier to handle due to the suppressed fundamental frequency. In this paper we perform a parametrization of the solution of the eigenvalue equation for lasing at odd harmonics, and present an explicit expression for FEL gain length, taking into account all essential effects. We propose and discuss methods for suppression of the fundamental harmonic. We also suggest a combined use of harmonic lasing and lasing at the retuned fundamental wavelength in order to reduce bandwidth and to increase brilliance of X-ray beam at saturation. Considering 3rd harmonic lasing as a practical example, we come to the conclusion that it is much more robust...
Harmonic analysis on symmetric spaces
Terras, Audrey
This text explores the geometry and analysis of higher rank analogues of the symmetric spaces introduced in volume one. To illuminate both the parallels and differences of the higher rank theory, the space of positive matrices is treated in a manner mirroring that of the upper-half space in volume one. This concrete example furnishes motivation for the general theory of noncompact symmetric spaces, which is outlined in the final chapter. The book emphasizes motivation and comprehensibility, concrete examples and explicit computations (by pen and paper, and by computer), history, and, above all, applications in mathematics, statistics, physics, and engineering. The second edition includes new sections on Donald St. P. Richards’s central limit theorem for O(n)-invariant random variables on the symmetric space of GL(n, R), on random matrix theory, and on advances in the theory of automorphic forms on arithmetic groups.
Papadogiannis, N A; Nersisyan, G; Goulielmakis, E; Rakitzis, T P; Hertz, E; Charalambidis, D; Tsakiris, G D; Witte, K
2002-09-01
By use of a transmission-grating-based Michelson interferometer, second-order interferometric as well as intensity autocorrelation traces of the third harmonic of a Ti:sapphire 50-fs laser beam produced in Ar have been measured. The duration of the harmonic is found to be that expected from lowest-order perturbation theory. At this wavelength, the performance of the interferometer with respect to pulse-front distortion and dispersion is found to be satisfactory. This result is a first step toward the use of the interferometer for the temporal characterization of higher harmonics or harmonic superposition forming attosecond pulse trains.
Ito diffusions, modified capacity and harmonic measure. Applications to Schrodinger operators
Denisov, S
2010-01-01
Using certain Ito's equation, we introduce the probability on the space of paths and show its relevance to the scattering properties of multidimensional Schrodinger operator. To relate the geometry of the support of potential to the spectral type we develop a special variant of Potential theory and prove some estimates on the modified Harmonic measure.
Campoamor-Stursberg, R.; Rausch de Traubenberg, M.
2017-04-01
The representation theory of three dimensional real and complex Lie groups is reviewed from the perspective of harmonic functions defined over certain appropriate manifolds. An explicit construction of all unitary representations is given. The realisations obtained are shown to be related with each other by either natural operations as real forms or Inönü-Wigner contractions.
2010-05-10
... future. Financial statement accounting, on the other hand, is intended to report the change in an entity... accommodate evolving changes in financial accounting theory and reporting as well as Congressional changes to...-standing provisions and clearly identifies the special accounting required for harmonization....
Harmonic Aspects of Offshore Wind Farms
Kocewiak, Lukasz Hubert; Bak, Claus Leth; Hjerrild, Jesper
2010-01-01
This paper presents the aim, the work and the findings of a PhD project entitled "Harmonics in Large Offshore Wind Farms". It focuses on the importance of harmonic analysis in order to obtain a better performance of future wind farms. The topic is investigated by the PhD project at Aalborg...... of offshore wind farm (OWF) systems....... University (AAU) and DONG Energy. The objective of the project is to improve and understand the nature of harmonic emission and propagation in wind farms (WFs), based on available information, measurement data and simulation tools. The aim of the project is to obtain validated models and analysis methods...
Double Harmonic Transmission (D.H.T.
Sava Ianici
2006-10-01
Full Text Available The paper presents the construction and functioning of a new type of harmonic drive named double harmonic transmission (D.H.T.. In the second part of this paper is presented the dynamic analysis of the double harmonic transmission, which is based on the results of the experimental researches on the D.H.T. This study of the stress status and the forces distribution is necessary for to determine the durability on the portant elements of the D.H.T.
Selective harmonic control for power converters
Zhou, Keliang; Yang, Yongheng; Blaabjerg, Frede;
2014-01-01
This paper proposes an Internal Model Principle (IMP) based Selective Harmonic Controller (SHC) for power converters. The proposed SHC offers an optimal control solution for power converters to mitigate power harmonics. It makes a good trade-off among cost, complexity and performance. It has high...... accuracy and fast transient response, and it is cost-effective, easy for real-time implementation, and compatible for design rules-of-thumb. An application on a three-phase PWM converter has confirmed the effectiveness of the proposed control scheme in terms of harmonic mitigation....
Harmonic Distortion in CMOS Current Mirrors
Bruun, Erik
1998-01-01
One of the origins of harmonic distortion in CMOS current mirrors is the inevitable mismatch between the MOS transistors involved. In this paper we examine both single current mirrors and complementary class AB current mirrors and develop an analytical model for the mismatch induced harmonic...... distortion. This analytical model is verified through simulations and is used for a discussion of the impact of mismatch on harmonic distortion properties of CMOS current mirrors. It is found that distortion levels somewhat below 1% can be attained by carefully matching the mirror transistors but ultra low...... distortion is not achievable with CMOS current mirrors...
Asymptotic porosity of planar harmonic measure
Graczyk, Jacek; Świaţek, Grzegorz
2013-04-01
We study the distribution of harmonic measure on connected Julia sets of unicritical polynomials. Harmonic measure on a full compact set in ℂ is always concentrated on a set which is porous for a positive density of scales. We prove that there is a topologically generic set {A} in the boundary of the Mandelbrot set such that for every cin {A}, β>0, and λ∈(0,1), the corresponding Julia set is a full compact set with harmonic measure concentrated on a set which is not β-porous in scale λ n for n from a set with positive density amongst natural numbers.
Harmonic analysis of a cruise ship network
Guerin, P.; Miegeville, L. [GE44, France (France); Sahnouni, K. [Chantiers de l' Atlantique (France)
2000-07-01
The number and the power rating of equipment using power electronics have been increasing on board of the ships for many years. At present, the harmonic disturbance must be taken into account from the design stage in order to ensure the smooth running of the installation. This paper presents a harmonic analysis of the electrical distribution system of a cruise ship. The comparison between the evaluated and the real harmonic levels allows us to discuss about the interest and the limits of the estimates. (authors)
Harmonic Oscillators and Elementary Particles
Sobouti, Y
2016-01-01
Two dynamical systems with same symmetry should have features in common, and as far as their shared symmetry is concerned, one may represent the other. The three light quark constituents of the hadrons, a) have an approximate flavor SU(3) symmetry, b) have an exact color SU(3) symmetry, and c) as spin 1/2 particles, have a Lorentz SO(3,1) symmetry. So does a 3D harmonic oscillator. a) Its Hamiltonian has the SU(3) symmetry, breakable if the 3 fundamental modes of oscillation are not identical. b) The 3 directions of oscillation have the permutation symmetry. This enables one to create three copies of unbreakable SU(3) symmetry for each mode of the oscillation, and mimic the color of the elementary particles. And c) The Lagrangian of the 3D oscillator has the SO(3,1) symmetry. This can be employed to accommodate the spin of the particles. In this paper we draw up a one-to-one correspondence between the eigen modes of the Poisson bracket operator of the 3D oscillator and the flavor multiplets of the particles, ...
Harmonization of immunotoxicology study guidelines
NakaK
2002-01-01
Guidance for immunotoxicology studies has been intensively discussed.The European Medicnes Evaluation Agency published the draft guidance on immunotoxicity on December 16,1999 and finalized it on July 27,2000.In the meantime,the US Food and Drug Administration (FDA) published the draft guidance on May 11,2001.The Japanese Ministry of Health,Labor and Welfare and the Japan Pharmaceutical Manufactures Association submitted their interim draft guidance to the International Conference of Harmonization of Technical Requirements for Registration of Pharmaceuticals for Human Use(ICH) for discussion of Decemeber 20,2001.The approaches are taken in these(draft) guidance documents.A major difference among the guidance of the three regions is that only the EU guidance requires some immune function tests for all new medicinal products.The informal expert working proup meeting held in the ICH on February 7,2002 resched the conchusion that the guidelines should be eventually hamonized after collecting more data.A scientific session on immunotoxicity testing will be included in the ICH6,Osake,November 2003.
High-order harmonics with frequency-varying polarization within each harmonic
Fleischer, Avner; Sidorenko, Pavel; Cohen, Oren
2014-01-01
We predict high-order harmonics in which the polarization within the spectral bandwidth of each harmonic varies continuously and significantly. For example, the interaction of counter-rotating circularly-polarized bichromatic drivers having close central frequencies with isotropic gas leads to the emission of polarization-fan harmonics which are nearly circularly-polarized in one tail of the harmonic peak, linear in the center of the peak and nearly circular with the opposite helicity in the opposite tail. Polarization fan harmonics are obtained as a result of multiple (at least two) head-on recollisions of electrons with their parent ions occurring from different angles. The process can be phase-matched using standard methods (e.g. pressure tuning phase matching) and maintains the single-atom polarization property through propagation. These polarization-fan harmonics may be used for exploring non-repetitive ultrafast chiral phenomena, e.g. dynamics of magnetic domains, in a single shot
Cavity-Enhanced Third Harmonic Generation
YANG Xiao-Xue; WU Ying
2005-01-01
We derive the analytical expression of microcavity-enhanced factor for third harmonic generation in terms of detunings, linewidths, and the Purcell factors of the relevant microcavity modes. It is suitable for microcavities with any dimensions and arbitrary geometric shapes.
On conformal supergravity and harmonic superspace
Butter, Daniel
2015-01-01
This paper describes a fully covariant approach to harmonic superspace. It is based on the conformal superspace description of conformal supergravity and involves extending the supermanifold M^{4|8} by the tangent bundle of CP^1. The resulting superspace M^{4|8} x TCP^1 can be identified in a certain gauge with the conventional harmonic superspace M^{4|8} x S^2. This approach not only makes the connection to projective superspace transparent, but simplifies calculations in harmonic superspace significantly by eliminating the need to deal directly with supergravity prepotentials. As an application of the covariant approach, we derive from harmonic superspace the full component action for the sigma model of a hyperkahler cone coupled to conformal supergravity. Further applications are also sketched.
Developing Castable Metal Harmonic Drives Project
National Aeronautics and Space Administration — This effort utilizes the high elastic strain limit and net-shaped processing of metallic glasses to fabricate low-cost harmonic drives that outperform steel. ...
SEVENTH HARMONIC 20 GHz CO-GENERATOR
Hirshfield, Jay L
2014-04-08
To satisfy the need for multi-MW rf sources in frequency ranges where commercial sources do not exist, a study was undertaken on a class of devices based on gyro-harmonic frequency multiplication. This mechanism relies upon adding energy in gyrating motion to a linear electron beam that traverses a rotating-mode TE111-mode drive cavity in a dc magnetic field. The beam then drifts along the magnetic field into a second cavity, operating in the TEn11-mode tuned to the nth harmonic of the drive cavity. Studies of this configuration have been carried out for 2 < n < 7. Results are given for multi-MW, efficient operation of a 7th harmonic device operating at 20 GHz, and a 2nd harmonic device operating at 22.4 GHz.
Reduction of Harmonics by 18-Pulse Rectifier
Stanislav Kocman
2008-01-01
Full Text Available Operation of such electrical devices as data processing and electronics devices, adjustable speed drives or uninterruptible power supply can cause problems by generating harmonic currents into the network, from which they are supplied. Effects of these harmonic currents are various, they can get worse the quality of supply voltage in the network or to have negative influences on devices connected to this network. There are various technical solutions for reduction of harmonics. One of them is using of multi-pulse rectifiers, whereas the 18-pulse rectifier in the structure of adjustable speed drive is briefly presented in this paper including some results of its behaviour. The examined experimental measurements confirmed its very good efficiency in the harmonic mitigation.
Terahertz optics: Terahertz-driven harmonics
Kim, K. Y.; You, Y. S.
2014-02-01
Researchers have demonstrated high-harmonic generation using strong terahertz pulses in a bulk solid without damaging it. The mechanism underpinning such an extreme nonlinearity also generates coherent electromagnetic radiation covering the terahertz, infrared and optical regions.
Multiculturalism, Europhilia and harmonization: harmony or disharmony?
Ruth Sefton-Green
2010-11-01
Full Text Available This paper examines the difficulties of reconciling the values promoted by multiculturalism with the objectives of harmonization. In the event of conflict, examples from English and French law show that harmonization of private law rules does not always achieve its aim of approximating national laws but, on the contrary, often backfires. The question of whether and why these divergences produce Europhile or Eurosceptic positions amongst Member States is addressed. It appears that when maximum harmonisation clashes with multiculturalism this can lead to legal nationalism, whereas minimum harmonization has less negative effects and can stimulate legal experimentation. It is suggested that harmonization requires a mutual listening and learning process in order to accommodate the multiculturalism of Member States and enable Europhilia to flourish in the European Union.
Artificial Satellite Theory: Contribution of the Tesseral Harmonic Coefficients
J. F. Palacían
2006-01-01
Full Text Available En el marco de la teoría del satélite artificial, se presenta aquí el estudio del caso de un satélite artificial moviéndose alrededor de un planeta similar a la Tierra. La fuerza de perturbación considerada es la debida a la inhomogeneidad del potencial gravitacional del planeta. El análisis que se presenta es puramente analítico y considera el truncamiento de las ecuaciones Hamiltonianas a partir del segundo orden, es decir, la influencia de los armónicos zonales y teserales hasta segundo orden. El sistema se formula como un Hamiltoniano con tres grados de libertad. Por medio de tres transformaciones de Lie sucesivas y sin hacer uso de expansiones de Taylor para la excentricidad ni de series de Fourier para las anomalías, el sistema se normaliza hasta orden cinco en un pequeño parámetro. El Hamiltoniano resultante define un sistema de un grado de libertad, que puede ser expresado en el espacio de fases en términos de una colección de variables que tienen en cuenta todas las simetrías del problema. El análisis de este sistema da como resultado la obtención de cuatro regiones de equilibrio relativo y dos tipos de bifurcaciones. La comparación de este problema reducido con el sistema original nos muestra la existencia de varias familias de toroides invariantes, trayectorias periódicas y cuasiperiódicas con el mismo tipo de bifurcaciones.
Theory of THz harmonic generation in semiconductor superlattices (Conference Presentation)
Pereira, Mauro F.; Winge, David O.; Wacker, Andreas
2016-10-01
Superlattices are artificial structures with a wide range of applications and open possibilities for controlling and study transport and optical [M.F. Pereira Jr., Phys. Rev. B 52, (1995)] properties of semiconductors. In this work, we start from the full Nonequilibrium Greens Functions approach [A. Wacker et a, IEEE Journal of Sel. Top. in Quantum Electron.,19 1200611, (2013),T. Schmielau and M.F. Pereira, Appl. Phys. Lett. 95 231111, (2009)] to obtain Voltage-Current curves and compare them with experiments. By adjusting the numerical solutions of the corresponding Dyson equations to a simple model, analytical solutions are given for the nonlinear response of a biased superlattice under sub-THz radiation. The frequency multiplication process leading to multiple harmonicgeneration is described. This hybrid approach leads to predictive simulations and may have important application for a new generation of devices where the superlattices are used as both sources and detectors and may be particular useful for high resolution transient spectroscopy [A.A. Yablokov et at, IEEE Transactions on THz Science and Technology 5, 845 (2015)].
Stable Stationary Harmonic Maps to Spheres
Fang Hua LIN; Chang You WANG
2006-01-01
For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable-stationary harmonic maps to the sphere Sk. We show that the singular set of stable-stationary harmonic maps from B5 to S3 is the union of finitely many isolated singular points and finitely many Holder continuous curves. We also discuss the minimization problem among continuous maps from Bn to S2.
Harmonic distortion in microwave photonic filters.
Rius, Manuel; Mora, José; Bolea, Mario; Capmany, José
2012-04-09
We present a theoretical and experimental analysis of nonlinear microwave photonic filters. Far from the conventional condition of low modulation index commonly used to neglect high-order terms, we have analyzed the harmonic distortion involved in microwave photonic structures with periodic and non-periodic frequency responses. We show that it is possible to design microwave photonic filters with reduced harmonic distortion and high linearity even under large signal operation.
Fractal harmonic law and waterproof/dustproof
Kong Hai-Yan
2014-01-01
Full Text Available The fractal harmonic law admits that the friction between the pure water and the moving surface is the minimum when fractal dimensions of water in Angstrom scale are equal to fractal dimensions of the moving surface in micro scale. In the paper, the fractal harmonic law is applied to demonstrate the mechanism of waterproof/ dustproof. The waterproof phenomenon of goose feathers and lotus leaves is illustrated to verify our results and experimental results agree well with our theoretical analysis.
Evaluation of harmonic detection methods for active power filter applications
Asiminoaei, Lucian; Blaabjerg, Frede; Hansen, Steffan
2005-01-01
filter is to use a good method for current/voltage reference generation. There exist many implementations supported by different theories (either in time- or frequency-domain), which continuously debate their performances proposing ever better solutions. This paper gives a survey of the common used...... theories. Then, the work here proposes a simulation setup that decouples the harmonic reference generator from the active filter model and its controller. In this way the selected methods can be equally analyzed and compared with respect to their performance, which helps anticipating possible...... implementation issues. The conclusions are collected and a comparison is given at the end, which is useful in deciding the future hardware setup implementation. The comparison shows that the choice of numerical filtering is a key factor for obtaining good accuracies and dynamics for an active filter....
Georgiev, Svetlin G
2015-01-01
This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.
Shen, Che-Chou; Shi, Tai-Yu
2011-07-01
Ultrasound tissue harmonic signal generally provides superior image quality as compared to the linear signal. However, since the generation of the tissue harmonic signal is based on finite amplitude distortion of the propagating waveform, the penetration and the sensitivity in tissue harmonic imaging are markedly limited because of the low signal-to-noise ratio (SNR). The method of third harmonic (3f(0)) transmit phasing can improve the tissue harmonic SNR by transmitting at both the fundamental (2.25MHz) and the 3f(0) (6.75MHz) frequencies to achieve mutual enhancement between the frequency-sum and the frequency-difference components of the second harmonic signal. To further increase the SNR without excessive transmit pressure, coded excitation can be incorporated in 3f(0) transmit phasing to boost the tissue harmonic generation. Our analyses indicate that the phase-encoded Golay excitation is suitable in 3f(0) transmit phasing due to its superior transmit bandwidth efficiency. The resultant frequency-sum and frequency-difference components of tissue harmonic signal can be simultaneously Golay-encoded for SNR improvement. The increase of the main-lobe signal with the Golay excitation in 3f(0) transmit phasing are consistent between the tissue harmonic measurements and the simulations. B-mode images of the speckle generating phantom also demonstrate the increases of tissue harmonic SNR for about 11dB without noticeable compression artifacts. For tissue harmonic imaging in combination with the 3f(0) transmit phasing method, the Golay excitation can provide further SNR improvement. Meanwhile, the axial resolution can be effectively restored by pulse compression while the lateral resolution remains unchanged. Copyright © 2010 Elsevier B.V. All rights reserved.
Harmonic Analysis and Group Representation
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.
Pulsed high harmonic generation of light due to pumped Bloch oscillations in noninteracting metals
Freericks, J K; Kemper, A F; Devereaux, T P; 10.1088/0031-8949/2012/T151/014062
2012-01-01
We derive a simple theory for high-order harmonic generation due to pumping a noninteracting metal with a large amplitude oscillating electric field. The model assumes that the radiated light field arises from the acceleration of electrons due to the time-varying current generated by the pump, and also assumes that the system has a constant density of photoexcited carriers, hence it ignores the dipole excitation between bands (which would create carriers in semiconductors). We examine the circumstances under which odd harmonic frequencies would be expected to dominate the spectrum of radiated light, and we also apply the model to real materials like ZnO, for which high-order harmonic generation has already been demonstrated in experiments.
The 3-Dimensional q-Deformed Harmonic Oscillator and Magic Numbers of Alkali Metal Clusters
Bonatsos, Dennis; Raychev, P P; Roussev, R P; Terziev, P A; Bonatsos, Dennis
1999-01-01
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3) > SOq(3) symmetry are compared to experimental data for alkali metal clusters, as well as to theoretical predictions of jellium models, Woods--Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. The 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry of systems of alkali metal clusters.
Buth, Christian; Ullrich, Joachim; Keitel, Christoph H; Hatsagortsyan, Karen Z
2013-01-01
High-order harmonic generation (HHG) in simultaneous intense near-infrared (NIR) laser light and brilliant x rays above an inner-shell absorption edge is examined. A tightly bound inner-shell electron is transferred into the continuum. Then, NIR light takes over and drives the liberated electron through the continuum until it eventually returns to the cation leading in some cases to recombination and emission of a high-harmonic photon that is upshifted by the x-ray photon energy. We develop a theory of this scenario and apply it to 1s electrons of neon atoms. The boosted high-harmonic light is used to generate a single attosecond pulse in the kiloelectronvolt regime. Prospects for nonlinear x-ray physics and HHG-based spectroscopy involving core orbitals are discussed.
Guo, Y.; Keller, J.; Parker, R. G.
2012-06-01
The dynamics of wind turbine planetary gears with gravity effects are investigated using an extended harmonic balance method that extends established harmonic balance formulations to include simultaneous internal and external excitations. The extended harmonic balance method with arc-length continuation and Floquet theory is applied to a lumped-parameter planetary gear model including gravity, fluctuating mesh stiffness, bearing clearance, and nonlinear tooth contact to obtain the planetary gear dynamic response. The calculated responses compare well with time domain integrated mathematical models and experimental results. Gravity is a fundamental vibration source in wind turbine planetary gears and plays an important role in system dynamics, causing hardening effects induced by tooth wedging and bearing-raceway contacts. Bearing clearance significantly reduces the lowest resonant frequencies of translational modes. Gravity and bearing clearance together lowers the speed at which tooth wedging occurs lower than the resonant frequency.
Hanson-Heine, Magnus W. D., E-mail: magnus.hansonheine@nottingham.ac.uk [School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)
2015-10-28
Carefully choosing a set of optimized coordinates for performing vibrational frequency calculations can significantly reduce the anharmonic correlation energy from the self-consistent field treatment of molecular vibrations. However, moving away from normal coordinates also introduces an additional source of correlation energy arising from mode-coupling at the harmonic level. The impact of this new component of the vibrational energy is examined for a range of molecules, and a method is proposed for correcting the resulting self-consistent field frequencies by adding the full coupling energy from connected pairs of harmonic and pseudoharmonic modes, termed vibrational self-consistent field (harmonic correlation). This approach is found to lift the vibrational degeneracies arising from coordinate optimization and provides better agreement with experimental and benchmark frequencies than uncorrected vibrational self-consistent field theory without relying on traditional correlated methods.
Singh, Navpreet; Gupta, Naveen; Singh, Arvinder
2016-12-01
This paper investigates second harmonic generation (SHG) of an intense Cosh-Gaussian (ChG) laser beam propagating through a preformed underdense collisional plasma with nonlinear absorption. Nonuniform heating of plasma electrons takes place due to the nonuniform irradiance of intensity along the wavefront of laser beam. This nonuniform heating of plasma leads to the self-focusing of the laser beam and thus produces strong density gradients in the transverse direction. The density gradients so generated excite an electron plasma wave (EPW) at pump frequency that interacts with the pump beam to produce its second harmonics. To envision the propagation dynamics of the ChG laser beam, moment theory in Wentzel-Kramers-Brillouin (W.K.B) approximation has been invoked. The effects of nonlinear absorption on self-focusing of the laser beam as well as on the conversion efficiency of its second harmonics have been theoretically investigated.
Digital model for harmonic interactions in AC/DC/AC systems
Guarini, A.P.; Rangel, R.D.; Pilotto, L.A.S.; Pinto, R.J.; Passos Junior, R. [Centro de Pesquisas de Energia Eletrica (CEPEL), Rio de Janeiro, RJ (Brazil)
1994-12-31
The main purpose of this paper is to present a model for calculation of HVdc converter harmonics taking into account the influence of the harmonic interactions between the ac systems in dc link transmissions. The ideas and methodologies used in the model development take into account the dc current ripple and ac voltage distortion in the ac systems. The theory of switching functions is applied to contemplate for the frequency conversions between the ac and dc sides, in an iterative process. It is possible then to obtain, even in balanced situations, non-characteristic harmonics that are produced by frequencies originated in the other terminal, which can be significant in a strongly coupled system, such as back-to-back configuration. (author) 9 refs., 3 figs.
Modified ADALINE algorithm for harmonic estimation and selective harmonic elimination in inverters
Vasumathi, B.; Moorthi, S.
2011-11-01
In digital signal processing, algorithms are very well developed for the estimation of harmonic components. In power electronic applications, an objective like fast response of a system is of primary importance. An effective method for the estimation of instantaneous harmonic components, along with conventional harmonic elimination technique, is presented in this article. The primary function is to eliminate undesirable higher harmonic components from the selected signal (current or voltage) and it requires only the knowledge of the frequency of the component to be eliminated. A signal processing technique using modified ADALINE algorithm has been proposed for harmonic estimation. The proposed method stays effective as it converges to a minimum error and brings out a finer estimation. A conventional control based on pulse width modulation for selective harmonic elimination is used to eliminate harmonic components after its estimation. This method can be applied to a wide range of equipment. The validity of the proposed method to estimate and eliminate voltage harmonics is proved with a dc/ac inverter as a simulation example. Then, the results are compared with existing ADALINE algorithm for illustrating its effectiveness.
Stoelinga, Christophe; Heo, Inseok; Long, Glenis; Lee, Jungmee; Lutfi, Robert; Chang, An-Chieh
2015-12-01
The human auditory system has a remarkable ability to "hear out" a wanted sound (target) in the background of unwanted sounds. One important property of sound which helps us hear-out the target is inharmonicity. When a single harmonic component of a harmonic complex is slightly mistuned, that component is heard to separate from the rest. At high harmonic numbers, where components are unresolved, the harmonic segregation effect is thought to result from detection of modulation of the time envelope (roughness cue) resulting from the mistuning. Neurophysiological research provides evidence that such envelope modulations are represented early in the auditory system, at the level of the auditory nerve. When the mistuned harmonic is a low harmonic, where components are resolved, the harmonic segregation is attributed to more centrally-located auditory processes, leading harmonic components to form a perceptual group heard separately from the mistuned component. Here we consider an alternative explanation that attributes the harmonic segregation to detection of modulation when both high and low harmonic numbers are mistuned. Specifically, we evaluate the possibility that distortion products in the cochlea generated by the mistuned component introduce detectable beating patterns for both high and low harmonic numbers. Distortion product otoacoustic emissions (DPOAEs) were measured using 3, 7, or 12-tone harmonic complexes with a fundamental frequency (F0) of 200 or 400 Hz. One of two harmonic components was mistuned at each F0: one when harmonics are expected to be resulted and the other from unresolved harmonics. Many non-harmonic DPOAEs are present whenever a harmonic component is mistuned. These non-harmonic DPOAEs are often separated by the amount of the mistuning (ΔF). This small frequency difference will generate a slow beating pattern at ΔF, because this beating is only present when a harmonic component is mistuned, it could provide a cue for behavioral detection
Ma, Qingyu; Zhang, Dong; Gong, Xiufen; Ma, Yong
2007-04-07
Second or higher order harmonic imaging shows significant improvement in image clarity but is degraded by low signal-noise ratio (SNR) compared with fundamental imaging. This paper presents a phase-coded multi-pulse technique to provide the enhancement of SNR for the desired high-order harmonic ultrasonic imaging. In this technique, with N phase-coded pulses excitation, the received Nth harmonic signal is enhanced by 20 log(10)N dB compared with that in the single-pulse mode, whereas the fundamental and other order harmonic components are efficiently suppressed to reduce image confusion. The principle of this technique is theoretically discussed based on the theory of the finite amplitude sound waves, and examined by measurements of the axial and lateral beam profiles as well as the phase shift of the harmonics. In the experimental imaging for two biological tissue specimens, a plane piston source at 2 MHz is used to transmit a sequence of multiple pulses with equidistant phase shift. The second to fifth harmonic images are obtained using this technique with N = 2 to 5, and compared with the images obtained at the fundamental frequency. Results demonstrate that this technique of relying on higher order harmonics seems to provide a better resolution and contrast of ultrasonic images.
Harmonic Interaction Analysis in Grid Connected Converter using Harmonic State Space (HSS) Modeling
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-model, are in...... behavior interaction and dynamic transfer procedure. Frequency domain as well as time domain simulation results are represented by means of HSS modeling to verify the theoretical analysis. Experimental results are also included to validate the method....... 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...
High-harmonic spectroscopy of molecular isomers
Wong, M. C. H.; Brichta, J.-P.; Bhardwaj, V. R. [Department of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario, K1N 6N5 (Canada); Spanner, M.; Patchkovskii, S. [National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario, K1A 0R6 (Canada)
2011-11-15
We demonstrate that high-order-harmonic generation (HHG) spectroscopy can be used to probe stereoisomers of randomly oriented 1,2-dichloroethylene (C{sub 2}H{sub 2}Cl{sub 2}) and 2-butene (C{sub 4}H{sub 8}). The high-harmonic spectra of these isomers are distinguishable over a range of laser intensities and wavelengths. Time-dependent numerical calculations of angle-dependent ionization yields for 1,2-dichloroethylene suggest that the harmonic spectra of molecular isomers reflect differences in their strong-field ionization. The subcycle ionization yields for the cis isomer are an order of magnitude higher than those for the trans isomer. The sensitivity in discrimination of the harmonic spectra of cis- and trans- isomers is greater than 8 and 5 for 1,2-dichloroethylene and 2-butene, respectively. We show that HHG spectroscopy cannot differentiate the harmonic spectra of the two enantiomers of the chiral molecule propylene oxide (C{sub 3}H{sub 6}O).
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
宁德志; 林红星; 滕斌; 邹青萍
2014-01-01
To investigate higher harmonics induced by a submerged obstacle in the presence of uniform current, a 2D fully nonlinear numerical wave flume (NWF) is developed by use of a time-domain higher-order boundary element method (HOBEM) based on potential flow theory. A four-point method is developed to decompose higher bound and free harmonic waves propagating upstream and downstream around the obstacle. The model predictions are in good agreement with the experimental data for free harmonics induced by a submerged horizontal cylinder in the absence of currents. This serves as a benchmark to reveal the current effects on higher harmonic waves. The peak value of non-dimensional second free harmonic amplitude is shifted upstream for the opposing current relative to that for zero current with the variation of current-free incident wave amplitude, and it is vice versa for the following current. The second-order analysis shows a resonant behavior which is related to the ratio of the cylinder diameter to the second bound mode wavelength over the cylinder. The second-order resonant position slightly downshifted for the opposing current and upshifted for the following current.
Hein, Annette; Larsen, Jakob Juul; Parsekian, Andrew D.
2017-02-01
Surface nuclear magnetic resonance (NMR) is a unique geophysical method due to its direct sensitivity to water. A key limitation to overcome is the difficulty of making surface NMR measurements in environments with anthropogenic electromagnetic noise, particularly constant frequency sources such as powerlines. Here we present a method of removing harmonic noise by utilizing frequency domain symmetry of surface NMR signals to reconstruct portions of the spectrum corrupted by frequency-domain noise peaks. This method supplements the existing NMR processing workflow and is applicable after despiking, coherent noise cancellation, and stacking. The symmetry based correction is simple, grounded in mathematical theory describing NMR signals, does not introduce errors into the data set, and requires no prior knowledge about the harmonics. Modelling and field examples show that symmetry based noise removal reduces the effects of harmonics. In one modelling example, symmetry based noise removal improved signal-to-noise ratio in the data by 10 per cent. This improvement had noticeable effects on inversion parameters including water content and the decay constant T2*. Within water content profiles, aquifer boundaries and water content are more accurate after harmonics are removed. Fewer spurious water content spikes appear within aquifers, which is especially useful for resolving multilayered structures. Within T2* profiles, estimates are more accurate after harmonics are removed, especially in the lower half of profiles.
Nelson, Christopher
2012-01-01
Solutions to Laplace's equation are called harmonic functions. Harmonic functions arise in many applications, such as physics and the theory of stochastic processes. Of interest classically are harmonic polynomials, which have a simple classification. Further, the work of Reznick, building on the work of others, namely Sylvester, Clifford, Rosanes, Gundelfinger, Cartan, Maass and Helgason, has led to a classification of all polynomial solutions to a differential equation of arising from a homogeneous polynomial over an algebraically closed field. The definition of harmonicity can be extended to the space of polynomials in free variables using the concept of a noncommutative Laplacian. Given a positive integer $\\ell$, the $\\ell$-Laplacian of a noncommutative (abbreviated NC) polynomial $p$ in the direction $h$ is defined to be $$ \\lap_{\\ell}[p,h] := \\sum_{i=1}^g \\frac{d^{\\ell}}{dt^{\\ell}} p(x_1,..., x_i + th,..., x_g).$$ A NC polynomial $p$ is said to be $\\ell$-harmonic if $\\lap_{\\ell}[p,h] = 0$. When $\\ell = ...
Harmonic analysis on triple spaces
Danielsen, Thomas Hjortgaard
In this thesis we study examples of triple spaces, both their structure theory, their invariant differential operators as well as analysis on them. The first major results provide us with some examples of triple spaces which are strongly spherical, i.e. satisfy some conditions reminiscent...... of properties of symmetric spaces. The algebras of invariant differential operators for these spaces are studied and the conclusion is that most of them are non-commutative. Finally, we restrict our attention to a single triple space, giving a specific polar decomposition and corresponding integration formula......, and studying the relations between open orbits of parabolic subgroups, multiplicities and distribution vectors....
Generation of high harmonics from silicon
Vampa, Giulio; Thiré, Nicolas; Schmidt, Bruno E; Légaré, Francois; Klug, Dennis D; Corkum, Paul B
2016-01-01
We generate high-order harmonics of a mid-infrared laser from a silicon single crystal and find their origin in the recollision of coherently accelerated electrons with their holes, analogously to the atomic and molecular case, and to ZnO [Vampa et al., Nature 522, 462-464 (2015)], a direct bandgap material. Therefore indirect bandgap materials are shown to sustain the recollision process as well as direct bandgap materials. Furthermore, we find that the generation is perturbed with electric fields as low as 30 V/$\\mu$m, equal to the DC damage threshold. Our results extend high-harmonic spectroscopy to the most technologically relevant material, and open the possibility to integrate high harmonics with conventional electronics.
Coded excitation for ultrasound tissue harmonic imaging.
Song, Jaehee; Kim, Sangwon; Sohn, Hak-Yeol; Song, Tai-Kyong; Yoo, Yang Mo
2010-05-01
Coded excitation can improve the signal-to-noise ratio (SNR) in ultrasound tissue harmonic imaging (THI). However, it could suffer from the increased sidelobe artifact caused by incomplete pulse compression due to the spectral overlap between the fundamental and harmonic components of ultrasound signal after nonlinear propagation in tissues. In this paper, three coded tissue harmonic imaging (CTHI) techniques based on bandpass filtering, power modulation and pulse inversion (i.e., CTHI-BF, CTHI-PM, and CTHI-PI) were evaluated by measuring the peak range sidelobe level (PRSL) with varying frequency bandwidths. From simulation and in vitro studies, the CTHI-PI outperforms the CTHI-BF and CTHI-PM methods in terms of the PRSL, e.g., -43.5dB vs. -24.8dB and -23.0dB, respectively. Copyright 2010 Elsevier B.V. All rights reserved.
Harmonic and complex analysis in several variables
Krantz, Steven G
2017-01-01
Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and...
High harmonic phase in molecular nitrogen
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.
Microscopic optical buffering in a harmonic potential
Sumetsky, M
2015-01-01
In the early days of quantum mechanics, Schr\\"odinger noticed that oscillations of a wave packet in a one-dimensional harmonic potential well are periodic and, in contrast to those in anharmonic potential wells, do not experience distortion over time. This original idea did not find applications up to now since an exact one-dimensional harmonic resonator does not exist in nature and has not been created artificially. However, an optical pulse propagating in a bottle microresonator (a dielectric cylinder with a nanoscale-high bump of the effective radius) can exactly imitate a quantum wave packet in the harmonic potential. Here, we propose a tuneable microresonator that can trap an optical pulse completely, hold it as long as the material losses permit, and release it without distortion. This result suggests the solution of the long standing problem of creating a microscopic optical buffer, the key element of the future optical signal processing devices.
Robust Speech Recognition Using a Harmonic Model
许超; 曹志刚
2004-01-01
Automatic speech recognition under conditions of a noisy environment remains a challenging problem. Traditionally, methods focused on noise structure, such as spectral subtraction, have been employed to address this problem, and thus the performance of such methods depends on the accuracy in noise estimation. In this paper, an alternative method, using a harmonic-based spectral reconstruction algorithm, is proposed for the enhancement of robust automatic speech recognition. Neither noise estimation nor noise-model training are required in the proposed approach. A spectral subtraction integrated autocorrelation function is proposed to determine the pitch for the harmonic model. Recognition results show that the harmonic-based spectral reconstruction approach outperforms spectral subtraction in the middle- and low-signal noise ratio (SNR) ranges. The advantage of the proposed method is more manifest for non-stationary noise, as the algorithm does not require an assumption of stationary noise.
Does high harmonic generation conserve angular momentum?
Fleischer, Avner; Diskin, Tzvi; Sidorenko, Pavel; Cohen, Oren
2013-01-01
High harmonic generation (HHG) is a unique and useful process in which infrared or visible radiation is frequency up converted into the extreme ultraviolet and x ray spectral regions. As a parametric process, high harmonic generation should conserve the radiation energy, momentum and angular momentum. Indeed, conservation of energy and momentum have been demonstrated. Angular momentum of optical beams can be divided into two components: orbital and spin (polarization). Orbital angular momentum is assumed to be conserved and recently observed deviations were attributed to propagation effects. On the other hand, conservation of spin angular momentum has thus far never been studied, neither experimentally nor theoretically. Here, we present the first study on the role of spin angular momentum in extreme nonlinear optics by experimentally generating high harmonics of bi chromatic elliptically polarized pump beams that interact with isotropic media. While observing that the selection rules qualitatively correspond...
RESEARCH ON THE INTERNATIONAL ACCOUNTING HARMONIZATION PROCESS
Tatiana Danescu
2016-12-01
Full Text Available During the last decades, the need of harmonization of the financial reporting frameworks has become more acute, mostly because the capital markets are not restricted anymore by country borders and capital movement has outlined the phenomenon of globalization and internationalism. A significant step in harmonizing the financial reporting was done in the process of normalization through different sets of rules and principles, recognized and applied in many states are the International Financial Reporting Standards (IFRS. The process of international recognition of these standards continues along with conceptual development which is based on epistemological research on specific markets, industries, economies open to international capital flows. In this context it becomes of interest to identify and understand generally accepted and applied accounting elements which carry forward the accounting harmonization process along with factors and circumstances that create diversity in nationally applied financial reporting frameworks.
Simulation of Second Harmonic Ultrasound Fields
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2010-01-01
A non-linear ultrasound imaging simulation software should be capable of simulating the non-linear fields for any kind of transducer, focusing, apodization, and attenuation. At present, a major issue is the overlong simulation time of the non-linear software. An Angular Spectrum Approach (ASA......) using a quasi-linear approximation for solving the Westervelt equation can simulate the second harmonic pressure at any distance. Therefore, it shortens the execution time compared with the operator splitting method. The purpose of this paper is to implement the monochromatic solution for the second......, and the fundamental pressure is calculated by Field II. The second harmonic pressure in k-space along the propagating direction is calculated as an auto-convolution of the fundamental pressure multiplied by an exponential propagating coefficient. In this case, the second harmonic pressure can be calculated using ASA...
Automatic Tooth Segmentation of Dental Mesh Based on Harmonic Fields
Sheng-hui Liao
2015-01-01
Full Text Available An important preprocess in computer-aided orthodontics is to segment teeth from the dental models accurately, which should involve manual interactions as few as possible. But fully automatic partition of all teeth is not a trivial task, since teeth occur in different shapes and their arrangements vary substantially from one individual to another. The difficulty is exacerbated when severe teeth malocclusion and crowding problems occur, which is a common occurrence in clinical cases. Most published methods in this area either are inaccurate or require lots of manual interactions. Motivated by the state-of-the-art general mesh segmentation methods that adopted the theory of harmonic field to detect partition boundaries, this paper proposes a novel, dental-targeted segmentation framework for dental meshes. With a specially designed weighting scheme and a strategy of a priori knowledge to guide the assignment of harmonic constraints, this method can identify teeth partition boundaries effectively. Extensive experiments and quantitative analysis demonstrate that the proposed method is able to partition high-quality teeth automatically with robustness and efficiency.
Automatic Tooth Segmentation of Dental Mesh Based on Harmonic Fields.
Liao, Sheng-hui; Liu, Shi-jian; Zou, Bei-ji; Ding, Xi; Liang, Ye; Huang, Jun-hui
2015-01-01
An important preprocess in computer-aided orthodontics is to segment teeth from the dental models accurately, which should involve manual interactions as few as possible. But fully automatic partition of all teeth is not a trivial task, since teeth occur in different shapes and their arrangements vary substantially from one individual to another. The difficulty is exacerbated when severe teeth malocclusion and crowding problems occur, which is a common occurrence in clinical cases. Most published methods in this area either are inaccurate or require lots of manual interactions. Motivated by the state-of-the-art general mesh segmentation methods that adopted the theory of harmonic field to detect partition boundaries, this paper proposes a novel, dental-targeted segmentation framework for dental meshes. With a specially designed weighting scheme and a strategy of a priori knowledge to guide the assignment of harmonic constraints, this method can identify teeth partition boundaries effectively. Extensive experiments and quantitative analysis demonstrate that the proposed method is able to partition high-quality teeth automatically with robustness and efficiency.
Harmonic Cavity Performance for NSLS-II
Blednykh, Alexei; Podobedov, Boris; Rose, James; Towne, Nathan A; Wang, Jiunn-Ming
2005-01-01
NSLS-II is a 3 GeV ultra-high brightness storage ring that is planned to succeed the present NSLS rings at Brookhaven. Ultra-low emittance bunch combined with a short bunch length results in the Touschek lifetime of only a few hours, which strongly advocates including harmonic RF in the baseline design of NSLS-II. This paper describes the required harmonic RF parameters, trade-offs between the possible choices and the expected system performance, including the implications on lifetime and instabilities.
Geometric Models of the Relativistic Harmonic Oscillator
Cotaescu, I I
1997-01-01
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.
Harmonic Inverse FEL Interaction at 800nm
Sears, C M S; Siemann, R; Spencer, J E
2005-01-01
The inverse Free Electron Laser (IFEL) interaction has recently been proposed and demonstrated as a premodulator for High Gain Harmonic Generation (HGHG) experiments. These experiments utilized the fundamental of the interaction between the laser field and electron bunch. In the current experiment, we explore the higher order resonances of the IFEL interaction from a 3 period, 1.8 centimeter wavelength undulator with a picosecond, 0.25 mJ/pulse laser at 800nm. The resonances are observed by adjusting the gap of the undulator while keeping the beam energy constant. The harmonic IFEL can add flexibility to HGHG FEL design.
Reconstruction of harmonic signals based on bispectrum
FAN Yangyu; SUN Jincai; LI Pingan; XU Jiadong; SHANG Jiuhao
2000-01-01
A method for accurate reconstruction of the harmonic signals from bispectrum is presented. Based on the analysis of the measured harmonic signal, a sinusoid signal with 0phase, 1-amplitude and half of the fundamental frequency combines with the measured signal to form a combined signal, and then the bispectrum analysis is carried out to reconstruct the phase and the amplitude of the measured signal accurately. Without the zero-phase assumption of the fundamental component, using the new method eliminates the phase shifting between the calculated Fourier phase and the true Fourier phase in the existing signal retrieval methods based on bispectrum. The simulation results show the effectiveness of the new method.
Fast algorithms for spherical harmonic expansions, III
Tygert, Mark
2009-01-01
We accelerate the computation of spherical harmonic transforms, using what is known as the butterfly scheme. This provides a convenient alternative to the approach taken in the second paper from this series on "Fast algorithms for spherical harmonic expansions." The requisite precomputations become manageable when organized as a "depth-first traversal" of the program's control-flow graph, rather than as the perhaps more natural "breadth-first traversal" that processes one-by-one each level of the multilevel procedure. We illustrate the results via several numerical examples.
Cascaded third harmonic generation in hybrid graphene-semiconductor waveguides
Smirnova, Daria A
2015-01-01
We study cascaded harmonic generation of hybrid surface plasmons in integrated planar waveguides composed of a graphene layer and a doped-semiconductor slab. We derive a comprehensive model of cascaded third harmonic generation through phase-matched nonlinear interaction of fundamental, second harmonic and third harmonic plasmonic modes supported by the structure. We show that hybrid graphene-semiconductor waveguides can simultaneously phase-match these three interacting harmonics, increasing the total third-harmonic output by a factor of 5 compared to the non-cascaded regime.
Harmonic and reactive behavior of the quasiparticle tunnel current in SIS junctions
Rashid, H.; Desmaris, V.; Pavolotsky, A.; Belitsky, V.
2016-04-01
In this paper, we show theoretically and experimentally that the reactive quasiparticle tunnel current of the superconductor tunnel junction could be directly measured at specific bias voltages for the higher harmonics of the quasiparticle tunnel current. We used the theory of quasiparticle tunneling to study the higher harmonics of the quasiparticle tunnel current in superconducting tunnel junction in the presence of rf irradiation. The impact of the reactive current on the harmonic behavior of the quasiparticle tunnel current was carefully studied by implementing a practical model with four parameters to model the dc I-V characteristics of the superconducting tunnel junction. The measured reactive current at the specific bias voltage is in good agreement with our theoretically calculated reactive current through the Kramers-Kronig transform. This study also shows that there is an excellent correspondence between the behavior of the predicted higher harmonics using the previously established theory of quasiparticle tunnel current in superconducting tunnel junctions by J.R. Tucker and M.J. Feldman and the measurements presented in this paper.
Harmonic and reactive behavior of the quasiparticle tunnel current in SIS junctions
H. Rashid
2016-04-01
Full Text Available In this paper, we show theoretically and experimentally that the reactive quasiparticle tunnel current of the superconductor tunnel junction could be directly measured at specific bias voltages for the higher harmonics of the quasiparticle tunnel current. We used the theory of quasiparticle tunneling to study the higher harmonics of the quasiparticle tunnel current in superconducting tunnel junction in the presence of rf irradiation. The impact of the reactive current on the harmonic behavior of the quasiparticle tunnel current was carefully studied by implementing a practical model with four parameters to model the dc I-V characteristics of the superconducting tunnel junction. The measured reactive current at the specific bias voltage is in good agreement with our theoretically calculated reactive current through the Kramers-Kronig transform. This study also shows that there is an excellent correspondence between the behavior of the predicted higher harmonics using the previously established theory of quasiparticle tunnel current in superconducting tunnel junctions by J.R. Tucker and M.J. Feldman and the measurements presented in this paper.
Badikyan, Karen
2016-01-01
The nonlinear theory of relyativistic strophotron is developed. Classical equations of motion are averaged over fast oscillations. The slow motion phase and saturation parameter are found different from usual undulator oscillation parameters. In the strong field approximation the analytical expression of gain is found on higher harmonics of main resonance frequency.
Governance and organizational theory
Carlos E. Quintero Castellanos
2017-07-01
Full Text Available The objective of this essay is to propose a way to link the theoretical body that has been weaved around governance and organizational theory. For this, a critical exposition is done about what is the theoretical core of governance, the opportunity areas are identified for the link of this theory with organizational theory. The essay concludes with a proposal for the organizational analysis of administrations in governance. The essay addresses with five sections. The first one is the introduction. In the second one, I present a synthesis of the governance in its current use. In the next one are presented the work lines of the good governance. In the fourth part, I show the organizational and managerial limits in the governance theory. The last part develops the harmonization proposal for the governance and organizational theories.
Chiral potential renormalized in harmonic-oscillator space
Yang, C -J
2016-01-01
We renormalize the chiral effective field theory (EFT) potential in harmonic-oscillator (HO) model space. The low energy constants (LECs) are utilized to absorb not just the ultra-violet part of the physics due to the cutoff, but also the infrared part due to the truncation of model space. We use the inverse J-matrix method to reproduce the nucleon-nucleon (NN) scattering phase shifts in the given model space. We demonstrate that by including the NLO correction, the nucleon-nucleon scattering in the continuum could be well reproduced in the truncated HO trap space up to laboratory energy $T_{lab}=100$ MeV with number of HO basis $n_{max}$ as small as 10. A perturbative power counting starts at subleading order is adopted in this work, and how to extract the perturbative contribution is demonstrated. Our work serves as the input to perform ab-initio calculations.
Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
Hod, Shahar
2015-06-01
The spheroidal harmonics Slm (θ ; c) have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues {Alm (c) } of these functions have been determined by many authors. However, it should be emphasized that all the previous asymptotic analyzes were restricted either to the regime m → ∞ with a fixed value of c, or to the complementary regime | c | → ∞ with a fixed value of m. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both m and c. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit m → ∞ and | c | → ∞ with a fixed m / c ratio.
Avalanche effect and gain saturation in high harmonic generation
Serrat, Carles; Budesca, Josep M; Seres, Jozsef; Seres, Enikoe; Aurand, Bastian; Hoffmann, Andreas; Namba, Shinichi; Kuehl, Thomas; Spielmann, Christian
2015-01-01
Optical amplifiers in all ranges of the electromagnetic spectrum exhibit two essential characteristics: i) the input signal during the propagation in the medium is multiplied by the avalanche effect of the stimulated emission to produce exponential growth and ii) the amplification saturates at increasing input signal. We demonstrate that the strong-field theory in the frame of high harmonic generation fully supports the appearance of both the avalanche and saturation effects in the amplification of extreme ultraviolet attosecond pulse trains. We confirm that the amplification takes place only if the seed pulses are perfectly synchronized with the driving strong field in the amplifier. We performed an experimental study and subsequent model calculation on He gas driven by intense 30-fs-long laser pulses, which was seeded with an attosecond pulse train at 110 eV generated in a separated Ne gas jet. The comparison of the performed calculations with the measurements clearly demonstrates that the pumped He gas med...
Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
Hod, Shahar
2015-01-01
The spheroidal harmonics $S_{lm}(\\theta;c)$ have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues $\\{A_{lm}(c)\\}$ of these functions have been determined by many authors. However, it should be emphasized that all previous asymptotic analyzes were restricted either to the regime $m\\to\\infty$ with a fixed value of $c$, or to the complementary regime $|c|\\to\\infty$ with a fixed value of $m$. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both $m$ and $c$. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit $m\\to\\infty$ and $|c|\\to\\infty$ with a fixed $m/c$ ratio.
Bond length, dipole moment, and harmonic frequency of CO
Barnes, Leslie A.; Liu, Bowen; Lindh, Roland
1993-01-01
A detailed comparison of some properties of CO is given, at the modified coupled-pair functional, single and double excitation coupled-cluster (CCSD), and CCSD(T) levels of theory (including a perturbational estimate for connected triple excitations), using a variety of basis sets. With very large one-particle basis sets, the CCSD(T) method gives excellent results for the bond distance, dipole moment, and harmonic frequency of CO. In a (6s 5p 4d 3f 2g 1h) + (1s 1p 1d) basis set, the bond distance is about 0.005a0 too large, the dipole moment about 0.005 a.u. too small, and the frequency about 6/cm too small, when compared with experimental results.
Second harmonic plasma emission involving ion sound waves
Cairns, Iver H.
1987-01-01
The theory for second harmonic plasma emission by the weak turbulence (or random phase) processes L + L + or - S to T, proceeding in two three-wave steps, L + or - S to L prime and L + L prime to T, where L, S and T denote Langmuir, ion sound and electromagnetic waves, respectively, is developed. Kinematic constraints on the characteristics and growth lengths of waves participating in the wave processes, and constraints on the characteristics of the source plasma, are derived. Limits on the brightness temperature of the radiation and the levels of the L prime and S waves are determined. Expressions for the growth rates and path-integrated wave temperatures are derived for simple models of the wave spectra and source plasma.
Nonlinear dynamic response of stay cables under axial harmonic excitation
Xu XIE; He ZHAN; Zhi-cheng ZHANG
2008-01-01
This paper proposes a new numerical simulation method for analyzing the parametric vibration of stay cables based on the theory of nonlinear dynamic response of structures under the asynchronous support excitation.The effects of important parameters related to parametric vibration of cables,I.e., characteristics of structure,excitation frequency,excitation amplitude,damping effect of the air and the viscous damping coefficient of the cables,were investigated by using the proposed method for the cables with significant length difference as examples.The analysis results show that nonlinear finite element method is a powerful technique in analyzing the parametric vibration of cables,the behavior of parametric vibration of the two cables with different Irvine parameters has similar properties,the amplitudes of parametric vibration of cables are related to the frequency and amplitude of harmonic support excitations and the effect of distributed viscous damping on parametric vibration of the cables is very small.
Optical Cherenkov radiation in ultrafast cascaded second-harmonic generation
Bache, Morten; Bang, Ole; Zhou, Binbin
2010-01-01
the dispersive wave. Finally, an investigation of recent experimental results uncovers a four-wave-mixing phenomenon related to Cherenkov radiation that is an additional generation mechanism of long-wavelength radiation that can occur during soliton compression. We discuss the conditions that lead......We show through theory and numerics that when few-cycle femtosecond solitons are generated through cascaded (phase-mismatched) second-harmonic generation, these broadband solitons can emit optical Cherenkov radiation in the form of linear dispersive waves located in the red part of the spectrum....... The beating between the dispersive wave and the soliton generates trailing temporal oscillations on the compressed soliton. Insertion of a simple short-wave pass filter after the crystal can restore a clean soliton. On the other hand, bandpass filtering around the dispersive wave peak results in near...
Perfusion harmonic imaging of the human brain
Metzler, Volker H.; Seidel, Guenter; Wiesmann, Martin; Meyer, Karsten; Aach, Til
2003-05-01
The fast visualisation of cerebral microcirculation supports diagnosis of acute cerebrovascular diseases. However, the commonly used CT/MRI-based methods are time consuming and, moreover, costly. Therefore we propose an alternative approach to brain perfusion imaging by means of ultrasonography. In spite of the low signal/noise-ratio of transcranial ultrasound and the high impedance of the skull, flow images of cerebral blood flow can be derived by capturing the kinetics of appropriate contrast agents by harmonic ultrasound image sequences. In this paper we propose three different methods for human brain perfusion imaging, each of which yielding flow images indicating the status of the patient's cerebral microcirculation by visualising local flow parameters. Bolus harmonic imaging (BHI) displays the flow kinetics of bolus injections, while replenishment (RHI) and diminution harmonic imaging (DHI) compute flow characteristics from contrast agent continuous infusions. RHI measures the contrast agents kinetics in the influx phase and DHI displays the diminution kinetics of the contrast agent acquired from the decay phase. In clinical studies, BHI- and RHI-parameter images were found to represent comprehensive and reproducible distributions of physiological cerebral blood flow. For DHI it is shown, that bubble destruction and hence perfusion phenomena principally can be displayed. Generally, perfusion harmonic imaging enables reliable and fast bedside imaging of human brain perfusion. Due to its cost efficiency it complements cerebrovascular diagnostics by established CT/MRI-based methods.
Challenges and Opportunities for Harmonizing Research Methodology
van Hees, V. T.; Thaler-Kall, K.; Wolf, K. H.
2016-01-01
Objectives: Raw accelerometry is increasingly being used in physical activity research, but diversity in sensor design, attachment and signal processing challenges the comparability of research results. Therefore, efforts are needed to harmonize the methodology. In this article we reflect on how ...
determination of determination of total harmonic distortion
eobe
Harmonic Distortion (THD) of the Distribution lines in the 33kV distri .... guidelines based on industrial distribution system design. IEEE 519-1992 defines ..... studies and also reviewed issues related to the concept. The results of power flow and ...
Sobolev Spaces Associated to the Harmonic Oscillator
B Bongioanni; J L Torrea
2006-08-01
We define the Hermite-Sobolev spaces naturally associated to the harmonic oscillator $H= - + |x|^2$. Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrödinger equation are also considered.
Spatial mode discrimination using second harmonic generation
Delaubert, Vincent; Lassen, Mikael Østergaard; Pulford, David
2007-01-01
Second harmonic generation can be used as a technique for controlling the spatial mode structure of optical beams. We demonstrate experimentally the generation of higher order spatial modes, and that it is possible to use nonlinear phase matching as a predictable and robust technique for the conv...
The Berry Phase for Simple Harmonic Oscillators
Suslov, Sergei K
2011-01-01
We evaluate the Berry phase for a "missing" family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables. It is obtained by the action of the maximal kinematical invariance group on the standard solutions. An explicit simple formula for the phase is found by integration with the help of a computer algebra system.
Collective excitations of harmonically trapped ideal gases
Van Schaeybroeck, B.; Lazarides, A.
2009-01-01
We theoretically study the collective excitations of an ideal gas confined in an isotropic harmonic trap. We give an exact solution to the Boltzmann-Vlasov equation; as expected for a single-component system, the associated mode frequencies are integer multiples of the trapping frequency. We show
Harmonic generation with multiple wiggler schemes
Bonifacio, R.; De Salvo, L.; Pierini, P. [Universita degli Studi, Milano (Italy)
1995-02-01
In this paper the authors give a simple theoretical description of the basic physics of the single pass high gain free electron laser (FEL), describing in some detail the FEL bunching properties and the harmonic generation technique with a multiple-wiggler scheme or a high gain optical klystron configuration.
Regularity of harmonic maps with the potential
CHU; Yuming
2006-01-01
The aim of this work is to prove the partial regularity of the harmonic maps with potential. The main difficulty caused by the potential is how to find the equation satisfied by the scaling function. Under the assumption on the potential we can obtain the equation, however, for a general potential, even if it is smooth, the partial regularity is still open.
Parameter estimation of harmonic polluting industrial loads
Maza-Ortega, J.M.; Gomez-Exposito, A.; Trigo-Garcia, J.L.; Burgos-Payan, M. [University of Sevilla, Sevilla (Spain). Department of Electrical Engineering
2005-12-01
This paper develops a methodology for the estimation of relevant parameters characterizing harmonic polluting industrial loads through a set of measurements acquired at the point of common coupling. The proposed method is capable of obtaining an accurate load model in absence of detailed information about its internal structure and composition. (author)
Transducer for harmonic intravascular ultrasound imaging
Vos, Hendrik J.; Frijlink, Martijn E.; Droog, E.J.; Goertz, David E.; Blacquiere, Gerrit; Gisolf, Anton; de Jong, N.; van der Steen, Antonius F.W.
2005-01-01
A recent study has shown the feasibility of tissue harmonic imaging (THI) using an intravascular ultrasound (IVUS) transducer. This correspondence describes the design, fabrication, and characterization of a THI-optimized piezoelectric transducer with oval aperture of 0.75 mm by 1 mm. The transducer
Feasibility of 3D harmonic contrast imaging
Voormolen, M.M.; Bouakaz, A.; Krenning, B.J.; Lancée, C.; ten Cate, F.; de Jong, N.
2004-01-01
Improved endocardial border delineation with the application of contrast agents should allow for less complex and faster tracing algorithms for left ventricular volume analysis. We developed a fast rotating phased array transducer for 3D imaging of the heart with harmonic capabilities making it
Toeplitz operators on harmonic Bergman spaces
Choe, Boo Rim; Lee, Young Joo; Na, Kyunguk
2004-01-01
We study Toeplitz operators on the harmonic Bergman spaces on bounded smooth domains. Two classes of symbols are considered; one is the class of positive symbols and the other is the class of uniformly continuous symbols. For positive symbols, boundedness, compactness, and membership in the Schatten classes are characterized. For uniformly continuous symbols, the essential spectra are described.
Local Dynamics in an Infinite Harmonic Chain
M. Howard Lee
2016-04-01
Full Text Available By the method of recurrence relations, the time evolution in a local variable in a harmonic chain is obtained. In particular, the autocorrelation function is obtained analytically. Using this result, a number of important dynamical quantities are obtained, including the memory function of the generalized Langevin equation. Also studied are the ergodicity and chaos in a local dynamical variable.
The Harmonic Oscillator–A Simplified Approach
L. R. Ganesan
2008-01-01
Full Text Available Among the early problems in quantum chemistry, the one dimensional harmonic oscillator problem is an important one, providing a valuable exercise in the study of quantum mechanical methods. There are several approaches to this problem, the time honoured infinite series method, the ladder operator method etc. A method which is much shorter, mathematically simpler is presented here.
Coherent control of High-harmonic generation
Barreaux, J.L.P.
2012-01-01
High-harmonic generation (HHG) is a non-linear optical process that can convert laser light with standard wavelengths, such as infrared light, into coherent radiation at much shorter wavelengths in the XUV (extreme ultraviolet) or soft X-ray regime. As opposed to low-order nonlinear frequency
ACCOUNTING HARMONIZATION AND HISTORICAL COST ACCOUNTING
Valentin Gabriel CRISTEA
2017-05-01
Full Text Available There is a huge interest in accounting harmonization and historical costs accounting, in what they offer us. In this article, different valuation models are discussed. Although one notices the movement from historical cost accounting to fair value accounting, each one has its advantages.
Psychoacoustic Approaches for Harmonic Music Mixing
Roman B. Gebhardt
2016-05-01
Full Text Available The practice of harmonic mixing is a technique used by DJs for the beat-synchronous and harmonic alignment of two or more pieces of music. In this paper, we present a new harmonic mixing method based on psychoacoustic principles. Unlike existing commercial DJ-mixing software, which determines compatible matches between songs via key estimation and harmonic relationships in the circle of fifths, our approach is built around the measurement of musical consonance. Given two tracks, we first extract a set of partials using a sinusoidal model and average this information over sixteenth note temporal frames. By scaling the partials of one track over ±6 semitones (in 1/8th semitone steps, we determine the pitch-shift that maximizes the consonance of the resulting mix. For this, we measure the consonance between all combinations of dyads within each frame according to psychoacoustic models of roughness and pitch commonality. To evaluate our method, we conducted a listening test where short musical excerpts were mixed together under different pitch shifts and rated according to consonance and pleasantness. Results demonstrate that sensory roughness computed from a small number of partials in each of the musical audio signals constitutes a reliable indicator to yield maximum perceptual consonance and pleasantness ratings by musically-trained listeners.
Harmonic cascade FEL designs for LUX
Penn, G.; Reinsch, M.; Wurtele, J.; Corlett, J.N.; Fawley, W.M.; Zholents, A.; Wan, W.
2004-07-16
LUX is a design concept for an ultrafast X-ray science facility, based on an electron beam accelerated to GeV energies in are circulating linac. Included in the design are short duration (200 fs or shorter FWHM) light sources using multiple stages of higher harmonic generation, seeded by a 200-250 nm laser of similar duration. This laser modulates the energy of a group of electrons within the electron bunch; this section of the electron bunch then produces radiation at a higher harmonic after entering a second, differently tuned undulator. Repeated stages in a cascade yield increasing photon energies up to 1 keV. Most of the undulators in the cascade operate in the low-gain FEL regime. Harmonic cascades have been designed for each pass of the recirculating linac up to a final electron beam energy of 3.1 GeV. For a given cascade, the photon energy can be selected over a wide range by varying the seed laser frequency and the field strength in the undulators. We present simulation results using the codes GENESIS and GINGER, as well as the results of analytical models which predict FEL performance. We discuss lattice considerations pertinent for harmonic cascade FELs, as well as sensitivity studies and requirements on the electron beam.
Spatial mode discrimination using second harmonic generation
Delaubert, Vincent; Lassen, Mikael Østergaard; Pulford, David
2007-01-01
Second harmonic generation can be used as a technique for controlling the spatial mode structure of optical beams. We demonstrate experimentally the generation of higher order spatial modes, and that it is possible to use nonlinear phase matching as a predictable and robust technique for the conv...
Virial expansion coefficients in the harmonic approximation
R. Armstrong, J.; Zinner, Nikolaj Thomas; V. Fedorov, D.
2012-01-01
The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated...
Probabilistic Aspects of Harmonic Emission of Large Offshore Wind Farms
Jensen, Christian Flytkjær; Bak, Claus Leth; Kocewiak, Lukasz Hubert
2011-01-01
In this article, a new probabilistic method of as-sessment of harmonic emission of large offshore wind farms is presented. Based on measurements from the British wind farm Burbo Banks, probability density functions are estimated for the dominating low order harmonic currents injected by a single...... turbine. The degree and type of dependence between the harmonic emission and the operating point of a single turbine is established. A model of Burbo Banks, suitable for harmonic load flow studies, is created in DIgSILENT Power Factory along with a DPL-script that deals with the probabilistic issues...... of the harmonic emission. The simulated harmonic distortion at the PCC is compared to measurement. This reveals some diffi-culties regarding harmonic load flow studies. The harmonic background distortion in the grid to where the wind farm is connected must be included in the study. Furthermore, a very detailed...
Estimates on Bloch constants for planar harmonic mappings
无
2009-01-01
The Bloch constants for quasiregular harmonic mappings and open planar harmonic mappings are considered. Better estimates are obtained. The results, presented in this paper, improve the one made by Chen et al. and Grigoryan.
harmonics mitigation on industrial loads using series and parallel ...
user
This work compared the use of series and parallel resonant harmonic filters in suppressing harmonics ... industrial applications high technology devices related to communication .... magnification is large because of high circuit Q-factor or.
Product of Toeplitz Operators on the Harmonic Dirichlet Space
Lian Kuo ZHAO
2012-01-01
In this paper,we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space,and show that the product of two Toeplitz operators is another Toeplitz operator only if one factor is constant.
Strongly Dispersive Transient Bragg Grating for High Harmonics
Farrell, J.; Spector, L.S.; /SLAC, PULSE /Stanford U., Phys. Dept. /Stanford U., Appl. Phys. Dept.; Gaarde, M.B.; /SLAC, PULSE /Louisiana State U.; McFarland, B.K.; Bucksbaum, P.H.; Guhr, Markus; /SLAC, PULSE /Stanford U., Phys. Dept. /Stanford U., Appl. Phys. Dept.
2010-06-04
We create a transient Bragg grating in a high harmonic generation medium using two counterpropagating pulses. The Bragg grating disperses the harmonics in angle and can diffract a large bandwidth with temporal resolution limited only by the source size.
Johansen, Steffen Kjær; Baldi, Pascal
2004-01-01
A new scheme for nondestructive characterization of quasi-phase-matching grating structures and temperature gradients through inverse Fourier theory using second-harmonic-generation experiments is proposed. By inserting a mirror to reflect the signals back through the sample, we show how it is po......A new scheme for nondestructive characterization of quasi-phase-matching grating structures and temperature gradients through inverse Fourier theory using second-harmonic-generation experiments is proposed. By inserting a mirror to reflect the signals back through the sample, we show how...... it is possible to retrieve the relevant information by measuring only the generated second-harmonic power, avoiding more complicated phase measurements. The potential of the scheme is emphasized through theoretical and numerical investigations in the case of periodically poled lithium niobate bulk crystals...
Deterministic and Stochastic Study of Wind Farm Harmonic Currents
Sainz, Luis; Mesas, Juan Jose; Teodorescu, Remus;
2010-01-01
Wind farm harmonic emissions are a well-known power quality problem, but little data based on actual wind farm measurements are available in literature. In this paper, harmonic emissions of an 18 MW wind farm are investigated using extensive measurements, and the deterministic and stochastic...... characterization of wind farm harmonic currents is analyzed. Specific issues addressed in the paper include the harmonic variation with the wind farm operating point and the random characteristics of their magnitude and phase angle....
RHIC susceptibility to variations in systematic magnetic harmonic errors
Dell, G.F.; Peggs, S.; Pilat, F.; Satogata, T.; Tepikian, S.; Trbojevic, D.; Wei, J.
1994-08-01
Results of a study to determine the sensitivity of tune to uncertainties of the systematic magnetic harmonic errors in the 8 cm dipoles of RHIC are reported. Tolerances specified to the manufacturer for tooling and fabrication can result in systematic harmonics different from the expected values. Limits on the range of systematic harmonics have been established from magnet calculations, and the impact on tune from such harmonics has been established.
The current issues of internal control and internal audit harmonization
Синюгіна, Наталія Вікторівна
2013-01-01
The relevance of topics related to a harmonization of internal control and internal audit system of internal financial control is being proved. It is high lightened the essence of harmonization period by reviewing existing thoughts on this object, a concept of 'harmonization of internal control and internal audit", and provided reasonably practical recommendations to ensure such harmonization in the modern world. The scientific impact of this research is to clarify the concept of "harmonizati...
Lipschitz spaces and bounded mean oscillation of harmonic mappings
Chen, Sh; Vuorinen, M; Wang, X
2012-01-01
In this paper, we first study the bounded mean oscillation of planar harmonic mappings, then a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings is established. At last, we obtain sharp estimates on Lipschitz number of planar harmonic mappings in terms of bounded mean oscillation norm, which shows that the harmonic Bloch space is isomorphic to $BMO_{2}$ as a Banach space.
Second-Harmonic Generation of Bessel Beams in Lossy Media
丁德胜; 许坚毅; 王耀俊
2002-01-01
We present a further analysis for the second-harmonic generation of Bessel beams in lossy media. The emphasis is put on the effect of absorption to the radial pattern of the second-harmonic beam. It is shown that within the absorption length of the second harmonic, the Bessel second-harmonic beam approaches limited diffraction in the radial direction and behaves as in the case of lossless media.
A Designated Harmonic Suppression Technology for Sampled SPWM
YANG Ping
2005-01-01
Sampled SPWM is an excellent VVVF method of motor speed control, meanwhile the harmonic components of the output wave impairs its applications in practice. A designated harmonic suppression technology is presented for sampled SPWM, which is an improved algorithm for the harmonic suppression in high voltage and high frequency spectrum. As the technology is applied in whole speed adjusting range, the voltage can be conveniently controlled and high frequency harmonic of SP WM is also improved.
A Look at Damped Harmonic Oscillators through the Phase Plane
Daneshbod, Yousef; Latulippe, Joe
2011-01-01
Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the…
Harmonic Mitigation Methods in Large Offshore Wind Power Plants
Kocewiak, Łukasz Hubert; Chaudhary, Sanjay; Hesselbæk, Bo
2013-01-01
Various sources of harmonic problems in large wind power plants (WPPs) and optimized harmonic mitigation methods are presented in this paper. The harmonic problems such as sources of harmonic emission and amplification as well as harmonic stability are identified. Also modern preventive and remed......Various sources of harmonic problems in large wind power plants (WPPs) and optimized harmonic mitigation methods are presented in this paper. The harmonic problems such as sources of harmonic emission and amplification as well as harmonic stability are identified. Also modern preventive...... and remedial harmonic mitigation methods in terms of passive and active filtering are described. It is shown that WPP components such as long HVAC cables and park transformers can introduce significant low-frequency resonances which can affect wind turbine control system operation and overall WPP stability...... as well as amplification of harmonic distortion. It is underlined that there is a potential in terms of active filtering in modern grid-side converters in e.g. wind turbines, STATCOMs or HVDC stations utilized in modern large WPPs. It is also emphasized that the grid-side converter controller should...
Harmonic calculation software for industrial applications with ASDs
Blaabjerg, Frede; Asiminoaei, Lucian; Hansen, Steffan
2007-01-01
This article describes the evaluation of new harmonic calculation software. By using a combination of a prestored database and new interpolation techniques the software can provide the harmonic data on real applications of a very fast speed. The harmonic results obtained with this software have a...
The harmonic force field and absolute infrared intensities of diacetylene
Koops, Th.; Visser, T.; Smit, W.M.A.
1984-01-01
The frequencies, harmonic force field and absolute IR intensities for C4H2 and C4D2 are reported. The experimental harmonized frequencies obey the Teller—Redlich product rule very well. An approximate harmonic force field was obtained from a refinement procedure in which the starting values are adj
Twenty-Four Tuba Harmonics Using a Single Pipe Length
Holmes, Bud; Ruiz, Michael J.
2017-01-01
Harmonics arise naturally from the resonances in strings and pipes. A video demonstration (Ruiz 2016 "YouTube: Tuba Harmonics" (https://youtu.be/souhEzOP9c4)) is provided where a tubist (coauthor Holmes) produces a phenomenal 24 harmonics using a single tuba pipe length by controlling the buzz of his lips. The frequencies of the…
Harmonic Calculation Software for Industrial Applications with Adjustable Speed Drives
Asiminoaei, Lucian; Hansen, S.; Blaabjerg, Frede
2005-01-01
This paper describes the evaluation of a new harmonic software. By using a combination of a pre-stored database and new interpolation techniques the software can very fast provide the harmonic data on real applications. The harmonic results obtained with this software have acceptable precision even...
Double-Undulator Fel for Governing by the Harmonics Generation
Tulupov, A. V.
1993-01-01
Generation of harmonics in the double-undulator FEL based on the additional cyclotron resonance is considered. It is shown that efficient control of harmonics generation is feasible. Only one selected harmonic is generated while the others are suppressed. This effect takes place under a small value
Demonstration of the dual-tripler scheme for increased-bandwidth third-harmonic generation.
Babushkin, A; Craxton, R S; Oskoui, S; Guardalben, M J; Keck, R L; Seka, W
1998-06-15
The dual-tripler scheme for enhancing the bandwidth of third-harmonic generation proposed by Eimerl et al. [Opt. Lett. 22, 1208 (1997)] is experimentally demonstrated for the conversion of 1054-nm radiation to 351 nm. It is shown that the spacing between the triplers must be carefully controlled. The results are in excellent agreement with theory and indicate that fusion lasers can be frequency tripled with a threefold increase in bandwidth.
(3+1)-Dimensional Quantum Mechanics from Monte Carlo Hamiltonian: Harmonic Oscillator
LUO Xiang-Qian; XU Hao; YANG Jie-Chao; WANG Yu-Li; CHANG Di; LIN Yin; Helmut Kroger
2001-01-01
In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions ora quantum theory via Monte Carlo methods. Recently, we developed a Monte Carlo Hamiltonian method for investigating this hard problem and tested the algorithm in quantum-mechanical systems in 1+1 and 2t1 dimensions. In this paper we apply it to the study of thelow-energy quantum physics of the (3+1)-dimensional harmonic oscillator.``
Solution to the Master Equation of a Free Damped Harmonic Oscillator with Linear Driving
杨洁; 逯怀新; 赵博; 赵梅生; 张永德
2003-01-01
We use the Lie algebra representation theory for superoperators to solve the master equation for a harmonic oscillator with a linear driving term in a squeezed thermal reservoir. By using the quantum displacement transformation and squeeze transformation, we show that the master equation has an su(1, 1) Lie algebra structure,with which we obtain the explicit solution to the master equation. A simple but typical example is given to illustrate our method.
CPT/Lorentz Invariance Violation and Quantum Field Theory
Arias, P; Gamboa-Rios, J; López-Sarrion, J; Méndez, F; Arias, Paola; Das, Ashok; Gamboa, Jorge; Lopez-Sarrion, Justo; Mendez, Fernando
2006-01-01
Analogies between the noncommutative harmonic oscillator and noncommutative fields are analyzed. Following this analogy we construct examples of quantum fields theories with explicit CPT and Lorentz symmetry breaking. Some applications to baryogenesis and neutrino oscillation are also discussed
Wang, Xiongfei; Blaabjerg, Frede; Chen, Zhe
2012-01-01
This paper proposes a harmonic impedance synthesis technique for voltage-controlled distributed generation inverters in order to damp harmonic voltage distortion on a distribution network. The approach employs a multiloop control scheme, where a selective harmonic load current feedforward loop ba...
Wang, Xiongfei; Blaabjerg, Frede; Chen, Zhe
2012-01-01
This paper proposes a harmonic impedance synthesis technique for voltage-controlled distributed generation inverter in order to damp harmonic voltage distortion on a distribution network. The approach employs a multiloop control scheme, where a selective load harmonic current feedforward loop bas...
Addition theorems for spin spherical harmonics: II. Results
Bouzas, Antonio O, E-mail: abouzas@mda.cinvestav.mx [Departamento de Fisica Aplicada, CINVESTAV-IPN, Carretera Antigua a Progreso Km. 6, Apdo. Postal 73 ' Cordemex' , Merida 97310, Yucatan (Mexico)
2011-04-22
Based on the results of part I (2011 J. Phys. A: Math. Theor. 44 165301), we obtain the general form of the addition theorem for spin spherical harmonics and give explicit results in the cases involving one spin-s' and one spin-s spherical harmonics with s', s = 1/2, 1, 3/2, and |s' - s| = 0, 1. We also obtain a fully general addition theorem for one scalar and one tensor spherical harmonic of arbitrary rank. A variety of bilocal sums of ordinary and spin spherical harmonics are given in explicit form, including a general explicit expression for bilocal spherical harmonics.
Twenty-four tuba harmonics using a single pipe length
Holmes, Bud; Ruiz, Michael J.
2017-03-01
Harmonics arise naturally from the resonances in strings and pipes. A video demonstration (Ruiz 2016 YouTube: Tuba Harmonics (https://youtu.be/souhEzOP9c4)) is provided where a tubist (coauthor Holmes) produces a phenomenal 24 harmonics using a single tuba pipe length by controlling the buzz of his lips. The frequencies of the harmonics, measured with the free software program Audacity, fall excellently on a linear fit using a spreadsheet. The skillful musical production of so many harmonics with a fixed pipe length is an extraordinary illustration of physics.
Harmonics in large offshore wind farms
Kocewiak, Lukasz Hubert
harmonic origin and observe short-term variation. Non-parametric spectrum estimation is successfully applied to interpolated signals adjusted according to the varying power system frequency. Different data processing techniques are presented and applied depending on the signal (i.e. stationary or non...... suitable data processing methods. Before any of the above aspects could be seriously taken into consideration, a reliable and robust measurement system is needed. This is achieved by carefully designing the hardware and the software layers of the measurement system. It is explained in the report...... that it is of great importance to know the nature of generated harmonics in large offshore wind farms in order to apply the most suitable data processing technique. Time-frequency analysis based on multiresolution wavelet transform is used in order to perform time-frequency domain analysis helpful to distinguish...
Shunt Active Filter in Damping Harmonics Propagation
BERBAOUI, B.
2010-08-01
Full Text Available This paper deals with a hybrid shunt active power filter applied on 500 kV HVDC, after a description of the causes and effects harmonic pollution which may damage equipments and interrupt electric power customers service; in this paper we present the deferent solutions of this problem among one has to study the two most recent types of filtering: passive and hybrid filter. The hybrid filter consists of active filter connected in shunt with passive filter. The hybrid shunt active filter proposed is based on three levels PWM inverter and characterized by detecting the harmonic current flowing into the passive filter and controlled by notch algorithm. This structure has been applied on a test HVDC power system, is presented as a technical solution makes it possible to eliminate the disadvantages from passive filtering, and also economic price of active filtering part. The simulation results justified the effectiveness of this type of filter face of the classic passive filter.
Super/subradiant second harmonic generation
Koganov, Gennady A.; Shuker, Reuben
2017-04-01
A scheme for active second harmonics generation is suggested. The system comprises N three-level atoms in ladder configuration, situated into a resonant cavity. The system generates the field whose frequency is twice the frequency of the pumping laser, and the field phase is locked to the phase of the pumping field. It is found that the system can lase in either superradiant or subradiant regime, depending on the number of atoms N. When N passes some critical value the transition from the super to subradiance occurs in a phase-transition-like manner. Stability study of the steady state supports this conclusion. For experimental realization of the super/subradiant second harmonics generation we propose semiconductor quantum well structures, superconducting quantum circuits, and evanescently coupled waveguides in which equally spaced levels relevant to this study exist.
A remark on infinity harmonic functions
Michael G. Crandall
2001-01-01
Full Text Available A real-valued function $u$ is said to be {it infinity harmonic} if it solves the nonlinear degenerate elliptic equation $-sum_{i,j=1}^nu_{x_1}u_{x_j}u_{x_ix_j}=0$ in the viscosity sense. This is equivalent to the requirement that $u$ enjoys comparison with cones, an elementary notion explained below. Perhaps the primary open problem concerning infinity harmonic functions is to determine whether or not they are continuously differentiable. Results in this note reduce the problem of whether or not a function $u$ which enjoys comparison with cones has a derivative at a point $x_0$ in its domain to determining whether or not maximum points of $u$ relative to spheres centered at $x_0$ have a limiting direction as the radius shrinks to zero.
Harmonic oscillator model for the helium atom
Carlsen, Martin
2015-01-01
A harmonic oscillator model in four dimensions is presented for the helium atom to estimate the distance to the inner and outer electron from the nucleus, the angle between electrons and the energy levels. The method is algebraic and is not based on the choice of correct trial wave function. Three harmonic oscillators and thus three quantum numbers are sufficient to describe the two-electron system. We derive a simple formula for the energy in the general case and in the special case of the Wannier Ridge. For a set of quantum numbers the distance to the electrons and the angle between the electrons are uniquely determined as the intersection between three surfaces. We show that the excited states converge either towards ionization thresholds or towards extreme parallel or antiparallel states and provide an estimate of the ground state energy.
Harmonic beam splitter design and fabrication
Xiaofeng Ma(马小凤); Yingjian Wang(王英剑); Zhengxiu Fan(范正修); Jianda Shao(邵建达)
2004-01-01
Two problems of half-wave hole and high ripples in the transmittance region for a harmonic beam splitter had been pointed out and analyzed. Based on the application of a half-wavelength control and a new admittance matching methods, a harmonic beam splitter was designed and fabricated. The former method eliminated the half-wave hole fundamentally, and the latter smoothed high ripples in the transmittance region effectively. The matching stack consisted of a symmetrically periodic structure and provided a complete matching at the desired wavelength, i.e., both conditions for the equivalent admittance and phase thickness were fulfilled. Furthermore, both the theoretical and the tested curves had been given, and a good agreement between them was obtained.
Harmonic dynamical behaviour of thallous halides
Sarvesh K Tiwari; L J Shukla; K S Upadhyaya
2010-05-01
Harmonic dynamical behaviour of thallous halides (TlCl and TlBr) have been studied using the new van der Waals three-body force shell model (VTSM), which incorporates the effects of the van der Waals interaction along with long-range Coulomb interactions, three-body interactions and short-range second neighbour interactions in the framework of rigid shell model (RSM). Phonon dispersion curves (PDC), variations of Debye temperature with absolute temperature and phonon density of state (PDS) curves have been reported for thallous halides using VTSM. Comparison of experimental values with those of VTSM and TSM are also reported in the paper and a good agreement between experimental and VTSM values has been found, from which it may be inferred that the incorporation of van der Waals interactions is essential for the complete harmonic dynamical behaviour of thallous halides.
Quantum Harmonic Oscillator Algebra and Link Invariants
Gómez, C
1991-01-01
The $q$--deformation $U_q (h_4)$ of the harmonic oscillator algebra is defined and proved to be a Ribbon Hopf algebra.Associated with this Hopf algebra we define an infinite dimensional braid group representation on the Hilbert space of the harmonic oscillator, and an extended Yang--Baxter system in the sense of Turaev. The corresponding link invariant is computed in some particular cases and coincides with the inverse of the Alexander--Conway polynomial. The $R$ matrix of $U_q (h_4)$ can be interpreted as defining a baxterization of the intertwiners for semicyclic representations of $SU(2)_q$ at $q=e^{2 \\pi i/N}$ in the $N \\rightarrow \\infty$ limit.Finally we define new multicolored braid group representations and study their relation to the multivariable Alexander--Conway polynomial.
Effects of harmonic roving on pitch discrimination
Santurette, Sébastien; de Kérangal, Mathilde le Gal; Joshi, Suyash Narendra
2015-01-01
Performance in pitch discrimination tasks is limited by variability intrinsic to listeners which may arise from peripheral auditory coding limitations or more central noise sources. Perceptual limitations may be characterized by measuring an observer’s change in performance when introducting...... external noise in the physical stimulus (Lu and Dosher, 2008). The present study used this approach to attempt to quantify the “internal noise” involved in pitch coding of harmonic complex tones by estimating the amount of harmonic roving required to impair pitch discrimination performance. It remains...... a matter of debate whether pitch perception of natural complex sounds mostly relies on either spectral excitation-based information or temporal periodicity information. Comparing the way internal noise affects the internal representations of such information to how it affects pitch discrimination...
Harmonics in a Wind Power Plant: Preprint
Preciado, V.; Madrigal, M.; Muljadi, E.; Gevorgian, V.
2015-04-02
Wind power generation has been growing at a very fast pace for the past decade, and its influence and impact on the electric power grid is significant. As in a conventional power plant, a wind power plant (WPP) must ensure that the quality of the power being delivered to the grid is excellent. At the same time, the wind turbine should be able to operate immune to small disturbances coming from the grid. Harmonics are one of the more common power quality issues presented by large WPPs because of the high switching frequency of the power converters and the possible nonlinear behavior from electric machines (generator, transformer, reactors) within a power plant. This paper presents a summary of the most important issues related to harmonics in WPPs and discusses practical experiences with actual Type 1 and Type 3 wind turbines in two WPPs.
X-ray FEL based on harmonics generation and electron beam outcoupling
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.
Topological string in harmonic space and correlation functions in $S^3$ stringy cosmology
Saidi, E H; Saidi, El Hassan; Sedra, Moulay Brahim
2006-01-01
We develop the harmonic space method for conifold and use it to study local complex deformations of $T^{\\ast}S^{3}$ preserving manifestly $SL(2,C) $ isometry. We derive the perturbative manifestly $SL(2,C) $ invariant partition function $\\mathcal{Z}_{top}$ of topological string B model on locally deformed conifold. Generic $n$ momentum and winding modes of 2D $c=1$ non critical theory are described by highest $% \\upsilon _{(n,0)}$ and lowest components $\\upsilon_{(0,n)}$ of $SL(2,C) $ spin $s=\\frac{n}{2}$ multiplets $% (\\upsilon _{(n-k,k)}) $, $0\\leq k\\leq n$ and are shown to be naturally captured by harmonic monomials. Isodoublets ($n=1$) describe uncoupled units of momentum and winding modes and are exactly realized as the $SL(2,C) $ harmonic variables $U_{\\alpha}^{+}$ and $V_{\\alpha}^{-}$. We also derive a dictionary giving the passage from Laurent (Fourier) analysis on $T^{\\ast }S^{1}$ ($S^{1}$) to the harmonic method on $T^{\\ast}S^{3}$ ($S^{3}$). The manifestly $SU(2,C) $ covariant correlation functions ...
Topological string in harmonic space and correlation functions in S{sup 3} stringy cosmology
Saidi, El Hassan [Lab/UFR-Physique des Hautes Energies, Faculte des Sciences de Rabat (Morocco) and GNPHE, Groupement National de Physique des Hautes Energies, Siege focal, FS Rabat (Morocco) and Virtual African Centre for Basic Science and Technology, VACBT, Focal point, LabUFR-PHE, Rabat (Morocco)]. E-mail: h-saidi@fsr.ac.ma; Sedra, Moulay Brahim [Lab/UFR-Physique des Hautes Energies, Faculte des Sciences de Rabat (Morocco) and Lab Physique de la Matiere et Rayonnement, Faculte des Sciences Kenitra (Morocco) and GNPHE, Groupement National de Physique des Hautes Energies, Siege focal, FS Rabat (Morocco) and Virtual African Centre for Basic Science and Technology, VACBT, Focal point, LabUFR-PHE, Rabat (Morocco)]. E-mail: sedra@ictp.it
2006-08-07
We develop the harmonic space method for conifold and use it to study local complex deformations of T*S{sup 3} preserving manifestly SL(2,C) isometry. We derive the perturbative manifestly SL(2,C) invariant partition function Z{sub top} of topological string B model on locally deformed conifold. Generic n momentum and winding modes of 2D c=1 noncritical theory are described by highest {upsilon}{sub (n,0)} and lowest components {upsilon}{sub (0,n)} of SL(2,C) spin s=n2 multiplets ({upsilon}{sub (n-k,k)}), 0=
X-ray FEL based on harmonics generation and electron beam outcoupling
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.
Rectification Efficiency of Two Harmonically Coupled Particles
SUN Lian-Xiu
2009-01-01
@@ Transportation properties of two harmonically coupled particles moving in a flashing or rocking ratchet potential are investigated in terms of Langevin simulation. The efficiency for rectification of non-equilibrium fluctuation is calculated by using a new definition. The results show that both the average current and efficiency of two coupled particles in the flashing ratchet are larger than that of a single particle and these quantities are non-monotonous functions of the potential remaining time.
Interpolating Spherical Harmonics for Computing Antenna Patterns
2011-07-01
the specific radon-transform algorithms of ISAR. 28 References [1] Arfken , George [1970] Mathematical Methods for Physicists, second edi- tion...approximation methods . Section 2 sets out two antenna patterns to be tested in the spline algorithm. Section 3 reviews the spherical harmonic functions Y mn...number of samples on the sphere [12]. This compressed sensing result will not reduce the method of moment computations. All the current must be
Harmonic analysis of Doubly Fed Induction Generators
Lindholm, Morten; Rasmussen, Tonny Wederberg
2003-01-01
This paper gives an overview of the frequency spectrum of the stator and rotor currents in a doubly fed induction generator (DFIG) used in wind power applications. The paper also presents a method to eliminate higher harmonics and interharmonics in the DFIG stator current. The method is implemented...... on a 40 kW laboratory model connected to the utility-grid, where the DFIG is supplied by a back-to-back 3-level NPC-converter....
Curvature and bubble convergence of harmonic maps
Kokarev, Gerasim
2010-01-01
We explore geometric aspects of bubble convergence for harmonic maps. More precisely, we show that the formation of bubbles is characterised by the local excess of curvature on the target manifold. We give a universal estimate for curvature concentration masses at each bubble point and show that there is no curvature loss in the necks. Our principal hypothesis is that the target manifold is Kaehler.
Rotating field transformers eliminate rectifier harmonics
Pastor, C.E. [Westinghouse Motor Co., Round Rock, TX (United States); Buckle, K.A. [Univ. of South Florida, Tampa, FL (United States); Luce, J.W. [Luce (John W.), Tampa, FL (United States)
1995-10-01
The rotating field transformer is a static device that has the same magnetic field as a three phase motor. When used to feed diode rectifiers, it converts ac to dc with low ripple on the output voltage and remarkably low current distortion on the input. Filters are not needed. This is a timely development because it is an economical and very effective solution to the growing problem of power system harmonics.
Harmonic Resonances in Wind Power Plants
Fernandez, Francisco Daniel Freijedo; Chaudhary, Sanjay; Teodorescu, Remus
2015-01-01
converters. Subsequently, pros and cons of frequency and time domain analysis methods are outlined. The next sections are devoted to mitigation methods implemented in the power electronics converters. From the wind turbine perspective, different techniques to enhance the robustness of the controller...... are analyzed. Subsequently, the suitability for active damping of harmonics using STATCOM devices is assessed, with focus both on control techniques and power converter technologies....
Fischer decomposition in symplectic harmonic analysis
Brackx, Fred; De Schepper, Hennie; Eelbode, David; Lávička, Roman; Soucek, Vladimir
2014-01-01
In the framework of quaternionic Clifford analysis in Euclidean space , which constitutes a refinement of Euclidean and Hermitian Clifford analysis, the Fischer decomposition of the space of complex valued polynomials is obtained in terms of spaces of so-called (adjoint) symplectic spherical harmonics, which are irreducible modules for the symplectic group Sp. Its Howe dual partner is determined to be sl(2, C) circle plus sl(2, C) = so(4, C).
Food legislation and its harmonization in Russia.
Shamtsyan, Mark
2014-08-01
Bringing Russian legislation into compliance with international norms and standards is necessary after its accession to the World Trade Organization. Harmonization of food legislation and of sanitary and phytosanitary measures are among the problems that had to be solved first. Many Russian food and trade regulations had been changed or are still in the process of being reformed, largely owing to a policy of integration pursued by the Customs Union of Russia, Belarus and Kazakhstan. However, as a member of the Eurasian Economic Community, Russia is also engaged not only in harmonization throughout the Customs Union but also Kirgizstan and Tajikistan, and Armenia, Moldova and Ukraine as observer countries. Russia also continues to coordinate policy reforms closely with the European Union, its primary trade partner, ultimately bringing Russian food and sanitary norms closer to international standards (e.g. Codex). Today, all participants in the Russian food production chain, processing and sale of foods have to deal with growing numbers of security standards. Many organizations are certified under several schemes, which leads to unnecessary costs. Harmonization of standards has helped promote solutions in the domestic market as well as import-export of foods and raw materials for production. Priorities have included food safety for human health, consumer protection, removal of hazardous and/or adulterated products and increased competition within the domestic food market as well as mutual recognition of certification in bilateral and multilateral (inter)national agreements. © 2013 Society of Chemical Industry.
Harmonics of circadian gene transcription in mammals.
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.
Harmonics of circadian gene transcription in mammals.
Hughes, Michael E; DiTacchio, Luciano; Hayes, Kevin R; Vollmers, Christopher; Pulivarthy, S; Baggs, Julie E; Panda, Satchidananda; Hogenesch, John B
2009-04-01
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.
Means of Harmonization in Religious Discourse
Irina Ščukina
2012-12-01
Full Text Available Means of harmonization of religious discourse are considered by studying communicational behaviour (verbal and nonverbal between the religion institution and believers. The following factors defining specificity of realization of harmonization in Orthodox and other religious texts are taken into account: the communication channel between the author and the reader, a defining speech genre, the command of language (communication code, and extra-linguistic factors. It is shown that sharing the general social, historical and national experience, as well as a lexical overlapping of actors on both sides of the communication channel are the deciding elements of the harmonization process. The analysis also shows that usage of rational argumentation is more likely to lead to harmonisation in comparison to other rhetoric tools (i. e. affective ones or story-telling. Rational and unemotional sermonic discourse is perceived as a sign of respect (namely, for the listener's intelligence. Another successful and much-applied way seems to be evoking a feeling of equality, unity and/or identity between clerics and their flocks.
Breuer, G D; Chow, J H; Lindh, C B; Miller, N W; Numrich, F H; Price, W W; Turner, A E; Whitney, R R
1982-09-01
Improved methods are needed to characterize ac system harmonic behavior for ac filter design for HVDC systems. The purpose of this General Electric Company RP1138 research is to evaluate the present filter design practice and to investigate methods for calculating system harmonic impedances. An overview of ac filter design for HVDC systems and a survey of literature related to filter design have been performed. Two methods for calculating system harmonic impedances have been investigated. In the measurement method, an instrumentation system for measuring system voltage and current has been assembled. Different schemes of using the measurements to calculate system harmonic impedances have been studied. In the analytical method, a procedure to include various operating conditions has been proposed. Computer programs for both methods have been prepared, and the results of the measurement and analytical methods analyzed. A conclusion of the project is that the measurement and analytical methods both provided reasonable results. There are correlations between the measured and analytical results for most harmonics, although there are discrepancies between the assumptions used in the two methods. A sensitivity approach has been proposed to further correlate the results. From the results of the analysis, it is recommended that both methods should be tested further. For the measurement method, more testing should be done to cover different system operating conditions. In the analytical method, more detailed models for representing system components should be studied. In addition, alternative statistical and sensitivity approaches should be attempted.
Breuer, G D; Chow, J H; Lindh, C B; Miller, N W; Numrich, F H; Price, W W; Turner, A E; Whitney, R R
1982-09-01
Improved methods are needed to characterize ac system harmonic behavior for ac filter design for HVDC systems. The purpose of this General Electric Company RP1138 research is to evaluate the present filter design practice and to investigate methods for calculating system harmonic impedances. An overview of ac filter design for HVDC systems and a survey of literature related to filter design have been performed. Two methods for calculating system harmonic impedances have been investigated. In the measurement method, an instrumentation system for measuring system voltage and current has been assembled. Different schemes of using the measurements to calculate system harmonic impedances have been studied. In the analytical method, a procedure to include various operating conditions has been proposed. Computer programs for both methods have been prepared, and the results of the measurement and analytical methods analyzed. A conclusion of the project is that the measurement and analytical methods both provided reasonable results. There are correlations between the measured and analytical results for most harmonics, although there are discrepancies between the assumptions used in the two methods. A sensitivity approach has been proposed to further correlate the results. From the results of the analysis, it is recommended that both methods should be tested further. For the measurement method, more testing should be done to cover different system operating conditions. In the analytical method, more detailed models for representing system components should be studied. In addition, alternative statistical and sensitivity approaches should be attempted.
Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator
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.
Salieres, P.
1995-07-03
In this thesis is presented an experimental and theoretical study of the harmonic generation in intense field and coherence properties of this radiation. The first part reminds the main harmonic specter characteristics. Follow then experimental studies of the tray extension with the laser lighting, the harmonic generation by ions, and the influence of the laser field on the efficiency of generation. The second part presents the quantum model of the harmonic generation in tunnel regime that we have used for the calculation of the dipoles. We compare dependence in lighting of some harmonic, by insisting on the characteristic behavior of the atomic phase. The theory of the propagation is presented in third part. After the reminder of the case of a perturbative polarization, we develop the case of the polarization in tunnel regime. With the help of numerical simulations, we show the influence of the atomic phase on the agreement of phase, and therefore on the efficiency of conversion and profiles of generation in the medium. The importance of the geometry of the interaction is underlined. The part IV presents the study of the spatial coherence of the harmonic radiation. We develop first consequences of the theory of the agreement of phase for profiles of emission. Then the comparison with experimental profiles is detailed in function of the different parameters( order of non linearity, laser lighting, position of the focus by report in the gaseous medium). The study of the spectral and temporal coherence of the part V begins with the experimental effect investigation of the ionization on specters of the harmonic of weak order. We present then theoretical predictions of the preceding model for spectral and temporal profiles of the harmonic of highest order, generated in tunnel regime. The part VI is devoted to the UVX source aspect of the harmonic radiation. (Abstract Truncated)
Transition operators in electromagnetic-wave diffraction theory - General theory
Hahne, G. E.
1992-01-01
A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.
Imaging parameters on third harmonic transmit phasing for tissue harmonic generation.
Shen, Che-Chou; Wang, Yu-Chun; Yeh, Chih-Kuang
2008-06-01
In third harmonic (3f0) transmit phasing, transmit waveforms comprising fundamental (f0) signal and 3f0 signal are used to generate both frequency-sum and frequency-difference components for manipulation of tissue harmonic amplitude. Nevertheless, the acoustic propagation of 3f0 transmit signal suffers from more severe attenuation and phase aberration than the f0 signal and hence degrades the performance of 3f0 transmit phasing. Besides, 3f0 transmit parameters such as aperture size and signal bandwidth are also influential in 3f0 transmit phasing. In this study, extensive simulations were performed to investigate the effects of these imaging parameters. Results indicate that the harmonic enhancement and suppression in 3f0 transmit phasing are compromised when the magnitude of frequency-difference component decreases in the presence of tissue attenuation and phase aberration. To compensate for the reduced frequency-difference component, a higher 3f0 transmit amplitude can be used. When the transmit parameters are concerned, a smaller 3f0 transmit aperture can provide more axially uniform harmonic enhancement and more effective suppression of harmonic amplitude. In addition, the spectral leakage signal also interferes with tissue harmonics and degrades the efficacy of 3f0 transmit phasing. Our results suggest that, in the method of 3f0 transmit phasing, the transmit amplitude, phase and aperture size of 3f0 signal should remain adjustable for optimization of clinical performance. Besides, multipulse sequences such as pulse inversion are also favorable for leakage removal in 3f0 transmit phasing.
Second Harmonic Generation in Scanning Probe Microscopy for Edge Localization
HU Xiao-Gen; LI Yu-He; LIN Hao-Shan; WANG Dong-Sheng; QI Xin
2011-01-01
We present an approach of second harmonic generation for edge localization of nano-scale defects measurement,based on the impact of the oscillating tip on the sample that induces higher harmonics of the excitation frequency.The harmonic signals of tip motion are measured by the heterodyne interferornetry. The edge amplitude ratio for the edge characterization can be calculated by a mechanics model and the threshold of edge localization is experimentally determined by second harmonic profiles. This approach has been successfully utilized to measure the pitch of a standard sample. The results show that the second harmonic is sensitive to locating the edge of nano-scale defects with high accuracy.%@@ We present an approach of second harmonic generation for edge localization of nano-scale defects measurement,based on the impact of the oscillating tip on the sample that induces higher harmonics of the excitation frequency.The harmonic signals of tip motion are measured by the heterodyne interferometry.The edge amplitude ratio for the edge characterization can be calculated by a mechanics model and the threshold of edge localization is experimentally determined by second harmonic profiles.This approach has been successfully utilized to measure the pitch of a standard sample.The results show that the second harmonic is sensitive to locating the edge of nano-scale defects with high accuracy.
Influence of Harmonics in Laboratory due to Nonlinear Loads
Risnidar Chan
2012-03-01
Full Text Available This research was focused on the customer’s side of the meter which is the effect of harmonics on a laboratory in Electrical System Engineering School at K.Wai Perlis. Harmonic currents in equipments can cause them to experience overheating and increased losses, while harmonic voltage produces magnetic fields rotating at a speed corresponding to the harmonic frequency. This also results in equipments heating, mechanical vibrations and noise, reduced efficiency, reduced life, and voltage stress on insulation of equipment windings. The loads in this research are computers, Compact Fluorescent Lamps CFLs, Air Conditions and printers,which all of the loads are harmonic significant The instrument to measure and monitoring is Fluke 435 Power Quality Analyzer. With the operation of varying nonlinear loads, the injected harmonic current magnitudes and phase angles vary in a random way. This research offers the advantage of providing the utility a wealth of information on the effects of harmonics in their equipments. This will subsequently make them aware of the causes of increased cost and reduced efficiency that may be experienced by using these equipments. This paper describes the investigation cost of harmonic effect as THD, and harmonic energy losses cost. Keywords: harmonics, nonlinear loads, Energy losses cost, THD.
The sheath effect on the floating harmonic method
Lee, Jaewon; Kim, Kyung-Hyun; Chung, Chin-Wook, E-mail: joykang@hanyang.ac.kr [Department of Electrical Engineering, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 133-791 (Korea, Republic of)
2015-12-15
The floating harmonic method biases sinusoidal voltage to a probe sheath, and as its response, harmonic currents can be obtained. These currents can be used to determine the plasma parameters. However, different shapes of probes have different shapes of sheaths that can affect the diagnostic results. However, no research has been done on the sheath effect on the floating harmonic method. Therefore, we investigate the effect of the sheath during floating harmonic diagnostics by comparing cylindrical and planar probes. While the sinusoidal voltages were applied to a probe, because the sheath oscillated, the time variant ion current and their harmonic currents were added to the electron harmonic currents. In the floating harmonic method, the harmonic currents are composed of only the electron harmonic currents. Therefore, the ion harmonic currents affect the diagnostic results. In particular, the electron temperature obtained by the small probe tip was higher than that of the large probe tip. This effect was exacerbated when the ratio of the probe tip radius to the sheath length was smaller.
Toward Rigorous Data Harmonization in Cancer Epidemiology Research: One Approach.
Rolland, Betsy; Reid, Suzanna; Stelling, Deanna; Warnick, Greg; Thornquist, Mark; Feng, Ziding; Potter, John D
2015-12-15
Cancer epidemiologists have a long history of combining data sets in pooled analyses, often harmonizing heterogeneous data from multiple studies into 1 large data set. Although there are useful websites on data harmonization with recommendations and support, there is little research on best practices in data harmonization; each project conducts harmonization according to its own internal standards. The field would be greatly served by charting the process of data harmonization to enhance the quality of the harmonized data. Here, we describe the data harmonization process utilized at the Fred Hutchinson Cancer Research Center (Seattle, Washington) by the coordinating centers of several research projects. We describe a 6-step harmonization process, including: 1) identification of questions the harmonized data set is required to answer; 2) identification of high-level data concepts to answer those questions; 3) assessment of data availability for data concepts; 4) development of common data elements for each data concept; 5) mapping and transformation of individual data points to common data elements; and 6) quality-control procedures. Our aim here is not to claim a "correct" way of doing data harmonization but to encourage others to describe their processes in order that we can begin to create rigorous approaches. We also propose a research agenda around this issue. © The Author 2015. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Coherent harmonic production using a two-section undulator FEL
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.
Liu, Xi; Li, Liang; Li, Yang; Zhang, Qingbin; Lan, Pengfei; Lu, Peixiang
2016-01-01
The selection rules of high harmonic generation (HHG) are investigated using three-dimensional time-dependent density functional theory (TDDFT). From the harmonic spectra obtained with various real molecules and different forms of laser fields, several factors that contribute to selection rules are revealed. Extending the targets to stereoscopic molecules, it is shown that the allowed harmonics are dependent on the symmetries of the projections of molecules. Moreover, it is found that the dynamical directivities of the laser fields play an important role on the selection rules. Our study presents a more general form of selection rules, which can be extended to the HHG for more complex molecules and various forms of laser fields.
XU Yu-xiu; HU Hai-yan; WEN Bang-chun
2006-01-01
The 1/3 sub-harmonic solution for the Duffing's with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.
Algal Supply System Design - Harmonized Version
Jared Abodeely; Daniel Stevens; Allison Ray; Debor
2013-03-01
The objective of this design report is to provide an assessment of current technologies used for production, dewatering, and converting microalgae cultivated in open-pond systems to biofuel. The original draft design was created in 2011 and has subsequently been brought into agreement with the DOE harmonized model. The design report extends beyond this harmonized model to discuss some of the challenges with assessing algal production systems, including the ability to (1) quickly assess alternative algal production system designs, (2) assess spatial and temporal variability, and (3) perform large-scale assessments considering multiple scenarios for thousands of potential sites. The Algae Logistics Model (ALM) was developed to address each of these limitations of current modeling efforts to enable assessment of the economic feasibility of algal production systems across the United States. The (ALM) enables (1) dynamic assessments using spatiotemporal conditions, (2) exploration of algal production system design configurations, (3) investigation of algal production system operating assumptions, and (4) trade-off assessments with technology decisions and operating assumptions. The report discusses results from the ALM, which is used to assess the baseline design determined by harmonization efforts between U.S. DOE national laboratories. Productivity and resource assessment data is provided by coupling the ALM with the Biomass Assessment Tool developed at PNNL. This high-fidelity data is dynamically passed to the ALM and used to help better understand the impacts of spatial and temporal constraints on algal production systems by providing a cost for producing extracted algal lipids annually for each potential site.
IDENTIFICATION OF HARMONIC SOURCES IN DEREGULATED POWER SECTOR
KRITI VAID,
2011-03-01
Full Text Available In this paper identification of origin of harmonic source in deregulated power sector has been carried out. Critical impedance method (CIM for detection of harmonic disturbances caused between utility and source side has already been reported in literature. The method is based on direction of reactive power flow in the power system when there is the presence of harmonic load. Taking the CIM as the base method harmonic sources are identified in deregulated power sector. Due to unavailability of practical data simulation approach has been adopted. A five bus system model with two Generation ompanies (GENCOS has been simulated for power transfer from GENCO to the considered five bus system. Harmonic current is injected into the system by using a three phase diode rectifier. The results obtainedusing the CIM clearly identifies whether the harmonic source is present in GENCO side or the load side.
The Obstacle Problem for the A-Harmonic Equation
Zhenhua Cao
2010-01-01
Full Text Available Firstly, we define an order for differential forms. Secondly, we also define the supersolution and subsolution of the A-harmonic equation and the obstacle problems for differential forms which satisfy the A-harmonic equation, and we obtain the relations between the solutions to A-harmonic equation and the solution to the obstacle problem of the A-harmonic equation. Finally, as an application of the obstacle problem, we prove the existence and uniqueness of the solution to the A-harmonic equation on a bounded domain Ω with a smooth boundary ∂Ω, where the A-harmonic equation satisfies d⋆A(x,du=0,x∈Ω; u=ρ,x∈∂Ω, where ρ is any given differential form which belongs to W1,p(Ω,Λl-1.
Relationships between Harmonic Characteristics and Different Types of Voltage Source
Yusniati Yusniati
2012-06-01
Full Text Available This paper discusses about harmonic characteristics due to different types of voltage sources. Usually, the voltage source is sinusoidal. But in actual condition the load that receive voltage sources through the elements where the output voltage of element as input to the load is not pure sinusoidal, for example voltage source at (PCC between transformer and linear load and nonlinear load. This research has been done with Schhafner Power Quality Analyzer and PM300 Power Quality Analyzer, was focused to all harmonic characteristics as power, voltage, current, power factor (p.f., Harmonic Distortion, and harmonic energy losses cost. The load is Induction Motor with Adjustable Speed Drive (ASD because the Induction Motor with Adjustable Speed Drive (ASD is one of electronic device causes harmonics. The voltage sources in this research are sine wave, square wave and harmonic order combinations of 3rd, 5th and 7th which can create from Schhafner Power Quality Analyzer.
Second-harmonic imaging of semiconductor quantum dots
Østergaard, John Erland; Bozhevolnyi, Sergey I.; Pedersen, Kjeld;
2000-01-01
Resonant second-harmonic generation is observed at room temperature in reflection from self-assembled InAlGaAs quantum dots grown on a GaAs (001) substrate. The detected second-harmonic signal peaks at a pump wavelength of similar to 885 nm corresponding to the quantum-dot photoluminescence maximum....... In addition, the second-harmonic spectrum exhibits another smaller but well-pronounced peak at 765 nm not found in the linear experiments. We attribute this peak to the generation of second-harmonic radiation in the AlGaAs spacer layer enhanced by the local symmetry at the quantum-dot interface. We further...... observe that second-harmonic images of the quantum-dot surface structure show wavelength-dependent spatial variations. Imaging at different wavelength is used to demonstrate second-harmonic generation from the semiconductor quantum dots. (C) 2000 American Institute of Physics....
APF for harmonic voltage resonance suppression in distribution system
Sun, Xiaofeng; Zeng, Jian; Chen, Zhe
2010-01-01
Traditional active power filter (APF) can prevent harmonic current from injecting into power system, but can not damp harmonic propagation in distribution system whereas voltage detection can do. This paper proposes a compound control method of APF based on detection of load current and harmonic...... voltage at the point of installation. In addition, based on the relationship between the rated volt-ampere of APF and the load volt-ampere, the conductance value could automatic adjustment. The objective of the shunt active filter is not only to compensate the harmonic but also to damp the harmonic. When...... the rated volt-ampere is limit, the harmonic compensation is prior considered. Computer simulation and experiment result are performed to verify the validity and effectiveness of the shunt active filter equipped with the compound control. © 2010 IEEE....
Intense harmonics generation with customized photon frequency and optical vortex
Zhang, Xiaomei; Shen, Baifei; Shi, Yin; Zhang, Lingang; Ji, Liangliang; Wang, Xiaofeng; Xu, Zhizhan; Tajima, Toshiki
2016-08-01
An optical vortex with orbital angular momentum (OAM) enriches the light and matter interaction process, and helps reveal unexpected information in relativistic nonlinear optics. A scheme is proposed for the first time to explore the origin of photons in the generated harmonics, and produce relativistic intense harmonics with expected frequency and an optical vortex. When two counter-propagating Laguerre-Gaussian laser pulses impinge on a solid thin foil and interact with each other, the contribution of each input pulse in producing harmonics can be distinguished with the help of angular momentum conservation of photons, which is almost impossible for harmonic generation without an optical vortex. The generation of tunable, intense vortex harmonics with different photon topological charge is predicted based on the theoretical analysis and three-dimensional particle-in-cell simulations. Inheriting the properties of OAM and harmonics, the obtained intense vortex beam can be applied in a wide range of fields, including atom or molecule control and manipulation.
Relationships between Harmonic Characteristics and Different Types of Voltage Source
Syafruddin H
2012-06-01
Full Text Available This paper discusses about harmonic characteristics due to different types of voltage sources. Usually, the voltage source is sinusoidal. But in actual condition the load that receive voltage sources through the elements where the output voltage of element as input to the load is not pure sinusoidal, for example voltage source at (PCC between transformer and linear load and nonlinear load. This research has been done with Schhafner Power Quality Analyzer and PM300 Power Quality Analyzer, was focused to all harmonic characteristics as power, voltage, current, power factor (p.f., Harmonic Distortion, and harmonic energy losses cost. The load is Induction Motor with Adjustable Speed Drive (ASD because the Induction Motor with Adjustable Speed Drive (ASD is one of electronic device causes harmonics. The voltage sources in this research are sine wave, square wave and harmonic order combinations of 3rd, 5th and 7th which can create from Schhafner Power Quality Analyzer.
High-order harmonic generation from the dressed autoionizing states
Fareed, M. A.; Strelkov, V. V.; Thiré, N.; Mondal, S.; Schmidt, B. E.; Légaré, F.; Ozaki, T.
2017-07-01
In high-order harmonic generation, resonant harmonics (RH) are sources of intense, coherent extreme-ultraviolet radiation. However, intensity enhancement of RH only occurs for a single harmonic order, making it challenging to generate short attosecond pulses. Moreover, the mechanism involved behind such RH was circumstantial, because of the lack of direct experimental proofs. Here, we demonstrate the exact quantum paths that electron follows for RH generation using tin, showing that it involves not only the autoionizing state, but also a harmonic generation from dressed-AIS that appears as two coherent satellite harmonics at frequencies +/-2Ω from the RH (Ω represents laser frequency). Our observations of harmonic emission from dressed states open the possibilities of generating intense and broadband attosecond pulses, thus contributing to future applications in attosecond science, as well as the perspective of studying the femtosecond and attosecond dynamics of autoionizing states.
On harmonic operation of Shanghai deep UV free electron laser
无
2008-01-01
By choosing parameters in the modulator,the dispersive section and the seed laser,the spatial bunching of the electron beam can be correlated to then-th harmonic of ther adiator radiation,instead of the fundamental radiation in conventional high-gain harmonic generation(HGHG).Thus,the radiator undulator is operated at high harmonic mode.In this paper,the possibility of harmonic operation of Shanghai deep ultraviolet(SDUV)free electron laser (FEL)is studied.Discussions on the principle of harmonic operation,the simulation code development,the simulation results.and the proposed experimental procedure for verification of harmonic operation at the SDUV FEL are also presented.
Gain of harmonic generation in high gain free electron laser
DENG Hai-Xiao; DAI Zhi-Min
2008-01-01
In a planar undulator employed free electron laser(FEL),each harmonic radiation starts from linear amplification and ends with nonlinear harmonic interactions of the lower nonlinear harmonics and the fundamental radiation.In this paper,we investigate the harmonic generation based on the dispersion relation driven from the coupled Maxwell-Vlasov equations,taking into account the effects due to energy spread,emittance,betatron oscillation of electron beam as well as diffraction guiding of the radiation field.A 3D universal scaling function for gain of the linear harmonic generation and a 1D universal scaling function for gain of the nonlinear harmonic generation are presented,which promise rapid computation in FEL design and optimization.The analytical approaches have been validated by 3D simulation results in large range.
A new method based on the harmonic balance method for nonlinear oscillators
Chen, Y.M. [Department of Mechanics, Zhongshan University, Guangzhou 510275 (China); Liu, J.K. [Department of Mechanics, Zhongshan University, Guangzhou 510275 (China)], E-mail: jikeliu@hotmail.com
2007-08-27
The harmonic balance (HB) method as an analytical approach is widely used for nonlinear oscillators, in which the initial conditions are generally simplified by setting velocity or displacement to be zero. Based on HB, we establish a new theory to address nonlinear conservative systems with arbitrary initial conditions, and deduce a set of over-determined algebraic equations. Since these deduced algebraic equations are not solved directly, a minimization problem is constructed instead and an iterative algorithm is employed to seek the minimization point. Taking Duffing and Duffing-harmonic equations as numerical examples, we find that these attained solutions are not only with high degree of accuracy, but also uniformly valid in the whole solution domain.
High-harmonic generation in alpha-quartz by the electron-hole recombination
Otobe, T
2016-01-01
The first-principle calculation for the high-harmonic generation (HHG) in an alpha-quartz employing the time-dependent density-functional theory is reported. The photon energy is set to 1.55 eV, and the cutoff energy of the plateau region is found to be limited at the 19th harmonics (30 eV). The laser intensity dependence of HHG efficiency at the cutoff energy region is consistent with that of the hole density in the lowest-lying valence band. Numerical results indicate that the electron-hole recombination plays a crucial role in HHG in alpha-quartz. It is found that the 200 attosecond pulse train is generated utilizing HHG around the plateau cutoff energy.
High-harmonic generation in α -quartz by electron-hole recombination
Otobe, T.
2016-12-01
A calculation of the high-harmonic generation (HHG) in α -quartz using the time-dependent density functional theory is reported. The interband process is attributed to the dominant in HHG above the band gap. The photon energy is set to 1.55 eV, and the cutoff energy of the plateau region is found to be limited at the 19th harmonic (30 eV). The dependence of the HHG efficiency at the cutoff energy region on laser intensity is consistent with that of the hole density in the lowest-lying valence band. Numerical results indicate that electron-hole recombination plays a crucial role in HHG in α -quartz. It is found that a 200 attosecond pulse train is produced using HHG around the plateau cutoff energy.
Wang, Y. Q.; Guo, X. H.; Li, Y. G.; Li, J.
2010-03-01
This is a study of nonlinear traveling wave response of a cantilever circular cylindrical shell subjected to a concentrated harmonic force moving in a concentric circular path at a constant velocity. Donnell's shallow-shell theory is used, so that moderately large vibrations are analyzed. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. Frequency-responses for six different mode expansions are studied and compared with that for single mode to find the more contracted and accurate mode expansion investigating traveling wave vibration. The method of harmonic balance is applied to study the nonlinear dynamic response in forced oscillations of this system. Results obtained with analytical method are compared with numerical simulation, and the agreement between them bespeaks the validity of the method developed in this paper. The stability of the period solutions is also examined in detail.
Mygind, Jesper; Pedersen, Niels Falsig; Sørensen, O. H.
1976-01-01
The first direct observation of the parametrically generated half-harmonic voltage in a Josephson tunnel junction is reported. A microwave signal at f=17.25 GHz is applied to the junction dc current biased at zero voltage such that the Josephson plasma resonance fp=f/2. Under these conditions a l...... a large-amplitude microwave signal is emitted at fp provided the input power exceeds a threshold value. The results are compared to existing theory. Applied Physics Letters is copyrighted by The American Institute of Physics.......The first direct observation of the parametrically generated half-harmonic voltage in a Josephson tunnel junction is reported. A microwave signal at f=17.25 GHz is applied to the junction dc current biased at zero voltage such that the Josephson plasma resonance fp=f/2. Under these conditions...
Kashinski, D. O.; Nelson, R. G.; Chase, G. M.; di Nallo, O. E.; Byrd, E. F. C.
2016-05-01
We are investigating the accuracy of theoretical models used to predict the visible, ultraviolet, and infrared spectra, as well as other properties, of product materials ejected from the muzzle of currently fielded systems. Recent advances in solid propellants has made the management of muzzle signature (flash) a principle issue in weapons development across the calibers. A priori prediction of the electromagnetic spectra of formulations will allow researchers to tailor blends that yield desired signatures and determine spectrographic detection ranges. Quantum chemistry methods at various levels of sophistication have been employed to optimize molecular geometries, compute unscaled harmonic frequencies, and determine the optical spectra of specific gas-phase species. Electronic excitations are being computed using Time Dependent Density Functional Theory (TD-DFT). Calculation of approximate global harmonic frequency scaling factors for specific DFT functionals is also in progress. A full statistical analysis and reliability assessment of computational results is currently underway. Work supported by the ARL, DoD-HPCMP, and USMA.
Policy Autonomy, Coordination or Harmonization in the Persistently Heterogeneous European Union?
Kouba Luděk
2016-03-01
Full Text Available Within the context of the continuing integration process in Europe, this paper addresses the question of whether policies in the EU should head towards autonomy, coordination or harmonization. Taking the path dependence effect into account, it is the authors’ opinion that Europe has gone too far in its integration process to be able to continue with policies being fully under the competences of individual member countries. However, the habitual question still arises: does fiscal policy need to be harmonized to a level comparable to monetary policy as these two policies, necessarily, complement each other? This paper argues that it does not. There are three main arguments discussed. Firstly, the authors build on the theory of fiscal federalism. Secondly, there are significantly different regimes of welfare states and extents of social policies among European countries, which strongly determine the character of public finance. And thirdly, the tax systems across Europe are also highly divergent, with many features of continuing tax competition.
Real-Time Method for Detecting Harmonic and Reactive Currents of Single-Phase Circuits
Zhang Xiufeng; Ding Juxia
2006-01-01
According to the characteristics of single-phase circuits and demand of using active filter for real-time detecting harmonic and reactive currents, a detecting method based on Fryze's power definition is proposed. The results of theoretical analysis and simulation show that the proposed method is effective in real-time detecting of instantaneous harmonic and reactive currents in single-phase circuits. When only detecting the total reactive currents, this method does not need a phase-locked loop circuit, and it also can be used in some special applications to provide different compensations on the ground of different requirements of electric network. Compared with the other methods based on the theory of instantaneous reactive power, this method is simple and easy to realize.
Second-harmonic generation from bimetal composites doped with metal nanoparticles
Daneshfar, Nader
2016-05-01
In the present paper, we study the nonlinear optical response of the bimetal composites doped with metal nanoparticles in the framework of nonlinear Mie theory combined with the Maxwell-Garnett model. We concentrate on the second-order harmonic generation from bimetal nanocomposites including silver and gold particles, since sometimes the nonlinear optical response is sensitive to the more accurate of material structure than linear optical response. We show that optical second harmonic generation is strongly sensitive to temperature as an environmental parameter, interparticle plasmon coupling between Au and Ag nanoparticles (the filling factor of inclusions), the particle size and the surrounding medium. However, this work shows good potential of bimetal composites for nonlinear optics at the nanoscale.
Reimagining a Riemannian symbology for the structural harmonic analysis of 19th-century tonal music.
Marcus Alessi Bittencourt
2013-12-01
Full Text Available In the context of a preview of central topics taken from a larger research work, this article presents and explains a proposition of a functional analytical symbology which is currently being developed as a tool for the structural harmonic analysis of tonal music. This symbology constitutes a key component for a proposal of an analytical methodology for 19th century extended tonality, which is the core of the aforementioned larger research work. Based on a critical revision of the history of music theory and analysis, this methodology is mainly the result of the recasting and the amplification of thoughts and concepts developed by 19th century theorists such as Hugo Riemann and Arthur von Oettingen. The article introduces the proposed analytical symbology through a comparison to its historical counterparts, and it also highlights the ability of the proposed symbols to graph the harmonic language of 19th century extended tonality by means of a few analytical examples.
On the harmonic index of graph operations
B. Shwetha Shetty
2015-12-01
Full Text Available The harmonic index of a connected graph G , denoted by H(G , is defined as H(G=∑ uv∈E(G 2d u +d v where d v is the degree of a vertex v in G. In this paper, expressions for the Harary indices of the join, corona product, Cartesian product, composition and symmetric difference of graphs are derived.
On the harmonic index of graph operations
B. Shwetha Shetty; V. Lokesha; Ranjini, P.S.
2015-01-01
The harmonic index of a connected graph G , denoted by H(G) , is defined as H(G)=∑ uv∈E(G) 2d u +d v where d v is the degree of a vertex v in G. In this paper, expressions for the Harary indices of the join, corona product, Cartesian product, composition and symmetric difference of graphs are derived.
Power quality and harmonic instrumentation selection
Stebbins, W.L.; Golden, P.
1996-05-01
The proliferation of adjustable speed drive (ASD) systems in commercial and industrial settings has prompted a new awareness of the impact of harmonics and other power quality (PQ) concerns. The PQ issues have a direct bearing on the reliability of these systems and the ability to perform the desired tasks in an interruption free manner. Details presented include identifying power quality problems, selecting the proper type of monitoring instruments, and interpretation of data. Included are typical instrument specifications and cost. Additionally the advent of artificial intelligence tools for PQ analysis and the resulting impact on providing solutions is described.
Contrast-enhanced harmonic endoscopic ultrasound
Săftoiu, A; Dietrich, C F; Vilmann, P
2012-01-01
Second-generation intravenous blood-pool ultrasound contrast agents are increasingly used in endoscopic ultrasound (EUS) for characterization of microvascularization, differential diagnosis of benign and malignant focal lesions, and improving staging and guidance of therapeutic procedures. Although...... contrast-enhanced harmonic EUS based on a very low mechanical index (0.08 - 0.12). Quantification techniques based on dynamic contrast-enhanced ultrasound have been recommended for perfusion imaging and monitoring of anti-angiogenic treatment, mainly based on time-intensity curve analysis. Most...
Information cloning of harmonic oscillator coherent states
N D Hari Dass; Pradeep Ganesh
2002-08-01
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 of this perfect information cloning it would be possible to estimate the original state through measurements and make arbitrary number of copies of the estimator. We deﬁne the notion of a measurement ﬁdelity and calculate it for our case as well as for the Gaussian cloners.
Perturbing rational harmonic functions by poles
Sète, Olivier; Liesen, Jörg
2014-01-01
We study how adding certain poles to rational harmonic functions of the form $R(z)-\\bar{z}$, with $R(z)$ rational and of degree $d\\geq 2$, affects the number of zeros of the resulting functions. Our results are motivated by and generalize a construction of Rhie derived in the context of gravitational microlensing (ArXiv e-print 2003). Of particular interest is the construction and the behavior of rational functions $R(z)$ that are {\\em extremal} in the sense that $R(z)-\\bar{z}$ has the maximal possible number of $5(d-1)$ zeros.
Harmonic Vibrational Analysis in Delocalized Internal Coordinates.
Jensen, Frank; Palmer, David S
2011-01-11
It is shown that a principal component analysis of a large set of internal coordinates can be used to define a nonredundant set of delocalized internal coordinates suitable for the calculation of harmonic vibrational normal modes. The selection of internal coordinates and the principal component analysis provide large degrees of freedom in extracting a nonredundant set of coordinates, and thus influence how the vibrational normal modes are described. It is shown that long-range coordinates may be especially suitable for describing low-frequency global deformation modes in proteins.
Glass devices for efficient second harmonic generation
Fage-Pedersen, Jacob; Jacobsen, Rune Shim; Kristensen, Martin
2005-01-01
We show here that quasi-phase matched (QPM) planar nonlinear devices of high quality can be fabricated by means of periodic poling of the glass. The devices, used for second-harmonic generation (SHG), have accurately-controlled centre wavelengths, and the normalised conversion efficiencies...... are approximately one order of magnitude higher than what has previously been reported for periodically poled glass. In conclusion, we have demonstrated that high-quality nonlinear QPM devices can be fabricated in glass-on-silicon. The technology is easily adaptable to any desired wavelength (e.g. 1550 nm) and can...
Harmonic and Monogenic Potentials in Euclidean Halfspace
Brackx, F.; De Bie, H.; De Schepper, H.
2011-09-01
In the framework of Clifford analysis a chain of harmonic and monogenic potentials is constructed in the upper half of Euclidean space Rm+1. Their distributional limits at the boundary are computed, obtaining in this way well-known distributions in Rm such as the Dirac distribution, the Hilbert kernel, the square root of the negative Laplace operator, and the like. It is shown how each of those potentials may be recovered from an adjacent kernel in the chain by an appropriate convolution with such a distributional limit.
Properties of the Third Harmonic of the SASE FEL Radiation
Saldin, E L; Schneidmiller, E
2005-01-01
Recent theoretical and experimental studies have shown that SASE FEL with a planar undulator holds a potential for generation of relatively strong coherent radiation at the third harmonic of the fundamental frequency. Here we present detailed study of the nonlinear harmonic generation in SASE FEL obtained with time-dependent FEL simulation code FAST. Using similarity techniques we present universal dependencies for temporal, spectral, and statistical properties of the third harmonic radiation from SASE FEL.
Relativistic surface-plasmon enhanced harmonic generation from gratings
Fedeli, Luca; Cantono, Giada; Macchi, Andrea
2016-01-01
The role of relativistic surface plasmons (SPs) in high order harmonic emission from laser-irradiated grating targets has been investigated by means of particle-in-cell simulations. SP excitation drives a strong enhancement of the intensity of harmonics, particularly in the direction close to the surface tangent. The SP-driven enhancement overlaps with the angular separation of harmonics generated by the grating, which is beneficial for applications requiring monochromatic XUV pulses.
Harmonic maps of finite uniton number into $G_2$
Correia, N
2010-01-01
We establish explicit formulae for canonical factorizations of extended solutions corresponding to harmonic maps of finite uniton number into the exceptional Lie group $G_2$ in terms of the Grassmannian model for the group of based algebraic loops in $G_2$. A description of the ``Frenet frame data" for such harmonic maps is given. In particular, we show that harmonic spheres into $G_2$ correspond to solutions of certain algebraic systems of quadratic and cubic equations.
Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators
王雪红; 郭军义; 李艳
2012-01-01
In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ?/?λ,where the λ is a real number.When λ=0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.
Andreica Horia Tudor
2010-12-01
Full Text Available The new configuration of the international economic relations which are in a general globalization process determined by the international capital circulation requires the compatibility and comparison of the information provided by the financial statements. The investors and the entrepreneurs wish to understand and to be able to compare the entities financial situation and performances, no matter the juridical and accounting system which are subdued to by their localization. The differences between the important variety of the accounting systems were identified long time ago and since then there have been efforts made in order to conceive a economic financial reporting structure, accessible to the entire accounting world. Therefore, there is the need of normalization, harmonization, and convergence in accounting. Our intention in the current paper is to bring again into discussion the problem of accounting harmonization, emphasizing a few aspects which in the Romanian context we consider to be controversial and which require some clarifications. This paper represents a brief review of the evolution of the accounting harmonization in Romania, analyzing the difficult moments and mainly it is focused on the conceptual understanding of the concepts of harmonization, convergence, and conformity in the Romanian accounting. Our approach is not an exhaustive one, but it has as objective to reflect on the importance of the stages of accounting modernization in Romania. In the last part of this paper, the conclusions that we reached after study, are presented synthetically, as well as the continuation of the approach initiated in other papers.
A Harmonic Impedance Measurement System for Reduction of Harmonics in the Electricity Grid
Heskes, P.J.M.; Myrzik, J.M.A.; Kling, W.L.
2009-01-01
This paper describes the development of a Complex Harmonic Impedance Measurement system, called the CHIME-system. This system performs on-line impedance measurements in the electricity grid and will be designed for implementation in Digital Signal Processor (DSP) control systems of grid-connected el
Chiou, See-Ying; Forsberg, Flemming; Fox, Traci B; Needleman, Laurence
2007-11-01
The purpose of this study was to compare fundamental gray scale sonography, tissue harmonic imaging (THI), and differential tissue harmonic imaging (DTHI) for depicting normal and abnormal livers. The in vitro lateral resolution of DTHI, THI, and sonography was assessed in a phantom. Sagittal and transverse images of right and left hepatic lobes of 5 volunteers and 20 patients and images of 27 liver lesions were also acquired. Three independent blinded readers scored all randomized images for noise, detail resolution, image quality, and margin (for lesions) on a 7-point scale. Next, images from the same location obtained with all 3 modes were compared blindly side by side and rated by all readers. Contrast-to-noise ratios were calculated for the lesions, and the depth of penetration (centimeters) was determined for all images. In vitro, the lateral resolution of DTHI was significantly better than fundamental sonography (P = .009) and showed a trend toward significance versus THI (P = .06). In the far field, DTHI performed better than both modes (P images were scored, and for all parameters, DTHI and THI did better than sonography (P tissue harmonic imaging scored significantly higher than THI with regard to detail resolution and image quality (P Tissue harmonic imaging and DTHI do better than fundamental sonography for hepatic imaging, with DTHI being rated the best of the 3 techniques.
Rajarshi Chakrabarti
2009-04-01
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 do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.
Electric-Field Switchable Second-Harmonic Generation in Bilayer MoS2 by Inversion Symmetry Breaking.
Klein, J; Wierzbowski, J; Steinhoff, A; Florian, M; Rösner, M; Heimbach, F; Müller, K; Jahnke, F; Wehling, T O; Finley, J J; Kaniber, M
2017-01-11
We demonstrate pronounced electric-field-induced second-harmonic generation in naturally inversion symmetric 2H stacked bilayer MoS2 embedded into microcapacitor devices. By applying strong external electric field perturbations (|F| = ±2.6 MV cm(-1)) perpendicular to the basal plane of the crystal, we control the inversion symmetry breaking and, hereby, tune the nonlinear conversion efficiency. Strong tunability of the nonlinear response is observed throughout the energy range (Eω ∼ 1.25-1.47 eV) probed by measuring the second-harmonic response at E2ω, spectrally detuned from both the A- and B-exciton resonances. A 60-fold enhancement of the second-order nonlinear signal is obtained for emission at E2ω = 2.49 eV, energetically detuned by ΔE = E2ω - EC = -0.26 eV from the C-resonance (EC = 2.75 eV). The pronounced spectral dependence of the electric-field-induced second-harmonic generation signal reflects the bandstructure and wave function admixture and exhibits particularly strong tunability below the C-resonance, in good agreement with density functional theory calculations. Moreover, we show that the field-induced second-harmonic generation relies on the interlayer coupling in the bilayer. Our findings strongly suggest that the strong tunability of the electric-field-induced second-harmonic generation signal in bilayer transition metal dichalcogenides may find applications in miniaturized electrically switchable nonlinear devices.
Zhou, Qinghua; Xiao, Fuliang; Yang, Chang; Liu, Si; He, Yihua; Baker, D. N.; Spence, H. E.; Reeves, G. D.; Funsten, H. O.
2017-06-01
Electrostatic electron cyclotron harmonic (ECH) waves generated by the electron loss cone distribution can produce efficient scattering loss of plasma sheet electrons, which has a significant effect on the dynamics in the outer magnetosphere. Here we report two ECH emission events around the same location L≈ 5.7-5.8, MLT ≈ 12 from Van Allen Probes on 11 February (event A) and 9 January 2014 (event B), respectively. The spectrum of ECH waves was centered at the lower half of the harmonic bands during event A, but the upper half during event B. The observed electron phase space density in both events is fitted by the subtracted bi-Maxwellian distribution, and the fitting functions are used to evaluate the local growth rates of ECH waves based on a linear theory for homogeneous plasmas. ECH waves are excited by the loss cone instability of 50 eV-1 keV electrons in the lower half of harmonic bands in the low-density plasmasphere in event A, and 1-10 keV electrons in the upper half of harmonic bands in a relatively high-density region in event B. The current results successfully explain observations and provide a first direct evidence on how ECH waves are generated in the lower and upper half of harmonic frequency bands.
Comparative Analysis of Instruments Measuring Time Varying Harmonics
Belchior, Fernando Nunes; Ribeiro, Paulo Fernando; Carvalho, Frederico Marques
2016-08-01
This paper aims to evaluate the performance of commercial class A and class S power quality (PQ) instruments when measuring time-varying harmonics. By using a high precision programmable voltage and current source, two meters from different manufacturers are analyzed and compared. Three-phase voltage signals are applied to PQ instruments, considering 3 situations of time-varying harmonic distortions, whose harmonic distortion values are in accordance with typical values found in power systems. This work is relevant considering that international standardization documents do not pay much attention to this aspect of harmonic distortion.
Higher Harmonics Generation in Tapping Mode Atomic Force Microscope
LI Yuan; QIAN Jian-Qiang
2009-01-01
The contribution of higher harmonics to the movement of a micro rectangular cantilever in tapping mode AFM is investigated. The dependence between the phase lag of the higher harmonic components and tip-sample separation are found to be an order of magnitude higher than the base one, reflecting an increasing sensitivity to local variations of surface properties compared to the normal phase signal.The strong correlation between the higher harmonic amplitude and average sample deformation implies that the higher harmonic amplitude can be taken to monitor the tapping force or as feedback variable to fulfill a constant repulsive force mode.
Image Formation in Second-Harmonic Near-Field Microscopy
Bozhevolnyi, Sergey I.; Lozovski, Valeri Z.; Pedersen, Kjeld
1999-01-01
A macroscopic self-consistent approach that enables one to rigorously describe image formation in scanning near-field optical second-harmonic generation microscopy is developed. The self-consistent second-harmonic field is determined by taking into account both the linear and nonlinear contributi......A macroscopic self-consistent approach that enables one to rigorously describe image formation in scanning near-field optical second-harmonic generation microscopy is developed. The self-consistent second-harmonic field is determined by taking into account both the linear and nonlinear...
Role of Excited States In High-order Harmonic Generation
Beaulieu, S.; Camp, S.; Descamps, D.; Comby, A.; Wanie, V.; Petit, S.; Légaré, F.; Schafer, K. J.; Gaarde, M. B.; Catoire, F.; Mairesse, Y.
2016-11-01
We investigate the role of excited states in high-order harmonic generation by studying the spectral, spatial, and temporal characteristics of the radiation produced near the ionization threshold of argon by few-cycle laser pulses. We show that the population of excited states can lead either to direct extreme ultraviolet emission through free induction decay or to the generation of high-order harmonics through ionization from these states and recombination to the ground state. By using the attosecond lighthouse technique, we demonstrate that the high-harmonic emission from excited states is temporally delayed by a few femtoseconds compared to the usual harmonics, leading to a strong nonadiabatic spectral redshift.
The location of critical points of analytic and harmonic functions
Walsh, J L
1950-01-01
This book is concerned with the critical points of analytic and harmonic functions. A critical point of an analytic function means a zero of its derivative, and a critical point of a harmonic function means a point where both partial derivatives vanish. The analytic functions considered are largely polynomials, rational functions, and certain periodic, entire, and meromorphic functions. The harmonic functions considered are largely Green's functions, harmonic measures, and various linear combinations of them. The interest in these functions centers around the approximate location of their crit
Tissue Characterization on Ultrasound Harmonic Signals using Nakagami Statistics
Lin, Fanglue; Cristea, Anca; Cachard, Christian; Basset, Olivier
Quantitative ultrasound (QUS) imaging provides a way to characterize biological tissue. The QUS estimates can be obtained from the envelope statistics. Previous studies are mainly based on the whole backscattered signals analysis. However, the ultrasound propagation is a nonlinear process and the harmonic signals can therefore reveal the nonlinear nature of a biological medium. The present study investigates the statistics of harmonic signal envelopes to relate the distribution parameters to the nonlinear coefficients. The main results demonstrate that the distributions exhibit a different behavior for fundamental and harmonic signals and that media with different nonlinearities can be distinguished, when using Nakagami statistics on the harmonic signal envelopes.
ON REGULARITY THEOREMS FOR LINEARLY INVARIANT FAMILIES OF HARMONIC FUNCTIONS
E. G. Ganenkova
2015-05-01
Full Text Available The classical theorem of growth regularity in the class S of analytic and univalent in the unit disc ∆ functions ƒ describes the growth character of different functionals of ƒ Є S and z Є ∆ as z tends to δ∆. Earlier the authors proved the theorems of growth and decrease regularity for harmonic and sense-preserving in ∆ functions which generalized the classical result for the class S. In the presented paper we establish new properties of harmonic sense-preserving functions, connected with the regularity theorems. The effects both common for analytic and harmonic case and specific for harmonic functions are displayed.
Effective harmonic oscillator description of anharmonic molecular vibrations
Tapta Kanchan Roy; M Durga Prasad
2009-09-01
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 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.
Goos-Hänchen shifts in harmonic generation from metals.
Yallapragada, V J; Gopal, Achanta Venu; Agarwal, G S
2013-05-06
We present the first calculation of the Goos-Hänchen shifts in the context of the nonlinear generation of fields. We specifically concentrate on shifts of second harmonic generated at metallic surfaces. At metallic surfaces the second harmonic primarily arises from discontinuities of the field at surfaces which not only result in large harmonic generation but also in significant Goos-Hänchen shifts of the generated second harmonic. Our results can be extended to other shifts like angular shifts and Fedorov-Imbert shifts.
High-order harmonic generation from eld-distorted orbitals
Spiewanowski, Maciek; Etches, Adam; Madsen, Lars Bojer
We investigate the eect on high-order harmonic generation of the distortion of molecular orbitals by the driving laser eld. Calculations for high-order harmonic generation including orbital distortion are performed for N2 (high polarizability). Our results allow us to suggest that field-distortio......We investigate the eect on high-order harmonic generation of the distortion of molecular orbitals by the driving laser eld. Calculations for high-order harmonic generation including orbital distortion are performed for N2 (high polarizability). Our results allow us to suggest that field...
Analysing harmonic motions with an iPhone’s magnetometer
Yavuz, Ahmet; Kağan Temiz, Burak
2016-05-01
In this paper, we propose an experiment for analysing harmonic motion using an iPhone’s (or iPad’s) magnetometer. This experiment consists of the detection of magnetic field variations obtained from an iPhone’s magnetometer sensor. A graph of harmonic motion is directly displayed on the iPhone’s screen using the Sensor Kinetics application. Data from this application was analysed with Eureqa software to establish the equation of the harmonic motion. Analyses show that the use of an iPhone’s magnetometer to analyse harmonic motion is a practical and effective method for small oscillations and frequencies less than 15-20 Hz.
Microgrid Reactive and Harmonic Power Sharing Using Enhanced Virtual Impedance
He, Jinwei; Wei Li, Yun; Guerrero, Josep M.
2013-01-01
To address the load sharing problem in islanding microgrids, this paper proposes an improved approach which regulates the distributed generation (DG) unit interfacing virtual impedance at fundamental and selected harmonic frequencies. In contrast to the conventional virtual impedance control where...... feeder impedances can be properly compensated, resulting in accurate reactive and harmonic power sharing at the same time. In addition, this paper shows that the microgrid PCC harmonic voltages can be mitigated by reducing the magnitude of DG unit equivalent harmonic impedance. Finally, an improved...
Harmonics Mitigation Using Active Power Filter
Sourabh Gupta
2013-06-01
Full Text Available This paper is proposed to reconsider the development of active power filter (APF technologies that are routinely utilized to mitigate harmonics in utility power lines. This reconsider can furthermore be considered as a “tutorial-type paper” as it provides a holistic coverage of the APF technologies by omitting the tedious details, but without losing the major essence of the subject matter. It is wanted that by this approach, it would be likely to lure more power engineering readers to be involved in this important and growing area. The discussion starts with a short overview of harmonic distortion difficulties and their impacts on electric power and powered value. The operation of common APF topologies, namely the shunt, sequence and hybrid APFs are recounted in minutia. This is followed by a reconsider on different types of reference pointer estimation extraction methods. In specific, the application of the p-q and elongation p-q theorems to extract the quotation pointers are elaborated, as they are the most commonly discovered in practical APF systems eventually, an overview of the APF command schemes is provided. A short consideration on the APF-solar photovoltaic scheme is furthermore granted. At the end of the paper, important references are cited to aid readers who are interested to discover the subject in larger detail.
Optimization Issues in a Harmonic Cascade FEL
De Ninno, G
2005-01-01
Presently there is significant interest by multiple groups (e.g. BNL, ELETTRA, LBNL, BESSY, MIT) to reach short output wavelengths via a harmonic cascade FEL using an external seed laser. In a multistage device, there are a number of "free" parameters such as the nominal power of the input seed, the lengths of the individual modulator and radiator undulators, the strengths (i.e. the R56's) of the dispersive sections, the choice of the actual harmonic numbers to reach a given wavelength, etc., whose optimization is a non-trivial exercise. In particular, one can choose whether to operate predominantly in the "high gain" regime such as was proposed by Yu [1] in which case each radiator undulator is many gain lengths long or, alternatively, in the "low gain" regime in which case all undulators (except possibly the last radiator) are a couple gain lengths or less long and the output from each radiator essentially corresponds to coherent spontaneous emission from a pre-bunched beam. With particular emphasis upon th...
Tissue harmonic synthetic aperture ultrasound imaging.
Hemmsen, Martin Christian; Rasmussen, Joachim Hee; Jensen, Jørgen Arendt
2014-10-01
Synthetic aperture sequential beamforming (SASB) and tissue harmonic imaging (THI) are combined to improve the image quality of medical ultrasound imaging. The technique is evaluated in a comparative study against dynamic receive focusing (DRF). The objective is to investigate if SASB combined with THI improves the image quality compared to DRF-THI. The major benefit of SASB is a reduced bandwidth between the probe and processing unit. A BK Medical 2202 Ultraview ultrasound scanner was used to acquire beamformed RF data for offline evaluation. The acquisition was made interleaved between methods, and data were recorded with and without pulse inversion for tissue harmonic imaging. Data were acquired using a Sound Technology 192 element convex array transducer from both a wire phantom and a tissue mimicking phantom to investigate spatial resolution and penetration. In vivo scans were also performed for a visual comparison. The spatial resolution for SASB-THI is on average 19% better than DRI-THI, and the investigation of penetration showed equally good signal-to-noise ratio. In vivo B-mode scans were made and compared. The comparison showed that SASB-THI reduces the artifact and noise interference and improves image contrast and spatial resolution.
Dark-Matter Harmonics Beyond Annual Modulation
Lee, Samuel K; Safdi, Benjamin R
2013-01-01
The count rate at dark-matter direct-detection experiments should modulate annually due to the motion of the Earth around the Sun. We show that higher-frequency modulations, including daily modulation, are also present and in some cases are nearly as strong as the annual modulation. These higher-order modes are particularly relevant if (i) the dark matter is light, O(10) GeV, (ii) the scattering is inelastic, or (iii) velocity substructure is present; for these cases, the higher-frequency modes are potentially observable at current and ton-scale detectors. We derive simple expressions for the harmonic modes as functions of the astrophysical and geophysical parameters describing the Earth's orbit, using an updated expression for the Earth's velocity that corrects a common error in the literature. For an isotropic halo velocity distribution, certain ratios of the modes are approximately constant as a function of nuclear recoil energy. Anisotropic distributions can also leave observable features in the harmonic ...
Ricci flow coupled with harmonic map flow
Müller, Reto
2009-01-01
We investigate a new geometric flow which consists of a coupled system of the Ricci flow on a closed manifold M with the harmonic map flow of a map phi from M to some closed target manifold N with a (possibly time-dependent) positive coupling constant alpha. This system can be interpreted as the gradient flow of an energy functional F_alpha which is a modification of Perelman's energy F for the Ricci flow, including the Dirichlet energy for the map phi. Surprisingly, the coupled system may be less singular than the Ricci flow or the harmonic map flow alone. In particular, we can always rule out energy concentration of phi a-priori - without any assumptions on the curvature of the target manifold N - by choosing alpha large enough. Moreover, if alpha is bounded away from zero it suffices to bound the curvature of (M,g(t)) to also obtain control of phi and all its derivatives - a result which is clearly not true for alpha = 0. Besides these new phenomena, the flow shares many good properties with the Ricci flow...
Holliday, Ezekiel S. (Inventor)
2014-01-01
Vibrations at harmonic frequencies are reduced by injecting harmonic balancing signals into the armature of a linear motor/alternator coupled to a Stirling machine. The vibrations are sensed to provide a signal representing the mechanical vibrations. A harmonic balancing signal is generated for selected harmonics of the operating frequency by processing the sensed vibration signal with adaptive filter algorithms of adaptive filters for each harmonic. Reference inputs for each harmonic are applied to the adaptive filter algorithms at the frequency of the selected harmonic. The harmonic balancing signals for all of the harmonics are summed with a principal control signal. The harmonic balancing signals modify the principal electrical drive voltage and drive the motor/alternator with a drive voltage component in opposition to the vibration at each harmonic.
Measuring signal generators theory & design
Rybin, Yuriy K
2014-01-01
The book brings together the following issues: Theory of deterministic, random and discrete signals reproducible in oscillatory systems of generators; Generation of periodic signals with a specified spectrum, harmonic distortion factor and random signals with specified probability density function and spectral density; Synthesis of oscillatory system structures; Analysis of oscillatory systems with non-linear elements and oscillation amplitude stabilization systems; It considers the conditions and criteria of steady-state modes in signal generators on active four-pole elements with unidirectional and bidirectional transmission of signals and on two-pole elements; analogues of Barkhausen criteria; Optimization of oscillatory system structures by harmonic distortion level, minimization of a frequency error and set-up time of the steady state mode; Theory of construction of random signal generators; Construction of discrete and digital signal generators; Practical design of main units of generators; Practical bl...
Matthews, Sinéad M; Shiddiky, Muhammad J A; Yunus, Kamran; Elton, Darrell M; Duffy, Noel W; Gu, Yunfeng; Fisher, Adrian C; Bond, Alan M
2012-08-07
The flow rate dependencies of the aperiodic direct current (dc) and fundamental to eighth alternating current (ac) harmonic components derived from large-amplitude Fourier transformed ac (FT-ac) voltammetry have been evaluated in a microfluidic flow cell containing a 25 μm gold microband electrode. For the oxidation of ferrocenemethanol ([FcMeOH]/[FcMeOH](+) process) in aqueous 0.1 M KNO(3) electrolyte, standard "Levich-like" dc behavior is observed for the aperiodic dc component, which enables the diffusion coefficient for FcMeOH to be obtained. In experimental studies, the first and second ac harmonic components contain contributions from the double layer capacitance current, thereby allowing details of the non-Faradaic current to be established. In contrast, the higher order harmonics and dc aperiodic component are essentially devoid of double layer capacitance contributions allowing the faradaic current dependence on flow rate to be studied. Significantly, flow rate independent data conforming to linear diffusion controlled theory are found in the sixth and higher ac harmonics at a frequency of 15 Hz and for all ac harmonics at a frequency of ≥ 90 Hz. Analysis of FT-ac voltammograms by theory based on stationary microband or planar electrode configurations confirms that stationary microband and planar electrode configurations and experimental data all converge for the higher order harmonics and establishes that the electrode kinetics are very fast (≥1 cms(-1)). The ability to locate, from a single experiment, a dc Faradaic component displaying Levich behavior, fundamental and second harmonics that contain details of the double layer capacitance, and Faradaic ac higher order harmonic currents that are devoid of capacitance, independent of the volume flow rate and also conform closely to mass transport by planar diffusion, provides enhanced flexibility in mass transport and electrode kinetic analysis and in understanding the performance of hydrodynamic
Harmonic factors in the perception of tonal melodies
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 faci
Spectral inverse problem for q-deformed harmonic oscillator
P K Bera; J Datta
2006-12-01
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 spectral inverse method.
A Law and Economics View on Harmonization of Procedural Law
L.T. Visscher (Louis)
2010-01-01
textabstractAbstract Even though there exists an extensive Law and Economics literature on the topics of procedural law and harmonization of law, very little has been written on harmonization of procedural law as such. In this paper I first provide a brief overview of the economic approach to legal
A REMARK ON THE QUASI-HARMONIC SPHERES
XuDeliang; ZhouChunqin
2002-01-01
Several theorems on the finiteness of energy for quasi-harmonic spheres are proved,some counter-examples which state that the energy of quasi-harmonic sphere may be infinite are given. The results support some conditions of a question posed by Lin Fanghua and Wang Changyou.
Interpretation of Plateau in High-Harmonic Generation
程太旺; 李晓峰; 敖淑艳; 傅盘铭
2003-01-01
The plateau in high-harmonic generation is investigated in the frequency domain. Probability density of an electron in an electromagnetic field is obtained through analysing the quantized-field Volkov state. The plateau of high-harmonic generation reflects the spectral density of the electron at the location of nucleus after abovethreshold ionization.
Frequency Adaptive Selective Harmonic Control for Grid-Connected Inverters
Yang, Yongheng; Zhou, Keliang; Wang, Huai
2015-01-01
SHC scheme consists of multiple parallel recursive (nk±m)-order (k = 0, 1, 2, . . ., and m ≤ n/2) harmonic control modules with independent control gains, which can be optimally weighted in accordance with the harmonic distribution. The hybrid SHC thus offers an optimal trade-off among cost...
Analysing Harmonic Motions with an iPhone's Magnetometer
Yavuz, Ahmet; Temiz, Burak Kagan
2016-01-01
In this paper, we propose an experiment for analysing harmonic motion using an iPhone's (or iPad's) magnetometer. This experiment consists of the detection of magnetic field variations obtained from an iPhone's magnetometer sensor. A graph of harmonic motion is directly displayed on the iPhone's screen using the "Sensor Kinetics"…
Harmonic Generation with Single-Cycle Light Pulses
Sukhorukov A.A.
2013-03-01
Full Text Available We study theoretically spatiotemporal pulse dynamics in cubic nonlinear media with instant response, nonresonant absorption and normal group velocity dispersion and reveal new features of harmonic generation when the pulse duration is reduced, including the suppression of third-harmonic generation for single-cycle light pulses.
High-order-harmonic generation from field-distorted orbitals
Spiewanowski, Maciek; Etches, Adam; Madsen, Lars Bojer
2013-01-01
We investigate the effect on high-order-harmonic generation of the distortion of molecular orbitals by the driving laser field. Calculations for high-order-harmonic generation including orbital distortion are performed for N2. Our results allow us to suggest that field distortion is the reason why...