Renormalization for free harmonic oscillators
Sonoda, H.
2013-01-01
We introduce a model of free harmonic oscillators that requires renormalization. The model is similar to but simpler than the soluble Lee model. We introduce two concrete examples: the first, resembling the three dimensional $\\phi^4$ theory, needs only mass renormalization, and the second, resembling the four dimensional $\\phi^4$ theory and the Lee model, needs additional renormalization of a coupling and a wave function.
Effective harmonic oscillator description of anharmonic molecular ...
Indian Academy of Sciences (India)
Administrator
Abstract. The validity of an effective harmonic oscillator approximation for anharmonic molecular vibrations is tested and compared with vibrational self consistent field and vibrational configurational interaction results. The effective harmonic oscillator is constructed variationally, by taking the trial wave function as a harmonic ...
Making space for harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Michelotti, Leo; /Fermilab
2004-11-01
If we restrict the number of harmonic oscillator energy eigenstates to some finite value, N, then the discrete spectrum of the corresponding position operator comprise the roots of the Hermite polynomial H{sub N+1}. Its range is just large enough to accommodate classical motion at high energy. A negative energy term must be added to the Hamiltonian which affects only the last eigenstate, |N>, suggesting it is concentrated at the extrema of this finite ''space''. Calculations support a conjecture that, in the limit of large N, the global distribution of points approaches the differential form for classical action.
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
First harmonic injection locking of 24-GHz-oscillators
Directory of Open Access Journals (Sweden)
M. R. Kühn
2003-01-01
Full Text Available An increasing number of applications is proposed for the 24 GHz ISM-band, like automotive radar systems and short-range communication links. These applications demand for oscillators providing moderate output power of a few mW and moderate frequency stability of about 0.5%. The maximum oscillation frequency of low-cost off-theshelf transistors is too low for stable operation of a fundamental 24GHz oscillator. Thus, we designed a 24 GHz first harmonic oscillator, where the power generated at the fundamental frequency (12 GHz is reflected resulting in effective generation of output power at the first harmonic. We measured a radiated power from an integrated planar antenna of more than 1mW. Though this oscillator provides superior frequency stability compared to fundamental oscillators, for some applications additional stabilization is required. As a low-cost measure, injection locking can be used to phase lock oscillators that provide sufficient stability in free running mode. Due to our harmonic oscillator concept injection locking has to be achieved at the first harmonic, since only the antenna is accessible for signal injection. We designed, fabricated and characterized a harmonic oscillator using the antenna as a port for injection locking. The locking range was measured versus various parameters. In addition, phase-noise improvement was investigated. A theoretical approach for the mechanism of first harmonic injection locking is presented.
Effective harmonic oscillator description of anharmonic molecular ...
Indian Academy of Sciences (India)
... a harmonic oscillator eigenfunction with the centroid and width parameter as variational paraeters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar to the vibrational self consistent field results. Coriolis coupling is also included in these studies.
Truong, D. D.; Fonck, R. J.; McKee, G. R.; Yan, Z.; Grierson, B. A.
2016-10-01
The UF-CHERS (Ultra Fast CHarge Exchange Recombination Spectroscopy) diagnostic at DIII-D measures local, long-wavelength ion temperature and toroidal velocity fluctuations at turbulence-relevant spatiotemporal scales from emission of the CVI n=8 ->7 transition. During Quiescent H-mode (QH-mode) plasmas, which offer ELM-free improved confinement, UF-CHERS measurements observed coherent, low frequency (fo 10kHz) pedestal oscillations in Ti and vtor at the Edge Harmonic Oscillation (EHO) frequency while several modes between 35-75 kHz are suppressed when the EHO appears. Although broadband ion temperature and density fluctuations were reduced by the EHO, the toroidal rotation showed increased fluctuation amplitude. Investigating ion temperature and toroidal fluctuations associated with the EHO may provide insights into the saturated instability driving the EHO. Supported by DOE Grants DE-FG02-08ER54999, DE-FC02-04ER54698, and NSF GRFP Grant DGE-1256259.
Chen, Xi; Burrell, K. H.; Osborne, T. H.; Barada, K.; Ferraro, N. M.; Garofalo, A. M.; Groebner, R. J.; McKee, G. R.; Petty, C. C.; Porkolab, M.; Rhodes, T. L.; Rost, J. C.; Snyder, P. B.; Solomon, W. M.; Yan, Z.; The DIII-D Team
2017-08-01
New experimental studies and modelling of the coherent edge harmonic oscillation (EHO), which regulates the conventional Quiescent H-mode (QH-mode) edge, validate the proposed hypothesis of edge rotational shear in destabilizing the low-n kink-peeling mode as the additional drive mechanism for the EHO. The observed minimum edge E × B shear required for the EHO decreases linearly with pedestal collisionality ν \\text{e}\\ast , which is favorable for operating QH-mode in machines with low collisionality and low rotation such as ITER. In addition, the QH-mode regime in DIII-D has recently been found to bifurcate into a new ‘wide-pedestal’ state at low torque in double-null shaped plasmas, characterized by increased pedestal height, width and thermal energy confinement (Burrell 2016 Phys. Plasmas 23 056103, Chen 2017 Nucl. Fusion 57 022007). This potentially provides an alternate path for achieving high performance ELM-stable operation at low torque, in addition to the low-torque QH-mode sustained with applied 3D fields. Multi-branch low-k and intermediate-k turbulences are observed in the ‘wide-pedestal’. New experiments support the hypothesis that the decreased edge E × B shear enables destabilization of broadband turbulence, which relaxes edge pressure gradients, improves peeling-ballooning stability and allows a wider and thus higher pedestal. The ability to accurately predict the critical E × B shear for EHO and maintain high performance QH-mode at low torque is an essential requirement for projecting QH-mode operation to ITER and future machines.
Pure Gaussian states from quantum harmonic oscillator chains with a single local dissipative process
Ma, Shan; Woolley, Matthew J.; Petersen, Ian R.; Yamamoto, Naoki
2017-03-01
We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of (2\\aleph +1) quantum harmonic oscillators where the central oscillator of the chain is coupled to a single reservoir. We then completely parametrize the class of (2\\aleph +1) -mode pure Gaussian states that can be prepared by this type of quantum harmonic oscillator chain. This parametrization allows us to determine the steady-state entanglement properties of such quantum harmonic oscillator chains.
Harmonic Oscillator SUSY Partners and Evolution Loops
Directory of Open Access Journals (Sweden)
David J. Fernández
2012-07-01
Full Text Available Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner Hamiltonians of the harmonic oscillator can produce evolution loops. The corresponding geometric phases will be as well studied.
Fundamental and Harmonic Oscillations in Neighboring Coronal Loops
Li, Hongbo; Liu, Yu; Vai Tam, Kuan
2017-06-01
We present observations of multimode (fundamental and harmonic) oscillations in a loop system, which appear to be simultaneously excited by a GOES C-class flare. Analysis of the periodic oscillations reveals that (1) the primary loop with a period of P a ≈ 4 minutes and a secondary loop with two periods of P a ≈ 4 minutes and P b ≈ 2 minutes are detected simultaneously in closely spaced loop strands; (2) both oscillation components have their peak amplitudes near the loop apex, while in the second loop the low-frequency component P a dominates in a loop segment that is two times larger than the high-frequency component P b ; (3) the harmonic mode P b shows the largest deviation from a sinusoidal loop shape at the loop apex. We conclude that multiple harmonic modes with different displacement profiles can be excited simultaneously even in closely spaced strands, similar to the overtones of a violin string.
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.
Information cloning of harmonic oscillator coherent states
Indian Academy of Sciences (India)
Abstract. We show that in the case of unknown harmonic oscillator coherent states it is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state.
Hyperchaotic circuit with damped harmonic oscillators
DEFF Research Database (Denmark)
Lindberg, Erik; Murali, K.; Tamasevicius, A.
2001-01-01
A simple fourth-order hyperchaotic circuit with damped harmonic oscillators is described. ANP3 and PSpice simulations including an eigenvalue study of the linearized Jacobian are presented together with a hardware implementation. The circuit contains two inductors with series resistance, two ideal...
Information cloning of harmonic oscillator coherent states
Indian Academy of Sciences (India)
We show that in the case of unknown harmonic oscillator coherent statesit is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state. By making use ...
Sobolev spaces associated to the harmonic oscillator
Indian Academy of Sciences (India)
2Departamento de Matemática, Facultad de Ciencias, Universidad Autónoma de. Madrid, Spain. E-mail: bbongio@math.unl.edu.ar; joseluis.torrea@uam.es. MS received 27 September 2005. Abstract. We define the Hermite–Sobolev spaces naturally associated to the harmonic oscillator H = − + |x|2. Structural properties ...
Supersymmetry, quark confinement and the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Bruce, S A; Minning, P C [Department of Physics, University of Concepcion, PO Box 160C, Concepcion (Chile)
2007-12-07
We study some quantum systems described by noncanonical commutation relations formally expressed as [q-hat,p-hat] = i h-bar(I-hat+{chi}-hatH-hat{sub HO}), where H-hat{sub HO} is the associated (harmonic-oscillator-like) Hamiltonian of the system and {chi}-hat is a Hermitian (constant) operator, i.e. [H-hat{sub HO},{chi}-hat]=O-hat. In passing, we also consider a simple ({chi}-hat=O-hat canonical) model, in the framework of a relativistic Klein-Gordon-like wave equation.
Spectral inverse problem for q-deformed harmonic oscillator
Indian Academy of Sciences (India)
The supersymmetric quantization condition is used to study the wave functions of SWKB equivalent -deformed harmonic oscillator which are obtained by using only the knowledge of bound-state spectra of -deformed harmonic oscillator. We have also studied the nonuniqueness of the obtained interactions by this ...
Coherent states for the relativistic harmonic oscillator
Aldaya, Victor; Guerrero, J.
1995-01-01
Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.
Spatial mode discrimination using second harmonic generation
DEFF Research Database (Denmark)
Delaubert, Vincent; Lassen, Mikael Østergaard; Pulford, David
2007-01-01
-Kleinmann analysis, taking into account the full description of the multi-mode field inside the nonlinear crystal in a type I phase-maching condition. The good agreement between experiments and theory shows that the effect is well understood and that we have reliable models required for the design of novel photonics......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 conversion of transverse electric modes of the second harmonic output. For a given TEMn0 pump mode the output mode can be altered continuously by adjusting the laser wavelength, the focusing of the pump or the temperature of the nonlinear medium. We make quantitative comparisons with a generalized Boyd...
On quantum harmonic oscillator being subjected to absolute ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 88; Issue 1. On quantum ... In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. ... This new function, which corresponds to new sets of particles, has scope to raise the quantum oscillator energy (QOE) up to infinity.
Generation of higher harmonic internal waves by oscillating spheroids
Shmakova, Natalia; Ermanyuk, Evgeny; Flór, Jan-Bert
2017-11-01
Oscillating bodies in stratified fluids may emit higher harmonics in addition to fundamental waves. In the present experimental study, we consider higher harmonics of an internal wave field generated by a horizontally oscillating spheroid in a linearly stratified fluid for moderate to high oscillation amplitudes, i.e., scaled oscillation amplitude A /a ≥0.5 , with a the minor radius of the spheroid. Three different spheroid shapes are tested. The results are discussed in the context of the different theories on the generation of higher harmonics. Higher harmonics are observed at the intersections of fundamental wave beams, and at the critical points of the topography where the topographic slope equals the wave slope. The velocity amplitudes of the fundamental, second, and third harmonic waves grow respectively linearly, quadratically, and with the third power of the scaled oscillation amplitude A /a . Though these amplitudes are generally higher when the object's slope is larger, the increase in amplitude above and below the axisymmetric oscillating objects is found to be due to the effect of focusing. In order to discern the relative importance of the harmonics to the fundamental wave, the horizontal structure of the wave amplitude is measured. The results suggest that the n th harmonic of the internal wave field is associated with a radiation diagram corresponding to a multipole of order 2n, with 2 n directions of propagation.
Driven damped harmonic oscillator resonance with an Arduino
Goncalves, A. M. B.; Cena, C. R.; Bozano, D. F.
2017-07-01
In this paper we propose a simple experimental apparatus that can be used to show quantitative and qualitative results of resonance in a driven damped harmonic oscillator. The driven oscillation is made by a servo motor, and the oscillation amplitude is measured by an ultrasonic position sensor. Both are controlled by an Arduino board. The frequency of free oscillation measured was campatible with the resonance frequency that was measured.
A harmonic oscillator having “volleyball damping”
Mickens, R. E.; Oyedeji, K.; Rucker, S. A.
2006-05-01
Volleyball damping corresponds to linear damping up to a certain critical velocity, with zero damping above this value. The dynamics of a linear harmonic oscillator is investigated with this damping mechanism.
Harmonic Brain Modes: A Unifying Framework for Linking Space and Time in Brain Dynamics.
Atasoy, Selen; Deco, Gustavo; Kringelbach, Morten L; Pearson, Joel
2017-09-01
A fundamental characteristic of spontaneous brain activity is coherent oscillations covering a wide range of frequencies. Interestingly, these temporal oscillations are highly correlated among spatially distributed cortical areas forming structured correlation patterns known as the resting state networks, although the brain is never truly at "rest." Here, we introduce the concept of harmonic brain modes-fundamental building blocks of complex spatiotemporal patterns of neural activity. We define these elementary harmonic brain modes as harmonic modes of structural connectivity; that is, connectome harmonics, yielding fully synchronous neural activity patterns with different frequency oscillations emerging on and constrained by the particular structure of the brain. Hence, this particular definition implicitly links the hitherto poorly understood dimensions of space and time in brain dynamics and its underlying anatomy. Further we show how harmonic brain modes can explain the relationship between neurophysiological, temporal, and network-level changes in the brain across different mental states ( wakefulness, sleep, anesthesia, psychedelic). Notably, when decoded as activation of connectome harmonics, spatial and temporal characteristics of neural activity naturally emerge from the interplay between excitation and inhibition and this critical relation fits the spatial, temporal, and neurophysiological changes associated with different mental states. Thus, the introduced framework of harmonic brain modes not only establishes a relation between the spatial structure of correlation patterns and temporal oscillations (linking space and time in brain dynamics), but also enables a new dimension of tools for understanding fundamental principles underlying brain dynamics in different states of consciousness.
The Study of Damped Harmonic Oscillations Using an Electronic Counter
Wadhwa, Ajay
2009-01-01
We study damped harmonic oscillations in mechanical systems like the loaded spring and simple pendulum with the help of an oscillation measuring electronic counter. The experimental data are used in a software program that solves the differential equation for damped vibrations of any system and determines its position, velocity and acceleration as…
Energy Technology Data Exchange (ETDEWEB)
Goldstein, J.C.; Warren, R.W.; Newnam, B.E.
1990-01-01
We study, using numerical simulation methods, the design requirements for the electron beam, wiggler, and optical resonator of an extreme-ultraviolet (XUV, 100 nm {ge} {lambda} {ge} 10 nm) free-electron laser oscillator operating on a higher harmonic. Our previous theoretical studies of an XUV FEL oscillator have assumed operation at the fundamental wavelength. Higher harmonic operation is attractive because the energy of the electrons can be reduced, thus reducing the cost of the linac. A further reduction in beam energy is possible with the use of short-period wigglers: in the present work, we use the expected properties of pulsed-wire wigglers. Operation of an FEL oscillator on the third harmonic has been experimentally demonstrated at Stanford University and Los Alamos, and this mode of operation may also be both possible and desirable for an XUV device. 12 refs., 2 tabs.
Harmonic oscillator in an elastic medium with a spiral dislocation
Maia, A. V. D. M.; Bakke, K.
2018-02-01
We investigate the behaviour of a two-dimensional harmonic oscillator in an elastic medium that possesses a spiral dislocation (an edge dislocation). We show that the Schrödinger equation for harmonic oscillator in the presence of a spiral dislocation can be solved analytically. Further, we discuss the effects of this topological defect on the confinement to a hard-wall confining potential. In both cases, we analyse if the effects of the topology of the spiral dislocation gives rise to an Aharonov-Bohm-type effect for bound states.
Violation of smooth observable macroscopic realism in a harmonic oscillator.
Leshem, Amir; Gat, Omri
2009-08-14
We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. We demonstrate a breakdown of dynamical realism in a wide parameter range that is maximized in a scaling limit of extreme squeezing, where it is based on measurements of smooth observables, implying that macroscopic realism is not valid in the harmonic oscillator. We propose an indirect experimental test of these predictions with entangled photons by demonstrating that local realism in a composite system implies dynamical realism in a subsystem.
Predicting charmonium and bottomonium spectra with a quark harmonic oscillator
Norbury, J. W.; Badavi, F. F.; Townsend, L. W.
1986-01-01
The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.
Adomian Decomposition approach to solve the simple harmonic quantum oscillator
Jaradat, Adnan; Adnan Jardat Team; Maen Gharaibeh Team; Mohammad Qaseer Team; Abdalla Obeidat Team
2015-04-01
The simple harmonic quantum oscillator problem has been solved using two methods namely, the algebraic method where the raising and lower operators used and the Frobenius method. Here, we will adopt the Adomian decomposition method to solve this problem and derive the Hermite polynomials in much easier way than the above mentioned methods. This work is supported by Jordan University of Science and Technolgy.
Spectral inverse problem for q-deformed harmonic oscillator
Indian Academy of Sciences (India)
only the knowledge of bound-state spectra of q-deformed harmonic oscillator. We have also studied the ... that these will be continued both at sophisticated and pedagogical levels [2]. In an interesting work, Engelke ... concepts, exact knowledge of the spectrum is not enough for the reconstruction of the potential. For a given ...
Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps
Pendrill, Ann-Marie; Eager, David
2015-01-01
Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…
Coherent states of general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
The wave function can then be found easily, by making use of these ladder operators. Glauber proposed standard coherent states for a harmonic oscillator which is the prototype for most of the coherent states [3,4]. The coherent states form a very convenient representation for problems of quantum mechanics and can be ...
Maximal Regularity of the Discrete Harmonic Oscillator Equation
Directory of Open Access Journals (Sweden)
Airton Castro
2009-01-01
Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.
Thermal state of the general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. The uncertainty relation of the system is always larger than ħ=2 not only in number but also in the thermal state as expected. We used the diagonal elements of density operator ...
The harmonic oscillator in a space with a screw dislocation
Amore, Paolo; Fernández, Francisco M.
2018-01-01
We obtain the eigenvalues of the harmonic oscillator in a space with a screw dislocation. By means of a suitable nonorthogonal basis set with variational parameters we obtain sufficiently accurate eigenvalues for an arbitrary range of values of the space-deformation parameter. The energies exhibit a rich structure of avoided crossings in terms of such model parameter.
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
2017-02-22
Feb 22, 2017 ... Phase-space quantum mechanics; coherent states; harmonic oscillator; Husimi distribution; cross- ... is the Weyl operator assigned to the phase-space ...... formulae used in this work. The Hermite polynomials satisfy the following relations: 1. [19, Section 5.6.4],. Hη(y + σ) = η. ∑ k=0. ( η k. ) Hk(y)(2σ)η−k. = η.
Quantum theory of damped harmonic oscillator | Antia | Global ...
African Journals Online (AJOL)
The exact solutions of the Schrödinger equation for damped harmonic oscillator with pulsating mass and modified Caldirola-Kanai Hamiltonian are evaluated. We also investigated the case of under-damped for the two models constructed and the results obtained in both cases do not violate Heisenberg uncertainty principle ...
Harmonic oscillator in Snyder space: The classical case and the ...
Indian Academy of Sciences (India)
This modified parameters give us a modified energy spectrum also. Keywords. Harmonic oscillator ... time where the non-commutativity of space operators is proportional to non-linear combinations of phase ... in §4. 2. The classical case. Classical n dimensional Snyder space is characterized by its non-linear commutation.
Harmonic oscillator in Snyder space: The classical case and the ...
Indian Academy of Sciences (India)
The harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. An effective cut-off to high frequencies is found. The quantum version is developed and an equivalent usual ...
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the ...
Brownian motion with adhesion: harmonic oscillator with fluctuating mass.
Gitterman, M; Klyatskin, V I
2010-05-01
In contrast to the cases usually studied of a harmonic oscillator subject to a random force (Brownian motion) or having random frequency or random damping, we consider a random mass which corresponds to an oscillator for which the particles of the surrounding medium adhere to it for some (random) time after the collision, thereby changing the oscillator mass. This model, which describes Brownian motion with adhesion, can be useful for the analysis of chemical and biological solutions as well as nanotechnological devices. We consider dichotomous noise and its limiting case, white noise.
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearity...... in the coupling transconductances, in conjunction with a finite amplitude relaxation time and de-tuning of the individual oscillators, cause close-to-carrier AM-to-PM noise conversion. A discussion is presented of how the theoretic results translate into design rules for quadrature oscillator ICs. SPECTRE RF...
Geometric phase and nonadiabatic effects in an electronic harmonic oscillator.
Pechal, M; Berger, S; Abdumalikov, A A; Fink, J M; Mlynek, J A; Steffen, L; Wallraff, A; Filipp, S
2012-04-27
Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe its experimental observation in an electronic harmonic oscillator. We use a superconducting qubit as a nonlinear probe of the phase, which is otherwise unobservable due to the linearity of the oscillator. We show that the geometric phase is, for a variety of cyclic paths, proportional to the area enclosed in the quadrature plane. At the transition to the nonadiabatic regime, we study corrections to the phase and dephasing of the qubit caused by qubit-resonator entanglement. In particular, we identify parameters for which this dephasing mechanism is negligible even in the nonadiabatic regime. The demonstrated controllability makes our system a versatile tool to study geometric phases in open quantum systems and to investigate their potential for quantum information processing.
The q-harmonic oscillators, q-coherent states and the q-symplecton
Biedenharn, L. C.; Lohe, M. A.; Nomura, Masao
1993-01-01
The recently introduced notion of a quantum group is discussed conceptually and then related to deformed harmonic oscillators ('q-harmonic oscillators'). Two developments in applying q-harmonic oscillators are reviewed: q-coherent states and the q-symplecton.
Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator
Energy Technology Data Exchange (ETDEWEB)
Belendez, Augusto [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Pascual, Carolina [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-11-19
The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A.
Energy Technology Data Exchange (ETDEWEB)
Rosu, H.C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosi, S.L.P. (Mexico); Khmelnytskaya, K.V. [Universidad Autonoma de Queretaro, Centro Universitario, Cerro de las Campanas s/n, C.P. 76010 Santiago de Queretaro, Qro. (Mexico)
2011-09-19
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned. -- Highlights: → A particular Riccati solution of the classical harmonic oscillator is shifted by a constant. → Such a solution is used in the factorization brackets to get different equations of motion. → The properties of the parametric oscillators obtained in this way are examined.
Quantum harmonic oscillator: an elementary derivation of the energy spectrum
Borghi, Riccardo
2017-03-01
An elementary treatment of the quantum harmonic oscillator is proposed. No previous knowledge of linear differential equation theory or Fourier analysis are required, but rather only a few basics of elementary calculus. The pivotal role in our analysis is played by the sole particle localization constraint, which implies square integrability of stationary-state wavefunctions. The oscillator ground-state characterization is then achieved in a way that could be grasped, in principle, even by first-year undergraduates. A very elementary approach to build up and to characterize all higher-level energy eigenstates completes our analysis.
Pisot q-coherent states quantization of the harmonic oscillator
Gazeau, J. P.; del Olmo, M. A.
2013-03-01
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0states form an overcomplete set that resolves the unity with respect to an explicit measure. We restrict our study to the case in which q-1 is a quadratic unit Pisot number, since then the q-deformed integers form Fibonacci-like sequences of integers. We then examine the main characteristics of the corresponding quantum oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories.
Nonlinear oscillations of TM-mode gyrotrons
Chang, Tsun-Hsu; Yao, Hsin-Yu; Su, Bo-Yuan; Huang, Wei-Chen; Wei, Bo-Yuan
2017-12-01
This study investigates the interaction between the relativistic electrons and the waves in cavities with fixed field profiles. Both the transverse electric (TE) and the transverse magnetic (TM) cavity modes are examined, including three first-axial modes, TE011, TM011, and TM111, and two zero-axial modes, TM010 and TM110. The first-axial modes have the same resonant frequency, so a direct comparison can be made. By sweeping the electron pitch factor (α) and the electron transit angle (Θ), the optimal converting efficiency of TM modes occurs at α = 1.5 and Θ = 1.5π, unlike the TE mode of α = 2.0 and Θ = 1.0π. The converting efficiencies of both the first-axial TM modes are much lower than that of TE011 mode. The starting currents of TM011 and TM111 modes are four times higher than that of TE011 mode, indicating that these two TM modes are very difficult to oscillate. This evidences that under the traditional operating conditions, the TM-mode gyrotrons are insignificant. However, the two unique, zero-axial TM modes have relatively high converting efficiency. The highest converting efficiency of TM110 is 27.4%, the same value as that of TE011 mode. The starting currents of TM110 mode and TE011 mode are at the same level. The results suggest that some TM-mode gyrotron oscillators are feasible and deserve further theoretical and experimental studies.
Quantum Harmonic Oscillator State Control in a Squeezed Fock Basis.
Kienzler, D; Lo, H-Y; Negnevitsky, V; Flühmann, C; Marinelli, M; Home, J P
2017-07-21
We demonstrate control of a trapped-ion quantum harmonic oscillator in a squeezed Fock state basis, using engineered Hamiltonians analogous to the Jaynes-Cummings and anti-Jaynes-Cummings forms. We demonstrate that for squeezed Fock states with low n the engineered Hamiltonians reproduce the sqrt[n] scaling of the matrix elements which is typical of Jaynes-Cummings physics, and also examine deviations due to the finite wavelength of our control fields. Starting from a squeezed vacuum state, we apply sequences of alternating transfer pulses which allow us to climb the squeezed Fock state ladder, creating states up to excitations of n=6 with up to 8.7 dB of squeezing, as well as demonstrating superpositions of these states. These techniques offer access to new sets of states of the harmonic oscillator which may be applicable for precision metrology or quantum information science.
Detection of the Second Harmonic of Decay-less Kink Oscillations in the Solar Corona
Duckenfield, T.; Anfinogentov, S. A.; Pascoe, D. J.; Nakariakov, V. M.
2018-02-01
EUV observations of a multi-thermal coronal loop, taken by the Atmospheric Imaging Assembly of the Solar Dynamics Observatory, which exhibits decay-less kink oscillations are presented. The data cube of the quiet-Sun coronal loop was passed through a motion magnification algorithm to accentuate transverse oscillations. Time–distance maps are made from multiple slits evenly spaced along the loop axis and oriented orthogonal to the loop axis. Displacements of the intensity peak are tracked to generate time series of the loop displacement. Fourier analysis on the time series shows the presence of two periods within the loop: {P}1={10.3}-1.7+1.5 minutes and {P}2={7.4}-1.3+1.1 minutes. The longer period component is greatest in amplitude at the apex and remains in phase throughout the loop length. The shorter period component is strongest further down from the apex on both legs and displays an anti-phase behavior between the two loop legs. We interpret these results as the coexistence of the fundamental and second harmonics of the standing kink mode within the loop in the decay-less oscillation regime. An illustration of seismological application using the ratio P 1/2P 2 ∼ 0.7 to estimate the density scale height is presented. The existence of multiple harmonics has implications for understanding the driving and damping mechanisms for decay-less oscillations and adds credence to their interpretation as standing kink mode oscillations.
Pisot q-coherent states quantization of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Gazeau, J.P., E-mail: gazeau@apc.univ-paris7.fr [Laboratoire APC, Univ. Paris Diderot, Sorbonne Paris Cite, 75205 Paris (France); Olmo, M.A. del, E-mail: olmo@fta.uva.es [Departamento de Fisica Teorica and IMEVA, Universidad de Valladolid, E-47005, Valladolid (Spain)
2013-03-15
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories. - Highlights: Black-Right-Pointing-Pointer Quantized version of the harmonic oscillator (HO) through a q-family of coherent states. Black-Right-Pointing-Pointer For q,0
oscillator.
Detecting the harmonics of oscillations with time-variable frequencies
Sheppard, L. W.; Stefanovska, A.; McClintock, P. V. E.
2011-01-01
A method is introduced for the spectral analysis of complex noisy signals containing several frequency components. It enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency. The method is based on mutual information and surrogate testing combined with the wavelet transform, and it is applicable to relatively short time series containing frequencies that are time variable. Where the fundamental frequency and harmonics of a process can be identified, the characteristic shape of the corresponding oscillation can be determined, enabling adaptive filtering to remove other components and nonoscillatory noise from the signal. Thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately. The method is first demonstrated on numerical examples. It is then used to identify the higher harmonics of oscillations in human skin blood flow, both spontaneous and associated with periodic iontophoresis of a vasodilatory agent. The method should be equally relevant to all situations where signals of comparable complexity are encountered, including applications in astrophysics, engineering, and electrical circuits, as well as in other areas of physiology and biology.
Epsilon coherent states with polyanalytic coefficients for the harmonic oscillator
Mouayn, Zouhaïr
2017-12-01
We construct a new class of coherent states indexed by points z of the complex plane and depending on two positive parameters m and ɛ >0 by replacing the coefficients zn/√{n!} of the canonical coherent states by polyanalytic functions. These states solve the identity of the states Hilbert space of the harmonic oscillator at the limit ɛ → 0+ and obey a thermal stability property. Their wavefunctions are obtained in a closed form and their associated Bargmann-type transform is also discussed.
Spatial Mode Control of High-Order Harmonics
Energy Technology Data Exchange (ETDEWEB)
Mercer, I.; Mevel, E.; Zerne, R.; LHuillier, A.; Antoine, P.; Wahlstroem, C. [Department of Physics, Lund Institute of Technology, S-221 00 Lund (Sweden)]|[Commissariat a l`Energie Atomique, DSM/DRECAM/SPAM, Centre d`Etudes de Saclay, 91191 Gif-sur-Yvette (France)
1996-08-01
We demonstrate that the spatial mode of high-order harmonics can be continuously controlled. The control is achieved by spatially modulating the degree of elliptical polarization of the fundamental field using birefringent optics. A highly sensitive relationship between the efficiency of harmonic generation and the degree of laser elliptical polarization leads to atoms emitting harmonics only in regions of linear polarization. The harmonics are emitted as annular beams whose angles of divergence can be continuously varied. {copyright} {ital 1996 The American Physical Society.}
The two capacitor problem revisited: simple harmonic oscillator model approach
Lee, Keeyung
2012-01-01
The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that \\emph {exactly half} the work done by a constant applied force is dissipated irrespective of the form of dissipation mechanism when the system comes to a new equilibrium after a constant force is abruptly applied. This model is then applied to the energy loss mechanism in the capacitor charging problem or the two-capacitor problem. This approach allows a simple explanation of the energy dissipation mechanism in these problems and shows that the dissipated energy should always be \\emph {exactly half} the supplied energy whether that is caused by the Joule heat or by the radiation. This paper which provides a simple treatment of the energy dissipation mechanism in the two-capacitor problem is suitable for all undergraduate...
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
Chou, Chia-Chun
2016-10-01
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton-Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Directory of Open Access Journals (Sweden)
P. A. Deymier
2016-12-01
Full Text Available We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.
Earl, Boyd L.
2008-01-01
A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…
Modeling stock return distributions with a quantum harmonic oscillator
Ahn, K.; Choi, M. Y.; Dai, B.; Sohn, S.; Yang, B.
2017-11-01
We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.
Spectral theory of non-commutative harmonic oscillators an introduction
Parmeggiani, Alberto
2010-01-01
This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of “classical” invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.
DAMPING OF SUBSYNCHRONOUS MODES OF OSCILLATIONS
Directory of Open Access Journals (Sweden)
JAGADEESH PASUPULETI
2006-06-01
Full Text Available The IEEE bench mark model 2 series compensated system is considered for analysis. It consists of single machine supplying power to infinite bus through two parallel lines one of which is series compensated. The mechanical system considered consists of six mass, viz, high pressure turbine, intermediate pressure turbine, two low pressure turbines, generator and an exciter. The excitation system considered is IEEE type 1 with saturation. The auxiliary controls considered to damp the unstable subsynchronous modes of oscillations are Power System Stabilizer (PSS and Static var Compensator (SVC. The different cases of power system stabilizer and reactive power controls are adapted to study the effectiveness of damping these unstable subsynchronous modes of oscillations.
Harmonic and anharmonic quantum-mechanical oscillators in noninteger dimensions
Energy Technology Data Exchange (ETDEWEB)
Sandev, Trifce, E-mail: trifce.sandev@drs.gov.mk [Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje (Macedonia, The Former Yugoslav Republic of); Petreska, Irina, E-mail: irina.petreska@pmf.ukim.mk [Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss Cyril and Methodius University, P.O. Box 162, 1001 Skopje (Macedonia, The Former Yugoslav Republic of); Lenzi, Ervin K., E-mail: eklenzi@dfi.uem.br [Departamento de Fisica, Universidade Estadual de Maringá, Avenida Colombo 5790, Maringá, 87020-900, PR (Brazil)
2014-01-10
We present new results for time-independent solutions for a Schrödinger equation with noninteger dimension by considering different, harmonic and anharmonic, forms for the potential energy. The solutions obtained for these potentials are exact and expressed in terms of the special functions such as Laguerre and Gegenbauer polynomials, associated Legendre functions, and hypergeometric functions. Graphical comparison of the probability density function with the ones for two-dimensional and three-dimensional case is given. We derive the mean values r{sup β}sin{sup δ}θ{sup ¯} for the harmonic oscillator in noninteger dimensions, which may be of interest in the perturbation theory for calculation of energy corrections. We consider anharmonic Kratzer potential energy function and we obtain bound and scattering states. Exact results in case of different forms of θ-dependent potentials are presented. In addition, they can be connected to rich variety of situations which enable us to model anisotropic interactions in real space.
Mixed Mode Oscillations due to the Generalized Canard Phenomenon
DEFF Research Database (Denmark)
Brøns, Morten; Krupa, Martin; Wechselberger, Martin
2006-01-01
Mixed mode oscillations combine features of small oscillations and large oscillations of relaxation type. We describe a mechanism for mixed mode oscillations based on the presence of canard solutions, which are trajectories passing from a stable to an unstable slow manifold. An important ingredient...... on mixed mode periodic orbits with Farey sequences of the form 1s. We also show how to generalize the context of one fast variable to an arbitrary number of fast variables....
The quantum harmonic oscillator on a circle and a deformed quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Rego-Monteiro, M.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). E-mail: regomont@cbpf.br
2001-05-01
We construct a deformed free quantum field theory with an standard Hilbert space based on a deformed Heisenberg algebra. This deformed algebra is a Heisenberg-type algebra describing the first levels of the quantum harmonic oscillator on a circle of large length L. The successive energy levels of this quantum harmonic oscillator on a circle of large length L are interpreted, similarly to the standard quantum one-dimensional harmonic oscillator on an infinite line, as being obtained by the creation of a quantum particle of frequency w at very high energies. (author)
West Coast Swing Dancing as a Driven Harmonic Oscillator Model
Ferrara, Davon; Holzer, Marie; Kyere, Shirley
The study of physics in sports not only provides valuable insight for improved athletic performance and injury prevention, but offers undergraduate students an opportunity to engage in both short- and long-term research efforts. In this project, conducted by two non-physics majors, we hypothesized that a driven harmonic oscillator model can be used to better understand the interaction between two west coast swing dancers since the stiffness of the physical connection between dance partners is a known factor in the dynamics of the dance. The hypothesis was tested by video analysis of two dancers performing a west coast swing basic, the sugar push, while changing the stiffness of the physical connection. The difference in stiffness of the connection from the ideal was estimated by the leader; the position with time data from the video was used to measure changes in the amplitude and phase difference between the leader and follower. While several aspects of our results agree with the proposed model, some key characteristics do not, possibly due to the follower relying on visual leads. Corresponding author and principal investigator.
Calorimetric measurement of work for a driven harmonic oscillator
Sampaio, Rui; Suomela, Samu; Ala-Nissila, Tapio
2016-12-01
A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.
Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise.
Viñales, A D; Wang, K G; Despósito, M A
2009-07-01
The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using the Laplace analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions and its derivatives from a generalized Langevin equation. Our results show that the oscillator displays an anomalous diffusive behavior. In the strictly asymptotic limit, the dynamics of the harmonic oscillator corresponds to an oscillator driven by a noise with a pure power-law autocorrelation function. However, at short and intermediate times the dynamics has qualitative difference due to the presence of the characteristic time of the noise.
Maamache, M.; Bencheikh, K.; Hachemi, H.
1999-04-01
The correct wave function for the problem of a harmonic oscillator of time-dependent mass and frequency is obtained following the same approach used in the paper of Dantas et al. [Phys. Rev. A 45, 1320 (1992)].
Supersymmetry and the constants of motion of the two-dimensional isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Torres del Castillo, G.F. [Departamento de Fisica Matematica, Instituto de Ciencias, Universidad Autonoma de Puebla, 72570 Puebla (Mexico); Tepper G, T. [Escuela de Ciencias, Departamento de Fisica y Matematicas, Universidad de Las Americas-Puebla, Santa Catarina Martir, 72820 Cholula, Puebla (Mexico)
2002-07-01
It is shown that the constants of motion of the two-dimensional isotropic harmonic oscillator not related to the rotational invariance of the Hamiltonian can be derived using the ideas of supersymmetric quantum mechanics. (Author)
Yeon, Kyu-Hwang; Um, Chung-In; George, Thomas F.; Pandey, Lakshmi N.
1993-01-01
Starting with evaluations of propagator and wave function for the damped harmonic oscillator with time-dependent frequency, exact coherent states are constructed. These coherent states satisfy the properties which coherent states should generally have.
Boonengering, J.M.; Gloster, L.A.W.; Veer, van der W.E.; McKinnie, I.T.; King, T.A.; Hogervorst, W.
1995-01-01
A new coupled-cavity design for single-longitudinal-mode operation of an optical parametric oscillator (OPO) is presented. The OPO is based on a beta-BaB2O4 crystal and is pumped by the third harmonic of a Nd:YAG laser. With this design, we achieved single-longitudinal-mode operation of the OPO with
Exact diagonalization of the D-dimensional spatially confined quantum harmonic oscillator
Directory of Open Access Journals (Sweden)
Kunle Adegoke
2016-01-01
Full Text Available In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.
Phase of the quantum harmonic oscillator with applications to optical polarization
Shepard, Scott R.
1993-01-01
The phase of the quantum harmonic oscillator, the temporal distribution of a particle in a square-well potential, and a quantum theory of angles are derived from a general theory of complementarity. Schwinger's harmonic oscillator model of angular momenta is modified for the case of photons. Angular distributions for systems of identical and distinguishable particles are discussed. Unitary and antiunitary time reversal operators are then presented and applied to optical polarization states in birefringent media.
"Good Vibrations": A workshop on oscillations and normal modes
Barbieri, Sara; Carpineti, Marina; Giliberti, Marco; Rigon, Enrico; Stellato, Marco; Tamborini, Marina
2016-05-01
We describe some theatrical strategies adopted in a two hour workshop in order to show some meaningful experiments and the underlying useful ideas to describe a secondary school path on oscillations, that develops from harmonic motion to normal modes of oscillations, and makes extensive use of video analysis, data logging, slow motions and applet simulations. Theatre is an extremely useful tool to stimulate motivation starting from positive emotions. That is the reason why the theatrical approach to the presentation of physical themes has been explored by the group "Lo spettacolo della Fisica" (http://spettacolo.fisica.unimi.it) of the Physics Department of University of Milano for the last ten years (Carpineti et al., JCOM, 10 (2011) 1; Nuovo Cimento B, 121 (2006) 901) and has been inserted also in the European FP7 Project TEMI (Teaching Enquiry with Mysteries Incorporated, see http://teachingmysteries.eu/en) which involves 13 different partners coming from 11 European countries, among which the Italian (Milan) group. According to the TEMI guidelines, this workshop has a written script based on emotionally engaging activities of presenting mysteries to be solved while participants have been involved in nice experiments following the developed path.
Directory of Open Access Journals (Sweden)
Yu-Shan Chen
2015-04-01
Full Text Available We reported that the photonic crystal fiber (PCF filled with TI:Bi2Te3 nanosheets solution could act as an effective saturable absorber (SA. Employing this TI-PCF SA device; we constructed an ytterbium-doped all-fiber laser oscillator and achieved the evanescent wave mode-locking operation. Due to the large cavity dispersion; the fundamental mode-locking pulse had the large full width at half maximum (FWHM of 2.33 ns with the repetition rate of ~1.11 MHz; and the radio frequency (RF spectrum with signal-to-noise ratio (SNR of 61 dB. In addition; the transition dynamics from a bunched state of pulses to harmonic mode-locking (HML was also observed; which was up to 26th order.
Single longitudinal mode operation of a solid-state dye laser oscillator
Lim, G; Kim, H S; Cha, B H; Lee, J M
2000-01-01
We have operated a single longitudinal mode of a solid-state dye laser oscillator in a Littman configuration. The host material of the solid-state gain medium was rhodamine dye-doped poly (methyl methacrylate). The pumping source was the second harmonic of a Nd:YAG laser with a repetition rate of 10 Hz. The measured linewidth of the laser output was about 1.5 GHz.
Thermal state of the general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
the thermal state. In Ü2, we investigate quantum mechanical solution of the general time-dependent har- monic oscillator. The thermal state of the system is discussed in Ü3 on the basis of. Liouville–von Neumann approach. InÜ4, we will apply our theory for a special case which is the forced Caldirola–Kanai oscillator.
Modes of nanosatellite aerodynamic oscillations in atmosphere
Gerasimov, Yu V.; Ivanov, E. A.; Karetnikov, G. K.; Konstantinova, I. A.; Selivanov, A. B.
2017-11-01
The paper is devoted to the results of investigating the dependencies of nanosatellite aerodynamic oscillations frequency on attack angle at different altitudes up to 70 km are defined. The oscillations bandwidths are determined with respect to the geometric parameters for a nanosatellite with 10 kg mass and 6000 kg/m3 average density. The model allows estimating the bandwidth aerodynamic oscillations in the suborbital nanosatellite trajectory based on the given geometry and mass-dimensional parameters.
Directory of Open Access Journals (Sweden)
Yilun Shang
2012-07-01
Full Text Available In this paper, we investigate the leader-follower synchronization ofcoupled second-order linear harmonic oscillators with the presence ofrandom noises and time delays. The interaction topology is modeledby a weighted directed graph and the weights are perturbed by whitenoise. On the basis of stability theory of stochastic differential delayequations, algebraic graph theory and matrix theory, we show that thecoupled harmonic oscillators can be synchronized almost surely withrandom perturbation and time delays. Numerical examples are presentedto illustrate our theoretical results.
Planck scale corrections to the harmonic oscillator, coherent, and squeezed states
Bosso, Pasquale; Das, Saurya; Mann, Robert B.
2017-09-01
The generalized uncertainty principle (GUP) is a modification of Heisenberg's Principle predicted by several theories of quantum gravity. It consists of a modified commutator between the position and momentum. In this work, we compute potentially observable effects that GUP implies for the harmonic oscillator, coherent, and squeezed states in quantum mechanics. In particular, we rigorously analyze the GUP-perturbed harmonic oscillator Hamiltonian, defining new operators that act as ladder operators on the perturbed states. We use these operators to define the new coherent and squeezed states. We comment on potential applications.
Time dependent quantum harmonic oscillator subject to a sudden change of mass: continuous solution
Energy Technology Data Exchange (ETDEWEB)
Moya C, H. [INAOE, Coordinacion de Optica, AP 51 y 216, 72000 Puebla (Mexico); Fernandez G, M. [Depto. de Fisica, CBI, Universidad Autonoma Metropolitana - Iztapalapa, 09340, Mexico, D.F. AP 55-534 (Mexico)
2007-07-01
We show that a harmonic oscillator subject to a sudden change of mass produces squeezed states. Our study is based on an approximate analytic solution to the time-dependent harmonic oscillator equation with a sub period function parameter. This continuous treatment differs from former studies that involve the matching of two time-independent solutions at the discontinuity. This formalism requires an ad hoc transformation of the original differential equation and is also applicable for rapid, although not necessarily instantaneous, mass variations. (Author)
Leaci, Paola; Ortolan, Antonello
2007-12-01
We discuss limitations in precision measurements of a weak classical force coupled to quantum mechanical systems, the so-called standard quantum limit (SQL). Among the several contexts exploiting the measurement of classical signals, gravitational wave (GW) detection is of paramount importance. In this framework, we analyze the quantum limited sensitivity of a free test mass, a quantum mechanical harmonic oscillator, two harmonic oscillators with equal masses and different resonance frequencies, and finally two mechanical oscillators with different masses and resonating at the same frequency. The sensitivity analysis of the latter two cases illustrates the potentialities of back-action reduction and classical impedance matching schemes, respectively. By examining coupled quantum oscillators as detectors of classical signals, we found a viable path to approach the SQL for planned or operating GW detectors, such as DUAL and AURIGA.
Collective modes of coupled phase oscillators with delayed coupling
Ares, Saúl; Morelli, Luis G.; Jörg, David J.; Andrew C. Oates; Jülicher, Frank
2012-01-01
We study the effects of delayed coupling on timing and pattern formation in spatially extended systems of dynamic oscillators. Starting from a discrete lattice of coupled oscillators, we derive a generic continuum theory for collective modes of long wavelength. We use this approach to study spatial phase profiles of cellular oscillators in the segmentation clock, a dynamic patterning system of vertebrate embryos. Collective wave patterns result from the interplay of coupling delays and moving...
Asymptotic behavior of a harmonic oscillator driven by a generalized Mittag-Leffler noise
Energy Technology Data Exchange (ETDEWEB)
Sandev, Trifce [Radiation Safety Directorate, Blv. Partizanski Odredi 143, PO Box 22, 1020 Skopje (Macedonia, The Former Yugoslav Republic of); Tomovski, Zivorad, E-mail: trifce.sandev@avis.gov.m, E-mail: tomovski@iunona.pmf.ukim.edu.m [Faculty of Natural Sciences and Mathematics, Institute of Mathematics, 1000 Skopje (Macedonia, The Former Yugoslav Republic of)
2010-12-15
The asymptotic behavior of a harmonic oscillator driven by a generalized Mittag-Leffler noise was studied by analyzing the generalized Langevin equation. The mean square displacement (MSD) and the velocity autocorrelation function (VACF) of a diffusing particle were obtained by using the Laplace transform method and Tauberian theorem. It was found that the MSD and VACF for various values of the parameters show a power-law decay, i.e. an anomalous diffusive behavior of the oscillator.
Quantum/classical mode evolution in free electron laser oscillators
Bosco, P.; Colson, W. B.; Freedman, R. A.
1983-01-01
The problem of oscillator evolution and mode competition in free electron lasers is studied. Relativistic quantum field theory is used to calculate electron wave functions, the angular distribution of spontaneous emission, and the transition rates for stimulated emission and absorption in each mode. The photon rate equation for the weakfield regime is presented. This rate equation is applied to oscillator evolution with a conventional undulator, a two-stage optical klystron, and a tapered undulator. The effects of noise are briefly discussed.
Nonlinear Analysis of a Cross-Coupled Quadrature Harmonic Oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2004-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator leading to an expression for the trade-off between signal quadrature and close-in phase noise. The theory shows that nonlinearity in the coupling transconductance results in AM-PM noise close to the carrier, which...... increases with the coupling strength. The results are compared with SPECTRE RF simulations....
Pascoe, D. J.; Russell, A. J. B.; Anfinogentov, S. A.; Simões, P. J. A.; Goddard, C. R.; Nakariakov, V. M.; Fletcher, L.
2017-10-01
Aims: We extend recently developed seismological methods to analyse oscillating loops which feature a large initial shift in the equilibrium position and investigate additional observational signatures related to the loop environment and oscillation driver. Methods: We model the motion of coronal loops as a kink oscillation damped by mode coupling, accounting for any change in loop length and the possible presence of parallel harmonics in addition to the fundamental mode. We apply our model to a loop which rapidly contracts due to a post-flare implosion (SOL2012-03-09) and a loop with a large lateral displacement (SOL2012-10-20). Results: The seismological method is used to calculate plasma parameters of the oscillating loops including the transverse density profile, magnetic field strength, and phase mixing timescale. For SOL2012-03-09 the period of oscillation has a linear correlation with the contracting motion and suggests the kink speed remains constant during the oscillation. The implosion excitation mechanism is found to be associated with an absence of additional parallel harmonics. Conclusions: The improved Bayesian analysis of the coronal loop motion allows for accurate seismology of plasma parameters, and the evolution of the period of oscillation compared with the background trend can be used to distinguish between loop motions in the plane of the loop and those perpendicular to it. The seismologically inferred kink speed and density contrast imply sub-Alfvénic (MA = 0.16 ± 0.03) propagation of the magnetic reconfiguration associated with the implosion, as opposed to triggering by a wave propagating at the Alfvén speed.
On approximations of first integrals for a system of weakly nonlinear, coupled harmonic oscillators
Waluya, S.B.; van Horssen, W.T.
2001-01-01
In this paper a system of weakly nonlinear, coupled harmonic oscillators will be studied. It will be shown that the recently developed perturbation method based on integrating vectors can be used to approximate rst integrals and periodic solutions. To show how this perturbation method works the
Generalized Uncertainty Principle Corrections to the Simple Harmonic Oscillator in Phase Space
Das, Saurya; Walton, Mark A
2016-01-01
We compute Wigner functions for the harmonic oscillator including corrections from generalized uncertainty principles (GUPs), and study the corresponding marginal probability densities and other properties. We show that the GUP corrections to the Wigner functions can be significant, and comment on their potential measurability in the laboratory.
Energy-dependent harmonic oscillator in noncommutative space: A path integral approach
Benchikha, A.; Merad, M.
2017-11-01
In the context of noncommutative quantum mechanics, the energy-dependent harmonic oscillator problem is solved via path integral approach. The propagator of the system is calculated using polar coordinates. The normalized wave functions and the energy eigenvalues are obtained in two different cases.
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
DEFF Research Database (Denmark)
Jensen, Arne; Yajima, Kenji
2010-01-01
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials which grow at spatial infinity slower than quadratic but faster than linear functions and whose Hessian matrices have a fixed sign. We prove that the fundamental...
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
DEFF Research Database (Denmark)
Jensen, Arne; Yajima, Kenji
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials, which grow at spatial infinity slower than quadratic, but faster than linear functions, and whose Hessian matrices have a fixed sign. We prove that the fundamental...
Attainable conditions and exact invariant for the time-dependent harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)
2006-09-22
The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.
Directory of Open Access Journals (Sweden)
M. Döntgen
2016-09-01
Full Text Available Energy-level densities are key for obtaining various chemical properties. In chemical kinetics, energy-level densities are used to predict thermochemistry and microscopic reaction rates. Here, an analytic energy-level density formulation is derived using inverse Laplace transformation of harmonic oscillator partition functions. Anharmonic contributions to the energy-level density are considered approximately using a literature model for the transition from harmonic to free motions. The present analytic energy-level density formulation for rigid rotor-harmonic oscillator systems is validated against the well-studied CO+O˙H system. The approximate hindered rotor energy-level density corrections are validated against the well-studied H2O2 system. The presented analytic energy-level density formulation gives a basis for developing novel numerical simulation schemes for chemical processes.
Loganathan, Muthukumaran; Bristow, Douglas A
2014-04-01
This paper presents a method and cantilever design for improving the mechanical measurement sensitivity in the atomic force microscopy (AFM) tapping mode. The method uses two harmonics in the drive signal to generate a bi-harmonic tapping trajectory. Mathematical analysis demonstrates that the wide-valley bi-harmonic tapping trajectory is as much as 70% more sensitive to changes in the sample topography than the standard single-harmonic trajectory typically used. Although standard AFM cantilevers can be driven in the bi-harmonic tapping trajectory, they require large forcing at the second harmonic. A design is presented for a bi-harmonic cantilever that has a second resonant mode at twice its first resonant mode, thereby capable of generating bi-harmonic trajectories with small forcing signals. Bi-harmonic cantilevers are fabricated by milling a small cantilever on the interior of a standard cantilever probe using a focused ion beam. Bi-harmonic drive signals are derived for standard cantilevers and bi-harmonic cantilevers. Experimental results demonstrate better than 30% improvement in measurement sensitivity using the bi-harmonic cantilever. Images obtained through bi-harmonic tapping exhibit improved sharpness and surface tracking, especially at high scan speeds and low force fields.
Current and Voltage Mode Multiphase Sinusoidal Oscillators Using CBTAs
Directory of Open Access Journals (Sweden)
M. Sagbas
2013-04-01
Full Text Available Current-mode (CM and voltage-mode (VM multiphase sinusoidal oscillator (MSO structures using current backward transconductance amplifier (CBTA are proposed. The proposed oscillators can generate n current or voltage signals (n being even or odd equally spaced in phase. n+1 CBTAs, n grounded capacitors and a grounded resistor are used for nth-state oscillator. The oscillation frequency can be independently controlled through transconductance (gm of the CBTAs which are adjustable via their bias currents. The effects caused by the non-ideality of the CBTA on the oscillation frequency and condition have been analyzed. The performance of the proposed circuits is demonstrated on third-stage and fifth-stage MSOs by using PSPICE simulations based on the 0.25 µm TSMC level-7 CMOS technology parameters.
Nonradial oscillation modes of compact stars with a crust
Flores, Cesar Vásquez; Hall, Zack B.; Jaikumar, Prashanth
2017-12-01
Oscillation modes of isolated compact stars can, in principle, be a fingerprint of the equation of state (EoS) of dense matter. We study the non-radial high-frequency l =2 spheroidal modes of neutron stars and strange quark stars, adopting a two-component model (core and crust) for these two types of stars. Using perturbed fluid equations in the relativistic Cowling approximation, we explore the effect of a strangelet or hadronic crust on the oscillation modes of strange stars. The results differ from the case of neutron stars with a crust. In comparison to fluid-only configurations, we find that a solid crust on top of a neutron star increases the p -mode frequency slightly with little effect on the f -mode frequency, whereas for strange stars, a strangelet crust on top of a quark core significantly increases the f -mode frequency with little effect on the p -mode frequency.
Nonclassical phase-space trajectories for the damped harmonic quantum oscillator
Energy Technology Data Exchange (ETDEWEB)
Pachon, L.A. [Departamento de Fisica, Universidad Nacional de Colombia, Bogota D.C. (Colombia); Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany); CeiBA - Complejidad, Bogota D.C. (Colombia); Ingold, G.-L., E-mail: gert.ingold@physik.uni-augsburg.de [Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany); Dittrich, T. [Departamento de Fisica, Universidad Nacional de Colombia, Bogota D.C. (Colombia); CeiBA - Complejidad, Bogota D.C. (Colombia)
2010-10-05
Graphical abstract: The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation and the appearance of nonclassical trajectories is discussed. - Abstract: The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation. It is found that pairs of nonclassical trajectories contribute to the path-integral representation of the Wigner propagating function. Due to the linearity of the problem, the sum coordinate of a pair still satisfies the classical equation of motion. Furthermore, it is shown that the broadening of the Wigner propagating function of the damped oscillator arises due to the time-nonlocal interaction mediated by the heat bath.
Qin, Jie; Ning, Lijuan
2017-08-01
This paper addresses the entropy evolution of a damped harmonic oscillator driven by quasimonochromatic noise (QMN). Due to QMN is distinct from white noise, so this paper studied the effect of QMN noise on the upper bound of time derivative of entropy for a damped harmonic oscillator. Through the comparison of probability density function (PDF) and the upper bound for the time derivative of entropy, we find that the entropy evolution is also a useful tool to describe the system dynamic behavior. Then we discuss the interplay of the parameters of QMN, damping constant, the frequency of oscillator and external periodic force and their effects on the upper bound for the rate of entropy change. Finally, some beneficial conclusions are obtained.
Directory of Open Access Journals (Sweden)
Wayne Cheng-Wei Huang
2013-01-01
Full Text Available Stochastic electrodynamics (SED predicts a Gaussian probability distribution for a classical harmonic oscillator in the vacuum field. This probability distribution is identical to that of the ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and the Gaussian probability distribution, we perform a numerical simulation and follow the motion of the oscillator. The dynamical information obtained through the simulation provides insight to the connection between the classic double-peak probability distribution and the Gaussian probability distribution. A main objective for SED research is to establish to what extent the results of quantum mechanics can be obtained. The present simulation method can be applied to other physical systems, and it may assist in evaluating the validity range of SED.
Underdamped stochastic harmonic oscillator driven by Lévy noise
Dybiec, Bartłomiej; Gudowska-Nowak, Ewa; Sokolov, Igor M.
2017-10-01
We investigate the distribution of potential and kinetic energy in stationary states of the linearly damped stochastic oscillator driven by Lévy noises. In the long time limit distributions of kinetic and potential energies of the oscillator follow the power-law asymptotics and do not fulfill the equipartition theorem. The partition of the mechanical energy is controlled by the damping coefficient. In the limit of vanishing damping a stochastic analog of the equipartition theorem can be proposed, namely, the statistical properties of potential and kinetic energies attain distributions characterized by the same widths. For larger damping coefficient the larger fraction of energy is stored in its potential form. In the limit of very strong damping the contribution of kinetic energy becomes negligible. Finally, we demonstrate that the ratio of instantaneous kinetic and potential energies, which signifies departure from the mechanical energy equipartition, follows universal power-law asymptotics, regardless of the symmetric α -stable noise parameters. Altogether our investigations clearly indicate strongly nonequilibrium character of Lévy-stable fluctuations with the stability index α <2 .
Cooling a Harmonic Oscillator by Optomechanical Modification of Its Bath
Xu, Xunnong; Purdy, Thomas; Taylor, Jacob M.
2017-06-01
Optomechanical systems show tremendous promise for the high-sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce an additional damping channel to mechanical motion while keeping its thermal noise at the same level, and, as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of the temperature to the quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an approach for simultaneously reducing the thermal load on a mechanical resonator while improving its quality factor. In essence, we use the optical interaction to dynamically modify the dominant damping mechanism, providing an optomechanically induced effect analogous to a phononic band gap. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red-detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme.
Tunable Mode Coupling in Nanocontact Spin-Torque Oscillators
Zhang, Steven S.-L.; Iacocca, Ezio; Heinonen, Olle
2017-07-01
Recent experiments on spin-torque oscillators have revealed interactions between multiple magnetodynamic modes, including mode coexistence, mode hopping, and temperature-driven crossover between modes. The initial multimode theory indicates that a linear coupling between several dominant modes, arising from the interaction of the subdynamic system with a magnon bath, plays an essential role in the generation of various multimode behaviors, such as mode hopping and mode coexistence. In this work, we derive a set of rate equations to describe the dynamics of coupled magnetodynamic modes in a nanocontact spin-torque oscillator. Expressions for both linear and nonlinear coupling terms are obtained, which allow us to analyze the dependence of the coupled dynamic behaviors of modes on external experimental conditions as well as intrinsic magnetic properties. For a minimal two-mode system, we further map the energy and phase difference of the two modes onto a two-dimensional phase space and demonstrate in the phase portraits how the manifolds of periodic orbits and fixed points vary with an external magnetic field as well as with the temperature.
A classical limit-cycle system that mimics the quantum-mechanical harmonic oscillator
Zarmi, Yair
2017-11-01
Classical harmonic oscillators affected by appropriately chosen nonlinear dissipative perturbations can exhibit infinite sequences of limit cycles, which mimic quantized systems. For properly chosen perturbations, the large-amplitude limit cycles approach circles. The higher the amplitude of the limit cycle is, the smaller are the dissipative deviations from energy conservation. The weaker the perturbation is, the earlier on does the asymptotic behavior show up already in low-lying limit cycles. Simple modifications of the Rayleigh and van der Pol oscillators yield infinite sequences of limit cycles such that the energy spectrum of the higher-amplitude limit cycles tends to that of the quantum-mechanical particle in a box. For another judiciously chosen dissipative perturbation, the energy spectrum of the higher-amplitude limit cycles tends to that of the quantum-mechanical harmonic oscillator. In all cases, one first finds the limit-cycle solutions for dissipation strength, ε ≠ 0. The "energy of each limit cycle" then oscillates around an average value. In the limit ε → 0 these oscillations vanish, and the limit cycles in the infinite sequence attain constant values for their energies, a characteristic that is required for such classical systems to mimic Hamiltonian quantum-mechanical systems.
A Second Harmonic Self-Oscillating Mixer Incorporating Resonant Cell Structure
Directory of Open Access Journals (Sweden)
Leung Chiu
2012-01-01
Full Text Available A downconverting second harmonic self-oscillating mixer (SOM is developed for low-cost wireless communications applications. Incorporating resonant cell in the SOM, we can provide suitable oscillation for generating LO and terminations to all major unwanted mixing products, leading to high conversion gain design. The proposed SOM was measured with 8.5 dB downconversion gain at the RF frequency of 8.2 GHz RF, LO frequency of 4.0 GHz, and IF frequency of 0.2 GHz. The proposed design achieves higher conversion gain than that of the SOM without resonant cell.
Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method
Directory of Open Access Journals (Sweden)
A. M. El-Naggar
2015-11-01
Full Text Available Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.
Harmonic-oscillator pattern arising from an algebraic approach to chiral symmetry
Buccella, F; Savoy, C A
1972-01-01
The Weinberg equation for the (mass)/sup 2/ operator (Q/sub 5//sup +/, (Q/sub 5//sup +/, m/sup 2/))=0, between meson states, is saturated in a perturbative approach. The generator Z of the mixing operators is completely established as Z=(W*M)/sub z/, where W is the W-spin operator and M is the co-ordinate of the three-dimensional harmonic oscillator. In a perturbative expansion of the (mass)/sup 2/ operator, the lowest term consists of two parts, the harmonic-oscillator energy and a spin-orbit coupling of the form (-1)/sup L+1/(L.S+/sup 1///sub 2 /). The resulting (mass)/sup 2/ consists of families of equispaced linearly rising trajectories. (11 refs).
Quantum-trajectory approach to the stochastic thermodynamics of a forced harmonic oscillator.
Horowitz, Jordan M
2012-03-01
I formulate a quantum stochastic thermodynamics for the quantum trajectories of a continuously monitored forced harmonic oscillator coupled to a thermal reservoir. Consistent trajectory-dependent definitions are introduced for work, heat, and entropy, through engineering the thermal reservoir from a sequence of two-level systems. Within this formalism the connection between irreversibility and entropy production is analyzed and confirmed by proving a detailed fluctuation theorem for quantum trajectories. Finally, possible experimental verifications are discussed.
Quantum Trajectory Approach to the Stochastic Thermodynamics of a Forced Harmonic Oscillator
Horowitz, Jordan M.
2011-01-01
I formulate a quantum stochastic thermodynamics for the quantum trajectories of a continuously-monitored forced harmonic oscillator coupled to a thermal reservoir. Consistent trajectory-dependent definitions are introduced for work, heat, and entropy, through engineering the thermal reservoir from a sequence of two-level systems. Within this formalism the connection between irreversibility and entropy production is analyzed and confirmed by proving a detailed fluctuation theorem for quantum t...
Rabi oscillations and stimulated mode conversion on the subwavelength scale.
Zhang, Xiao; Ye, Fangwei; Kartashov, Yaroslav V; Chen, Xianfeng
2015-03-09
We study stimulated mode conversion and dynamics of Rabi-like oscillations of weights of guided modes in deeply subwavelength guiding structures, whose dielectric permittivity changes periodically in the direction of light propagation. We show that despite strong localization of the fields of eigenmodes on the scales below the wavelength of light, even weak longitudinal modulation couples modes of selected parity and causes periodic energy exchange between them, thereby opening the way for controllable transformation of the internal structure of subwavelength beams. The effect is reminiscent of Rabi oscillations in multilevel quantum systems subjected to the action of periodic external fields. By using rigorous numerical solution of the full set of the Maxwell's equations, we show that the effect takes place not only in purely dielectric, but also in metallic-dielectric structures, despite the energy dissipation inherent to the plasmonic waveguides. The stimulated conversion of subwavelength light modes is possible in both linear and nonlinear regimes.
Simultaneous Estimation of Electromechanical Modes and Forced Oscillations
Energy Technology Data Exchange (ETDEWEB)
Follum, Jim; Pierre, John W.; Martin, Russell
2017-09-01
Over the past several years, great strides have been made in the effort to monitor the small-signal stability of power systems. These efforts focus on estimating electromechanical modes, which are a property of the system that dictate how generators in different parts of the system exchange energy. Though the algorithms designed for this task are powerful and important for reliable operation of the power system, they are susceptible to severe bias when forced oscillations are present in the system. Forced oscillations are fundamentally different from electromechanical oscillations in that they are the result of a rogue input to the system, rather than a property of the system itself. To address the presence of forced oscillations, the frequently used AutoRegressive Moving Average (ARMA) model is adapted to include sinusoidal inputs, resulting in the AutoRegressive Moving Average plus Sinusoid (ARMA+S) model. From this model, a new Two-Stage Least Squares algorithm is derived to incorporate the forced oscillations, thereby enabling the simultaneous estimation of the electromechanical modes and the amplitude and phase of the forced oscillations. The method is validated using simulated power system data as well as data obtained from the western North American power system (wNAPS) and Eastern Interconnection (EI).
Energy Technology Data Exchange (ETDEWEB)
Dobaczewski, J.; Dudek, J. [Strasbourg-1 Univ., 67 (France). Centre de Recherches Nucleaires; Dobaczewski, J. [Warsaw Univ. (Poland)
1996-12-31
We describe a method of solving the nuclear Skyrme-Hartree-Fock problem by using a deformed Cartesian harmonic oscillator basis. The complete list of expressions required to calculate local densities, total energy, and self-consistent fields is presented, and an implementation of the self-consistent symmetries is discussed. Formulas to calculate matrix elements in the Cartesian harmonic oscillator basis are derived for the nuclear and Coulomb interactions. (authors). 39 refs.
Indicator for Separation of Structural and Harmonic Modes in Output-only Modal Testing
DEFF Research Database (Denmark)
Brincker, Rune; Andersen, Palle; Møller, Nis
2000-01-01
In this paper a technique for separation of harmonic and structural modes in output-only modal testing and identification is presented. The indicator is based on the basic differences of the statistical properties of a harmonic response and narrow-band stochastic response of a structural mode....... The indicator is demonstrated on an example where a plate is loaded by an engine rotating with quasi-stationary speed. An output-only modal identification is performed using a technique based on Frequency Domain Decomposition (FDD), and what appears to be three harmonic components and five structural modes were...
An Indicator for Separation of Structural and Harmonic Modes in Output-Only Modal Testing
DEFF Research Database (Denmark)
Brincker, Rune; Andersen, P.; Møller, N.
2000-01-01
In this paper a technique for separation of harmonic and structural modes in output-only modal testing and identification is presented. The indicator is based on the basic differences of the statistical properties of a harmonic response and narrow-band stochastic response of a structural mode....... The indicator is demonstrated on an example where a plate is loaded by an engine rotating with quasi-stationary speed. An output-only modal identification is performed using a technique based on Frequency Domain Decomposition (FDD), and what appears to be three harmonic components and five structural modes were...
An Indicator for Separation of Structural and Harmonic Modes in Output-Only Modal Testing
DEFF Research Database (Denmark)
Brincker, Rune; Andersen, P.; Møller, N.
2000-01-01
In this paper a technique for separation of harmonic and structural modes in output-only modal testing and identification is presented. The indicator is based on the basic differences of the statistical properties of a harmonic response and narrow-band stochastic response of a structural mode....... The indicator is demonstrated on an example where a plate is loaded by an engine rotating with quasi-stationary speed. An output-only modal identification is performed using a technique based on Frequency Domain Decomposition (FDD), and what appeared to be three harmonic components and five structural modes...
Dynamics of entanglement between two harmonic modes in stable and unstable regimes
Rebón, Lorena; Canosa, Norma; Rossignoli, Raúl Dante
2014-01-01
The exact dynamics of the entanglement between two harmonic modes generated by an angular momentum coupling is examined. Such system arises when considering a particle in a rotating anisotropic harmonic trap or a charged particle in a fixed harmonic potential in a magnetic field, and exhibits a rich dynamical structure, with stable, unstable and critical regimes according to the values of the rotational frequency or field and trap parameters. Consequently, it is shown that the entanglement ge...
Kinetic freeze-out, particle spectra and harmonic flow coefficients from mode-by-mode hydrodynamics
Floerchinger, Stefan
2014-01-01
The kinetic freeze-out for the hydrodynamical description of relativistic heavy ion collisions is discussed using a background-fluctuation splitting of the hydrodynamical fields. For a single event, the particle spectrum, or its logarithm, can be written as the sum of background part that is symmetric with respect to azimuthal rotations and longitudinal boosts and a part containing the contribution of fluctuations or deviations from the background. Using a complete orthonormal basis to characterize the initial state allows one to write the double differential harmonic flow coefficients determined by the two-particle correlation method as matrix expressions involving the initial fluid correlations. We discuss the use of these expressions for a mode-by-mode analysis of fluctuating initial conditions in heavy ion collisions.
Tunable passively harmonic mode-locked Yb-doped fiber laser with Lyot-Sagnac filter.
Li, Ming; Zou, Xin; Wu, Jian; Shi, Jindan; Qiu, Jifang; Hong, Xiaobin
2015-10-10
A novel passively harmonic mode-locked dissipative soliton Yb-doped fiber laser with all normal dispersion is proposed and experimentally demonstrated based on a semiconductor saturable absorption mirror and tunable Lyot-Sagnac filter. By only tuning the bandwidth of the filter at fixed pump power, the repetition rate of 9.87 to 167.8 MHz (corresponding to 17th-order harmonic) is obtained. This is the highest repetition rate and harmonic order for a passively harmonic mode-locked dissipative soliton Yb-doped fiber laser with all-normal dispersion to the best of our knowledge. The signal-to-noise ratio and super-mode suppression ratio for all harmonic orders are higher than 65 and 35 dB, respectively, which shows the high stability of the fiber laser.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-09-22
An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities.
ELM-free and inter-ELM divertor heat flux broadening induced by edge harmonics oscillation in NSTX
Gan, K. F.; Ahn, J.-W.; Gray, T. K.; Zweben, S. J.; Fredrickson, E. D.; Scotti, F.; Maingi, R.; Park, J.-K.; Canal, G. P.; Soukhanovskii, V. A.; Mclean, A. G.; Wirth, B. D.
2017-12-01
A new n = 1 dominated edge harmonic oscillation (EHO) has been found in NSTX. The new EHO, rotating toroidally in the counter-current direction and the opposite direction of the neutral beam, was observed during certain inter-ELM and ELM-free periods of H-mode operation. This EHO is associated with a significant broadening of the integral heat flux width ({λ\\operatorname{int}} ) by up to 150%, and a decrease in the divertor peak heat flux by >60%. An EHO induced filament was also observed by the gas puff imaging diagnostic. The toroidal rotating filaments could change the edge magnetic topology resulting in toroidal rotating strike point splitting and heat flux broadening. Experimental result of the counter current rotation of strike points splitting is consistent with the counter-current EHO.
Voltage Harmonic Compensation of a Microgrid Operating in Islanded and Grid-Connected Modes
DEFF Research Database (Denmark)
Savaghebi, Mehdi; Jalilian, Alireza; Vasquez, Juan C.
2011-01-01
In this paper, a method for voltage harmonic compensation in a microgrid operating in islanded and gridconnected modes is presented. Harmonic compensation is done through proper control of distributed generators (DGs) interface converters. In order to achieve proper sharing of the compensation...
Dispersion Management in a Harmonically Mode-Locked Fiber Soliton Laser
National Research Council Canada - National Science Library
Carruthers, Thomas F; Duling, III, Irl N; Horowitz, Moshe; Menyuk, Curtis R
1999-01-01
Harmonically mode-locked Er-fiber soliton lasers have become a reliable source of high-repetition-rate picosecond pulses in high-speed communications and photonic analog-to-digital conversion systems...
Tearing mode dynamics and sawtooth oscillation in Hall-MHD
Ma, Zhiwei; Zhang, Wei; Wang, Sheng
2017-10-01
Tearing mode instability is one of the most important dynamic processes in space and laboratory plasmas. Hall effects, resulted from the decoupling of electron and ion motions, could cause the fast development and perturbation structure rotation of the tearing mode and become non-negligible. We independently developed high accuracy nonlinear MHD code (CLT) to study Hall effects on the dynamic evolution of tearing modes with Tokamak geometries. It is found that the rotation frequency of the mode in the electron diamagnetic direction is in a good agreement with analytical prediction. The linear growth rate increases with increase of the ion inertial length, which is contradictory to analytical solution in the slab geometry. We further find that the self-consistently generated rotation largely alters the dynamic behavior of the double tearing mode and the sawtooth oscillation. National Magnetic Confinement Fusion Science Program of China under Grant No. 2013GB104004 and 2013GB111004.
Fleyer, Michael; Horowitz, Moshe
2017-05-01
Homogeneously broadened delay-line oscillators such as lasers or optoelectronic oscillators (OEOs) can potentially oscillate in a large number of cavity modes that are supported by their amplifier bandwidth. In a continuous wave operating mode, the oscillating mode is selected between one or few cavity modes that experience the highest small-signal gain. In this manuscript, we show that the oscillation mode of a homogeneously broadened oscillator can be selected from a large number of modes in a frequency region that can be broader than the full width at half maximum of the effective cavity filter. The mode is selected by a short-time injection of an external signal into the oscillator. After the external signal is turned off, the oscillation is maintained in the selected mode even if this mode has a significantly lower small-signal gain than that of other cavity modes. The stability of the oscillation is obtained due to nonlinear saturation effect in the oscillator amplifier. We demonstrate, experimentally and theoretically, mode selection in a long cavity OEO. We could select any desired mode between 400 cavity modes while maintaining ultra-low phase noise in the selected mode and in the non-oscillating modes. No mode-hopping was observed during our maximum measurement duration of about 24 hours.
Linear stability analysis of collective neutrino oscillations without spurious modes
Morinaga, Taiki; Yamada, Shoichi
2018-01-01
Collective neutrino oscillations are induced by the presence of neutrinos themselves. As such, they are intrinsically nonlinear phenomena and are much more complex than linear counterparts such as the vacuum or Mikheyev-Smirnov-Wolfenstein oscillations. They obey integro-differential equations, for which it is also very challenging to obtain numerical solutions. If one focuses on the onset of collective oscillations, on the other hand, the equations can be linearized and the technique of linear analysis can be employed. Unfortunately, however, it is well known that such an analysis, when applied with discretizations of continuous angular distributions, suffers from the appearance of so-called spurious modes: unphysical eigenmodes of the discretized linear equations. In this paper, we analyze in detail the origin of these unphysical modes and present a simple solution to this annoying problem. We find that the spurious modes originate from the artificial production of pole singularities instead of a branch cut on the Riemann surface by the discretizations. The branching point singularities on the Riemann surface for the original nondiscretized equations can be recovered by approximating the angular distributions with polynomials and then performing the integrals analytically. We demonstrate for some examples that this simple prescription does remove the spurious modes. We also propose an even simpler method: a piecewise linear approximation to the angular distribution. It is shown that the same methodology is applicable to the multienergy case as well as to the dispersion relation approach that was proposed very recently.
Verreault, René
2017-08-01
In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes' dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2-3 orders of magnitude is achieved.
Tang, Sai Chun; Clement, Gregory T
2008-02-01
The aim of this study is to evaluate the feasibility of using harmonic cancellation for a therapeutic ultrasound transducer excited by a switched-mode power converter without an additional output filter. A switching waveform without the third harmonic was created by cascading two switched-mode power inverter modules at which their output waveforms were pi/3 phase shifted from each other. A PSPICE simulation model for the power converter output stage was developed. The simulated results were in good agreement with the measurement. The waveform and harmonic contents of the acoustic pressure generated by a 1-MHz, self-focused piezoelectric transducer with and without harmonic cancellation have been evaluated. Measured results indicated that the acoustic third harmonicto- fundamental ratio at the focus was small (-48 dB) with harmonic cancellation, compared to that without harmonic cancellation (-20 dB). The measured acoustic levels of the fifth harmonic for both cases with and without harmonic cancellation also were small (-46 dB) compared to the fundamental. This study shows that it is viable to drive a piezoelectric ultrasound transducer using a switched-mode power converter without the requirement of an additional output filter in many high-intensity focused ultrasound (HIFU) applications.
DEFF Research Database (Denmark)
Zou, Zhixiang; Wang, Zheng; Cheng, Ming
2012-01-01
This paper presents an digital dual-mode-structure repetitive control approach for the single-phase shunt active power filter (APF), which aims to enhance the tracking ability and eliminate arbitrary order harmonic. The proposed repetitive control scheme blends the characteristics of both odd......-harmonic repetitive control and even-harmonic repetitive control. Moreover, the convergence rate is faster than conventional repetitive controller. Additionally, the parameters have been designed and optimized for the dual-mode structure repetitive control to improve the performance of APF system. Experimental...... results on a laboratory setup are given to verify the proposed control scheme....
Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2014-09-02
A complete equation of state (EOS) for a molecular solid is derived utilizing a Helmholtz free energy. Assuming that the solid is nonconducting, phonon excitations dominate the specific heat. Phonons are approximated as independent quasi-harmonic oscillators with vibrational frequencies depending on the specific volume. The model is suitable for calibrating an EOS based on isothermal compression data and infrared/Raman spectroscopy data from high pressure measurements utilizing a diamond anvil cell. In contrast to a Mie-Gruneisen EOS developed for an atomic solid, the specific heat and Gruneisen coefficient depend on both density and temperature.
Structure of the harmonic oscillator in the space of n-particle Glauber correlators
Zubizarreta Casalengua, E.; López Carreño, J. C.; del Valle, E.; Laussy, F. P.
2017-06-01
We map the Hilbert space of the quantum harmonic oscillator to the space of Glauber's nth-order intensity correlators, in effect showing "the correlations between the correlators" for a random sampling of the quantum states. In particular, we show how the popular g(2) function is correlated to the mean population and how a recurrent criterion to identify single-particle states or emitters, namely, g ( 2 ) physically more intuitive way that can be used to classify quantum sources by surveying which territory they can access.
Instrumentation and control of harmonic oscillators via a single-board microprocessor-FPGA device.
Picone, Rico A R; Davis, Solomon; Devine, Cameron; Garbini, Joseph L; Sidles, John A
2017-04-01
We report the development of an instrumentation and control system instantiated on a microprocessor-field programmable gate array (FPGA) device for a harmonic oscillator comprising a portion of a magnetic resonance force microscope. The specific advantages of the system are that it minimizes computation, increases maintainability, and reduces the technical barrier required to enter the experimental field of magnetic resonance force microscopy. Heterodyne digital control and measurement yields computational advantages. A single microprocessor-FPGA device improves system maintainability by using a single programming language. The system presented requires significantly less technical expertise to instantiate than the instrumentation of previous systems, yet integrity of performance is retained and demonstrated with experimental data.
Instrumentation and control of harmonic oscillators via a single-board microprocessor-FPGA device
Picone, Rico A. R.; Davis, Solomon; Devine, Cameron; Garbini, Joseph L.; Sidles, John A.
2017-04-01
We report the development of an instrumentation and control system instantiated on a microprocessor-field programmable gate array (FPGA) device for a harmonic oscillator comprising a portion of a magnetic resonance force microscope. The specific advantages of the system are that it minimizes computation, increases maintainability, and reduces the technical barrier required to enter the experimental field of magnetic resonance force microscopy. Heterodyne digital control and measurement yields computational advantages. A single microprocessor-FPGA device improves system maintainability by using a single programming language. The system presented requires significantly less technical expertise to instantiate than the instrumentation of previous systems, yet integrity of performance is retained and demonstrated with experimental data.
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung [Department of Physics, HCMC University of Pedagogy, 280 An Duong Vuong, Ward 10, Dist. 5, Ho Chi Minh City (Viet Nam)
2009-05-01
We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./.
de Ponte, M. A.; Mizrahi, S. S.; Moussa, M. H. Y.
2009-09-01
In this paper we extend the results presented in (de Ponte, Mizrahi and Moussa 2007 Phys. Rev. A 76 032101) to treat quantitatively the effects of reservoirs at finite temperature in a bosonic dissipative network: a chain of coupled harmonic oscillators whatever its topology, i.e., whichever the way the oscillators are coupled together, the strength of their couplings and their natural frequencies. Starting with the case where distinct reservoirs are considered, each one coupled to a corresponding oscillator, we also analyze the case where a common reservoir is assigned to the whole network. Master equations are derived for both situations and both regimes of weak and strong coupling strengths between the network oscillators. Solutions of these master equations are presented through the normal ordered characteristic function. These solutions are shown to be significantly involved when temperature effects are considered, making difficult the analysis of collective decoherence and dispersion in dissipative bosonic networks. To circumvent these difficulties, we turn to the Wigner distribution function which enables us to present a technique to estimate the decoherence time of network states. Our technique proceeds by computing separately the effects of dispersion and the attenuation of the interference terms of the Wigner function. A detailed analysis of the dispersion mechanism is also presented through the evolution of the Wigner function. The interesting collective dispersion effects are discussed and applied to the analysis of decoherence of a class of network states. Finally, the entropy and the entanglement of a pure bipartite system are discussed.
Energy Technology Data Exchange (ETDEWEB)
De Ponte, M A; Mizrahi, S S [Departamento de Fisica, Universidade Federal de Sao Carlos, Caixa Postal 676, Sao Carlos, 13565-905, Sao Paulo (Brazil); Moussa, M H Y [Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, Caixa Postal 369, 13560-590 Sao Carlos, SP (Brazil)
2009-09-11
In this paper we extend the results presented in (de Ponte, Mizrahi and Moussa 2007 Phys. Rev. A 76 032101) to treat quantitatively the effects of reservoirs at finite temperature in a bosonic dissipative network: a chain of coupled harmonic oscillators whatever its topology, i.e., whichever the way the oscillators are coupled together, the strength of their couplings and their natural frequencies. Starting with the case where distinct reservoirs are considered, each one coupled to a corresponding oscillator, we also analyze the case where a common reservoir is assigned to the whole network. Master equations are derived for both situations and both regimes of weak and strong coupling strengths between the network oscillators. Solutions of these master equations are presented through the normal ordered characteristic function. These solutions are shown to be significantly involved when temperature effects are considered, making difficult the analysis of collective decoherence and dispersion in dissipative bosonic networks. To circumvent these difficulties, we turn to the Wigner distribution function which enables us to present a technique to estimate the decoherence time of network states. Our technique proceeds by computing separately the effects of dispersion and the attenuation of the interference terms of the Wigner function. A detailed analysis of the dispersion mechanism is also presented through the evolution of the Wigner function. The interesting collective dispersion effects are discussed and applied to the analysis of decoherence of a class of network states. Finally, the entropy and the entanglement of a pure bipartite system are discussed.
Guseinov, I. I.; Mamedov, B. A.
2017-04-01
In this paper, the physical nature of quantum usual and self-friction (SF) harmonic oscillators is presented. The procedure for studying these harmonic oscillators is identical; therefore, we can benefit from the theory of the usual harmonic oscillator. To study the SF harmonic oscillator, using analytical formulae for the L^{{(pl^{ * } )}}-SF Laguerre polynomials (L^{{(pl^{ * } )}}-SFLPs) and L^{{(α^{*} )}}-modified SFLPs (L^{{(α^{*} )}}-MSFLPs) in standard convention, the V^{{(pl^{ * } )}}-SF potentials (V^{{(pl^{ * } )}}-SFPs), V^{{(α^{*} )}}-modified SFPs (V^{{(α^{*} )}}-MSFPs), F^{{(pl^{ * } )}}-SF forces (F^{{(pl^{ * } )}}-SFFs) and F^{{(α^{*} )}}-modified SFFs (F^{{(α^{*} )}}-MSFFs) are investigated, where pl^{ * } = 2l + 2 - α^{*} and α^{*} is the integer (α^{*} = α, - ∞ forces (F^{{(pl^{ * } )}}-SFFs and F^{{(α^{*} )}}-MSFFs), respectively, are independent functions. It is shown that the numerical values of these independent functions are the same, i.e., V_{num}^{{(pl^{ * } )}} = V_{num}^{{(α^{*} )}} and F_{num}^{{(pl^{ * } )}} = F_{num}^{{(α^{*} )}}. The dependence of the SF harmonic oscillator as a function of the distance is analyzed. The presented relationships are valid for arbitrary values of parameters.
Generation of higher order Gauss-Laguerre modes in single-pass 2nd harmonic generation
DEFF Research Database (Denmark)
Buchhave, Preben; Tidemand-Lichtenberg, Peter
2008-01-01
We present a realistic method for dynamic simulation of the development of higher order modes in second harmonic generation. The deformation of the wave fronts due to the nonlinear interaction is expressed by expansion in higher order Gauss-Laguerre modes....
On the local virial theorems for linear and isotropic harmonic oscillator potentials in d dimensions
Bencheikh, K.; Nieto, L. M.
2010-09-01
For the system of noninteracting fermions in a one-body potential V(\\overrightarrow{\\vphantom{A}r}), the local virial theorems (LVT) are relations, at a given point \\overrightarrow{\\vphantom{A}r} in space, between this potential, kinetic energy and particle densities. It was recently shown (Brack et al 2010 J. Phys. A: Math. Theor. 43 255204) that for d-dimensional linear and also for isotropic harmonic oscillator potentials these LVTs are exactly satisfied. We present alternative and simple proofs of these theorems, by consideration of the canonical or Bloch density matrix and its relation to the kinetic energy density. The explicit analytical forms of the Bloch density matrix are used for the above-mentioned potentials to achieve the proofs. For the case of linear potential, we obtain a more general result for the so-called semilocal virial theorem, and for the harmonic oscillator potential case we derive a new relationship between the diagonal part of the canonical bloch density and the kinetic energy density.
Solving a fuzzy initial value problem of a harmonic oscillator model
Karim, M. A.; Gunawan, A. Y.; Apri, M.; Sidarto, K. A.
2017-03-01
Modeling in systems biology is often faced with challenges in terms of measurement uncertainty. This is possibly either due to limitations of available data, environmental or demographic changes. One of typical behavior that commonly appears in the systems biology is a periodic behavior. Since uncertainties would get involved into the systems, the change of solution behavior of the periodic system should be taken into account. To get insight into this issue, in this work a simple mathematical model describing periodic behavior, i.e. a harmonic oscillator model, is considered by assuming its initial value has uncertainty in terms of fuzzy number. The system is known as Fuzzy Initial Value Problems. Some methods to determine the solutions are discussed. First, solutions are examined using two types of fuzzy differentials, namely Hukuhara Differential (HD) and Generalized Hukuhara Differential (GHD). Application of fuzzy arithmetic leads that each type of HD and GHD are formed into α-cut deterministic systems, and then are solved by the Runge-Kutta method. The HD type produces a solution with increasing uncertainty starting from the initial condition. While, GHD type produces an oscillatory solution but only until a certain time and above it the uncertainty becomes monotonic increasing. Solutions of both types certainly do not provide the accuracy for harmonic oscillator model during its evolution. Therefore, we propose the third method, so called Fuzzy Differential Inclusions (FDI), to attack the problem. Using this method, we obtain oscillatory solutions during its evolution.
On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on R
Álvarez Nodarse, Renato; Atakishiyeva Kyazim Zade, Messouma; Atakishiyev Mektiyev, Natig
2005-01-01
We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics, based on a q-extension of the classical Hermite polynomials Hn(x), recently introduced by us in [1] R. Alvarez-Nodarse, M. K. Atakishiyeva, and N. M. Atakishiyev.. On a q-extension of the Hermite polynomials Hn(x) with the continuous orthogonality property on R. Boletín de la Sociedad Matemática Mexicana (3), 8, No.2, pp.127–139, 2002. The wave functions in this q-model of the quantum harmonic oscillator posses...
On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on ℝ
Alvarez-Nodarse, R.; Atakishiyeva, M. K.; Atakishiyev, N. M.
2005-11-01
We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics based on a q-extension of the classical Hermite polynomials H n ( x) recently introduced by us in R. Alvarez-Nodarse et al.: Boletin de la Sociedad Matematica Mexicana (3) 8 (2002) 127. The wave functions in this q-model of the quantum harmonic oscillator possess the continuous orthogonality property on the whole real line ℝ with respect to a positive weight function. A detailed description of the corresponding q-system is carried out.
Directory of Open Access Journals (Sweden)
Cornelia A. Bulucea
2012-03-01
Full Text Available Over the last several decades, it has become increasingly accepted that the term xenobiotic relates to environmental impact, since environmental xenobiotics are understood to be substances foreign to a biological system, which did not exist in nature before their synthesis by humans. In this context, xenobiotics are persistent pollutants such as dioxins and polychlorinated biphenyls, as well as plastics and pesticides. Dangerous and unstable situations can result from the presence of environmental xenobiotics since their harmful effects on humans and ecosystems are often unpredictable. For instance, the immune system is extremely vulnerable and sensitive to modulation by environmental xenobitics. Various experimental assays could be performed to ascertain the immunotoxic potential of environmental xenobiotics, taking into account genetic factors, the route of xenobiotic penetration, and the amount and duration of exposure, as well as the wave shape of the xenobiotic. In this paper, we propose an approach for the analysis of xenobiotic metabolism using mathematical models and corresponding methods. This study focuses on a pattern depicting mathematically modeled processes of resonant absorption of a xenobiotic harmonic oscillation by an organism modulated as an absorbing oscillator structure. We represent the xenobiotic concentration degree through a spatial concentration vector, and we model and simulate the oscillating regime of environmental xenobiotic absorption. It is anticipated that the results could be used to facilitate the assessment of the processes of environmental xenobiotic absorption, distribution, biotransformation and removal within the framework of compartmental analysis, by establishing appropriate mathematical models and simulations.
DEFF Research Database (Denmark)
Nielsen, Dennis; Knott, Arnold; Andersen, Michael A. E.
2013-01-01
A hysteretic self-oscillating bandpass current mode control (BPCM) scheme for Class D audio amplifiers driving capacitive transducers are presented. The scheme provides excellent stability margins and low distortion over a wide range of operating conditions. Small-signal behavior of the amplifier...... is analysis through transfer function based linear control methodology. Measurements are performed on a single-ended ± 300 V half-bridge amplifier driving a capacitive load of 100 nF. Total Harmonic Distortion plus noise (THD+N) below 0.1 % are reported. Transducers representing a capacitive load and obeying...... the rules of electrostatics have been known as very interesting alternatives to the traditional inefficient electrodynamic transducers. When driving capacitive transducers from a Class D audio amplifier the high impedance nature of the load represents a key challenge. The BPCM control scheme ensures a flat...
Effect of localized microstructural evolution on higher harmonic generation of guided wave modes
Choi, Gloria; Liu, Yang; Yao, Xiaochu; Lissenden, Cliff J.
2015-03-01
Higher harmonic generation of ultrasonic waves has the potential to be used to detect precursors to macroscale damage of phenomenon like fatigue due to microstructural evolution contributing to nonlinear material behavior. Aluminum plates having various plastic zone sizes were plastically deformed to different levels. The fundamental shear horizontal mode was then generated in the plate samples via a magnetostrictive transducer. After propagating through the plastic zone the primary wave mode (SH0) and its third harmonic (sh0) were received by a second transducer. Results of a parallel numerical study using the S1-s2 Lamb mode pair, where sensitivity to changes in third order elastic constants were investigated, are described within the context of the experimental results. Specimens used within both studies are geometrically similar and have double edge notches for dog bone samples that introduce localized plastic deformation. Through both studies, the size of the plastic zone with respect to the propagation distance and damage intensity influence the higher harmonics.
Minimizing Crosstalk in Self Oscillating Switch Mode Audio Power Amplifiers
DEFF Research Database (Denmark)
Knott, Arnold; Ploug, Rasmus Overgaard
2012-01-01
The varying switching frequencies of self oscillating switch mode audio amplifiers have been known to cause interchannel intermodulation disturbances in multi channel configurations. This crosstalk phenomenon has a negative impact on the audio performance. The goal of this paper is to present...... a method to minimize this phenomenon by improving the integrity of the various power distribution systems of the amplifier. The method is then applied to an amplifier built for this investigation. The results show that the crosstalk is suppressed with 30 dB, but is not entirely eliminated...
Electron-bunch lengthening on higher-harmonic oscillations in storage-ring free-electron lasers.
Sei, Norihiro; Ogawa, Hiroshi; Okuda, Shuichi
2017-09-01
The influence of higher-harmonic free-electron laser (FEL) oscillations on an electron beam have been studied by measuring its bunch length at the NIJI-IV storage ring. The bunch length and the lifetime of the electron beam were measured, and were observed to have become longer owing to harmonic lasing, which is in accord with the increase of the FEL gain. It was demonstrated that the saturated FEL power could be described by the theory of bunch heating, even for the harmonic lasing. Cavity-length detuning curves were measured for the harmonic lasing, and it was found that the width of the detuning curve was proportional to a parameter that depended on the bunch length. These experimental results will be useful for developing compact resonator-type FELs by using higher harmonics in the extreme-ultraviolet and the X-ray regions.
Energy Technology Data Exchange (ETDEWEB)
Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)
2012-10-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Rodes, J.J. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fuentes, R.; Pascual, I. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2009-02-16
The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed.
Plastic bottle oscillator: Rhythmicity and mode bifurcation of fluid flow
Kohira, Masahiro I.; Magome, Nobuyuki; Kitahata, Hiroyuki; Yoshikawa, Kenichi
2007-10-01
The oscillatory flow of water draining from an upside-down plastic bottle with a thin pipe attached to its head is studied as an example of a dissipative structure generated under far-from-equilibrium conditions. Mode bifurcation was observed in the water/air flow: no flow, oscillatory flow, and counter flow were found when the inner diameter of the thin pipe was changed. The modes are stable against perturbations. A coupled two-bottle system exhibits either in-phase or anti-phase self-synchronization. These characteristic behaviors imply that the essential features of the oscillatory flow in a single bottle system can be described as a limit-cycle oscillation.
Energy Technology Data Exchange (ETDEWEB)
Yazdanpannah, M.M.; Dehghanzadeh, M. [Shahid Bahonar University of Kerman, Faculty of Physics, Kerman (Iran, Islamic Republic of); Mirjalili, A. [Yazd University, Physics Department, P.O. Box 89195-741, Yazd (Iran, Islamic Republic of)
2012-11-15
The solution of the Dirac equation with a generalized harmonic oscillator potential is used to extract the constituent bare parton densities. The results are firstly in spatial space which are converted to momentum space, using the Fourier transformation. The final results are presented in terms of the Bjorken x-variable. Employing the effective chiral quark model and the related convolutions, the parton densities inside the proton are obtained. Choosing an appropriate radius of proton, they indicate reasonable behavior. Although the initial framework is completely theoretical, the results for the sea and valence quark densities and also the ratio of d to u valence quarks inside the proton are in good agreement with the available experimental data and some theoretical models. (orig.)
Dynamical Relation between Quantum Squeezing and Entanglement in Coupled Harmonic Oscillator System
Directory of Open Access Journals (Sweden)
Lock Yue Chew
2014-04-01
Full Text Available In this paper, we investigate into the numerical and analytical relationship between the dynamically generated quadrature squeezing and entanglement within a coupled harmonic oscillator system. The dynamical relation between these two quantum features is observed to vary monotically, such that an enhancement in entanglement is attained at a fixed squeezing for a larger coupling constant. Surprisingly, the maximum attainable values of these two quantum entities are found to consistently equal to the squeezing and entanglement of the system ground state. In addition, we demonstrate that the inclusion of a small anharmonic perturbation has the effect of modifying the squeezing versus entanglement relation into a nonunique form and also extending the maximum squeezing to a value beyond the system ground state.
The optimal performance of a quantum refrigeration cycle working with harmonic oscillators
Lin Bi Hong; Hua Ben
2003-01-01
The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here ...
A dynamical systems approach to Bohmian trajectories in a 2D harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Borondo, F [Departamento de Quimica, and Instituto Mixto de Ciencias Matematicas CSIC-UAM-UC3M-UCM, Universidad Autonoma de Madrid, Cantoblanco-28049 Madrid (Spain); Luque, A; Villanueva, J [Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya, 08028 Barcelona (Spain); Wisniacki, D A [Departamento de Fisica ' J. J. Giambiagi' , FCEN, UBA, Pabellon 1, Ciudad Universitaria, 1428 Buenos Aires (Argentina)], E-mail: f.borondo@uam.es, E-mail: alejandro.luque@upc.edu, E-mail: jordi.villanueva@upc.edu, E-mail: wisniacki@df.uba.ar
2009-12-11
Vortices are known to play a key role in the dynamics of the quantum trajectories defined within the framework of the de Broglie-Bohm formalism of quantum mechanics. It has been rigourously proved that the motion of a vortex in the associated velocity field can induce chaos in these trajectories, and numerical studies have explored the rich variety of behaviors that due to their influence can be observed. In this paper, we go one step further and show how the theory of dynamical systems can be used to construct a general and systematic classification of such dynamical behaviors. This should contribute to establish some firm grounds on which the studies on the intrinsic stochasticity of Bohm's quantum trajectories can be based. An application to the two-dimensional isotropic harmonic oscillator is presented as an illustration.
Sang, Nguyen Anh; Thu Thuy, Do Thi; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai
2017-06-01
Using the simple deformed three-level model (D3L model) proposed in our early work, we study the entanglement problem of composite bosons. Consider three first energy levels are known, we can get two energy separations, and can define the level deformation parameter δ. Using connection between q-deformed harmonic oscillator and Morse-like anharmonic potential, the deform parameter q also can be derived explicitly. Like the Einstein’s theory of special relativity, we introduce the observer e˙ects: out side observer (looking from outside the studying system) and inside observer (looking inside the studying system). Corresponding to those observers, the outside entanglement entropy and inside entanglement entropy will be defined.. Like the case of Foucault pendulum in the problem of Earth rotation, our deformation energy level investigation might be useful in prediction the environment e˙ect outside a confined box.
Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations
Schubert, O; Langer, F; Urbanek, B; Lange, C; Huttner, U; Golde, D; Meier, T; Kira, M; Koch, S W; Huber, R
2016-01-01
Ultrafast charge transport in strongly biased semiconductors is at the heart of highspeed electronics, electro-optics, and fundamental solid-state physics. Intense light pulses in the terahertz (THz) spectral range have opened fascinating vistas: Since THz photon energies are far below typical electronic interband resonances, a stable electromagnetic waveform may serve as a precisely adjustable bias. Novel quantum phenomena have been anticipated for THz amplitudes reaching atomic field strengths. We exploit controlled THz waveforms with peak fields of 72 MV/cm to drive coherent interband polarization combined with dynamical Bloch oscillations in semiconducting gallium selenide. These dynamics entail the emission of phase-stable high-harmonic transients, covering the entire THz-to-visible spectral domain between 0.1 and 675 THz. Quantum interference of different ionization paths of accelerated charge carriers is controlled via the waveform of the driving field and explained by a quantum theory of inter- and in...
Stochastic and superharmonic stochastic resonances of a confined overdamped harmonic oscillator
Zhang, Lu; Lai, Li; Peng, Hao; Tu, Zhe; Zhong, Suchuan
2018-01-01
The dynamics of many soft condensed matter and biological systems is affected by space limitations, which produce some peculiar effects on the systems' stochastic resonance (SR) behavior. In this study, we propose a model where SR can be observed: a confined overdamped harmonic oscillator that is subjected to a sinusoidal driving force and is under the influence of a multiplicative white noise. The output response of the system is a periodic signal with harmonic frequencies that are odd multiples of the driving frequency. We verify the amplitude resonances at the driving frequencies and superharmonic frequencies that are equal to three, five, and seven times the driving frequency, using a numerical method based on the stochastic Taylor expansion. The synergistic effect of the multiplicative white noise, constant boundaries, and periodic driving force that can induce a SR in the output amplitude at the driving and superharmonic frequencies is found. The SR phenomenon found in this paper is sensitive to the driving amplitude and frequency, inherent potential parameter, and boundary width, thus leading to various resonance conditions. Therefore, the mechanism found could be beneficial for the characterization of these confined systems and could constitute an important tool for controlling their basic properties.
The optimal performance of a quantum refrigeration cycle working with harmonic oscillators
Lin, Bihong; Chen, Jincan; Hua, Ben
2003-02-01
The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here are compared with those of an Ericsson or Stirling refrigeration cycle using an ideal gas as the working substance. Finally, the optimal performance of a harmonic quantum Carnot refrigeration cycle at high temperatures is derived easily.
Directory of Open Access Journals (Sweden)
Sibel Başkal
2014-06-01
Full Text Available The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group Sp(2. It is shown that this oscillator system contains the essential features of Wigner’s little groups dictating the internal space-time symmetries of particles in the Lorentz-covariant world. The little groups are the subgroups of the Lorentz group whose transformations leave the four-momentum of a given particle invariant. It is shown that the damping modes of the oscillator correspond to the little groups for massive and imaginary-mass particles respectively. When the system makes the transition from the oscillation to damping mode, it corresponds to the little group for massless particles. Rotations around the momentum leave the four-momentum invariant. This degree of freedom extends the Sp(2 symmetry to that of SL(2, c corresponding to the Lorentz group applicable to the four-dimensional Minkowski space. The Poincaré sphere contains the SL(2, c symmetry. In addition, it has a non-Lorentzian parameter allowing us to reduce the mass continuously to zero. It is thus possible to construct the little group for massless particles from that of the massive particle by reducing its mass to zero. Spin-1/2 particles and spin-1 particles are discussed in detail.
Steffen, T; Tanimura, Y
The quantum Fokker-Planck equation is derived for a system nonlinearly coupled to a harmonic oscillator bath. The system-bath interaction is assumed to be linear in the bath coordinates but quadratic in the system coordinate. The relaxation induced dynamics of a harmonic system are investigated by
MAVRI, J; BERENDSEN, HJC
A density-matrix evolution method [Berendsen and Mavri, J. Phys. Chem. 97, 13464 (1993)] coupled to a classical molecular dynamics simulation was applied to study a quantum harmonic oscillator immersed in a bath of Lennard-Jones particles. Eigenfunctions of the three, lowest levels of the
DEFF Research Database (Denmark)
Madsen, Christian Bruun; Abu-Samha, Mahmoud; Madsen, Lars Bojer
2010-01-01
as a nuclear correlation function. We express the nuclear correlation function in terms of Franck-Condon factors, which allows us to decompose nuclear motion into modes and identify the modes that are dominant in the high-order harmonic generation process. We show results for the isotopes CH4 and CD4......We present a generic approach for treating the effect of nuclear motion in high-order harmonic generation from polyatomic molecules. Our procedure relies on a separation of nuclear and electron dynamics where we account for the electronic part using the Lewenstein model and nuclear motion enters...... and thereby provide direct theoretical support for a recent experiment [S. Baker et al., Science 312, 424 (2006)] that uses high-order harmonic generation to probe the ultrafast structural nuclear rearrangement of ionized methane....
Castellanos-Gomez, A.
2013-01-01
A simple strobe setup with the potential to study higher-order eigenmodes and multifrequency oscillations in micromechanical resonators is described. It requires standard equipment, commonly found in many laboratories, and it can thus be employed for public demonstrations of mechanical resonances. Moreover, the work presented here can be used by undergraduate students and/or teachers to prepare practical work in laboratory courses at physics or engineering universities. The dynamics of a micromachined cantilever is analysed as an example. In fact, using our stroboscopic setup, the first and second flexural eigenmodes, as well as a multifrequency oscillation composed by a superposition of both modes, have been successfully filmed with a conventional optical microscope equipped with a digital camera.
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
Energy Technology Data Exchange (ETDEWEB)
Belendez, A., E-mail: a.belendez@ua.e [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Mendez, D.I. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Marini, S. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, I. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2009-08-03
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
Scaling of mode shapes from operational modal analysis using harmonic forces
Brandt, A.; Berardengo, M.; Manzoni, S.; Cigada, A.
2017-10-01
This paper presents a new method for scaling mode shapes obtained by means of operational modal analysis. The method is capable of scaling mode shapes on any structure, also structures with closely coupled modes, and the method can be used in the presence of ambient vibration from traffic or wind loads, etc. Harmonic excitation can be relatively easily accomplished by using general-purpose actuators, also for force levels necessary for driving large structures such as bridges and highrise buildings. The signal processing necessary for mode shape scaling by the proposed method is simple and the method can easily be implemented in most measurement systems capable of generating a sine wave output. The tests necessary to scale the modes are short compared to typical operational modal analysis test time. The proposed method is thus easy to apply and inexpensive relative to some other methods for scaling mode shapes that are available in literature. Although it is not necessary per se, we propose to excite the structure at, or close to, the eigenfrequencies of the modes to be scaled, since this provides better signal-to-noise ratio in the response sensors, thus permitting the use of smaller actuators. An extensive experimental activity on a real structure was carried out and the results reported demonstrate the feasibility and accuracy of the proposed method. Since the method utilizes harmonic excitation for the mode shape scaling, we propose to call the method OMAH.
Decoupling of Superfluid and Normal Oscillation Modes in Rotating Neutron Stars
Kantor, E. M.; Gusakov, M. E.
2012-12-01
It was shown in Gusakov & Kantor (2011) that equations governing oscillations of superfluid neutron stars can be split into two systems of weakly coupled equations, one describing the superfluid modes and another one, the normal modes. Here we demonstrate that similar decoupling of modes also occurs in rotating NSs. To this aim we formulated the relativistic hydrodynamics of superfluid mixtures allowing for vortices. Our results indicate, in particular, that emission of gravitational waves from superfluid oscillation modes is suppressed in comparison to that from normal modes. The proposed approach allows one to drastically simplify modeling of oscillations of superfluid rotating neutron stars.
The particle flow oscillations of rotating non-interacting gases in a two-dimensional harmonic trap
Energy Technology Data Exchange (ETDEWEB)
Li, Yushan [Department of Physics, University of Science and Technology Beijing, Beijing 100083 (China); Department of Physics, Heze University, Heze 274015 (China); Gu, Qiang, E-mail: qgu@ustb.edu.cn [Department of Physics, University of Science and Technology Beijing, Beijing 100083 (China)
2016-01-28
The spatial distribution of particle flow and atomic density of the two-dimensional, harmonically trapped, ideal atomic gases in synthetic magnetic field and rotating frame are systematically investigated in various regimes of temperature. The magnetization and particle flow of rotating fermions exhibit a de Haas–van Alphen-like oscillation at relatively low temperature. This phenomenon is analogous to the quantum oscillation of orbital magnetism and current in confined electron system. An elaborate comparison with Bose system is also proposed. - Highlights: • Oscillations of particle flow in rotating trapped gases are comprehensively studied. • Fermions exhibit de Haas–van Alphen-like oscillation at low temperature. • Rotating fermions can be easily used to illustrate magnetic properties of confined electrons. • Diamagnetism of bosons increases with increasing rotation frequency. • Characteristic dependency of magnetization on temperature is reflected in particle flow.
Energy Technology Data Exchange (ETDEWEB)
Viana-Gomes, J; Peres, N M R, E-mail: zgomes@fisica.uminho.pt [Physics Department, University of Minho, CFUM, P-4710-057 Braga (Portugal)
2011-09-15
We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the boundary conditions at the origin. This problem calls the attention of the students to an inaccurate statement in quantum mechanics textbooks often found in the context of the solution of the harmonic oscillator problem.
Xu, Wenrui; Lai, Dong
2017-10-01
In coalescing neutron star (NS) binaries, tidal force can resonantly excite low-frequency (≲500 Hz ) oscillation modes in the NS, transferring energy between the orbit and the NS. This resonant tide can induce phase shift in the gravitational waveforms, and potentially provide a new window of studying NS interior using gravitational waves. Previous works have considered tidal excitations of pure g-modes (due to stable stratification of the star) and pure inertial modes (due to Coriolis force), with the rotational effect treated in an approximate manner. However, for realistic NSs, the buoyancy and rotational effects can be comparable, giving rise to mixed inertial-gravity modes. We develop a nonperturbative numerical spectral code to compute the frequencies and tidal coupling coefficients of these modes. We then calculate the phase shift in the gravitational waveform due to each resonance during binary inspiral. Given the uncertainties in the NS equation of state and stratification property, we adopt polytropic NS models with a parametrized stratification. We derive relevant scaling relations and survey how the phase shift depends on various properties of the NS. We find that for canonical NSs (with mass M =1.4 M⊙ and radius R =10 km ) and modest rotation rates (≲300 Hz ), the gravitational wave phase shift due to a resonance is generally less than 0.01 radian. But the phase shift is a strong function of R and M , and can reach a radian or more for low-mass NSs with larger radii (R ≳15 km ). Significant phase shift can also be produced when the combination of stratification and rotation gives rise to a very low frequency (≲20 Hz in the inertial frame) modified g-mode. As a by-product of our precise calculation of oscillation modes in rotating NSs, we find that some inertial modes can be strongly affected by stratification; we also find that the m =1 r -mode, previously identified to have a small but finite inertial-frame frequency based on the Cowling
Radial index of Laguerre-Gaussian modes in high-order-harmonic generation
Géneaux, Romain; Chappuis, Céline; Auguste, Thierry; Beaulieu, Samuel; Gorman, Timothy T.; Lepetit, Fabien; DiMauro, Louis F.; Ruchon, Thierry
2017-05-01
High-order-harmonic generation (HHG) is a tabletop and tunable source of extreme ultraviolet (XUV) light. Its flexibility was lately evidenced by the production of Laguerre-Gaussian (LG) modes in the XUV with a known azimuthal index. Here we investigate the role of the radial index of LG modes in HHG. We show both numerically and experimentally that the mode content of the emitted XUV radiation can be tuned by controlling the weight of the different quantum trajectories involved in the process. The appearance of high-order radial modes is finally linked to the atomic dipole phase of HHG. These results extend the capabilities of shaping the spatial mode of ultrashort XUV pulses of light.
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators.
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
2016-07-01
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.
Shannon and Fisher entropy measures for a parity-restricted harmonic oscillator
Shi, Ye-Jiao; Sun, Guo-Hua; Jing, Jian; Dong, Shi-Hai
2017-12-01
We first present the analytical solutions to the Schrödinger equation with the parity-restricted harmonic oscillator V(x)=\\frac{1}{2}m{{ω }2}{{x}2} (x>0)~ and then calculate the Shannon information entropies Sxn and Spn both in position space and in momentum space. It is interesting to find that the variation of the Shannon information entropy Spn in momentum space is different from our previous studies, i.e. the Spn first increases with the quantum number n and then decreases with the number n. This is a new and abnormal phenomenon and may be explained by the parity-restricted system. The BBM inequality is verified to be saturated, but the sum of the entropies first increases with the number n and then decreases with it. The entropy densities ρ s (x) and ρ s (p) are also demonstrated. We find that the Fisher entropy is exactly given by {{I}F}=8n+6,n=0,1,2,\\ldots .
A new look at the quantum mechanics of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Kastrup, H.A.
2006-12-15
At first sight it is probably hard to believe that something new can be said about the harmonic oscillator (HO). But that is so indeed: Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables {phi} element of R mod 2{pi} and I>0. However, the transformation q= {radical}(2I)cos {phi}, p=-{radical}(2I)sin {phi} is only locally symplectic and singular for (q,p)=(0,0). Globally the phase space {l_brace}(q,p){r_brace} has the topological structure of the plane R{sup 2}, whereas the phase space {l_brace}({phi},I){r_brace} corresponds globally to the punctured plane R{sup 2}-(0,0) or to a simple cone S{sup 1} x R{sup +} with the tip deleted. This makes a qualitative difference as to the quantum theory of the two phase spaces: The quantizing canonical group for the plane R{sup 2} consists of the (centrally extended) translations generated by the Poisson Lie algebra basis {l_brace}q,p,1{r_brace}, whereas the corresponding canonical group of the phase space {l_brace}({phi},I){r_brace} is the group SO{up_arrow}(1,2)=Sp(2,R)/Z{sub 2}, where Sp(2,R) is the sympletic group of the plane, with the generating Poisson Lie algebra basis {l_brace}h{sub 0}=I,h{sub 1}=Icos{phi},h{sub 2}=-Isin{phi}{r_brace} which provides also the basic ''observables'' on {l_brace}({phi}, I){r_brace}. In the quantum mechanics of the ({phi},I)-model of the HO the three h{sub j} correspond to self-adjoint generators K{sub j}, j=0,1,2, of irreducible unitary representations from the positive discrete series of the group SO{up_arrow}(1,2) or one of its infinitely many covering groups, the representations parametrized by the Bargmann index k>0. This index k determines the ground state energy E{sub k,n=0}={Dirac_h}{omega}k of the ({phi},I)-Hamiltonian H(anti K)={Dirac_h}{omega}K{sub 0}. For an m-fold covering the lowest possible value for k is k=1/m, which can be made arbitrarily small by choosing m accordingly. This is not in contraction to
Chen, Y F; Tung, J C; Tuan, P H; Yu, Y T; Liang, H C; Huang, K F
2017-01-01
A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.
Energy Technology Data Exchange (ETDEWEB)
Guasti, M Fernandez [Depto de Fisica, CBI, Universidad A Metropolitana - Iztapalapa, 09340 Mexico, DF, Apdo Postal 55-534 (Mexico); Moya-Cessa, H [INAOE, Coordinacion de Optica, Apdo Postal 51 y 216, 72000 Puebla, Pue. (Mexico)
2003-02-28
An extension of the classical orthogonal functions invariant to the quantum domain is presented. This invariant is expressed in terms of the Hamiltonian. Unitary transformations which involve the auxiliary function of this quantum invariant are used to solve the time-dependent Schroedinger equation for a harmonic oscillator with time-dependent parameter. The solution thus obtained is in agreement with the results derived using other methods which invoke the Lewis invariant in their procedures.
I. Badran; A. L. Mahmood; M. T. Lazim
2008-01-01
n integral-cycle triggering mode of voltage control, subharmonic as well as higher order harmonic components are generated in the load voltage waveforms of a three-phase system. These harmonic components are found to be unbalanced in phase displacement. The correction of the unbalanced phase displacement angles of a particular subharmonic or higher order harmonic for this type of triggering is investigated to solve the limitation of use of this important type of control as a drive and many ot...
Local modes analysis of a rotating marine ship propeller with higher order harmonic elements
Feng, Chen; Yong, Chen; Hongxing, Hua
2016-09-01
An annular harmonic finite element for the computation of the local modes of a pretwisted ship propeller is developed. The elements take into account both the gyroscopic effect and centrifugal stiffening of the propeller blades. The displacement field is expressed by a truncated Fourier series along the angle and by polynomial shape functions in the radial direction. As an example, the dynamic behaviour, i.e. the nature frequency and local modes, of a ship propeller is studied, and compared with ANSYS, both of which have good consistency.
CSIR Research Space (South Africa)
Grobler, TL
2012-06-01
Full Text Available It is proposed that the time series extracted from moderate resolution imaging spectroradiometer satellite data be modeled as a simple harmonic oscillator with additive colored noise. The colored noise ismodeled with an Ornstein–Uhlenbeck process...
Long, Chang; Yin, Sheng; Wang, Wei; Li, Wei; Zhu, Jianfei; Guan, Jianguo
2016-01-01
By investigating a square-shaped metamaterial structure we discover that wave diffraction at diagonal corners of such a structure excites transverse magnetic harmonics of 210 mode (TM210 harmonics). Multi-layer overlapping and deliberately regulating period length between adjacent unit cells can significantly enhance TM210 harmonics, leading to a strong absorption waveband. On such a basis, a design strategy is proposed to achieve broadband, thin-thickness multi-layered metamaterial absorbers (MMAs). In this strategy big pyramidal arrays placed in the “white blanks” of a chessboard exhibit two isolated absorption bands due to their fundamental and TM210 harmonics, which are further connected by another absorption band from small pyramidal arrays in the “black blanks” of the chessboard. The as-designed MMA at a total thickness (h) of 4.36 mm shows an absorption of above 0.9 in the whole frequency range of 7–18 GHz, which is 38% broader with respect to previous design methods at the same h. This strategy provides an effective route to extend the absorption bandwidth of MMAs without increasing h. PMID:26888365
Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.
1995-08-01
The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.
Energy Technology Data Exchange (ETDEWEB)
Thantu, Napoleon; McMorrow, D.; Melinger, J. S.; Kleiman, V.; Lotshaw, W. T.
2001-07-01
The apparently-multicomponent subpicosecond intermolecular dynamics of carbon disulfide liquid are addressed in a unified manner in terms of an inhomogeneously broadened quantum mechanical harmonic oscillator model for a single vibrational coordinate. For an inhomogeneously broadened (Gaussian) distribution of oscillators, the model predicts naturally the bimodal character of the subpicosecond intermolecular dynamics of carbon disulfide liquid, and also the spectral evolution effects (spectral narrowing and saturation) that are observed for solutions of carbon disulfide in weakly interacting alkane solvents. The unique dynamical signature of these low-frequency vibrational coordinates is determined largely by the physical constraints on the coordinates (near equality of oscillator frequency, dephasing frequency, and inhomogeneous bandwidth), such that constructive and destructive interference effects play a dominant role in shaping the experimental observable.
Theerawisitpong, Somboon; Suzuki, Toshitatsu; Morita, Noboru; Utsumi, Yozo
The design of microstrip bandpass filters using stepped-impedance resonators (SIRs) is examined. The passband center frequency for the WCDMA-FDD (uplink band) Japanese cellular system is 1950MHz with a 60-MHz bandwidth. The SIR physical characteristic can be designed using a SIR characteristic chart based on second harmonic suppression. In our filter design, passband design charts were obtained through the design procedure. Tchebycheff and maximally flat bandpass filters of any bandwidth and any number of steps can be designed using these passband design charts. In addition, sharp skirt characteristics in the passband can be realized by having two transmission zeros at both adjacent frequency bands by using open-ended quarter-wavelength stubs at input and output ports. A new even-mode harmonics suppression technique is proposed to enable a wide rejection band having a high suppression level. The unloaded quality factor of the resonator used in the proposed filters is greater than 240.
Oscillation mode analysis considering the interaction between a DFIG-based wind turbine and the grid
Wu, Wangping; Xie, Da; Lu, Yupu; Zhao, Zuyi; Yu, Songtao
2017-01-01
Sub-synchronous interactions between wind farms and transmission networks with series compensation have drawn great attention. As most large wind farms in Europe and Asia employ doubly fed induction generator turbines, there has recently been a growing interest in studying this phenomenon. To study the stability of wind turbine with doubly fed induction generator after a small disturbance, a complete small signal system is built in this paper. By using eigenvalue and participation factor analysis, the relation between the modes and state variables can be discovered. Thereafter, the oscillation modes are classified into electrical resonance, sub-synchronous resonance, sub-synchronous oscillation, sub-synchronous control interaction, and low frequency oscillation. To verify the oscillation frequency of each oscillation mode, time-domain simulation based on MATLAB/Simulink is presented. The simulation results justify the effectiveness of the small-signal models.
Cluster synchronization modes in an ensemble of coupled chaotic oscillators
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Belykh, Igor V.; Mosekilde, Erik
2001-01-01
Considering systems of diffusively coupled identical chaotic oscillators, an effective method to determine the possible states of cluster synchronization and ensure their stability is presented. The method, which may find applications in communication engineering and other fields of science...
Directory of Open Access Journals (Sweden)
A. Schroeder
2012-09-01
Full Text Available This paper proposes a compression of far field matrices in the fast multipole method and its multilevel extension for electromagnetic problems. The compression is based on a spherical harmonic representation of radiation patterns in conjunction with a radiating mode expression of the surface current. The method is applied to study near field effects and the far field of an antenna placed on a ship surface. Furthermore, the electromagnetic scattering of an electrically large plate is investigated. It is demonstrated, that the proposed technique leads to a significant memory saving, making multipole algorithms even more efficient without compromising the accuracy.
Enhanced third harmonic generation from the epsilon-near-zero modes of ultrathin films
Energy Technology Data Exchange (ETDEWEB)
Luk, Ting S. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); De Ceglia, Domenico [National Research Council (AMRDEC), Redstone Arsenal, AL (United States); Liu, Sheng [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Keeler, Gordon Arthur [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Prasankumar, Rohit [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vincenti, Maria A [National Research Council (AMRDEC), Redstone Arsenal, AL (United States); Scalora, Michael [National Research Council (AMRDEC), Redstone Arsenal, AL (United States); Sinclair, Michael B. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); campione, salvatore [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-04-13
We demonstrate, through our experimentation, efficient third harmonic generation from an indium tin oxide nanofilm (λ/42 thick) on a glass substrate for a pump wavelength of 1.4 μm. A conversion efficiency of 3.3 × 10^{-6} is achieved by exploiting the field enhancement properties of the epsilon-near-zero mode with an enhancement factor of 200. Furthermore, this nanoscale frequency conversion method is applicable to other plasmonic materials and reststrahlen materials in proximity of the longitudinal optical phonon frequencies.
Enhanced third harmonic generation from the epsilon-near-zero modes of ultrathin films
Energy Technology Data Exchange (ETDEWEB)
Luk, Ting S., E-mail: tsluk@sandia.gov; Liu, Sheng; Campione, Salvatore [Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185 (United States); Center for Integrated Nanotechnologies (CINT), Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185 (United States); Ceglia, Domenico de; Vincenti, Maria A. [National Research Council–AMRDEC, Charles M. Bowden Research Laboratory, Redstone Arsenal, Alabama 35898 (United States); Keeler, Gordon A.; Sinclair, Michael B. [Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185 (United States); Prasankumar, Rohit P. [Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185 (United States); Center for Integrated Nanotechnologies (CINT-LANL), Los Alamos Laboratories, Los Alamos, New Mexico 87545 (United States); Scalora, Michael [Charles M. Bowden Research Laboratory, AMRDEC, U.S. Army RDECOM, Redstone Arsenal, Alabama 35898 (United States)
2015-04-13
We experimentally demonstrate efficient third harmonic generation from an indium tin oxide nanofilm (λ/42 thick) on a glass substrate for a pump wavelength of 1.4 μm. A conversion efficiency of 3.3 × 10{sup −6} is achieved by exploiting the field enhancement properties of the epsilon-near-zero mode with an enhancement factor of 200. This nanoscale frequency conversion method is applicable to other plasmonic materials and reststrahlen materials in proximity of the longitudinal optical phonon frequencies.
Oscillation mode frequencies of 61 main-sequence and subgiant stars observed by Kepler
DEFF Research Database (Denmark)
Appourchaux, T.; Chaplin, W. J.; García, R. A.
2012-01-01
Solar-like oscillations have been observed by Kepler and CoRoT in several solar-type stars, thereby providing a way to probe the stars using asteroseismology Aims. We provide the mode frequencies of the oscillations of various stars required to perform a comparison with those obtained from stella...
Observational Searches for Chromospheric g-Mode Oscillations ...
Indian Academy of Sciences (India)
time sequence of spectra in CaII H-line obtained at the Vacuum Tower Tele- ... An important parameter of the H-line profile, intensity at H2V(IH2V ), has .... a 3-min period of intensity oscillations. In the left side box of Fig. 1, the thick line represents the 3-min period of intensity oscillations, whereas the dotted line shows an.
DEFF Research Database (Denmark)
Lodahl, P.; Saffman, M.
1999-01-01
fundamental field, and its coupling to a pair of nondegenerate parametric fields. The parametric fields are driven by the nonresonant second-harmonic field. Analysis indicates the existence of transverse instability of the pump field alone, as well as the possibility of simultaneous instability of the pump......We theoretically investigate the generation of spatial patterns in intracavity second-harmonic generation. We consider a cavity with planar mirrors that is resonant at the fundamental frequency, but not at the second-harmonic frequency. A mean-field model is derived that describes the resonant...
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Tenorio, C. [Benemerita Universidad Autonoma de Puebla, 7200 Puebla (Mexico) and Universidad Autonoma del Estado de Mexico (Mexico)]. E-mail: celso1@hotmail.com; Belyaeva, T.L. [Universidad Autonoma del Estado de Mexico (Mexico); Serkin, V.N. [Benemerita Universidad Autonoma de Puebla, 7200 Puebla (Mexico)
2007-09-01
The dynamics of nonlinear solitary waves is studied in the framework of the nonlinear Schroedinger equation model with time-dependent harmonic oscillator potential. The model allows one to analyse on general basis a variety of nonlinear phenomena appearing both in Bose-Einstein condensate, condensed matter physics, nonlinear optics, and biophysics. The soliton parametric resonance is investigated by using two complementary methods: the adiabatic perturbation theory and direct numerical experiments. Conditions for reversible and irreversible denaturation of soliton bound states are also considered.
DEFF Research Database (Denmark)
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-01-01
-lapse recordings. Three applications are discussed: (i) The effects of finite sampling rate and time, described exactly here, are similar for other stochastic dynamical systems-e.g., motile microorganisms and their time-lapse-recorded trajectories. (ii) The same statistics is satisfied by any experimental system......The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...... of finite sampling rate and sampling time for these models as well....
Directory of Open Access Journals (Sweden)
Yongjun Wu
2011-01-01
Full Text Available We study the stochastic optimal bounded control for minimizing the stationary response of strongly nonlinear oscillators under combined harmonic and wide-band noise excitations. The stochastic averaging method and the dynamical programming principle are combined to obtain the fully averaged Itô stochastic differential equations which describe the original controlled strongly nonlinear system approximately. The stationary joint probability density of the amplitude and phase difference of the optimally controlled systems is obtained from solving the corresponding reduced Fokker-Planck-Kolmogorov (FPK equation. An example is given to illustrate the proposed procedure, and the theoretical results are verified by Monte Carlo simulation.
Yermachenko, VM; Karle, RA; Petrovskiy, VN; Protsenko, ED
The influence of intracavity second harmonic generation on the mode competition in a double-mode diode-pumped Nd:YAG laser is studied theoretically and experimentally. Various configurations of the optical cavity with II-type phase-matching frequency-doubling crystals are considered. The conditions
Theory of anomalous backscattering in second harmonic X-mode ECRH experiments
Energy Technology Data Exchange (ETDEWEB)
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.
Dispersal and noise: Various modes of synchrony in ecological oscillators
Bressloff, Paul C.
2012-10-21
We use the theory of noise-induced phase synchronization to analyze the effects of dispersal on the synchronization of a pair of predator-prey systems within a fluctuating environment (Moran effect). Assuming that each isolated local population acts as a limit cycle oscillator in the deterministic limit, we use phase reduction and averaging methods to derive a Fokker-Planck equation describing the evolution of the probability density for pairwise phase differences between the oscillators. In the case of common environmental noise, the oscillators ultimately synchronize. However the approach to synchrony depends on whether or not dispersal in the absence of noise supports any stable asynchronous states. We also show how the combination of partially correlated noise with dispersal can lead to a multistable steady-state probability density. © 2012 Springer-Verlag Berlin Heidelberg.
An Application of the Harmonic Oscillator Model to Verify Dunning’s Theory of the Economic Growth
Directory of Open Access Journals (Sweden)
Marcin Salamaga
2013-09-01
Full Text Available Analogies with mechanisms ruling the natural world have oft en been sought in the course of economic phenomena.Th is paper is also an attempt to combine the physical phenomenon of a harmonious oscillator withthe theory of economic growth by J. H. Dunning (1981. In his theory, Dunning distinguished stages of economicgrowth of countries that imply the dependency between the investment position of countries and theirGDP per capita, while the graph presenting this dependency reminds a trajectory of oscillating motion of adamped harmonic oscillator. Th is analogy has given inspiration to reinterpret the theory of economy on thegrounds of the mechanism of a physical model. In this paper, the harmonious oscillator motion equation wasadapted to the description of dependencies shown in the theory of economic growth by J. H. Dunning. Th emathematical solution of this equation is properly parameterised and parameters are estimated with the useof the Gauss-Newton algorithm. Th e main objective of this paper is to allocate a specifi c stage in the economicgrowth to each country on the basis of the values of parameter estimations of the proposed cyclical models ofchanges in the net investment indicator.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Neipp, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Belendez, T [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-02-15
A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient.
Red Giant Oscillations: Stellar Models and Mode Frequency Calculations
DEFF Research Database (Denmark)
Jendreieck, A.; Weiss, A.; Aguirre, Victor Silva
2012-01-01
We present preliminary results on modelling KIC 7693833, the so far most metal-poor red-giant star observed by {\\it Kepler}. From time series spanning several months, global oscillation parameters and individual frequencies were obtained and compared to theoretical calculations. Evolution models ...
Mode lifetimes of stellar oscillations. Implications for asteroseismology
DEFF Research Database (Denmark)
Chaplin, W.J.; Houdek, G.; Karoff, Christoffer
2009-01-01
is the effective temperature). When this relation is combined with the well-known scaling relation of Kjeldsen & Bedding for mode amplitudes observed in narrow-band intensity observations, we obtain the unexpected result that the height (the maximum power spectral density) of mode peaks in the frequency power...... as their hotter counterparts. When observations are instead made in Doppler velocity, our results imply that mode height does increase with increasing effective temperature....
Visualization of the Mode Shapes of Pressure Oscillation in a Cylindrical Cavity
Energy Technology Data Exchange (ETDEWEB)
He, Xin [Tsinghua Univ., Beijing (China); Qi, Yunliang [Tsinghua Univ., Beijing (China); Wang, Zhi [Tsinghua Univ., Beijing (China); Wang, Jianxin [Tsinghua Univ., Beijing (China); Shuai, Shijin [Tsinghua Univ., Beijing (China); Tao, Ling [National Renewable Energy Lab. (NREL), Golden, CO (United States)
2015-06-08
Our work describes a novel experimental method to visualize the mode shapes of pressure oscillation in a cylindrical cavity. Acoustic resonance in a cavity is a grand old problem that has been under investigation (using both analytical and numerical methods) for more than a century. In this article, a novel method based on high speed imaging of combustion chemiluminescence was presented to visualize the mode shapes of pressure oscillation in a cylindrical cavity. By generating high-temperature combustion gases and strong pressure waves simultaneously in a cylindrical cavity, the pressure oscillation can be inferred due to the chemiluminescence emissions of the combustion products. We can then visualized the mode shapes by reconstructing the images based on the amplitudes of the luminosity spectrum at the corresponding resonant frequencies. Up to 11 resonant mode shapes were clearly visualized, each matching very well with the analytical solutions.
Energy Technology Data Exchange (ETDEWEB)
Draganescu, Gheorghe Eugen [Department of Mechanics, Polytechnic University of Timisoara, Bd M Viteazu No1, Timisoara and Department of Physics, West University of Timisoara (Romania)
2012-08-17
We used the dicrete variable three-dimmensional Charlier oscillator. For a system of molecules interacting with the coherent radiation field the temporal variation of the refractive index has been established.
Application of He’s Energy Balance Method to Duffing-Harmonic Oscillators
DEFF Research Database (Denmark)
Momeni, M.; Jamshidi, j.; Barari, Amin
2011-01-01
In this article, He's energy balance method is applied for calculating angular frequencies of nonlinear Duffing oscillators. This method offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. We illustrate that the energy balance is very effective and convenient...... and does not require linearization or small perturbation. Contrary to the conventional methods, in energy balance, only one iteration leads to high accuracy of the solutions. It is predicted that the energy balance method finds wide applications in engineering problems....
Higher Order Modes for Beam Diagnostics in Third Harmonic 3.9 GHz Accelerating Modules
Baboi, N; Flisgen, T; Glock, H-W; Jones, R M; Shinton, I R R; Zhang, P
2011-01-01
An international team is currently investigating the best way to use Higher Order Modes (HOM) for beam diagnostics in 3.9 GHz cavities. HOMs are excited by charged particles when passing through an accelerating structure. Third harmonic cavities working at 3.9 GHz have been installed in FLASH to linearize the bunch energy profile. A proof-of-principle of using HOMs for beam monitoring has been made at FLASH in the TESLA 1.3 GHz cavities. Since the wakefields generated in the 3.9 GHz cavities are significantly larger, their impact on the beam should be carefully minimized. Therefore our target is to monitor HOMs and minimize them by aligning the beam on the cavity axis. The difficulty is that, in comparison to the 1.3 GHz cavities, the HOM-spectrum is dense, making it difficult to identify individual modes. Also, most modes propagate through the whole cryomodule containing several cavities, making it difficult to measure local beam properties. In this paper the options for the HOM-based beam position monitors ...
Report on first masing and single mode locking in a prebunched beam FEM oscillator
Energy Technology Data Exchange (ETDEWEB)
Cohen, M.; Eichenbaum, A.; Kleinman, H. [Tel-Aviv Univ., Ramat-Aviv (Israel)] [and others
1995-12-31
Radiation characteristics of a table-top free electron maser (FEM) are described in this paper. The FEM employs a prebunched electron beam and is operated as an oscillator in the low-gain collective (Raman) regime. Using electron beam prebunching single mode locking at any one of the possible oscillation modes was obtained. The electron beam is prebunched by a microwave tube section before it is injected into the wiggler. By tuning the electron beam bunching frequency, the FEM oscillation frequency can be locked to any eigen frequency of the resonant waveguide cavity which is within the frequency band of net gain of the FEM. The oscillation build up process is sped up, when the FEM operates with a prebunched electron beam, and the build-up time of radiation is shortened significantly. First measurements of masing with and without prebunching and characterization of the emitted radiation are reported.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Pei [Manchester Univ. (United Kingdom); Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Baboi, Nicoleta [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Jones, Roger M. [The Cockcroft Institute, Daresbury (United Kingdom)
2012-06-15
An electron beam entering an accelerating cavity excites a wakefield. This wakefield can be decomposed into a series of multi-poles or modes. The dominant component of the transverse wakefield is dipole. This report summarizes the higher order mode (HOM) signals of the third harmonic cavities of FLASH measured at various stages: transmission measurements in the single cavity test stand at Fermilab, at CMTB (Cryo- Module Test Bench) and at FLASH, and beam-excited measurements at FLASH. Modes in the first two dipole bands and the fifth dipole band have been identified using a global Lorentzian fit technique. The beam-pipe modes at approximately 4 GHz and some modes in the fifth dipole band have been observed as localized modes, while the first two dipole bands, containing some strong coupling cavity modes, propagate. This report also presents the dependence of the localized dipole modes on the transverse beam position. Linear dependence for various modes has been observed. This makes them suitable for beam position diagnostics. These modes, together with some propagating, strong coupling modes, have been considered in the design of a dedicated electronics for beam diagnostics with HOMs for the third harmonic cavities.
Energy Technology Data Exchange (ETDEWEB)
Wang, Yang; Song, Hai-Ying; Liu, H.Y.; Liu, Shi-Bing, E-mail: sbliu@bjut.edu.cn
2017-07-12
Highlights: • Proposed a valid mechanism of high harmonic generation by laser grating target interaction: oscillation of equivalent electric dipole (OEED). • Found that there also exist harmonic emission at large emission angle but not just near-surface direction as the former researches had pointed out. • Show the process of the formation and motion of electron bunches at the grating-target surface irradiating with femtosecond laser pulse. - Abstract: We theoretically study high-order harmonic generation (HHG) from relativistically driven overdense plasma targets with rectangularly grating-structured surfaces by femtosecond laser pulses. Our particle-in-cell (PIC) simulations show that, under the conditions of low laser intensity and plasma density, the harmonics emit principally along small angles deviating from the target surface. Further investigation of the surface electron dynamics reveals that the electron bunches are formed by the interaction between the laser field and the target surface, giving rise to the oscillation of equivalent electric-dipole (OEED), which enhances specific harmonic orders. Our work helps understand the mechanism of harmonic emissions from grating targets and the distinction from the planar harmonic scheme.
Plastic bottle oscillator: Rhythmicity and mode bifurcation of fluid flow
Kohira, Masahiro I.; Magome, Nobuyuki; Kitahata, Hiroyuki; Yoshikawa, Kenichi
2007-01-01
The oscillatory flow of water draining from an upside-down plastic bottle with a thin pipe attached to its head is studied as an example of a dissipative structure generated under far-from-equilibrium conditions. Mode bifurcation was observed in the water/air flow: no flow, oscillatory flow, and counter flow were found when the inner diameter of the thin pipe was changed. The modes are stable against perturbations. A coupled two-bottle system exhibits either in-phase or anti-phase self-synchr...
Directory of Open Access Journals (Sweden)
Sadolah Nasiri
2008-02-01
Full Text Available In a previous work the concept of quantum potential is generalized into extended phase space (EPS for a particle in linear and harmonic potentials. It was shown there that in contrast to the Schrödinger quantum mechanics by an appropriate extended canonical transformation one can obtain the Wigner representation of phase space quantum mechanics in which the quantum potential is removed from dynamical equation. In other words, one still has the form invariance of the ordinary Hamilton-Jacobi equation in this representation. The situation, mathematically, is similar to the disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates. Here we show that the Husimi representation is another possible representation where the quantum potential for the harmonic potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form. This happens when the parameter in the Husimi transformation assumes a specific value corresponding to Q-function.
The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation
Directory of Open Access Journals (Sweden)
Xi Fu
2016-01-01
Full Text Available Let B be the real unit ball in Rn and f∈CN(B. Given a multi-index m=(m1,…,mn of nonnegative integers with |m|=N, we set the quantity supx∈B,y∈E(x,r,x≠y(1-|x|2α(1-|y|2β|∂mf(x-∂mf(y|/|x-y|γ[x,y]1-γ, x≠y, where 0≤γ≤1 and α+β=N+1. In terms of it, we characterize harmonic Bloch and Besov spaces on the real unit ball. This generalizes the main results of Yoneda, 2002, into real harmonic setting.
59 fs mode-locked Yb:KGW oscillator pumped by a single-mode laser diode
Kowalczyk, M.; Sotor, J.; Abramski, K. M.
2016-03-01
In this letter we present a passively mode-locked Yb:KGW oscillator pumped by a low power single-mode laser diode. Contrary to high power operation, single-mode pumping enabled us to suppress parasitic thermal effects, while keeping the setup compact and its alignment straightforward. Undisturbed mode-locking (ML) stability was achieved without active cooling of the gain medium and the laser was entirely self-starting. Pulses 59 fs in duration were obtained in a semiconductor saturable absorber mirror (SESAM)-assisted Kerr-lens mode-locked regime. The corresponding spectrum was 20.2 nm broad at a central wavelength of 1036 nm approaching the performance limit of the crystal. To the best of our knowledge, these are the shortest pulses generated from a Yb:KGW laser.
Power System Oscillation Modes Identifications: Guidelines for Applying TLS-ESPRIT Method
Gajjar, Gopal R.; Soman, Shreevardhan
2013-05-01
Fast measurements of power system quantities available through wide-area measurement systems enables direct observations for power system electromechanical oscillations. But the raw observations data need to be processed to obtain the quantitative measures required to make any inference regarding the power system state. A detailed discussion is presented for the theory behind the general problem of oscillatory mode indentification. This paper presents some results on oscillation mode identification applied to a wide-area frequency measurements system. Guidelines for selection of parametes for obtaining most reliable results from the applied method are provided. Finally, some results on real measurements are presented with our inference on them.
Mixed mode and sequential oscillations in the cerium-bromate-4-aminophenol photoreaction
Energy Technology Data Exchange (ETDEWEB)
Bell, Jeffrey G.; Wang Jichang [Department of Chemistry and Biochemistry, University of Windsor, Windsor, Ontario N9B 3P4 (Canada)
2013-09-15
Cerium was introduced to the bromate-aminophenol photochemical oscillator to implement coupled autocatalytic feedbacks. Mixed mode and sequential oscillations emerged in the studied system, making it one of the few chemical oscillators known to support consecutive bifurcations in a batch system. The complex reaction behavior showed a strong dependence on the intensity of illumination supplied to the system. Removal of illumination during an oscillatory window affected both the frequency and amplitude of the oscillation but did not fully extinguish them, indicating that the cerium-bromate-4-aminophenol oscillator was photosensitive rather than photo-controlled. A moderate light intensity allowed for a slow evolution of the system, which proved to be critical for the emergence of transient complex oscillations. Variation of individual reaction parameters was carried out, which indicated that the development of complex oscillations occur in a narrow region and a phase diagram in the 4-aminophenol and sulfuric acid plane demonstrated this. Simulations provide strong support that transient complex oscillations observed experimentally arise from the coupling of two autocatalytic cycles.
Mixed mode and sequential oscillations in the cerium-bromate-4-aminophenol photoreaction
Bell, Jeffrey G.; Wang, Jichang
2013-09-01
Cerium was introduced to the bromate-aminophenol photochemical oscillator to implement coupled autocatalytic feedbacks. Mixed mode and sequential oscillations emerged in the studied system, making it one of the few chemical oscillators known to support consecutive bifurcations in a batch system. The complex reaction behavior showed a strong dependence on the intensity of illumination supplied to the system. Removal of illumination during an oscillatory window affected both the frequency and amplitude of the oscillation but did not fully extinguish them, indicating that the cerium-bromate-4-aminophenol oscillator was photosensitive rather than photo-controlled. A moderate light intensity allowed for a slow evolution of the system, which proved to be critical for the emergence of transient complex oscillations. Variation of individual reaction parameters was carried out, which indicated that the development of complex oscillations occur in a narrow region and a phase diagram in the 4-aminophenol and sulfuric acid plane demonstrated this. Simulations provide strong support that transient complex oscillations observed experimentally arise from the coupling of two autocatalytic cycles.
Energy Technology Data Exchange (ETDEWEB)
Dobaczewski, J.; Dudek, J. [Strasbourg-1 Univ., 67 (France). Centre de Recherches Nucleaires; Dobaczewski, J. [Warsaw Univ. (Poland)
1996-12-31
We describe the code HFODD which solves the nuclear Skyrme-Hartree-Fock problem by using the deformed Cartesian harmonic oscillator basis. The user has a possibility of choosing among various symmetries of the nuclear HF problem for rotating or non-rotating nuclei; they vary from the non-axial parity-invariant nuclear shapes, through those also breaking the intrinsic parity, towards the least-restrictive case corresponding to only one symmetry plane. The code provides a solution for a complete superdeformed rotational band in an A{approx}150 nucleus within one CPU hour of the CRAY C-90 supercomputer or within two-three CPU hours of a fast workstation. (authors). 22 refs.
Yu, Rong Mei; Zan, Li Rong; Jiao, Li Guang; Ho, Yew Kam
2017-09-01
Spatially confined atoms have been extensively investigated to model atomic systems in extreme pressures. For the simplest hydrogen-like atoms and isotropic harmonic oscillators, numerous physical quantities have been established with very high accuracy. However, the expectation value of which is of practical importance in many applications has significant discrepancies among calculations by different methods. In this work we employed the basis expansion method with cut-off Slater-type orbitals to investigate these two confined systems. Accurate values for several low-lying bound states were obtained by carefully examining the convergence with respect to the size of basis. A scaling law for was derived and it is used to verify the accuracy of numerical results. Comparison with other calculations show that the present results establish benchmark values for this quantity, which may be useful in future studies.
Transverse Electromagnetic Mode Conversion for High-Harmonic Self-Probing Spectroscopy
Directory of Open Access Journals (Sweden)
Antoine Camper
2015-02-01
Full Text Available We report on high-order harmonic (HHG two-source interferometry (TSI in molecular gases. We used a 0-\\(\\pi\\ phase plate to create two bright spots at the focus of a lens by converting a Gaussian laser beam into a TEM please define \\(_{01}\\ Transverse Electromagnetic Mode. The two bright foci produce two synchronized HHG sources. One of them is used to probe on-going dynamics in the generating medium, while the other serves to heterodyne the signal. The interference of the emissions in the far–field gives access to the phase difference between the two sources. In self–probing HHG phase spectroscopy, one of the two sources is used as a reference while the other one probes some on goin dynamics in the generating medium. We first compute overlap integrals to investigate the mode conversion efficiency. We then establish a clear relation between the laser phase-front curvature and the far-field overlap of the two HHG beams. Both Fresnel diffraction calculations and an experimental lens position scan are used to reveal variations of the phase front inclination in each source. We show that this arrangement offers \\(\\frac{\\lambda_{XUV}}{100}\\ precision, enabling extremely sensitive phase measurements. Finally, we use this compact setup for TSI and measure phase variations across the molecular alignment revival of nitrogen and in vibrating sulfur hexafluoride. In both gases, the phase variations change sign around the ionization threshold of the investigated molecule.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Pei
2013-02-15
Higher order modes (HOM) are electromagnetic resonant fields. They can be excited by an electron beam entering an accelerating cavity, and constitute a component of the wakefield. This wakefield has the potential to dilute the beam quality and, in the worst case, result in a beam-break-up instability. It is therefore important to ensure that these fields are well suppressed by extracting energy through special couplers. In addition, the effect of the transverse wakefield can be reduced by aligning the beam on the cavity axis. This is due to their strength depending on the transverse offset of the excitation beam. For suitably small offsets the dominant components of the transverse wakefield are dipole modes, with a linear dependence on the transverse offset of the excitation bunch. This fact enables the transverse beam position inside the cavity to be determined by measuring the dipole modes extracted from the couplers, similar to a cavity beam position monitor (BPM), but requires no additional vacuum instrumentation. At the FLASH facility in DESY, 1.3 GHz (known as TESLA) and 3.9 GHz (third harmonic) cavities are installed. Wakefields in 3.9 GHz cavities are significantly larger than in the 1.3 GHz cavities. It is therefore important to mitigate the adverse effects of HOMs to the beam by aligning the beam on the electric axis of the cavities. This alignment requires an accurate beam position diagnostics inside the 3.9 GHz cavities. It is this aspect that is focused on in this thesis. Although the principle of beam diagnostics with HOM has been demonstrated on 1.3 GHz cavities, the realization in 3.9 GHz cavities is considerably more challenging. This is due to the dense HOM spectrum and the relatively strong coupling of most HOMs amongst the four cavities in the third harmonic cryo-module. A comprehensive series of simulations and HOM spectra measurements have been performed in order to study the modal band structure of the 3.9 GHz cavities. The dependencies of
AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2006-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...... with the coupling strength. A simple linear time-domain model is employed to illustrate the results...
Robust identification of harmonic oscillator parameters using the adjoint Fokker-Planck equation
Boujo, E.; Noiray, N.
2017-04-01
We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator's damping and stiffness properties are postulated, guided by physical understanding of the oscillatory phenomena. The temporal dynamics and the probability density function of the oscillation amplitude are described by a Langevin equation and its associated Fokker-Planck equation, respectively. One method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values, obtained from data processing by taking the short-time limit of the first two transition moments. However, this limit estimation loses robustness in some situations-for instance when the data are band-pass filtered to isolate the spectral contents of the oscillatory phenomena of interest. In this paper, we use a robust alternative where the adjoint Fokker-Planck equation is solved to compute Kramers-Moyal coefficients exactly, and an iterative optimization yields the parameters that best fit the observed statistics simultaneously in a wide range of amplitudes and time scales. The method is illustrated with a stochastic Van der Pol oscillator serving as a prototypical model of thermoacoustic instabilities in practical combustors, where system identification is highly relevant to control.
Directory of Open Access Journals (Sweden)
M. K. Bahar
2013-01-01
Full Text Available Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.
Huveneers, R.
1994-01-01
In this paper we will study the 2D-harmonic oscillator in 1:1 resonance. We add a general third- and fourth order perturbation which is slowly time-dependent, and are interested in the resulting interaction between the unperturbed orbits (states). By treating this system quantummechanically we get a
Wu, Y.; Chen, Y. D.
2017-10-01
To achieve mode control of an X-band relativistic backward wave oscillator (RBWO) locked by a modulated electron beam, the mechanism of the parasitic mode oscillation and its influence on the working characteristics of the phase-locked RBWO are explored detailedly both in particle-in-cell simulation and in experiment. The experimental result agrees well with the simulation, which indicates that the TM11's excitation in the cavities and the TE11's coupling between the cavities are the main causes of the parasitic mode self-oscillation. Accordingly, RF lossy material is introduced to sever this coupling and suppress the parasitic mode oscillation. The suppression effect of the lossy material is also tested in the experiment, and the parasitic mode oscillation is eliminated. Finally, mode control of the phase-locked RBWO is accomplished experimentally. The phase jitter maintains at a level of ±10° in 50 ns.
Effect of oscillation mode on the free-molecule squeeze-film air damping
Gang Hong,
2010-01-01
A 3D Monte Carlo (MC) simulation approach is developed and employed to study the effect of the oscillation mode on the squeeze-film air damping in the free-molecule regime. By tracking individual gas molecule\\'s motion and its interaction with the resonator, the MC approach is by far the most accurate modeling approach for the modeling of squeeze-film damping in the free-molecule regime. The accuracy of this approach is demonstrated on several cases in which either analytical solutions or experimental measurements are available. It has been found that unlike the case when resonators oscillate in an unbounded domain, squeeze film damping is very sensitive to the mode shape, which implies that some of the existing modeling approaches based on rigid-resonator assumption may not be accurate when applied to model resonators oscillating at their deformed shape. ©2010 IEEE.
Oscillation mode linewidths of main-sequence and subgiant stars observed by Kepler
DEFF Research Database (Denmark)
Appourchaux, T.; Benomar, O.; Gruberbauer, M.
2012-01-01
Solar-like oscillations have been observed by {{\\it Kepler}} and CoRoT in several solar-type stars. We study the variations of stellar p-mode linewidth as a function of effective temperature. Time series of 9 months of Kepler data have been used. The power spectra of 42 cool main-sequence stars a...
Modelling of Trapped Plasma Mode Oscillations in a p+ n – n+ ...
African Journals Online (AJOL)
This paper proposes an approach for obtaining a relatively simple set of equations which apply to the description of TRAPATT phenomenon and applies it to model trappedplasma mode oscillations in a p+ n – n+ silicon diode. Typical voltage, conduction current, electric field and carrier charge wave-forms are presented for ...
Investigation of crosstalk in self oscillating switch mode audio power amplifier
DEFF Research Database (Denmark)
Birch, Thomas Haagen; Ploug, Rasmus Overgaard; Iversen, Niels Elkjær
2012-01-01
Self oscillating switch mode power ampliers are known to be susceptible to interchannel disturbances also known as crosstalk. This phenomenon has a signicant impact on the performance of an amplier of this type. The goal of this paper is to investigate the presence and origins of crosstalk in a two...
Wang, Yazhou; Li, Jianfeng; Zhang, Entao; Mo, Kundong; Wang, Yanyan; Liu, Fei; Zhou, Xiaojun; Liu, Yong
2017-07-24
Coexistence of harmonic mode-locking (HML) and noise-like pulse (NLP) were experimentally observed in a dual-wavelength mode-locked Tm-doped fiber laser for the first time. The coexistence patterns were self-started and maintained within a wide pump range by appropriately setting the intra-cavity polarization state. The HML was obtained at 1955.3 nm with a varied repetition rate range from 324 MHz to 1.138 GHz which benefits from the dispersion compensation, while the NLP observing at 1983.2 nm can operate at either fundamental repetition rate of 4.765 MHz or second harmonic state. Experimental investigations show that the coexistence patterns are caused by the wavelength-dependent phase delay of the mode-locked fiber cavity. Moreover, dual-wavelength NLP was also observed for the first time at 2 μm spectral region by changing the intra-cavity polarization state.
Energy Technology Data Exchange (ETDEWEB)
Marquette, Ian, E-mail: i.marquette@uq.edu.au [School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072 (Australia); Quesne, Christiane, E-mail: cquesne@ulb.ac.be [Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)
2016-05-15
The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent P{sub IV}, obtained in the context of second-order supersymmetric quantum mechanics and third-order ladder operators, with a hierarchy of families of quantum systems called k-step rational extensions of the harmonic oscillator and related with multi-indexed X{sub m{sub 1,m{sub 2,…,m{sub k}}}} Hermite exceptional orthogonal polynomials of type III. The connection between these exactly solvable models is established at the level of the equivalence of the Hamiltonians using rational solutions of the fourth Painlevé equation in terms of generalized Hermite and Okamoto polynomials. We also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving Darboux-Crum and Krein-Adler supercharges, their zero modes and the corresponding energies. These results will demonstrate and clarify the relation observed for a particular case in previous papers.
Ivanenko, Alexey; Kobtsev, Sergey; Smirnov, Sergey; Kemmer, Anna
2016-03-21
Combined lengthening of the cavity of a passive mode-locked fibre master oscillator and implementation of a new concept of intra-cavity power management led to achievement of a record-high pulse energy directly at the output of the mode-locked fibre master oscillator (without any subsequent amplification) exceeding 12 µJ. Output powers at the level of > 12 µJ obtainable from a long-cavity mode-locked fibre master oscillator open new possibilities of application of all pulse types that can be generated in such oscillators.
Energy Technology Data Exchange (ETDEWEB)
Dodonov, V V [Instituto de Fisica, Universidade de BrasIlia, Caixa Postal 04455, 70910-900 BrasIlia, DF (Brazil); Andreata, M A [Departamento de Fisica, Universidade Federal de Sao Carlos, Via Washington Luiz Km 235, Sao Carlos, 13565-905, SP (Brazil); Mizrahi, S S [Departamento de Fisica, Universidade Federal de Sao Carlos, Via Washington Luiz Km 235, Sao Carlos, 13565-905, SP (Brazil)
2005-12-01
We study the evolution of Wigner functions of arbitrary initial quantum states of field modes in a one-dimensional ideal cavity, whose boundary performs small harmonic oscillations at the frequency {omega}{sub W} = p{omega}{sub 1} (where {omega}{sub 1} is the fundamental field eigenfrequency). Special attention is paid to the case of initial even and odd coherent states, which serve as models of the 'Schroedinger cat states'. We show that the strong intermode interaction (due to the Doppler upshift of the fields reflected from the oscillating mirror) results in the decoherence of initial quantum superpositions in selected modes, even in the absence of any external 'environment'. Different quantitative measures of decoherence are discussed. The analytical solutions obtained show that any initial state of the field goes asymptotically to a highly mixed and moderately squeezed state in the 'principal resonance case' p = 2 and to the vacuum state in the 'semiresonance case' p = 1. It is shown that the decoherence process has several stages. In the first one, the interference between the components of the initial superposition is rapidly destroyed during the time of the primary decoherence, which is inversely proportional to the first power of the initial distance between the components, as opposed to the second power in the case of usual dissipative reservoirs. However, some weak traces of coherence (quantumness of states), such as the regions of negativity of the Wigner function, survive for much longer times, which do not depend on the size of the initial superposition.
A three-body force model for the harmonic and anharmonic oscillator
Directory of Open Access Journals (Sweden)
A. A. Rajabi
2005-06-01
Full Text Available We present a mathematical method to describe motion of a system based on 3 identical body forces. The 3-body forces are more easily introduced and treated within the hyperspherical harmonics. We have obtained an exact solution of the radial Schrödinger equation for a 3- body system in three dimensions. The interact potential V is assumed to depend on the hyperradius X only where X is a function of the Jacobi relative coordinates ρ and λ which are functions of the three identical particles, relative positions r12 , r23 and r31 . This method has been extensively used in nuclear and molecular physics. This work is interesting to those who are studying hadronic and bosonics physics and problems consisting three - body systems.
LBO optical parametric oscillator pumped by second harmonic of a Nd:YAG laser
Dabu, Razvan V.; Fenic, Constantin G.; Stratan, Aurel; Luculescu, C.; Muscalu, G. L.
1998-07-01
We describe a pulsed doubly resonant LiB3O5 (LBO) optical parametric oscillator (OPO) pumped with a frequency doubled Q- switched Nd:YAG laser amplifier. The threshold power density near degeneracy was found to be 29 MW/cm2. The OPO was continuously tuned from 970 nm to 1175 nm by rotation of the LBO crystal. The linewidth of the signal radiation at 998 nm, and idler radiation at 1136 nm wavelength, were found to be 10 nm, and 13 nm respectively. The OPO output pulse energy of signal and idler near degeneracy was 1.51 mJ for 18 mJ pump energy.
Low-Threshold Optical Parametric Oscillations in a Whispering Gallery Mode Resonator
DEFF Research Database (Denmark)
Fürst, J. U.; Strekalov, D. V.; Elser, D.
2010-01-01
In whispering gallery mode (WGM) resonator light is guided by continuous total internal reflection along a curved surface. Fabricating such resonators from an optically nonlinear material one takes advantage of their exceptionally high quality factors and small mode volumes to achieve extremely...... such an optical parametric oscillator (OPO) based on naturally phase-matched PDC in lithium niobate. We demonstrated a single-mode, strongly nondegenerate OPO with a threshold of 6.7 μW and linewidth under 10 MHz. This work demonstrates the remarkable capabilities of WGM-based OPOs....
Energy Technology Data Exchange (ETDEWEB)
Li, H.T. [Department of Engineering Mechanics, Northwestern Polytechnical University, Xian (China); Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, Ontario (Canada); Yang, Z.; Zu, J. [Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, Ontario (Canada); Qin, W. Y., E-mail: qinweiyang67@gmail.com [Department of Engineering Mechanics, Northwestern Polytechnical University, Xian (China)
2016-08-15
This paper presents the modeling and parametric analysis of the recently proposed nonlinear compressive-mode energy harvester (HC-PEH) under harmonic excitation. Both theoretical and experimental investigations are performed in this study over a range of excitation frequencies. Specially, a distributed parameter electro-elastic model is analytically developed by means of the energy-based method and the extended Hamilton’s principle. An analytical formulation of bending and stretching forces are derived to gain insight on the source of nonlinearity. Furthermore, the analytical model is validated against with experimental data and a good agreement is achieved. Both numerical simulations and experiment illustrate that the harvester exhibits a hardening nonlinearity and hence a broad frequency bandwidth, multiple coexisting solutions and a large-amplitude voltage response. Using the derived model, a parametric study is carried out to examine the effect of various parameters on the harvester voltage response. It is also shown from parametric analysis that the harvester’s performance can be further improved by selecting the proper length of elastic beams, proof mass and reducing the mechanical damping.
Haxton, Wick; Lunardini, Cecilia
2008-09-01
Semi-leptonic electroweak interactions in nuclei—such as β decay, μ capture, charged- and neutral-current neutrino reactions, and electron scattering—are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |p→|/M, where p→ and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q, where q is the magnitude of the three-momentum transfer. While results for such matrix elements are available in tabular form, with certain restriction on quantum numbers, the task of determining the analytic form of a response function can still be quite tedious, requiring the folding of the tabulated matrix elements with the nuclear density matrix, and subsequent algebra to evaluate products of operators. Here we provide a Mathematica script for generating these matrix elements, which will allow users to carry out all such calculations by symbolic manipulation. This will eliminate the errors that may accompany hand calculations and speed the calculation of electroweak nuclear cross sections and rates. We illustrate the use of the new script by calculating the cross sections for charged- and neutral-current neutrino scattering in 12C. Program summaryProgram title: SevenOperators Catalogue identifier: AEAY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Third Harmonic Mechanism in Complex Plasmonic Fano Structures.
Metzger, Bernd; Schumacher, Thorsten; Hentschel, Mario; Lippitz, Markus; Giessen, Harald
2014-06-18
We perform third harmonic spectroscopy of dolmen-type nanostructures, which exhibit plasmonic Fano resonances in the near-infrared. Strong third harmonic emission is predominantly radiated close to the low energy peak of the Fano resonance. Furthermore, we find that the third harmonic polarization of the subradiant mode interferes destructively and diminishes the nonlinear signal in the far-field. By comparing the experimental third harmonic spectra with finite element simulations and an anharmonic oscillator model, we find strong indications that the source of the third harmonic is the optical nonlinearity of the bare gold enhanced by the resonant plasmonic polarization.
Morin, Stéphane; Ahmaïdi, Saïd; Leprêtre, Pierre-Marie
2016-10-01
Positive and negative effects of training induce apparent oscillations of performance, suggesting that the delayed cumulative effects of training on daily performance capacity (DPC) are best fitted by sine waves damped over time. To compare the criterion validity of the impulse-response (IR) model of Banister et al and the damped harmonic oscillation (DHO) model for quantifying the training load (TL)-DPC relationship. Six female professional volleyball players (20.8 ± 2.4 y) were monitored using the session rating of perceived exertion (sRPE) for 9 mo to quantify TL. Countermovement-jump (CMJ) and 4-step-approach-CMJ (4sCMJ) performances were recorded once a month. Parameters of models were determined by minimizing residual-sum squares between predicted and real performances with a nonlinear regression. DPC was best fitted by the DHO model rather than the IR model (CMJ, R(2) = .80 ±.08 and.69 ±.20, respectively; 4sCMJ, R(2) = .86 ± .09 and .67 ± .29, respectively). The damping parameter θ and the period T were positively correlated with age (ρ = 0.81, P training and recovery days. DPC could be considered the expression of the individual process of accumulation and dissipation of fatigue induced by training. DHO-model parameters were correlated with age, which prompts one to postulate that expertise has a major influence on DPC. The DHO model will help coaches develop a greater understanding of training effects and make monitoring of the training process more effective.
Sanford, N A; Robinson, W C
1987-06-01
Second-harmonic generation in the form of Cerenkov radiation has been used to make direct, contact-free measurements of the effective indices of guided modes in LiNbO(3) channel waveguides. X-cut substrates were used, and channels oriented along the y axis were formed by either proton exchange or titanium indiffusion. For end-fire TE excitation, the Cerenkov harmonic radiates forward at a shallow angle into the substrate, leaves the output facet of the substrate, and appears as bright bands in the far field. These bands are seen to form a one-to-one correspondence with the m lines that are due to guided modes when a prism coupler is simultaneously clamped to the sample surface. The effective indices of the guided modes can be obtained by a simple calculation that involves only the substrate index and the angle at which the Cerenkov harmonic is radiated into the substrate. This technique permits effective index measurements of cladded waveguides where prism coupler measurements cannot be made. Examples of the technique in which index oil is used as a guide overlayer are given.
Chaos Control in Memristor-based Oscillators Using Intelligent Sliding Mode Control
Directory of Open Access Journals (Sweden)
Amir Hossein Abolmasoumi
2014-10-01
Full Text Available In this paper, Intelligent Sliding Mode Control of chaos in a memristor- based Chua’s oscillator is investigated. In order to gain stabilization and tracking of a sinusoidal input, an appropriate sliding surface is proposed and sliding gain is tuned. Also, to avoid the chattering phenomenon in traditional sliding mode controller, and to reduce the hitting time of the controlled system, an especial genetic algorithm optimization method is suggested. By defining a new objective function and searching for optimal the controller parameters the convergence time and chattering are reduced considerably. The usefulness of the proposed controller with intelligent tuning method for chaos control of memristorbased oscillators is demonstrated in memristor- based Chua's circuit.
Gasulla, Ivana; Sancho, Juan; Capmany, José; Lloret, Juan; Sales, Salvador
2010-12-06
We theoretically and experimentally evaluate the propagation, generation and amplification of signal, harmonic and intermodulation distortion terms inside a Semiconductor Optical Amplifier (SOA) under Coherent Population Oscillation (CPO) regime. For that purpose, we present a general optical field model, valid for any arbitrarily-spaced radiofrequency tones, which is necessary to correctly describe the operation of CPO based slow light Microwave Photonic phase shifters which comprise an electrooptic modulator and a SOA followed by an optical filter and supplements another recently published for true time delay operation based on the propagation of optical intensities. The phase shifter performance has been evaluated in terms of the nonlinear distortion up to 3rd order, for a modulating signal constituted of two tones, in function of the electrooptic modulator input RF power and the SOA input optical power, obtaining a very good agreement between theoretical and experimental results. A complete theoretical spectral analysis is also presented which shows that under small signal operation conditions, the 3rd order intermodulation products at 2Ω1 + Ω2 and 2Ω2 + Ω1 experience a power dip/phase transition characteristic of the fundamental tones phase shifting operation.
Zhang, P; Jones, R M
2012-01-01
An electron beam entering an accelerating cavity excites a wakefield. This wakefield can be decomposed into a series of multi-poles or modes. The dominant component of the transverse wakefield is dipole. This report summarizes the higher order mode (HOM) signals of the third harmonic cavities of FLASH measured at various stages: transmission measurements in the single cavity test stand at Fermilab, at CMTB (Cryo-Module Test Bench) and at FLASH, and beam-excited measurements at FLASH. Modes in the first two dipole bands and the fifth dipole band have been identified using a global Lorentzian fit technique. The beam-pipe modes at approximately 4 GHz and some modes in the fifth dipole band have been observed as localized modes, while the first two dipole bands, containing some strong coupling cavity modes, propagate. This report also presents the dependence of the localized dipole modes on the transverse beam position. Linear dependence for various modes has been observed. This makes them suitable for beam posit...
Introduction to focus issue: Mixed mode oscillations: Experiment, computation, and analysis
DEFF Research Database (Denmark)
Brøns, Morten; Kaper, T.J.; Rotstein, H.G.
2008-01-01
Mixed mode oscillations ( MMOs ) occur when a dynamical system switches between fast and slow motion and small and large amplitude. MMOs appear in a variety of systems in nature, and may be simple or complex. This focus issue presents a series of articles on theoretical, numerical, and experimental...... aspects of MMOs. The applications cover physical, chemical, and biological systems. c 2008 American Institute of Physics....
The oscillating collisions between the three solitons for a dual-mode fiber coupler system
Li, Bang-Qing; Ma, Yu-Lan; Yang, Tie-Mei
2017-10-01
The dynamical behaviors of the three-soliton collisions are investigated for a dual-mode fiber coupler system, which is modeled as coupled nonlinear Schrödinger equations describing optical pulse propagations. The three-soliton solutions are constructed by the bilinear method. A class of oscillating collisions is observed. The optical speckle intensity is controllable by setting parameters involved in soliton solution. It is valuable to inspire new ideas in optics and optical engineering.
Van Allen Probes observations of whistler-mode chorus with long-lived oscillating tones
Gao, Zhonglei; Su, Zhenpeng; Chen, Lunjin; Zheng, Huinan; Wang, Yuming; Wang, Shui
2017-06-01
Whistler-mode chorus plays an important role in the radiation belt electron dynamics. In the frequency-time spectrogram, chorus often appears as a hiss-like band and/or a series of short-lived (up to ˜1 s) discrete elements. Here we present some rarely reported chorus emissions with long-lived (up to 25 s) oscillating tones observed by the Van Allen Probes in the dayside (MLT ˜9-14) midlatitude (|MLAT|>15°) region. An oscillating tone can behave either regularly or irregularly and can even transform into a nearly constant tone (with a relatively narrow frequency sweep range). We suggest that these highly coherent oscillating tones were generated naturally rather than being related to some artificial VLF transmitters. Possible scenarios for the generation of the oscillating tone chorus are as follows: (1) being nonlinearly triggered by the accompanying hiss-like bands or (2) being caused by the modulation of the wave source. The details of the generation and evolution of such a long-lived oscillating tone chorus need to be investigated both theoretically and experimentally in the future.
Noise-induced oscillations in fluctuations of passively mode-locked pulses.
Katz, Michael; Gat, Omri; Fischer, Baruch
2010-02-01
We study the fluctuations of pulses in mode-locked lasers using the statistical light-mode dynamics approach. The analysis is based on a decomposition of the laser waveform into three parts: solitary pulse, intracavity noise continuum, and local overlap. We discover significant features in the fluctuation dynamics, beyond those known in existing theories that disregard the continuum component of the waveform, most notably oscillations in the autocorrelation functions of the pulse power and frequency parameters, and an enhancement of the phase jitter diffusion constant. The theoretical results are corroborated by numerical simulations.
Power system low frequency oscillation mode estimation using wide area measurement systems
Directory of Open Access Journals (Sweden)
Papia Ray
2017-04-01
Full Text Available Oscillations in power systems are triggered by a wide variety of events. The system damps most of the oscillations, but a few undamped oscillations may remain which may lead to system collapse. Therefore low frequency oscillations inspection is necessary in the context of recent power system operation and control. Ringdown portion of the signal provides rich information of the low frequency oscillatory modes which has been taken into analysis. This paper provides a practical case study in which seven signal processing based techniques i.e. Prony Analysis (PA, Fast Fourier Transform (FFT, S-Transform (ST, Wigner-Ville Distribution (WVD, Estimation of Signal Parameters by Rotational Invariance Technique (ESPRIT, Hilbert-Huang Transform (HHT and Matrix Pencil Method (MPM were presented for estimating the low frequency modes in a given ringdown signal. Preprocessing of the signal is done by detrending. The application of the signal processing techniques is illustrated using actual wide area measurement systems (WAMS data collected from four different Phasor Measurement Unit (PMU i.e. Dadri, Vindyachal, Kanpur and Moga which are located near the recent disturbance event at the Northern Grid of India. Simulation results show that the seven signal processing technique (FFT, PA, ST, WVD, ESPRIT, HHT and MPM estimates two common oscillatory frequency modes (0.2, 0.5 from the raw signal. Thus, these seven techniques provide satisfactory performance in determining small frequency modes of the signal without losing its valuable property. Also a comparative study of the seven signal processing techniques has been carried out in order to find the best one. It was found that FFT and ESPRIT gives exact frequency modes as compared to other techniques, so they are recommended for estimation of low frequency modes. Further investigations were also carried out to estimate low frequency oscillatory mode with another case study of Eastern Interconnect Phasor Project
Energy Technology Data Exchange (ETDEWEB)
Sharma, Raghav [Department of Physics, Indian Institute of Technology, Delhi, New Delhi 110016 (India); Dürrenfeld, P.; Iacocca, E. [Department of Physics, University of Gothenburg, Gothenburg 412 96 (Sweden); Heinonen, O. G. [Argonne National Laboratory, Materials Science Division, Lemont, Illinois 60439 (United States); Åkerman, J. [Department of Physics, University of Gothenburg, Gothenburg 412 96 (Sweden); Materials Physics, School of ICT, KTH-Royal Institute of Technology, Electrum 229, Kista 164 40 (Sweden); Muduli, P. K. [Department of Physics, Indian Institute of Technology, Delhi, New Delhi 110016 (India); Department of Physics, University of Gothenburg, Gothenburg 412 96 (Sweden)
2014-09-29
The frequency noise spectrum of a magnetic tunnel junction based spin torque oscillator is examined where multiple modes and mode-hopping events are observed. The frequency noise spectrum is found to consist of both white noise and 1/f frequency noise. We find a systematic and similar dependence of both white noise and 1/f frequency noise on bias current and the relative angle between the reference and free layers, which changes the effective damping and hence the mode-hopping behavior in this system. The frequency at which the 1/f frequency noise changes to white noise increases as the free layer is aligned away from the anti-parallel orientation w.r.t the reference layer. These results indicate that the origin of 1/f frequency noise is related to mode-hopping, which produces both white noise as well as 1/f frequency noise similar to the case of ring lasers.
Synchrony-induced modes of oscillation of a neural field model
Esnaola-Acebes, Jose M.; Roxin, Alex; Avitabile, Daniele; Montbrió, Ernest
2017-11-01
We investigate the modes of oscillation of heterogeneous ring networks of quadratic integrate-and-fire (QIF) neurons with nonlocal, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient standing waves with a specific temporal frequency, analogously to those in a tense string. In the neuronal network, the equilibrium corresponds to a spatially homogeneous, asynchronous state. Perturbations of this state excite the network's oscillatory modes, which reflect the interplay of episodes of synchronous spiking with the excitatory-inhibitory spatial interactions. In the thermodynamic limit, an exact low-dimensional neural field model describing the macroscopic dynamics of the network is derived. This allows us to obtain formulas for the Turing eigenvalues of the spatially homogeneous state and hence to obtain its stability boundary. We find that the frequency of each Turing mode depends on the corresponding Fourier coefficient of the synaptic pattern of connectivity. The decay rate instead is identical for all oscillation modes as a consequence of the heterogeneity-induced desynchronization of the neurons. Finally, we numerically compute the spectrum of spatially inhomogeneous solutions branching from the Turing bifurcation, showing that similar oscillatory modes operate in neural bump states and are maintained away from onset.
Simultaneous cooling of coupled mechanical oscillators using whispering gallery mode resonances.
Li, Ying Lia; Millen, James; Barker, P F
2016-01-25
We demonstrate simultaneous center-of-mass cooling of two coupled oscillators, consisting of a microsphere-cantilever and a tapered optical fiber. Excitation of a whispering gallery mode (WGM) of the microsphere, via the evanescent field of the taper, provides a transduction signal that continuously monitors the relative motion between these two microgram objects with a sensitivity of 3 pm. The cavity enhanced optical dipole force is used to provide feedback damping on the motion of the micron-diameter taper, whereas a piezo stack is used to damp the motion of the much larger (up to 180 μm in diameter), heavier (up to 1.5 × 10(-7) kg) and stiffer microsphere-cantilever. In each feedback scheme multiple mechanical modes of each oscillator can be cooled, and mode temperatures below 10 K are reached for the dominant mode, consistent with limits determined by the measurement noise of our system. This represents stabilization on the picometer level and is the first demonstration of using WGM resonances to cool the mechanical modes of both the WGM resonator and its coupling waveguide.
Energy Technology Data Exchange (ETDEWEB)
Noguera, Norman, E-mail: norman.noguera@ucr.ac.cr [Departamento de Matemática, Universidad de Costa Rica. S.O (Costa Rica); Rózga, Krzysztof, E-mail: krzysztof.rozga@upr.edu [Department of Mathematical Sciences, University of Puerto Rico, Mayagüez, Puerto Rico 00681-5000 (United States)
2015-07-15
In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case of a slightly more general potential than the one for harmonic oscillator.
Wan, Xiang; Tse, Peter W; Chen, Jingming; Xu, Guanghua; Zhang, Qing
2018-01-01
Second harmonic generation has been widely used in characterizing microstructural changes which are evenly distributed in a whole structure. However, few attention has been paid to evaluating localized micro-scale damages. In this paper, second harmonic reflection and transmission from the primary S0 mode Lamb wave interacting with a localized microstructural damage is numerically discussed. Schematic diagram for deriving fundamental temporal waveform and reconstructing the second harmonic temporal waveform based on Morlet wavelet transform is presented. Second harmonic reflection and transmission from an interface between the zones of linear elastic and nonlinear materials is firstly studied to verify the existence of interfacial nonlinearity. Compositions contributing to second harmonic components in the reflected and transmitted waves are analyzed. Amplitudes of the reflected and transmitted second harmonic components generated at an interface due to the interfacial nonlinearity are quantitatively evaluated. Then, second harmonic reflection and transmission from a localized microscale damage is investigated. The effects of the length and width of a microscale damage on WCPA (wavelet coefficient profile area) of the reflected and transmitted second harmonic components are studied respectively. It is found that the second harmonic component in the reflected waves mainly reflects the interfacial nonlinearity while second harmonic in the transmitted waves reflects the material nonlinearity. These findings provide some basis on using second harmonic generation for characterization and detection of localized microstructural changes. Copyright © 2017 Elsevier B.V. All rights reserved.
Chae, Jongchul; Litvinenko, Yuri E.
2017-08-01
The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D2 and Hα lines.
Energy Technology Data Exchange (ETDEWEB)
Chae, Jongchul [Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 08826 (Korea, Republic of); Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand)
2017-08-01
The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D{sub 2} and H α lines.
Li, Mingliang; Deng, Mingxi; Gao, Guangjian; Xiang, Yanxun
2018-01-01
The appropriate mode pairs of primary and double-frequency circumferential guided waves (CGWs) have been investigated and selected for generation of the cumulative second harmonics, which are applicable for quantitative assessment of damage/degradation in a circular tube. The selection criteria follow the requirements: the higher efficiency of cumulative second-harmonic generation (SHG) of primary CGW propagation, and the larger response sensitivity of cumulative SHG to material damage/degradation [characterized by variation in the third-order elastic (TOE) constants]. The acoustic nonlinearity parameter β of CGW propagation and the change rate of normalized β versus the TOE constants of tube material are, respectively, used to describe the efficiency of SHG and its response sensitivity to damage/degradation. Based on the selection criteria proposed, all the possible mode pairs of primary and double-frequency CGWs satisfying the phase velocity matching have been numerically examined. It has been found that there are indeed some mode pairs of CGW propagation with the larger values both of β and the change rate of normalized β versus the TOE constants. The CGW mode pairs found in this paper are of practical significance for quantitative assessment of damage/degradation in the circular tube. Copyright © 2017 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Yosef London
2017-04-01
Full Text Available An opto-electronic radio-frequency oscillator that is based on forward scattering by the guided acoustic modes of a standard single-mode optical fiber is proposed and demonstrated. An optical pump wave is used to stimulate narrowband, resonant guided acoustic modes, which introduce phase modulation to a co-propagating optical probe wave. The phase modulation is converted to an intensity signal at the output of a Sagnac interferometer loop. The intensity waveform is detected, amplified, and driven back to modulate the optical pump. Oscillations are achieved at a frequency of 319 MHz, which matches the resonance of the acoustic mode that provides the largest phase modulation of the probe wave. Oscillations at the frequencies of competing acoustic modes are suppressed by at least 40 dB. The linewidth of the acoustic resonance is sufficiently narrow to provide oscillations at a single longitudinal mode of the hybrid cavity. Competing longitudinal modes are suppressed by at least 38 dB as well. Unlike other opto-electronic oscillators, no radio-frequency filtering is required within the hybrid cavity. The frequency of oscillations is entirely determined by the fiber opto-mechanics.
Directory of Open Access Journals (Sweden)
Suhufa Alfarisa
2016-03-01
Full Text Available This research aims i to determine the density profile and calculate the ground state energy of a quantum dot in two dimensions (2D with a harmonic oscillator potential using orbital-free density functional theory, and ii to understand the effect of the harmonic oscillator potential strength on the electron density profiles in the quantum dot. This study determines the total energy functional of the quantum dot that is a functional of the density that depends only on spatial variables. The total energy functional consists of three terms. The first term is the kinetic energy functional, which is the Thomas–Fermi approximation in this case. The second term is the external potential. The harmonic oscillator potential is used in this study. The last term is the electron–electron interactions described by the Coulomb interaction. The functional is formally solved to obtain the electron density as a function of spatial variables. This equation cannot be solved analytically, and thus a numerical method is used to determine the profile of the electron density. Using the electron density profiles, the ground state energy of the quantum dot in 2D can be calculated. The ground state energies obtained are 2.464, 22.26, 90.1957, 252.437, and 496.658 au for 2, 6, 12, 20, and 56 electrons, respectively. The highest electron density is localized close to the middle of the quantum dot. The density profiles decrease with the increasing distance, and the lowest density is at the edge of the quantum dot. Generally, increasing the harmonic oscillator potential strength reduces the density profiles around the center of the quantum dot.
Synthetic free-oscillation spectra: an appraisal of various mode-coupling methods
Yang, Hsin-Ying; Tromp, Jeroen
2015-11-01
Normal-mode spectra may be used to investigate large-scale elastic and anelastic heterogeneity throughout the entire Earth. The relevant theory was developed a few decades ago, however-mainly due to computational limitations-several approximations are commonly employed, and thus far the full merits of the complete theory have not been taken advantage of. In this study, we present an exact algebraic form of the theory for an aspherical, anelastic and rotating Earth model in which either complex or real spherical harmonic bases are used. Physical dispersion is incorporated into the quadratic eigenvalue problem by expanding the logarithmic frequency term to second-order. Proper (re)normalization of modes in a 3-D Earth model is fully considered. Using a database of 41 earthquakes and more than 10 000 spectra containing 116 modes with frequencies less than 3 mHz, we carry out numerical experiments to quantitatively evaluate the accuracy of commonly used approximate mode synthetics. We confirm the importance of wideband coupling, that is, fully coupling all modes below a certain frequency. Neither narrowband coupling, in which nearby modes are grouped into isolated clusters, nor self-coupling, that is, incorporating coupling between singlets within the same multiplet, are sufficiently accurate approximations. Furthermore, we find that (1) effects of physical dispersion can be safely approximated based on either a fiducial frequency approximation or a quadratic approximation of the logarithmic dispersion associated with the absorption-band model; (2) neglecting the proper renormalization of the modes of a rotating, anelastic Earth model introduces only minor errors; (3) ignoring the frequency dependence of the Coriolis and kinematic matrices in a wideband coupling scheme can lead to ˜6 per cent errors in mode spectra at the lowest frequencies; notable differences also occur between narrowband coupling and quasi-degenerate perturbation theory, which linearizes the
Energy Technology Data Exchange (ETDEWEB)
Kuz’menko, A. P., E-mail: apkuzm@gmail.com; Saburov, S. V., E-mail: saburov58@yandex.ru [Russian Academy of Sciences, Computer Equipment Design Technology Institute, Siberian Branch (Russian Federation)
2016-07-15
The paper puts forward a method for processing data from detailed seismic assessments of HPP dams (dynamic tests). A detailed assessment (hundreds of observation points in dam galleries) is performed with consideration of operating dam equipment and the microseismic noise. It is shown that dynamic oscillation characteristics (natural oscillation frequencies and modes in the main dam axes, the velocities of propagation of elastic waves with given polarization, and so on.) can be determined with sufficient accuracy by using complex transfer functions and pulse characteristics. Monitoring data is processed using data from a detailed assessment, taking account of identified natural oscillation modes and determined ranges of natural frequencies. The spectra of characteristic frequencies thus obtained are used to choose substitution models and estimate the elastic characteristics of the “dam – rock bed” construction system, viz., the modulus of elasticity (the Young modulus), the Poisson ratio, the dam section stiffness with respect to shear, tension and compression and the elastic characteristics of the rock foundation.
Zhuang, W. Z.; Chang, M. T.; Su, K. W.; Huang, K. F.; Chen, Y. F.
2013-07-01
We report on high-power terahertz optical pulse generation with a dual-wavelength harmonically mode-locked Yb:YAG laser. A semiconductor saturable absorber mirror is developed to achieve synchronously mode-locked operation at two spectral bands centered at 1031.67 and 1049.42 nm with a pulse duration of 1.54 ps and a pulse repetition rate of 80.3 GHz. With a diamond heat spreader to improve the heat removal efficiency, the average output power can be up to 1.1 W at an absorbed pump power of 5.18 W. The autocorrelation traces reveal that the mode-locked pulse is modulated with a beat frequency of 4.92 THz and displays a modulation depth to be greater than 80%.
Directory of Open Access Journals (Sweden)
Xueyan Zheng
2013-01-01
Full Text Available Switching Mode Power Supply (SMPS has been widely applied in aeronautics, nuclear power, high-speed railways, and other areas related to national strategy and security. The degradation of MOSFET occupies a dominant position in the key factors affecting the reliability of SMPS. MOSFETs are used as low-voltage switches to regulate the DC voltage in SMPS. The studies have shown that die-attach degradation leads to an increase in on-state resistance due to its dependence on junction temperature. On-state resistance is the key indicator of the health of MOSFETs. In this paper, an online real-time method is presented for predicting the degradation of MOSFETs. First, the relationship between an oscillator signal of source and on-state resistance is introduced. Because oscillator signals change when they age, a feature is proposed to capture these changes and use them as indicators of the state of health of MOSFETs. A platform for testing characterizations is then established to monitor oscillator signals of source. Changes in oscillator signal measurement were observed with aged on-state resistance as a result of die-attach degradation. The experimental results demonstrate that the method is efficient. This study will enable a method to predict the failure of MOSFETs to be developed.
Steele, Richard H
2008-03-01
This article introduces quantum physics into biology in an intuitive and non-intimidating manner. It extends the quantum aspects of harmonic oscillators, and electromagnetic fields, to their functional roles in biology. Central to this process are the De Broglie wave-particle duality equation, and the adiabatic invariant parameters, magnetic moment, angular momentum and magnetic flux, determined by Ehrenfest as imposing quantum constraints on the dynamics of charges in motion. In mechanisms designed to explain the generation of low-level light emissions in biology we have adopted a biological analog of the electrical circuitry modeled on the parallel plated capacitor, traversed by helical protein structures, capable of generating electromagnetic radiation in the optical spectral region. The charge carrier required for the emissions is an accelerating electron driven, in a cyclotron-type mechanism, by ATP-induced reverse electron transfer with the radial, emission, components, mediated by coulombic forces within the helical configurations. Adenine, an essential nucleotide constituent of DNA, was examined with its long wavelength absorption maximum determining the energetic parameters for the calculations. The calculations were made for a virtual 5-turn helix where each turn of the helix emits a different frequency, generating a biological quantum series. The components of six adiabatic invariant equations were found to be embedded in Planck's constant rendering them discrete, finite, non-random, non-statistical-Planck's constant precludes probability. A mechanism for drug-induced hallucination is described that might provide insights as to the possible role of electromagnetic fields in consciousness. Sodium acceleration through a proposed nerve membrane helical channel generated electromagnetic emissions in the microwave region in confirmation of reported microwave emission for active nerves and may explain saltatory nerve conduction. Theoretical calculations for a
Tóthová, Mária; Nagy, Arpád; Treindl, Ľudovít.
1999-01-01
The periodical reduction of permanganate by hydrogen peroxide or by ninhydrin with transient oscillations in a closed system has been observed and discussed in relation to the first two permanganate oscillators described earlier. The mixed-mode oscillations of the permanganate-H 2O 2 oscillating system in a continuous-flow stirred tank reactor have been described.
An approach to the damping of local modes of oscillations resulting from large hydraulic transients
Energy Technology Data Exchange (ETDEWEB)
Dobrijevic, D.M.; Jankovic, M.V.
1999-09-01
A new method of damping of local modes of oscillations under large disturbance is presented in this paper. The digital governor controller is used. Controller operates in real time to improve the generating unit transients through the guide vane position and the runner blade position. The developed digital governor controller, whose control signals are adjusted using the on-line measurements, offers better damping effects for the generator oscillations under large disturbances than the conventional controller. Digital simulations of hydroelectric power plant equipped with low-head Kaplan turbine are performed and the comparisons between the digital governor control and the conventional governor control are presented. Simulation results show that the new controller offers better performances, than the conventional controller, when the system is subjected to large disturbances.
Yoshiki, Wataru; Chen-Jinnai, Akitoshi; Tetsumoto, Tomohiro; Tanabe, Takasumi
2015-11-30
We report the first experimental observation of an energy oscillation between two coupled ultra-high Q whispering gallery modes in the time domain. Two counter-propagating whispering gallery modes in a silica toroid microcavity were employed for this purpose. The combination of a large coupling coefficient between the two modes and an ultra-high Q factor, which creates a large Γ value of > 10, results in a clear energy oscillation. Our measurement is based on a drop-port measurement technique, which enables us to observe the light energy in the two modes directly. The oscillation period measured in the time domain precisely matched that inferred from mode splitting in the frequency domain, and the measured results showed excellent agreement with results calculated with the developed numerical model.
Oscillation modes of rapidly rotating neutron stars in scalar-tensor theories of gravity
Yazadjiev, Stoytcho S.; Doneva, Daniela D.; Kokkotas, Kostas D.
2017-09-01
We perform the first study of the oscillation frequencies of rapidly rotating neutron stars in alternative theories of gravity, focusing mainly on the fundamental f modes. We concentrated on a particular class of alternative theories—the (massive) scalar-tensor theories. The generalization to rapid rotation is important because on one hand the rapid rotation can magnify the deviations from general relativity compared to the static case and on the other hand some of the most efficient emitters of gravitational radiation, such as the binary neutron star merger remnants, are supposed to be rotating close to their Kepler (mass-shedding) limits shortly after their formation. We have constructed several sequences of models starting from the nonrotating case and reaching up to the Kepler limit, with different values of the scalar-tensor theory coupling constant and the scalar field mass. The results show that the deviations from pure Einstein's theory can be significant, especially in the case of nonzero scalar field mass. An important property of the oscillation modes of rapidly rotating stars is that they can become secularly unstable due to the emission of gravitational radiation, the so-called Chandrasekhar-Friedman-Schutz instability. Such unstable modes are efficient emitters of gravitational radiation. Our studies show that the inclusion of a nonzero scalar field would decrease the threshold value of the normalized angular momentum where this instability starts to operate, but the growth time of the instability seems to be increased compared to pure general relativity.
Quantifying Image Quality Improvement Using Elevated Acoustic Output in B-Mode Harmonic Imaging.
Deng, Yufeng; Palmeri, Mark L; Rouze, Ned C; Trahey, Gregg E; Haystead, Clare M; Nightingale, Kathryn R
2017-10-01
Tissue harmonic imaging has been widely used in abdominal imaging because of its significant reduction in acoustic noise compared with fundamental imaging. However, tissue harmonic imaging can be limited by both signal-to-noise ratio and penetration depth during clinical imaging, resulting in decreased diagnostic utility. A logical approach would be to increase the source pressure, but the in situ pressures used in diagnostic ultrasound are subject to a de facto upper limit based on the U.S. Food and Drug Administration guideline for the mechanical index (harmonic imaging using a transmit frequency of 1.8 MHz. The results indicate that harmonic imaging using elevated acoustic output leads to modest improvements (3%-7%) in contrast-to-noise ratio of hypo-echoic hepatic vessels and increases in imaging penetration depth on the order of 4 mm per mechanical index increase of 0.1 for a given focal depth. Difficult-to-image patients who suffer from poor ultrasound image quality exhibited larger improvements than easy-to-image study participants. Copyright © 2017 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.
Phononic High Harmonic Generation
Ganesan, Adarsh; Do, Cuong; Seshia, Ashwin A.
2016-01-01
This paper reports the first experimental evidence for phononic low-order to high-order harmonic conversion leading to high harmonic generation. Similar to parametric resonance, phononic high harmonic generation is also mediated by a threshold dependent instability of a driven phonon mode. Once the threshold for instability is met, a cascade of harmonic generation processes is triggered. Firstly, the up-conversion of first harmonic phonons into second harmonic phonons is established. Subseque...
Devgan, Preetpaul S; Lasri, Jacob; Tang, Renyong; Grigoryan, Vladimir S; Kath, William L; Kumar, Prem
2005-03-01
We demonstrate a regeneratively mode-locked fiber-optical parametric oscillator that utilizes intracavity dispersion compensation to generate pulses at a 10-GHz repetition rate in both soliton and nonsoliton regimes. At the threshold pump power the generated pulses are close to fundamental solitons. At higher pump powers we found a significant deviation of the pulses from the sech2 shape. In addition, the use of an ultralow-jitter self-starting pump-pulse source in a regenerative feedback loop allows for a significant reduction of the signal's timing jitter and amplitude noise.
Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model
DEFF Research Database (Denmark)
Brøns, Morten; Desroches, Mathieu; Krupa, Martin
2015-01-01
In a forest pest model, young trees are distinguished from old trees. The pest feeds on old trees. The pest grows on a fast scale, the young trees on an intermediate scale, and the old trees on a slow scale. A combination of a singular Hopf bifurcation and a “weak return” mechanism, characterized...... by a small change in one of the variables, determines the features of the mixed-mode oscillations. Period-doubling and saddle-node bifurcations lead to closed families (called isolas) of periodic solutions in a bifurcation corresponding to a singular Hopf bifurcation....
Energy Technology Data Exchange (ETDEWEB)
Kim, Sung Jin; Seo, Kyung; Song, Ho Taek; Park, Ah Young; Kim, Yaena; Yoon, Choon Sik [Gangnam Severance Hospital, Yonsei University College of Medicine, Seoul (Korea, Republic of); Suh, Jin Suck; Kim, Ah Hyun [Dept. of Radiology and Research Institute of Radiological Science, Severance Hospital, Yonsei University College of Medicine, Seoul (Korea, Republic of); Ryu, Jeong Ah [Dept. of Radiology, Guri Hospital, Hanyang University College of Medicine, Guri (Korea, Republic of); Park, Jeong Seon [Dept. of Radiology, Hanyang University Hospital, Hanyang University College of Medicine, Seoul (Korea, Republic of)
2012-09-15
To determine which mode of ultrasonography (US), among the conventional, spatial compound, and tissue-harmonic methods, exhibits the best performance for the detection of Implanon with respect to generation of posterior acoustic shadowing (PAS). A total of 21 patients, referred for localization of impalpable Implanon, underwent US, using the three modes with default settings (i.e., wide focal zone). Representative transverse images of the rods, according to each mode for all patients, were obtained. The resulting 63 images were reviewed by four observers. The observers provided a confidence score for the presence of PAS, using a five-point scale ranging from 1 (definitely absent) to 5 (definitely present), with scores of 4 or 5 for PAS being considered as detection. The average scores of PAS, obtained from the three different modes for each observer, were compared using one-way repeated measure ANOVA. The detection rates were compared using a weighted least square method. Statistically, the tissue harmonic mode was significantly superior to the other two modes, when comparing the average scores of PAS for all observers (p < 0.00-1). The detection rate was also highest for the tissue harmonic mode (p < 0.001). Tissue harmonic mode in US appears to be the most suitable in detecting subdermal contraceptive implant rods.
Meisenheimer, Sarah-Katharina; Fürst, Josef Urban; Schiller, Annelie; Holderied, Florian; Buse, Karsten; Breunig, Ingo
2016-06-27
Wavelength tuning of conventional mirror-based optical parametric oscillators (OPOs) exhibits parabolically-shaped tuning curves (type-0 and type-I phase matching) or tuning branches that cross each other with a finite slope (type-II phase matching). We predict and experimentally prove that whispering gallery OPOs based on type-0 phase matching show both tuning behaviors, depending on whether the mode numbers of the generated waves coincide or differ. We investigate the wavelength tuning of optical parametric oscillation in a millimeter-sized radially-poled lithium niobate disk pumped at 1 μm wavelength generating signal and idler waves between 1.7 and 2.6 μm wavelength. Our experimental findings excellently coincide with the theoretical predictions. The investigated whispering gallery optical parametric oscillator combines the employment of the highest nonlinear-optical coefficient of the material with a controlled type-II-like wavelength tuning and with the possibility of self-phase locking.
Bifurcations of mixed-mode oscillations in a stellate cell model
Wechselberger, Martin; Weckesser, Warren
2009-08-01
Experimental recordings of the membrane potential of stellate cells within the entorhinal cortex show a transition from subthreshold oscillations (STOs) via mixed-mode oscillations (MMOs) to relaxation oscillations under increased injection of depolarizing current. Acker et al. introduced a 7D conductance based model which reproduces many features of the oscillatory patterns observed in these experiments. For the first time, we present a comprehensive bifurcation analysis of this model by using the software package AUTO. In particular, we calculate the stable MMO branches within the bifurcation diagram of this model, as well as other MMO patterns which are unstable. We then use geometric singular perturbation theory to demonstrate how the bifurcations are governed by a 3D reduced model introduced by Rotstein et al. We extend their analysis to explain all observed MMO patterns within the bifurcation diagram. A key role in this bifurcation analysis is played by a novel homoclinic bifurcation structure connecting to a saddle equilibrium on the unstable branch of the corresponding critical manifold. This type of homoclinic connection is possible due to canards of folded node (folded saddle-node) type.
Vortex-induced vibration of a tension leg platform tendon: multi-mode limit cycle oscillations
Datta, Nabanita
2017-11-01
This paper studies the application of mathematical models to analyze the vortex-induced vibrations of the tendons of a given TLP along the Indian coastline, by using an analytical approach, analyzed using MATLAB. The tendon is subjected to a steady current load, which causes vortex-shedding downstream, leading to cross-flow vibrations. The magnitude of the excitation (lift and drag coefficients) depends on the vortex-shedding frequency. The resulting vibration is studied for possible resonant behavior. The excitation force is quantified empirically, the added mass by potential flow hydrodynamics, and the vibration by normal mode summation method. Non-linear viscous damping of the water is considered. The non-linear oscillations are studied by the phase-plane method, investigating the limit-cycle oscillations. The stable/unstable regions of the dynamic behavior are demarcated. The modal contribution to the total deflection is studied to establish the possibility of resonance of one of the wet modes with the vortex-shedding frequency.
Vortex-induced vibration of a tension leg platform tendon: Multi-mode limit cycle oscillations
Datta, Nabanita
2017-12-01
This paper studies the application of mathematical models to analyze the vortex-induced vibrations of the tendons of a given TLP along the Indian coastline, by using an analytical approach, analyzed using MATLAB. The tendon is subjected to a steady current load, which causes vortex-shedding downstream, leading to cross-flow vibrations. The magnitude of the excitation (lift and drag coefficients) depends on the vortex-shedding frequency. The resulting vibration is studied for possible resonant behavior. The excitation force is quantified empirically, the added mass by potential flow hydrodynamics, and the vibration by normal mode summation method. Non-linear viscous damping of the water is considered. The non-linear oscillations are studied by the phase-plane method, investigating the limit-cycle oscillations. The stable/unstable regions of the dynamic behavior are demarcated. The modal contribution to the total deflection is studied to establish the possibility of resonance of one of the wet modes with the vortex-shedding frequency.
Higher Order Modes in Third Harmonic Cavities for XFEL/FLASH
Energy Technology Data Exchange (ETDEWEB)
Shinton, I.R.R.; /Manchester U. /Cockcroft Inst. Accel. Sci. Tech.; Baboi, N.; /DESY; Eddy, N.; /Fermilab; Flisgen, T.; Glock, H.W.; /Rostock U.; Jones, R.M.; Juntong, N.; /Manchester U. /DESY; Khabiboulline, T.N.; /Fermilab; van Rienen, U; /Rostock U.; Zhang, P.; /Manchester U. /DESY /Cockcroft Inst. Accel. Sci. Tech.
2010-06-01
We analyse higher order modes in the 3.9 GHz bunch shaping cavities recently installed in the FLASH facility at DESY. We report on recent experimental results on the frequency spectrum from probe based measurements made at CMTB at DESY. These are compared to those predicted by finite difference and finite element computer codes. This study is focused mainly on the dipole component of the multi-pole expansion of the wakefield. The modes are readily identifiable as single-cavity modes provided the frequencies of these modes are below the cut-off of the inter-connecting beam pipes. The modes above cut-off are coupled to the 4 cavities and are distinct from single cavity modes.
Viscous damping of r-mode oscillations in compact stars with quark matter.
Energy Technology Data Exchange (ETDEWEB)
Jaikumar, P.; Rupak, G.; Steiner, A. W.; Physics; Inst. of Mathematical Sciences; North Carolina State Univ.; Michigan State Univ.
2008-12-01
We determine characteristic time scales for the viscous damping of r-mode oscillations in rapidly rotating compact stars that contain quark matter. We present results for the color-flavor-locked (CFL) phase of dense quark matter, in which the up, down, and strange quarks are gapped, as well as the normal (ungapped) quark phase. While the ungapped quark phase supports a temperature window 10{sup 8} K < = T < = 5 x 10{sup 9} K where the r mode is damped even for rapid rotation, the r mode in a rapidly rotating pure CFL star is not damped in the temperature range 10{sup 10} K < = T < = 10{sup 11} K. Rotating hybrid stars with quark matter cores display an instability window whose width is determined by the amount of quark matter present, and they can have large spin frequencies outside this window. Except at high temperatures T > = 10{sup 10} K, the presence of a quark phase allows for larger critical frequencies and smaller spin periods compared to rotating neutron stars. If low-mass x-ray binaries contain a large amount of ungapped or CFL quark matter, then our estimates of the r-mode instability suggest that there should be a population of rapidly rotating binaries at nu > {approx} 1000 Hz which have not yet been observed.
Directory of Open Access Journals (Sweden)
Abramski K.M.
2013-03-01
Full Text Available Passive harmonic-mode locking (PHML of erbium-doped fiber laser with multilayer graphene is presented. The laser could operate at several harmonics (from 2nd to 21st of the fundamental repetition frequency of the ring resonator (106 MHz. The highest achieved repetition rate was 2.22 GHz (which corresponds to the 21st harmonic with 900 fs pulse duration and 50 dB of the supermode noise suppression. The saturable absorber was formed by multilayer graphene, mechanically exfoliated from pure graphite block through Scotch-tape and deposited on the fiber ferrule.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A., E-mail: a.belendez@ua.e [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)] [Instituto Universitario de Fisica Aplicada a las Ciencias y las Tecnologias, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Rodes, J.J. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fuentes, R.; Pascual, I. [Instituto Universitario de Fisica Aplicada a las Ciencias y las Tecnologias, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)] [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2009-11-09
In a previous short communication [A. Belendez, E. Fernandez, J.J. Rodes, R. Fuentes, I. Pascual, Phys. Lett. A 373 (2009) 735] the nonlinear oscillations of a punctual charge in the electric field of a charged ring were analyzed. Approximate frequency-amplitude relations and periodic solutions were obtained using the harmonic balance method. Now we clarify an important aspect about of this oscillation charge. Taking into account Earnshaw's theorem, this punctual charge cannot be a free charge and so it must be confined, for example, on a finite conducting wire placed along the axis of the ring. Then, the oscillatory system may consist of a punctual charge on a conducting wire placed along the axis of the uniformly charged ring.
Directory of Open Access Journals (Sweden)
Ashfaque Ahmed Hashmani
2011-01-01
Full Text Available The objective of this paper is to design an H?-based local decentralized PSS (Power System Stabilizing controller. The controller is designed for separate damping of specific inter-area modes while considering time-delay. The controller uses remote signals, selected suitably from the whole system, as supplementary inputs. The wide area or global signals have been obtained where the oscillations in the remote network locations could be well observed. The PSS controller uses only those local and remote input signals in which the assigned single inter-area mode is most observable and is located at a generator which is most effective in controlling that mode. A long timedelay due to remote signal transmission and processing in WAMS (Wide Area Measurement System can cause system instability and degradation of system robustness. Therefore, this paper uses the time-delay compensation method that uses lead or lag adjustment method while integrates the gain scheduling to overcome the impacts of constant time-delay. The effectiveness of the resulting PSS controllers is established through simulations using three machine three area test power system.
National Aeronautics and Space Administration — A majority of millimeter wave based systems used for space exploration, communications and research, require a millimeter wave oscillator. These oscillators have...
Directory of Open Access Journals (Sweden)
Artit Hutem
2015-01-01
Full Text Available We aimed to evaluate the ground-state and excite-state energy eigenvalue (En, wave function, and the time-independent correlation function of the atomic density fluctuation of a particle under the harmonics oscillator Cosine asymmetric potential (Saad et al. 2013. Instead of using the 6-point kernel of 4 Green’s function (Cherroret and Skipetrov, 2008, averaged over disorder, we use the numerical shooting method (NSM to solve the Schrödinger equation of quantum mechanics system with Cosine asymmetric potential. Since our approach does not use complicated formulas, it requires much less computational effort when compared to the Green functions techniques (Cherroret and Skipetrov, 2008. We show that the idea of the program of evaluating time-independent correlation function of atomic density is underdamped motion for the Cosine asymmetric potential from the numerical shooting method of this problem. Comparison of the time-independent correlation function obtained from numerical shooting method by Boonchui and Hutem (2012 and correlation function experiment by Kasprzak et al. (2008. We show the intensity of atomic density fluctuation (δn(x=n~(x-m~(x in harmonics oscillator Cosine asymmetric potential by numerical shooting method.
Zhang, P; Jones, R M; Shinton, I R R; Flisgen, T; Glock, H W
2012-01-01
We investigate the feasibility of beam position diagnostics using Higher Order Mode (HOM) signals excited by an electron beam in the third harmonic 3.9 GHz superconducting accelerating cavities at FLASH. After careful theoretical and experimental assessment of the HOM spectrum, three modal choices have been narrowed down to fulfill different diagnostics requirements. These are localized dipole beam-pipe modes, trapped cavity modes from the fifth dipole band and propagating modes from the first two dipole bands. These modes are treated with various data analysis techniques: modal identification, direct linear regression (DLR) and singular value decomposition (SVD). Promising options for beam diagnostics are found from all three modal choices. This constitutes the first prediction, subsequently confirmed by experiments, of trapped HOMs in third harmonic cavities, and also the first direct comparison of DLR and SVD in the analysis of HOM-based beam diagnostics.
Diallo, Souleymane; Lin, Guoping; Chembo, Yanne K
2015-08-15
In this Letter, we show that giant thermo-optical oscillations can be triggered in millimeter (mm)-size whispering gallery mode (WGM) disk resonators when they are pumped by a resonant continuous-wave laser. Our resonator is an ultrahigh-Q barium fluoride cavity that features a positive thermo-optic coefficient and a negative thermo-elastic coefficient. We demonstrate for the first time, to our knowledge, that the complex interplay between these two thermic coefficients and the intrinsic Kerr nonlinearity yields very sharp slow-fast relaxation oscillations with a slow timescale that can be exceptionally large, typically of the order of 1 s. We use a time-domain model to gain understanding into this instability, and we find that both the experimental and theoretical results are in excellent agreement. The understanding of these thermal effects is an essential requirement for every WGM-related application and our study demonstrates that even in the case of mm-size resonators, such effects can still be accurately analyzed using nonlinear time-domain models.
Lee, T.; Ouarda, T. B. M. J.
2012-02-01
Nonstationary oscillation (NSO) processes are observed in a number of hydroclimatic data series. Stochastic simulation models are useful to study the impacts of the climatic variations induced by NSO processes into hydroclimatic regimes. Reproducing NSO processes in a stochastic time series model is, however, a difficult task because of the complexity of the nonstationary behaviors. In the current study, a novel stochastic simulation technique that reproduces the NSO processes embedded in hydroclimatic data series is presented. The proposed model reproduces NSO processes by utilizing empirical mode decomposition (EMD) and nonparametric simulation techniques (i.e., k-nearest-neighbor resampling and block bootstrapping). The model was first tested with synthetic data sets from trigonometric functions and the Rössler system. The North Atlantic Oscillation (NAO) index was then examined as a real case study. This NAO index was then employed as an exogenous variable for the stochastic simulation of streamflows at the Romaine River in the province of Quebec, Canada. The results of the application to the synthetic data sets and the real-world case studies indicate that the proposed model preserves well the NSO processes along with the key statistical characteristics of the observations. It was concluded that the proposed model possesses a reasonable simulation capacity and a high potential as a stochastic model, especially for hydroclimatic data sets that embed NSO processes.
One-dimensional modelling of limit-cycle oscillation and H-mode power scaling
DEFF Research Database (Denmark)
Wu, Xingquan; Xu, Guosheng; Wan, Baonian
2015-01-01
To understand the connection between the dynamics of microscopic turbulence and the macroscale power scaling in the L-I-H transition in magnetically confined plasmas, a new time-dependent, one-dimensional (in radius) model has been developed. The model investigates the radial force balance equation...... at the edge region of the plasma and applies the quenching effect of turbulence via the E x B flow shear rate exceeding the shear suppression threshold. By slightly ramping up the heating power, the spatio-temporal evolution of turbulence intensity, density and pressure profiles, poloidal flow and E x B flow...... and the turbulence intensity depending on which oscillation of the diamagnetic flow or poloidal flow is dominant. Specifically, by including the effects of boundary conditions of density and temperature, the model results in a linear dependence of the H-mode access power on the density and magnetic field...
14.5 GHz passive harmonic mode-locking in a dispersion compensated Tm-doped fiber laser.
Wang, Yazhou; Li, Jianfeng; Mo, Kundong; Wang, Yanyan; Liu, Fei; Liu, Yong
2017-08-10
We demonstrate a high repetition rate passive harmonic mode-locking (HML) based on nonlinear polarization evolution (NPE) technique in a Tm-doped ring fiber laser cavity. Small net anomalous cavity dispersion based on dispersion compensation benefited the generation of high repetition rate HML due to the low soliton splitting threshold. Stable HML with a repetition rate of up to 14.5 GHz and a super-mode suppression (SSR) of 19 dB was obtained at the center wavelength of 1982.3 nm, which is about ten times of state of the art at 2 μm band mode-locking fiber laser to our best knowledge. The repetition rate was selectable between 1 GHz to 14.5 GHz through changing the pump power and intra-cavity polarization state, and the SSR better than 25 dB was obtained as the repetition rate less than 5 GHz.
Keatley, Paul Steven; Redjai Sani, Sohrab; Hrkac, Gino; Majid Mohseni, Seyed; Dürrenfeld, Philipp; Åkerman, Johan; Hicken, Robert James
2017-04-01
Nano-contact spin-torque vortex oscillators (STVOs) are anticipated to find application as nanoscale sources of microwave emission in future technological applications. Presently the output power and phase stability of individual STVOs are not competitive with existing oscillator technologies. Synchronisation of multiple nano-contact STVOs via magnetisation dynamics has been proposed to enhance the microwave emission. The control of device-to-device variations, such as mode splitting of the microwave emission, is essential if multiple STVOs are to be successfully synchronised. In this work a combination of electrical measurements and time-resolved scanning Kerr microscopy (TRSKM) was used to demonstrate how mode splitting in the microwave emission of STVOs was related to the magnetisation dynamics that are generated. The free-running STVO response to a DC current only was used to identify devices and bias magnetic field configurations for which single and multiple modes of microwave emission were observed. Stroboscopic Kerr images were acquired by injecting a small amplitude RF current to phase lock the free-running STVO response. The images showed that the magnetisation dynamics of a multimode device with moderate splitting could be controlled by the injected RF current so that they exhibit similar spatial character to that of a single mode. Significant splitting was found to result from a complicated equilibrium magnetic state that was observed in Kerr images as irregular spatial characteristics of the magnetisation dynamics. Such dynamics were observed far from the nano-contact and so their presence cannot be detected in electrical measurements. This work demonstrates that TRSKM is a powerful tool for the direct observation of the magnetisation dynamics generated by STVOs that exhibit complicated microwave emission. Characterisation of such dynamics outside the nano-contact perimeter permits a deeper insight into the requirements for optimal phase-locking of
Mahnke, Peter; Wirth, Martin
2010-01-01
In this paper we present the dependency of a quantitative measurement of the first-order longitudinal mode beating of an injection-seeded optical parametric oscillator (OPO) on its injection-seeding state. We show the correlation of the intensity of the first-order longitudinal mode beating and the side-mode suppression of an injection-seeded OPO. We further demonstrate that the mode-beating intensity can be used as an indicator for the spectral purity of an injection-seeded OPO.
Bennett, Charles L.; Sewall, Noel; Boroa, Carl
2014-08-19
An engine based on a reciprocating piston engine that extracts work from pressurized working fluid. The engine includes a harmonic oscillator inlet valve capable of oscillating at a resonant frequency for controlling the flow of working fluid into of the engine. In particular, the inlet valve includes an inlet valve head and a spring arranged together as a harmonic oscillator so that the inlet valve head is moveable from an unbiased equilibrium position to a biased closed position occluding an inlet. Upon releasing the inlet valve the inlet valve head undergoes a single oscillation past the equilibrium positio to a maximum open position and returns to a biased return position close to the closed position to choke the flow and produce a pressure drop across the inlet valve causing the inlet valve to close. Protrusions carried either by the inlet valve head or piston head are used to bump open the inlet valve from the closed position and initiate the single oscillation of the inlet valve head, and protrusions carried either by the outlet valve head or piston head are used to close the outlet valve ahead of the bump opening of the inlet valve.
Naturally Phase-Matched Second-Harmonic Generation in a Whispering-Gallery-Mode Resonator
DEFF Research Database (Denmark)
Fürst, J. U.; Strekalov, D.V.; Elser, D.
2010-01-01
We demonstrate for the first time natural phase matching for optical frequency doubling in a high-Q whispering-gallery-mode resonator made of lithium niobate. A conversion efficiency of 9% is achieved at 30 μW in-coupled continuous wave pump power. The observed saturation pump power of 3.2 m...
Harmonic expressions for the eigen mode fields of step and graded index fibers
Energy Technology Data Exchange (ETDEWEB)
Guo Fuyuan; Li Lianhuang; Zheng Hua; Wang Yi; Dai Tiangui; Ke Jinrui, E-mail: guofy@fjnu.edu.cn [Key Laboratory of Optoelectronic Science and Technology for Medicine of Ministry of Education, Fujian Provincial Key Laboratory of Photonic Technology, Institute of Laser and Optoelectronics Technology, Fujian Normal University, 32 Shangsan Road, Cangshan, Fuzhou 350007 (China)
2011-02-01
For clarifying the mode field characteristics of step and graded index fibers, the Helmholtz's equation and local planar wave approximation are engaged, a novel idea that the eigenfunction of the traveling wave field in radial grade index dielectric is similar to positive or negative half order Hankel function is advanced. Then, the eigenfunction of core layer of graded index fiber is similar to the combination of half order Bessel function and half order Neumann function, the eigenfunction of cladding layer of graded index fiber is similar to the first kind half order imaginary parameter Hankel function, are suggested. The phase shift for total reflection effect at the turning point of grade fiber is proposed. The angular phase shift pi for the ray propagating along the fiber circumference is given. The eigen equation of new improved WKB method for analysing the mode field characteristics of graded index fiber is presented. Moreover, the eigen equation of new improved WKB method for analyzing the mode field characteristics of graded index fiber is held good for analysing the mode field characteristics of step index fiber too, it indicates that, the eigen equation of new improved WKB method is of universal significance.
High-power 200 fs Kerr-lens mode-locked Yb:YAG thin-disk oscillator.
Pronin, O; Brons, J; Grasse, C; Pervak, V; Boehm, G; Amann, M-C; Kalashnikov, V L; Apolonski, A; Krausz, F
2011-12-15
We demonstrate a power-scalable Kerr-lens mode-locked Yb:YAG thin-disk oscillator. It delivers 200 fs pulses at an average power of 17 W and a repetition rate of 40 MHz. At an increased (180 W) pump power level, the laser produces 270 fs 1.1 μJ pulses at an average power of 45 W (optical-to-optical efficiency of 25%). Semiconductor-saturable-absorber-mirror-assisted Kerr-lens mode locking (KLM) and pure KLM with a hard aperture show similar performance. To our knowledge, these are the shortest pulses achieved from a mode-locked Yb:YAG disk oscillator and this is the first demonstration of a Kerr-lens mode-locked thin-disk laser.
Bennett, Charles L [Livermore, CA
2009-10-20
A high efficiency harmonic engine based on a resonantly reciprocating piston expander that extracts work from heat and pressurizes working fluid in a reciprocating piston compressor. The engine preferably includes harmonic oscillator valves capable of oscillating at a resonant frequency for controlling the flow of working fluid into and out of the expander, and also preferably includes a shunt line connecting an expansion chamber of the expander to a buffer chamber of the expander for minimizing pressure variations in the fluidic circuit of the engine. The engine is especially designed to operate with very high temperature input to the expander and very low temperature input to the compressor, to produce very high thermal conversion efficiency.
Directory of Open Access Journals (Sweden)
Yuanjin Pan
2015-10-01
Full Text Available Modeling nonlinear vertical components of a GPS time series is critical to separating sources contributing to mass displacements. Improved vertical precision in GPS positioning at stations for velocity fields is key to resolving the mechanism of certain geophysical phenomena. In this paper, we use ensemble empirical mode decomposition (EEMD to analyze the daily GPS time series at 89 continuous GPS stations, spanning from 2002 to 2013. EEMD decomposes a GPS time series into different intrinsic mode functions (IMFs, which are used to identify different kinds of signals and secular terms. Our study suggests that the GPS records contain not only the well-known signals (such as semi-annual and annual signals but also the seldom-noted quasi-biennial oscillations (QBS. The quasi-biennial signals are explained by modeled loadings of atmosphere, non-tidal and hydrology that deform the surface around the GPS stations. In addition, the loadings derived from GRACE gravity changes are also consistent with the quasi-biennial deformations derived from the GPS observations. By removing the modeled components, the weighted root-mean-square (WRMS variation of the GPS time series is reduced by 7.1% to 42.3%, and especially, after removing the seasonal and QBO signals, the average improvement percentages for seasonal and QBO signals are 25.6% and 7.5%, respectively, suggesting that it is significant to consider the QBS signals in the GPS records to improve the observed vertical deformations.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Peng; Zhou, Ning; Abdollahi, Ali
2013-09-10
A Generalized Subspace-Least Mean Square (GSLMS) method is presented for accurate and robust estimation of oscillation modes from exponentially damped power system signals. The method is based on orthogonality of signal and noise eigenvectors of the signal autocorrelation matrix. Performance of the proposed method is evaluated using Monte Carlo simulation and compared with Prony method. Test results show that the GSLMS is highly resilient to noise and significantly dominates Prony method in tracking power system modes under noisy environments.
Chillara, Vamshi Krishna; Lissenden, Cliff J
2013-04-01
Theoretical formulation for the problem of second harmonic guided waves in pipes is presented from the principles of continuum mechanics. The formulation is carried out in the reference configuration of the pipe with an emphasis on the correct use of the "Divergence" operator in the reference configuration. Second harmonic guided wave generation from axis-symmetric longitudinal guided wave modes is studied. A large radius asymptotic approximation for the wave structures in pipe is studied and an error estimate for the same is obtained. Comparison with the corresponding modes in a plate and the analogy to second harmonic guided wave generation in plates is presented. Copyright © 2012 Elsevier B.V. All rights reserved.
Zhang, P; Baboi, Nicoleta
2012-01-01
Higher order modes (HOM) are electromagnetic resonant fields. They can be excited by an electron beam entering an accelerating cavity, and constitute a component of the wakefield. This wakefield has the potential to dilute the beam quality and, in the worst case, result in a beam-break-up instability. It is therefore important to ensure that these fields are well suppressed by extracting energy through special couplers. In addition, the effect of the transverse wakefield can be reduced by aligning the beam on the cavity axis. This is due to their strength depending on the transverse offset of the excitation beam. For suitably small offsets the dominant components of the transverse wakefield are dipole modes, with a linear dependence on the transverse offset of the excitation bunch. This fact enables the transverse beam position inside the cavity to be determined by measuring the dipole modes extracted from the couplers, similar to a cavity beam position monitor (BPM), but requires no additional vacuum instrum...
Zhang, Liwei; Zhang, Yewen; Yang, Yaping; Chen, Hong
2011-04-01
A special cavity based on effective near-zero-index paired structures containing ɛ-negative and μ-negative materials is realized by using composite right- or left-handed transmission lines. When an artificial magnetic "atom" is put into the cavity, unusual Rabi-type splitting appears because of the strong coupling between the artificial atom and the localized tunneling mode. The direct time domain energy exchanges between the cavity and the "atom" are experimentally observed after excited by a short pulse signal. Within the "atom" field attenuation time, more than one oscillations appear. Rabi-type splitting and the Rabi-type oscillation period are invariant with the scaling changes of the length but vary with the positions where the "atom" is put with different field intensity. Moreover, the decay time of Rabi-type oscillation becomes longer when the tunneling mode possesses smaller linewidth, which is in good agreement with numerical simulations.
Directory of Open Access Journals (Sweden)
Cheng Liu
2017-05-01
Full Text Available In this paper, a novel nonlinear robust damping controller is proposed to suppress power oscillation in interconnected power systems. The proposed power oscillation damping controller exhibits good nonlinearity and robustness. It can consider the strong nonlinearity of power oscillation and uncertainty of its model. First, through differential homeomorphic mapping, a mathematical model of the system can be transformed into the Brunovsky standard. Next, an extended state observer (ESO estimated and compensated for model errors and external disturbances as well as uncertain factors to achieve dynamic linearization of the nonlinear model. A power oscillation damping controller for interconnected power systems was designed on a backstepping-fractional order sliding mode variable structure control theory (BFSMC. Compared with traditional methods, the controller exhibits good dynamic performance and strong robustness. Simulations involving a four-generator two-area and partial test system of Northeast China were conducted under various disturbances to prove the effectiveness and robustness of the proposed damping control method.
Kuo, Paulina S; Bravo-Abad, Jorge; Solomon, Glenn S
2014-01-01
The 4 crystal symmetry in materials such as GaAs can enable quasi-phasematching for efficient optical frequency conversion without poling, twinning or other engineered domain inversions. 4 symmetry means that a 90° rotation is equivalent to a crystallographic inversion. Therefore, when light circulates about the 4 axis, as in GaAs whispering-gallery-mode microdisks, it encounters effective domain inversions that can produce quasi-phasematching. Microdisk resonators also offer resonant field enhancement, resulting in highly efficient frequency conversion in micrometre-scale volumes. These devices can be integrated in photonic circuits as compact frequency convertors, sources of radiation or entangled photons. Here we present the first experimental observation of second-harmonic generation in a whispering-gallery-mode microcavity utilizing -quasi-phasematching. We use a tapered fibre to couple into the 5-μm diameter microdisk resonator, resulting in a normalized conversion efficiency η≈5 × 10(-5)mW(-1). Simulations indicate that when accounting for fibre-cavity scattering, the normalized conversion efficiency is η≈3 × 10(-3)mW(-1).
Second-harmonic generation using -quasi-phasematching in a GaAs whispering-gallery-mode microcavity
Kuo, Paulina S.; Bravo-Abad, Jorge; Solomon, Glenn S.
2014-01-01
The crystal symmetry in materials such as GaAs can enable quasi-phasematching for efficient optical frequency conversion without poling, twinning or other engineered domain inversions. symmetry means that a 90° rotation is equivalent to a crystallographic inversion. Therefore, when light circulates about the axis, as in GaAs whispering-gallery-mode microdisks, it encounters effective domain inversions that can produce quasi-phasematching. Microdisk resonators also offer resonant field enhancement, resulting in highly efficient frequency conversion in micrometre-scale volumes. These devices can be integrated in photonic circuits as compact frequency convertors, sources of radiation or entangled photons. Here we present the first experimental observation of second-harmonic generation in a whispering-gallery-mode microcavity utilizing -quasi-phasematching. We use a tapered fibre to couple into the 5-μm diameter microdisk resonator, resulting in a normalized conversion efficiency η≈5 × 10−5 mW−1. Simulations indicate that when accounting for fibre-cavity scattering, the normalized conversion efficiency is η≈3 × 10−3 mW−1. PMID:24434576
Directory of Open Access Journals (Sweden)
V. I. Milykh
2013-12-01
Full Text Available The method of calculation of the magnetic field alternating component at the surface of the rotating rotor of turbo generator is presented. It is based on multiposition of the numerical calculations of the magnetic field with the rotor turns and changes of currents in the stator winding. Discrete time functions of the alternating component of the magnetic induction are selected in points of the surface . The harmonic analysis is conducted for them. The developed method is universal in terms of excitation modes, designs and the magnetic core saturation. The theory is confirmed by computational researches in the no-load and short circuit modes of large turbo generator. In it, the alternating component of the magnetic induction on the rotor surface in the short-circuit mode is much greater than in the no-load mode. Values and harmonic composition of the alternating component of the magnetic induction differ substantially at different points of the rotor surface. Harmonics are ponderable in the range from the level determined by the phase structure of stator winding to the level determined by the tooth structure of its core. The results obtained are qualitatively fit into the classical notion of oscillatory processes of the magnetic field on the rotor surface, but now the value and harmonic composition of the alternating component of the magnetic induction receive adequate numerical filling. The result of work can be used for designing of a turbogenerators and other synchronous machines.
Upadhyay, Ranjit Kumar; Mondal, Argha; Teka, Wondimu W.
The modified three-dimensional (3D) Morris-Lecar (M-L) model is very useful to understand the spiking activities of neurons. The present article addresses the random dynamical behavior of a modified M-L model driven by a white Gaussian noise with mean zero and unit spectral density. The applied stimulus can be expressed as a random term. Such random perturbations are represented by a white Gaussian noise current added through the electrical potential of membrane of the excitatory principal cells. The properties of the stochastic system (perturbed one) and noise induced mixed mode oscillation are analyzed. The Lyapunov spectrum is computed to present the nature of the system dynamics. The noise intensity is varied while keeping fixed the predominant parameters of the model in their ranges and also observed the changes in the dynamical behavior of the system. The dynamical synchronization is studied in the coupled M-L systems interconnected by excitatory and inhibitory neurons with noisy electrical coupling and verified with similarity functions. This result suggests the potential benefits of noise and noise induced oscillations which have been observed in real neurons and how that affects the dynamics of the neural model as well as the coupled systems. The analysis reports that the modified M-L system which has the limit cycle behavior can show a type of phase locking behavior which follows either period adding (i.e. 1:1, 2:1, 3:1, 4:1) sequences or Farey sequences. For the coupled neural systems, complete synchronization is shown for sufficient noisy coupling strength.
A generalized tool for accurate time-domain separation of excited modes in spin-torque oscillators
Energy Technology Data Exchange (ETDEWEB)
Siracusano, Giulio, E-mail: giuliosiracusano@gmail.com; Puliafito, Vito; Finocchio, Giovanni [Department of Electronic Engineering, Industrial Chemistry and Engineering, University of Messina, C.da Di Dio s/n, 98166 Messina (Italy); La Corte, Aurelio [Department of Informatic Engineering and Telecommunications, University of Catania, Viale Andrea Doria 6, 95125 Catania (Italy)
2014-05-07
We propose and develop an advanced signal processing technique that, combined with micromagnetic simulations, is able to deeply describe the non-stationary behavior of spin-torque oscillators, both in terms of time domain and spatial distribution of the magnetization dynamics. The Hilbert-Huang Transform is used for the identification of the time traces of each oscillation in a multimode excitation and enhanced with masking signals and the Ensemble Empirical Mode Decomposition. We emphasize that the technique developed here is general and can be used for any physical non-linear system in the presence of multimode dynamical excitation or intermittence.
Piezoelectric nonlinear vibration focusing on the second-harmonic vibration mode.
Ozaki, Ryohei; Liu, Yaoyang; Hosaka, Hiroshi; Morita, Takeshi
2018-01-01
Resonant piezoelectric devices are driven under high power condition. In such condition, a nonlinear piezoelectric vibration becomes apparent and this nonlinearity should be taken into account in the design procedure using the finite elemental method (FEM). The purpose of this study is to introduce the nonlinear parameter to the FEM and to establish the method for measuring the nonlinear parameter through evaluating a nonlinear model for a piezoelectric vibration. In a previous study about the nonlinear piezoelectric vibration, the third term was mainly focused on because the third mode vibration affects the fundamental vibration in the case of a simple bar-type transducer. On the other hand, we considered the second nonlinear parameter of the compliance to the piezoelectric constitutive equation. We observed that this parameter affects the vibration amplitude with each position and the velocity at the tip of the transducer with a double frequency at resonant. It was confirmed that two measured nonlinear parameters based on these two relationships were almost same. From these values, we concluded that the proposed model is reasonable. Copyright © 2017. Published by Elsevier B.V.
Zong, Weikai; Charpinet, Stéphane; Fu, Jian-Ning; Vauclair, Gérard; Niu, Jia-Shu; Su, Jie
2018-02-01
We present the first results of an ensemble and systematic survey of oscillation mode variability in pulsating hot B subdwarf (sdB) and white dwarf stars observed with the original Kepler mission. The satellite provides uninterrupted high-quality photometric data with a time baseline that can reach up to 4 yr collected on pulsating stars. This is a unique opportunity to characterize long-term behaviors of oscillation modes. A mode modulation in amplitude and frequency can be independently inferred by its fine structure in the Fourier spectrum, from the sLSP, or with prewhitening methods applied to various parts of the light curve. We apply all these techniques to the sdB star KIC 3527751, a long-period-dominated hybrid pulsator. We find that all the detected modes with sufficiently large amplitudes to be thoroughly studied show amplitude and/or frequency variations. Components of three identified quintuplets around 92, 114, and 253 μHz show signatures that can be linked to nonlinear interactions according to the resonant mode coupling theory. This interpretation is further supported by the fact that many oscillation modes are found to have amplitudes and frequencies showing correlated or anticorrelated variations, a behavior that can be linked to the amplitude equation formalism, where nonlinear frequency corrections are determined by their amplitude variations. Our results suggest that oscillation modes varying with diverse patterns are a very common phenomenon in pulsating sdB stars. Close structures around main frequencies therefore need to be carefully interpreted in light of this finding to secure a robust identification of real eigenfrequencies, which is crucial for seismic modeling. The various modulation patterns uncovered should encourage further developments in the field of nonlinear stellar oscillation theory. It also raises a warning to any long-term project aiming at measuring the rate of period change of pulsations caused by stellar evolution, or at
An Application of the Harmonic Oscillator Model to Verify Dunning’s Theory of the Economic Growth
Marcin Salamaga
2013-01-01
Analogies with mechanisms ruling the natural world have oft en been sought in the course of economic phenomena.Th is paper is also an attempt to combine the physical phenomenon of a harmonious oscillator withthe theory of economic growth by J. H. Dunning (1981). In his theory, Dunning distinguished stages of economicgrowth of countries that imply the dependency between the investment position of countries and theirGDP per capita, while the graph presenting this dependency reminds a trajectory...
Scafetta, Nicola
2013-01-01
Power spectra of global surface temperature (GST) records reveal major periodicities at about 9.1, 10-11, 19-22 and 59-62 years. The Coupled Model Intercomparison Project 5 (CMIP5) general circulation models (GCMs), to be used in the IPCC (2013), are analyzed and found not able to reconstruct this variability. From 2000 to 2013.5 a GST plateau is observed while the GCMs predicted a warming rate of about 2 K/century. In contrast, the hypothesis that the climate is regulated by specific natural oscillations more accurately fits the GST records at multiple time scales. The climate sensitivity to CO2 doubling should be reduced by half, e.g. from the IPCC-2007 2.0-4.5 K range to 1.0-2.3 K with 1.5 C median. Also modern paleoclimatic temperature reconstructions yield the same conclusion. The observed natural oscillations could be driven by astronomical forcings. Herein I propose a semi empirical climate model made of six specific astronomical oscillations as constructors of the natural climate variability spanning ...
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.
About the selection of transverse modes in the X-band oversized oscillator with 2.5 GW output power
Tsygankov, R. V.; Rostov, V. V.; Gunin, A. V.; Elchaninov, A. A.; Markov, A. B.; Ozur, G. E.
2017-05-01
The paper describes the numerical and experimental results of the microwave O-type oscillator based on an oversized slow wave structure (SWS). The feedback is applied to the design scheme, which provides intense modulation of the electron beam in the cathode-anode region and two special cavities before SWS. The selectivity of TM02 operating mode occurs due to increased diffraction loss of parasitic modes in the cathode part. The slow wave structure consists of two identical sections with the phase-shifting region in between. The use of this configuration leads to the formation of a locked TM01 wave, having good conditions for the transformation into the working mode TM02. In the experiments, a stable generation regime with pure TM02 mode at a frequency of 10 GHz with an efficiency of about 30% and the output power of 2.5 GW in the magnetic field below the cyclotron resonance was obtained.
Mancilla-Almonacid, D.; Arias, R. E.
2017-06-01
The excitation of the linear spin wave modes of a soft ferromagnetic free layer of a nanopillar structure through dc-ac currents that traverse the structure is studied, as well as with ac magnetic fields. There is interest in understanding the magnetization dynamics in these structures since they may be used as microwave sources when these nano-oscillators enter into auto-oscillatory regimes. The free layer is a soft ferromagnet, like Permalloy, in the shape of a circular disk, with a very small thickness in the range of the exchange length. Using a description of the magnetization dynamics in terms of a Hamiltonian for weakly interacting waves, we determine the spin wave modes of the structure under two approximations: a very thin film limit, and under a model that includes the effect of the full magnetostatic interaction. We consider direct and parametric excitations of different spin wave modes with ac currents, i.e., with exciting frequency approximately equal to the frequency of the mode or to twice its value, respectively. The Oersted field mainly plays a role in the direct resonant excitation of the modes. Our main conclusion is that for a dc current below the critical value necessary for the development of auto-oscillations, using parametric excitation, a very high value of the ac current is necessary to reach the auto-oscillatory behavior in this geometry. However, if the out-of-plane component of the spin transfer torque is high enough, the ac critical current for auto-oscillations is significantly reduced, leading to a signature for its detection. We comment on parallel pumping and transverse excitation using ac magnetic fields.
Giovan, Stefan M; Hanke, Andreas; Levene, Stephen D
2015-09-01
For much of the last three decades, Monte Carlo-simulation methods have been the standard approach for accurately calculating the cyclization probability, J, or J factor, for DNA models having sequence-dependent bends or inhomogeneous bending flexibility. Within the last 10 years approaches based on harmonic analysis of semi-flexible polymer models have been introduced, which offer much greater computational efficiency than Monte Carlo techniques. These methods consider the ensemble of molecular conformations in terms of harmonic fluctuations about a well-defined elastic-energy minimum. However, the harmonic approximation is only applicable for small systems, because the accessible conformation space of larger systems is increasingly dominated by anharmonic contributions. In the case of computed values of the J factor, deviations of the harmonic approximation from the exact value of J as a function of DNA length have not been characterized. Using a recent, numerically exact method that accounts for both anharmonic and harmonic contributions to J for wormlike chains of arbitrary size, we report here the apparent error that results from neglecting anharmonic behavior. For wormlike chains having contour lengths less than four times the persistence length, the error in J arising from the harmonic approximation is generally small, amounting to free energies less than the thermal energy, kB T. For larger systems, however, the deviations between harmonic and exact J values increase approximately linearly with size. © 2015 Wiley Periodicals, Inc.
Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators
Arroyo, Sebastián I
2014-01-01
We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, disclose new effects of nonlinearities on oscillating systems. First, we study the stability of periodic motion when the phase shift between the external force and the oscillation is controlled -contrary to the standard case, where the control parameter is the frequency of the force. Phase-shift control is the operational configuration under which self-sustained oscillators -and, in particular, micromechanical oscillators- provide a frequency reference useful for time keeping. We show that, contrary to the standard forced Duffing oscillator, under phase-shift control oscillations are stable over the whole resonance curve. Second, we analyze a model for the internal resonance between the main Duffing oscillation mode and a higher-harmonic mode of a vibrating solid bar clamped at its two ends. We focus on the stabilization of the oscillation frequency whe...
Energy Technology Data Exchange (ETDEWEB)
Ibarra-Sierra, V.G.; Sandoval-Santana, J.C. [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México D.F. (Mexico); Cardoso, J.L. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Kunold, A., E-mail: akb@correo.azc.uam.mx [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico)
2015-11-15
We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a
Oscillations in g-mode period spacings in red giants as a way to determine their state of evolution
Directory of Open Access Journals (Sweden)
Cunha M. S.
2015-01-01
Full Text Available In this work we consider the sensitivity of gravity-mode period spacings to sharp changes in the inner structure of red giant stars, more specifically in the buoyancy frequency inside the g-mode propagation cavity. Based on a comparison between the solutions to the linear pulsation equations in the Cowling approximation for pure g-modes with results obtained with a full oscillation code we identify and correctly interpret the signature of the above-mentioned sharp variations in the period spacings. Two examples, of red giant models in different evolutionary phases, are discussed. Detection of these signatures in CoRoT, Kepler or future PLATO red-giant stars would pin down their evolutionary state in an unprecedented way.
Coherent harmonic production using a two-section undulator FEL
Energy Technology Data Exchange (ETDEWEB)
Jaroszynski, D.A. [Commissariat a l`Energie, Bruyeres-le-Chatel (France); Prazeres, R.; Glotin, F. [Centre Universitaire Paris-Sud (France)] [and others
1995-12-31
We present measurements and a theoretical analysis of a new method of generating harmonic radiation in a free-electron laser oscillator with a two section undulator in a single optical cavity. To produce coherent harmonic radiation the undulator is arranged so that the downstream undulator section resonance frequency matches a harmonic of the upstream undulator. Both the fundamental and the harmonic optical fields evolve in the same optical cavity and are coupled out with different extraction fractions using a hole in one of the cavity mirrors. We present measurements that show that the optical power at the second and third harmonic can be enhanced by more than an order of magnitude in this fundamental/harmonic configuration. We compare the production of harmonic radiation of a two sectioned fundamental/harmonic undulator with that produced from a FEL operating at its highest efficiency with a step-tapered undulator, where the bunching at the end of the first section is very large. We examine, the dependence of the harmonic power on the intracavity power by adjusting the optical cavity desynchronism, {delta}L. We also examine the evolution of the fundamental and harmonic powers as a function of cavity roundtrip number to evaluate the importance of the small signal gain at the harmonic. We compare our measurements with predictions of a multi-electron numerical model that follows the evolution of fundamental and harmonic power to saturation. This fundamental/harmonic mode, of operation of the FEL may have useful applications in the production of coherent X-ray and VUV radiation, a spectral range where high reflectivity optical cavity mirrors are difficult or impossible to manufacture.
Propagator for a spin-Bose system with the Bose field coupled to a reservoir of harmonic oscillators
Banerjee, S
2003-01-01
We consider the general problem of a single two-level atom interacting with a multimode radiation field (without the rotating-wave approximation), and additionally take the field to be coupled to a thermal reservoir. Using the method of bosonization of the spin operators in the Hamiltonian, and working in the Bargmann representation for all the boson operators, we obtain the propagator for the composite system using the techniques of functional integration, under a reasonable approximation scheme. The propagator is explicitly evaluated for a simplified version of the system with one spin and a dynamically coupled single-mode field. The results are also checked on the known problem of quantum Brownian motion.
Directory of Open Access Journals (Sweden)
Chebabhi Ali
2015-01-01
Full Text Available In this paper, the four leg inverter controlled by the three dimensional space vector modulation (3D SVM is used as the shunt active power filter (SAPF for compensating the three phase four wire electrical network, by using the four leg inverter with 3D SVM advantages to eliminated zero sequence current, fixed switching frequency of inverter switches, and reduced switching losses. This four leg inverter is employed as shunt active power filter to minimizing harmonic currents, reducing magnitude of neutral wire current, eliminating zero sequence current caused by nonlinear single phase loads and compensating reactive power, and a nonlinear sliding mode control technique (SMC is proposed for harmonic currents and DC bus voltage control to improve the performances of the three phase four wire four leg shunt active power filter based on Synchronous Reference Frame (SRF theory in the dq0 axes, and to decoupling the four leg SAPF mathematical model.
Wang, C Y; Baldeck, P L; Budansky, Y; Alfano, R R
1989-05-15
15-THz trains of a few-tens-of-femtoseconds optical pulses were generated by modulation instability oscillation in a colliding-pulse mode-locked dye laser. A repeatable and stable modulation instability regime was obtained with the laser operating in the anomalous-dispersion regime and with a low saturable-absorber concentration. Autocorrelation measurements indicate that subpulses were completely separated in real time. Variations of the modulation with the pump power and the amount of dispersion in the cavity are in good agreement with modulation instability theory.
Booster Double Harmonic Setup Notes
Energy Technology Data Exchange (ETDEWEB)
Gardner, C. J. [Brookhaven National Lab. (BNL), Upton, NY (United States). Collider-Accelerator Dept.
2015-02-17
The motivation behind implementing a booster double harmonic include the reduced transverse space charge force from a reduced peak beam current and reduced momentum spread of the beam, both of which can be achieved from flattening the RF bucket. RF capture and acceleration of polarized protons (PP) is first set up in the single harmonic mode with RF harmonic h=1. Once capture and acceleration have been set up in the single harmonic mode, the second harmonic system is brought on and programmed to operate in concert with the single harmonic system.
Bisson, Scott E.; Armstrong, Karla M.; Kulp, Thomas J.; Hartings, Matthew
2001-11-01
We describe a broadly tunable, cw optical parametric oscillator (OPO) based on periodically poled lithium niobate. The OPO can be tuned over a broad region in the mid IR (2900 -3100 cm-1 ) covering the important C -H stretch region while a high spectral resolution ( volatile organic compounds.
Geodesic acoustic mode (GAM) like oscillations and RMP effect in the STOR-M tokamak
Basu, Debjyoti; Nakajima, Masaru; Melnikov, A. V.; McColl, David; Rohollahi, Akbar; Elgriw, Sayf; Xiao, Chijin; Hirose, Akira
2018-02-01
A new kind of quasi-coherent mode was observed in ohmic plasma in the STOR-M tokamak. It is featured with a clear solitary peak around 30–35 kHz in the power spectra of the ion saturation current (I_sat) of Langmuir probe as well as poloidal and toroidal mode numbers (m = 1,n = 0) as per the prediction of conventional geodesic acoustic mode (GAM) theory. The dispersion relation of the mode is also similar to GAM and it also shows collisional damping. In contrast to conventional GAM, the floating potential ϕ of the observed GAM-like mode does not show similar symmetric poloidal and toroidal mode numbers (m = 0,n = 0), but has (m = 1,n = 1). The GAM-like mode has also a pronounced magnetic component with mixed poloidal modes (m=3~and~m=5; n=1 ), as observed by Mirnov coils. This mode is suppressed by the application of resonance magnetic perturbations.
DEFF Research Database (Denmark)
Verhoef, A. J.; Zhu, L.; Israelsen, Stine Møller
2015-01-01
We present an Yb-fiber oscillator with an all-polarizationmaintaining cavity with a higher-order-mode fiber for dispersion compensation. The polarization maintaining higher order mode fiber introduces not only negative second order dispersion but also negative third order dispersion in the cavity...
Megalingam, Mariammal; Hari Prakash, N.; Solomon, Infant; Sarma, Arun; Sarma, Bornali
2017-04-01
Experimental evidence of different kinds of oscillations in floating potential fluctuations of glow discharge magnetized plasma is being reported. A spherical gridded cage is inserted into the ambient plasma volume for creating plasma bubbles. Plasma is produced between a spherical mesh grid and chamber. The spherical mesh grid of 80% optical transparency is connected to the positive terminal of power supply and considered as anode. Two Langmuir probes are kept in the ambient plasma to measure the floating potential fluctuations in different positions within the system, viz., inside and outside the spherical mesh grid. At certain conditions of discharge voltage (Vd) and magnetic field, irregular to regular mode appears, and it shows chronological changes with respect to magnetic field. Further various nonlinear analyses such as Recurrence Plot, Hurst exponent, and Lyapunov exponent have been carried out to investigate the dynamics of oscillation at a range of discharge voltages and external magnetic fields. Determinism, entropy, and Lmax are important measures of Recurrence Quantification Analysis which indicate an irregular to regular transition in the dynamics of the fluctuations. Furthermore, behavior of the plasma oscillation is characterized by the technique called multifractal detrended fluctuation analysis to explore the nature of the fluctuations. It reveals that it has a multifractal nature and behaves as a long range correlated process.
Controlled excitation of resonance self-oscillations in one-dimensional distributed systems
Izrailovich, M. Ya.
2004-03-01
On the basis of the method of equivalent linearization combined with the method of moments, laws of self-oscillation excitation are obtained that provide the modes with maximum intensity of resonance (or quasi-resonance) oscillations in one-dimensional systems with distributed parameters. A restriction of a general type is imposed on the law of excitation. In the particular case of an integral quadratic restriction, the law of excitation leads to the generation of purely harmonic self-oscillations. The use of an extended (multiplicatively stabilizing) control provides the uniqueness and stability of the quasi-optimal mode of self-oscillation.
Tanimura, Y; Steffen, T
2000-01-01
The relaxation processes in a quantum system nonlinearly coupled to a harmonic Gaussian-Markovian heat bath are investigated by the quantum Fokker-Planck equation in the hierarchy form. This model describes frequency fluctuations in the quantum system with an arbitrary correlation time and thus
Bachelard, Nicolas; Sebbah, Patrick; Vanneste, Christian
2014-01-01
We use time-domain numerical simulations of a two-dimensional (2D) scattering system to study the interaction of a collection of emitters resonantly coupled to an Anderson-localized mode. For a small electric field intensity, we observe the strong coupling between the emitters and the mode, which is characterized by linear Rabi oscillations. Remarkably, a larger intensity induces non-linear interaction between the emitters and the mode, referred to as the dynamical Stark effect, resulting in non-linear Rabi oscillations. The transition between both regimes is observed and an analytical model is proposed which accurately describes our numerical observations.
Blanco, Esteban
2016-01-01
A superconducting 800 MHz second harmonic RF system is one of the considered options as a Landau damping mechanism for HiLumi LHC. The Higher Order Mode (HOM) coupler designs require tight manufacturing tolerances in order to operate at the design specifications. The project consists of defining the mechanical tolerances for the different components of both the probe-type and hook-type HOM coupler. With the use of electromagnetic field simulation software it is possible to identify the critical components of the HOM coupler and to quantify their respective tolerances. The obtained results are discussed in this paper.
A Multi-Site Campaign to Measure Solar-Like Oscillations in Procyon. II. Mode Frequencies
DEFF Research Database (Denmark)
Bedding, Timothy R.; Kjeldsen, Hans; Campante, Tiago L.
2010-01-01
We have analyzed data from a multi-site campaign to observe oscillations in the F5 star Procyon. The data consist of high-precision velocities that we obtained over more than three weeks with 11 telescopes. A new method for adjusting the data weights allows us to suppress the sidelobes in the p...... We have analyzed data from a multi-site campaign to observe oscillations in the F5 star Procyon. The data consist of high-precision velocities that we obtained over more than three weeks with 11 telescopes. A new method for adjusting the data weights allows us to suppress the sidelobes...... with mixed character. We show that the frequencies of the ridge centroids and their separations are useful diagnostics for asteroseismology. In particular, variations in the large separation appear to indicate a glitch in the sound-speed profile at an acoustic depth of similar to 1000 s. We list frequencies...
Self-oscillating mode for frequency modulation noncontact atomic force microscopy
Giessibl, Franz J.; Tortonese, Marco
1997-01-01
Frequency modulation atomic force microscopy (FM-AFM) has made imaging of surfaces in ultrahigh vacuum with atomic resolution possible. Here, we demonstrate a new approach which simplifies the implementation of FM-AFM considerably and enhances force sensitivity by directly exciting the cantilever with the thermal effects involved in the deflection measurement process. This approach reduces the mechanically oscillating mass by 6 to 8 orders of magnitude as compared to conventional FM-AFM, beca...
Mixed-mode oscillations in a three-store calcium dynamics model
Liu, Peng; Liu, Xijun; Yu, Pei
2017-11-01
Calcium ions are important in cell process, which control cell functions. Many models on calcium oscillation have been proposed. Most of existing literature analyzed calcium oscillations using numerical methods, and found rich dynamical behaviours. In this paper, we explore a further study on an established three-store model, which contains endoplasmic reticulum (ER), mitochondria and calcium binding proteins. We conduct bifurcation analysis to identify two Hopf bifurcations, and apply normal form theory to study their stability and show that one of them is supercritical while the other is subcritical. Further, we transform the model into a slow-fast system, and then apply the geometrical singular perturbation theory to investigate the mechanism of generating slow-fast motions. The study reveals that the mechanism of generating the slow-fast oscillating behaviour in the three-store calcium model for certain parameter values is due to the relative fast change in the free calcium in cytosol, and relative slow changes in the free calcium in mitochondria and in the bounded Ca2+ binding sites on the cytosolic proteins. A further parametric study may provide some useful information for controlling harmful effect, by adjusting the amount of calcium in a human body. Numerical simulations are present to demonstrate the correct analytical predictions.
Distinguishing newly born strange stars from neutron stars with g-mode oscillations.
Fu, Wei-Jie; Wei, Hai-Qing; Liu, Yu-Xin
2008-10-31
The gravity-mode (g-mode) eigenfrequencies of newly born strange quark stars (SQSs) and neutron stars (NSs) are studied. It is found that the eigenfrequencies in SQSs are much lower than those in NSs by almost 1 order of magnitude, since the components of a SQS are all extremely relativistic particles while nucleons in a NS are nonrelativistic. We therefore propose that newly born SQSs can be distinguished from the NSs by detecting the eigenfrequencies of the g-mode pulsations of supernovae cores through gravitational radiation by LIGO-class detectors.
Energy Technology Data Exchange (ETDEWEB)
Breitzke, M.
1990-02-09
A normal mode summation process and a frequency harmonic process for the modelling, recomposition and migration of dispersive seismic surveys. The use of underground seismic surveys to locate seams and to position small techtonic or atechtonic faults predominantly used in coal mining requires, because of the dispersive seismic waves, special computer processing. This work is concerned with two such techniques. The first is a normal mode summation process for modelling and recompression, this means the time-dependent deconvolution of dispersive waves from underground transmission data with any number of superimposed modes. The second is a recursive frequency harmonics migration process for dispersive waves from underground reflexion data. (orig.).
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
Canards and mixed-mode oscillations in a forest pest model
DEFF Research Database (Denmark)
Brøns, Morten; Kaasen, Rune
2010-01-01
We consider a three-variable forest pest model, proposed by Rinaldi & Muratori (1992) [Rinaldi, S., Muratori, S., 1992. Limit cycles in slow-fast forest-pest models. Theor. Popul. Biol. 41,26-43]. The model allows relaxation oscillations where long pest-free periods are interspersed with outbreak...... of the model, and is expected to be applicable in a larger class of multiple timescale dynamical models.......We consider a three-variable forest pest model, proposed by Rinaldi & Muratori (1992) [Rinaldi, S., Muratori, S., 1992. Limit cycles in slow-fast forest-pest models. Theor. Popul. Biol. 41,26-43]. The model allows relaxation oscillations where long pest-free periods are interspersed with outbreaks...... of high pest concentration. For small values of the timescale of the young trees, the model can be reduced to a two-dimensional model. By a geometrical analysis we identify a canard explosion in the reduced model, that is, a change over a narrow parameter interval from outbreak dynamics to small...
Lee, Eunae; Kang, Jeong Won; Kim, Ki-Sub; Kwon, Oh-Kuen
2016-02-01
Superlubricity in nanoscale graphene structures has been of interest for developing graphene-based nanoelectromechanical systems, as well as for the study of basic mechanical properties. Here, we investigated the translational and rotational motions of a square graphene nanoflake with retracting motions by performing classical molecular dynamics simulations. Our results show that the kinetic energy of the translational motion was exchanged into the kinetic energy of the rotational motion. Thus, square graphene nanoflake oscillators have very low quality factors in translational motions. We discuss that square graphene nanoflakes have great potential to be a core component in nanoelectromechanical systems by detecting their motions with ultrahigh sensitivity to facilitate the development of sensor, memory, and quantum computing.
Persistent positive North Atlantic oscillation mode dominated the Medieval Climate Anomaly.
Trouet, Valérie; Esper, Jan; Graham, Nicholas E; Baker, Andy; Scourse, James D; Frank, David C
2009-04-03
The Medieval Climate Anomaly (MCA) was the most recent pre-industrial era warm interval of European climate, yet its driving mechanisms remain uncertain. We present here a 947-year-long multidecadal North Atlantic Oscillation (NAO) reconstruction and find a persistent positive NAO during the MCA. Supplementary reconstructions based on climate model results and proxy data indicate a clear shift to weaker NAO conditions into the Little Ice Age (LIA). Globally distributed proxy data suggest that this NAO shift is one aspect of a global MCA-LIA climate transition that probably was coupled to prevailing La Niña-like conditions amplified by an intensified Atlantic meridional overturning circulation during the MCA.
Wang, Yajun; Yang, Wenhai; Li, Zhixiu; Zheng, Yaohui
2017-02-01
Non-classical squeezed states of light at a compatible atomic wavelength have a potential application in quantum information protocols for quantum states delaying or storaging. An optical parametric oscillator (OPO) with periodically poled potassium titanyl phosphate (PPKTP) is the most effective method for generating this squeezed state. However, it is a challege for the nonlinear interaction in PPKTP crystal at the D1 line of rubidium atomic, due to a strong blue-light-induced infrared absorption (BLIIRA). In this paper, we report an indirect measurement method for the BLIIRA through measuring the mode-matching efficiency in an optical parametric oscillator. In contrast to previous works, our method is not limited by the absolute power variation induced from the change of frequency conversion loss and the impedance matching originated from the change of absorption loss. Therefore, the measurement process is performed at the phase-matching condition. The measured results show that BLIIRA coefficient is quadratic dependence of blue light intensity below 1 kW per square centimeter in our PPKTP device, which will provide important basis for optimizing squeezed state generation at 795 nm.
Kwok, Ron; Comiso, Josefino C.; Koblinsky, Chester J. (Technical Monitor)
2002-01-01
The 17-year (1982-1998) trend in surface temperature shows a general cooling over the Antarctic continent, warming of the sea ice zone, with moderate changes over the oceans. Warming of the peripheral seas is associated with negative trends in the regional sea ice extent. Effects of the Southern Hemisphere Annular Mode (SAM) and the extrapolar Southern Oscillation (SO) on surface temperature are quantified through regression analysis. Positive polarities of the SAM are associated with cold anomalies over most of Antarctica, with the most notable exception of the Antarctic Peninsula. Positive temperature anomalies and ice edge retreat in the Pacific sector are associated with El Nino episodes. Over the past two decades, the drift towards high polarity in the SAM and negative polarity in the SO indices couple to produce a spatial pattern with warmer temperatures in the Antarctic Peninsula and peripheral seas, and cooler temperatures over much of East Antarctica.
Directory of Open Access Journals (Sweden)
Yanghai Li
2016-01-01
Full Text Available Through the analysis of the control theory for steam turbine, the transfer function of the steam turbine control modes in the parallel operation was obtained. The frequency domain analysis indicated that different control modes of turbine control system have different influence on the damping characteristics of the power system. The comparative analysis shows the direction and the degree of the influence under the different oscillation frequency range. This can provide the theory for the suppression of the low-frequency oscillation from turbine side and has a guiding significance for the stability of power system. The results of simulation tests are consistent with the theoretic analysis.
Zheng, Xueyan; Wu, Lifeng; Guan, Yong; Li, Xiaojuan
2013-01-01
Switching Mode Power Supply (SMPS) has been widely applied in aeronautics, nuclear power, high-speed railways, and other areas related to national strategy and security. The degradation of MOSFET occupies a dominant position in the key factors affecting the reliability of SMPS. MOSFETs are used as low-voltage switches to regulate the DC voltage in SMPS. The studies have shown that die-attach degradation leads to an increase in on-state resistance due to its dependence on junction temperature....
Thompson, Lee M; Lasoroski, Aurélie; Champion, Paul M; Sage, J Timothy; Frisch, Michael J; van Thor, Jasper J; Bearpark, Michael J
2014-02-11
A systematic comparison of different environmental effects on the vibrational modes of the 4-hydroxybenzylidene-2,3-dimethylimidazolinone (HBDI) chromophore using the ONIOM method allows us to model how the molecule's spectroscopic transitions are modified in the Green Fluorescent Protein (GFP). ONIOM(QM:MM) reduces the expense of normal mode calculations when computing the majority of second derivatives only at the MM level. New developments described here for the efficient solution of the CPHF equations, including contributions from electrostatic interactions with environment charges, mean that QM model systems of ∼100 atoms can be embedded within a much larger MM environment of ∼5000 atoms. The resulting vibrational normal modes, their associated frequencies, and dipole derivative vectors have been used to interpret experimental difference spectra (GFPI2-GFPA), chromophore vibrational Stark shifts, and changes in the difference between electronic and vibrational transition dipoles (mode angles) in the protein environment.
Oscillation center theory and ponderomotive stabilization of low-frequency plasma modes
Similon, Philippe L.; Kaufman, Allan N.; Holm, Darryl D.
1986-06-01
Nonlinear, nondissipative ponderomotive theory is developed in relation to recent experimental results showing that externally imposed rf fields can stabilize an axisymmetric mirror plasma. First, the ponderomotive force problem is reexamined, with emphasis on self-consistency of the interaction between the plasma and high-frequency field. The averaged action principle for the antenna-plasma system yields self-consistent plasma and electromagnetic field dynamics on the oscillation-center time scale. The plasma equilibrium condition is expressed as a balance among plasma and magnetic pressure forces, including interchange, ponderomotive, and magnetization forces. Next, the spectral stability of such static equilibria is studied in the low-frequency magnetohydrodynamic (MHD) approximation, with a ΔW principle that incorporates the various ponderomotive contributions: particle effects, magnetization effects, and self-consistent adjustment of the rf field resulting from displacements of the plasma away from equilibrium. The ponderomotive potential energy functional is related to the antenna inductance and antenna current amplitude. Finally, the noncanonical Hamiltonian formulation for the system's dynamics is given, in terms of Eulerian fields. It allows the construction of nonlinearly conserved functionals, which yield criteria for linearized Lyapunov stability, for both multifluid and MHD models. The Lyapunov stability conditions are related to the modified ΔW variational principle.
Blagoveshchenskaya, N. F.; Borisova, T. D.; Kalishin, A. S.; Yeoman, T. K.; Häggström, I.
2017-03-01
We provide the first experimental evidence of the sensitivity of phenomena induced by extraordinary (X-mode) polarized HF high power radio waves to pump frequency stepping across the fifth electron gyro-harmonic (5fce) from below to above. The results were obtained at the EISCAT (European Incoherent Scatter Scientific Association) HF heater facility near Tromsø under effective radiated powers of 456-715 MW, when the HF pump wave was transmitted into the magnetic zenith. We have analyzed the behavior and intensities of various spectral lines in the narrowband stimulated electromagnetic emission (SEE) spectra observed far from the heater, HF-enhanced plasma and ion lines (HFPL and HFIL) from EISCAT UHF incoherent scatter radar spectra, and artificial field-aligned irregularities from CUTLASS (Co-operative UK Twin Located Auroral Sounding System) observations, depending on the frequency offset of the pump field relative to the 5fce. At pump frequencies below 5fce the narrowband SEE spectra exhibited very intense so-called stimulated ion Bernstein scatter (SIBS), accompanied by other spectral components, associated with stimulated Brillouin scatter (SBS), which are greatly suppressed and disappeared in the vicinity of 5fce and did not reappear at fH>5fce. As the pump frequency reached 5fce, the abrupt enhancements of the HFPL and HFIL power, the appearance of cascade lines in the plasma line spectra, and the onset of increasing CUTLASS backscatter power occurred. That is opposite to the ordinary mode (O-mode) effects in the vicinity of 5fce. The X-mode pumping at frequencies below and in the vicinity of the fifth electron gyro-harmonic clearly demonstrated an ascending altitude of generation of induced plasma and ion lines from the initial interaction height, whereas for O-mode heating the region of interaction descended. The observations are consistent with the coexistence of the electron acceleration along and across the geomagnetic field at fH<5fce, while only very
Classical oscillator driven by an oscillating chirped force
Khachatryan, A.G.; van Goor, F.A.; Boller, Klaus J.
2006-01-01
The motion of a classical (harmonic) oscillator is studied in the case where the oscillator is driven by a pulsed oscillating force with a frequency varying in time (frequency chirp). The amplitude and phase of the oscillations left after the pulsed force in dependence on the profile and strength of
Schlup, Philip; W. Baxter, Glenn; McKinnie, Iain T.
2000-10-01
We have demonstrated a simple grazing-incidence optical parametric oscillator (OPO) based on periodically poled lithium niobate (PPLN) capable of generating single-mode visible (619-640 nm) and infrared (3.16-3.77 μm) radiation. The single-mode (poly(methyl methacrylate) disc was used to amplify the signal wavelength up to 114 μJ in a single pass without broadening the optical bandwidth.
Dynamical evolution of quantum oscillators toward equilibrium.
Usha Devi, A R; Rajagopal, A K
2009-07-01
A pure quantum state of large number N of oscillators, interacting via harmonic coupling, evolves such that any small subsystem n
Energy Technology Data Exchange (ETDEWEB)
Carlsson, J. A., E-mail: carlsson@pppl.gov [Crow Radio and Plasma Science, Princeton, New Jersey 08540 (United States); Wilson, J. R.; Hosea, J. C.; Greenough, N. L.; Perkins, R. J. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543-0451 (United States)
2016-06-15
Third-order spectral analysis, in particular, the auto bicoherence, was applied to probe signals from high-harmonic fast-wave heating experiments in the National Spherical Torus Experiment. Strong evidence was found for parametric decay of the 30 MHz radio-frequency (RF) pump wave, with a low-frequency daughter wave at 2.7 MHz, the local majority-ion cyclotron frequency. The primary decay modes have auto bicoherence values around 0.85, very close to the theoretical value of one, which corresponds to total phase coherence with the pump wave. The threshold RF pump power for onset of parametric decay was found to be between 200 kW and 400 kW.
Location identification of closed crack based on Duffing oscillator transient transition
Liu, Xiaofeng; Bo, Lin; Liu, Yaolu; Zhao, Youxuan; Zhang, Jun; Deng, Mingxi; Hu, Ning
2018-02-01
The existence of a closed micro-crack in plates can be detected by using the nonlinear harmonic characteristics of the Lamb wave. However, its location identification is difficult. By considering the transient nonlinear Lamb under the noise interference, we proposed a location identification method for the closed crack based on the quantitative measurement of Duffing oscillator transient transfer in the phase space. The sliding short-time window was used to create a window truncation of to-be-detected signal. And then, the periodic extension processing for transient nonlinear Lamb wave was performed to ensure that the Duffing oscillator has adequate response time to reach a steady state. The transient autocorrelation method was used to reduce the occurrence of missed harmonic detection due to the random variable phase of nonlinear Lamb wave. Moreover, to overcome the deficiency in the quantitative analysis of Duffing system state by phase trajectory diagram and eliminate the misjudgment caused by harmonic frequency component contained in broadband noise, logic operation method of oscillator state transition function based on circular zone partition was adopted to establish the mapping relation between the oscillator transition state and the nonlinear harmonic time domain information. Final state transition discriminant function of Duffing oscillator was used as basis for identifying the reflected and transmitted harmonics from the crack. Chirplet time-frequency analysis was conducted to identify the mode of generated harmonics and determine the propagation speed. Through these steps, accurate position identification of the closed crack was achieved.
Collective modes of a two-dimensional spin-1/2 Fermi gas in a harmonic trap
DEFF Research Database (Denmark)
Baur, Stefan; Vogt, Enrico; Köhl, Michael
2013-01-01
We derive analytical expressions for the frequency and damping of the lowest collective modes of a two-dimensional Fermi gas using kinetic theory. For strong coupling, we furthermore show that pairing correlations overcompensate the effects of Pauli blocking on the collision rate for a large range...... of temperatures, resulting in a rate which is larger than that of a classical gas. Our results agree well with experimental data, and they recover the observed crossover from collisionless to hydrodynamic behavior with increasing coupling for the quadruple mode. Finally, we show that a trap anisotropy within...
Energy Technology Data Exchange (ETDEWEB)
Lal, A K; Pathania, Ankush [School of Mathematics and Computer Applications, Thapar University, Patiala, Punjab (India); Bhalla, Alka [Department of Mathematics, N.I.T., Jalandhar, Punjab (India); Mohan, C [Professor of Mathematics (Retd.), IIT Roorkee, Uttarakhand (India)], E-mail: aklal@thapar.edu
2009-12-04
Mohan et al (1992 Astrophys. Space. Sci. 193 69) (1998 Indian J. Pure Appl. Math. 29 199) investigated the problem of equilibrium structures and periods of small adiabatic oscillations of differentially rotating stellar models using a law of differential rotation of the type {omega}{sup 2} = b{sub 0} + b{sub 1}s{sup 2} + b{sub 2}s{sup 4} (here {omega} is a nondimensional measure of the angular velocity of rotation of a fluid element at a distance s from the axis of rotation and b's are suitably chosen constant parameters). This law of differential rotation assumes cylindrical symmetry for the rotating fluid elements. In the present paper, we have extended their study and used a more general law of differential rotation of the type {omega}{sup 2} = b{sub 0} + b{sub 1}s{sup 2} + b{sub 2}s{sup 4} + b{sub 3}z{sup 2} + b{sub 4}z{sup 4} + b{sub 5}z{sup 2}s{sup 2} in which the angular velocity of rotation of a fluid element is assumed to depend both on its distance s from the axis of rotation and on its distance z from the plane through the center of the star perpendicular to the axis of rotation. The main objective of this study has been to investigate whether the dependence of angular velocity of rotation on the parameter z in addition to the parameter s substantially alters the behavior of the eigenfrequencies of small adiabatic barotropic modes of oscillations of differentially rotating stars or not.
Blaise, Paul
2011-01-01
An invaluable reference for an overall but simple approach to the complexity of quantum mechanics viewed through quantum oscillators Quantum oscillators play a fundamental role in many areas of physics; for instance, in chemical physics with molecular normal modes, in solid state physics with phonons, and in quantum theory of light with photons. Quantum Oscillators is a timely and visionary book which presents these intricate topics, broadly covering the properties of quantum oscillators which are usually dispersed in the literature at varying levels of detail and often combined with other p
Dobaczewski, J.; Olbratowski, P.
2005-05-01
We describe the new version (v2.08k) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. Similarly as in the previous version (v2.08i), all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. In the new version, three minor errors have been corrected. New Version Program SummaryTitle of program: HFODD; version: 2.08k Catalogue number: ADVA Catalogue number of previous version: ADTO (Comput. Phys. Comm. 158 (2004) 158) Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Does the new version supersede the previous one: yes Computers on which this or another recent version has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems under which the program has been tested: UNIX, LINUX, Windows-2000 Programming language used: Fortran Memory required to execute with typical data: 10M words No. of bits in a word: 64 No. of lines in distributed program, including test data, etc.: 52 631 No. of bytes in distributed program, including test data, etc.: 266 885 Distribution format:tar.gz Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero
Kim, S.; Choi, M.; Song, J. Y.; Lee, J. H.; Kim, Y.
2017-02-01
Fiber ultrafast pulses such as mode-locked and noise-like pulses have useful optical characteristics for high precision metrology applications. In this study, we develop an ytterbium doped fiber laser with all normal dispersion which can selectively generate two pulse modes, mode-locked and noise-like pulses, by a turn-key system including polarization control and selective detection parts. The spectral and temporal characteristics of two pulses generated from the single oscillator are analyzed and compared with each other through optical spectrum, RF spectrum and autocorrelation. Furthermore, spectral coherence characteristics are verified through interference signals generated by balanced and unbalanced arm interferometers.
8.5-W mode-locked Yb:Lu$_{1.5}$Y$_{1.5}$Al$_5$O$_{12}$ laser with master oscillator power amplifiers
Wang, Fuyong; Xie, Guoqiang; Yuan, Peng; Qian, Liejia; Xu, Xiaodong; Xu, Jun
2014-01-01
We report on a diode-pumped passively mode-locked Yb:Lu$_{1.5}$Y$_{1.5}$Al$_5$O$_{12}$ (Yb:LuYAG) laser for the first time to our knowledge. With the mixed crystal of Yb:LuYAG as gain medium, the mode-locked laser generated 2.2 W of average output power with a repetition rate of 83.9 MHz and pulse duration of 2.2 ps at the wavelength of 1030 nm. In order to obtain higher output power, the output from the mode-locked oscillator was further amplified to 8.5 W by two-stage single-pass amplifiers. The high-power picosecond laser is very useful for applications such as pumping of mid-infrared optical parametric oscillators, material micro-processing, and UV light generation, etc.
Matsunaga, Ryusuke; Tsuji, Naoto; Makise, Kazumasa; Terai, Hirotaka; Aoki, Hideo; Shimano, Ryo
2017-07-01
Recent advances in time-domain terahertz (THz) spectroscopy have unveiled that resonantly enhanced strong THz third-harmonic generation (THG) mediated by the collective Higgs amplitude mode occurs in s -wave superconductors, where charge-density fluctuations (CDFs) have been shown to also contribute to the nonlinear third-order susceptibility. It has been theoretically proposed that the nonlinear responses of Higgs and CDF exhibit essentially different polarization dependences. Here we experimentally discriminate the two contributions by polarization-resolved intense THz transmission spectroscopy for a single-crystal NbN film. The result shows that the resonant THG in the transmitted light always appears in the polarization parallel to that of the incident light with no appreciable polarization-angle dependence relative to the crystal axis. When we compare this with the theoretical calculation here with the BCS approximation and the dynamical mean-field theory for a model of NbN constructed from first principles, the experimental result strongly indicates that the Higgs mode rather than the CDF dominates the THG resonance in NbN. A possible mechanism for this is the retardation effect in the phonon-mediated pairing interaction beyond BCS.
Kutsaev, Sergey V.; Agustsson, Ronald; Boucher, Salime; Fischer, Richard; Murokh, Alex; Mustapha, Brahim; Nassiri, Alireza; Ostroumov, Peter N.; Plastun, Alexander; Savin, Evgeny; Smirnov, Alexander Yu.
2017-12-01
The development of high-gradient accelerating structures for low-β particles is the key for compact hadron linear accelerators. A particular example of such a machine is a hadron therapy linac, which is a promising alternative to cyclic machines, traditionally used for cancer treatment. Currently, the practical utilization of linear accelerators in radiation therapy is limited by the requirement to be under 50 m in length. A usable device for cancer therapy should produce 200-250 MeV protons and/or 400 - 450 MeV /u carbon ions, which sets the requirement of having 35 MV /m average "real-estate gradient" or gradient per unit of actual accelerator length, including different accelerating sections, focusing elements and beam transport lines, and at least 50 MV /m accelerating gradients in the high-energy section of the linac. Such high accelerating gradients for ion linacs have recently become feasible for operations at S-band frequencies. However, the reasonable application of traditional S-band structures is practically limited to β =v /c >0.4 . However, the simulations show that for lower phase velocities, these structures have either high surface fields (>200 MV /m ) or low shunt impedances (<35 M Ω /m ). At the same time, a significant (˜10 % ) reduction in the linac length can be achieved by using the 50 MV /m structures starting from β ˜0.3 . To address this issue, we have designed a novel radio frequency structure where the beam is synchronous with the higher spatial harmonic of the electromagnetic field. In this paper, we discuss the principles of this approach, the related beam dynamics and especially the electromagnetic and thermomechanical designs of this novel structure. Besides the application to ion therapy, the technology described in this paper can be applied to future high gradient normal conducting ion linacs and high energy physics machines, such as a compact hadron collider. This approach preserves linac compactness in settings with limited
Quantum harmonically kicked environments
Custódio, M. S.; Strunz, W. T.; Beims, M. W.
2017-11-01
In this work we derive a generalized map which describes the time evolution of a quantum system coupled to a quantum environment composed by a finite number of free particles kicked harmonically at periodic times. Dissipation is introduced via the interaction between system and environment, which is switched on and off simultaneously at regular time intervals. The dynamics of the environmental particles occurs along rotated ellipsis in phase space and can be described by unrotated harmonic oscillators with a new frequency which depends on the kicking time. With the definition of a thermal bath we show that our quantum kicked environment induces an unusual fluctuation-dissipation relation.
Bando, T.; Ohdachi, S.; Suzuki, Y.; Sakamoto, R.; Narushima, Y.; Takemura, Y.; Watanabe, K. Y.; Sakakibara, S.; Du, X. D.; Motojima, G.; Tanaka, K.; Morisaki, T.; LHD Experiment Group
2018-01-01
Two types of oscillation phenomena are found just after hydrogen ice pellet injections in the Large Helical Device (LHD). Oscillation phenomena appear when the deposition profile of a hydrogen ice pellet is localized around the rotational transform ι = 1 rational surface. At first, damping oscillations (type-I) appear only in the soft X-ray (SX) emission. They are followed by the second type of oscillations (type-II) where the magnetic fluctuations and density fluctuations synchronized to the SX fluctuations are observed. Both oscillations have poloidal/toroidal mode number, m/n = 1/1. Since the type-II oscillations appear when the local pressure is large and/or the local magnetic Reynold's number is small, it is reasonable that type-II oscillations are caused by the resistive interchange modes. Because both types of oscillations appear simultaneously at slightly different locations and with slightly different frequencies, it is certain that type-I oscillations are different from type-II oscillations, which we believe is the MHD instability. It is possible that type-I oscillations are caused by the asymmetric concentration of the impurities. The type-I oscillations are similar to the impurity snake phenomena observed in tokamaks though type-I oscillations survive only several tens of milliseconds in LHD.
Directory of Open Access Journals (Sweden)
Sergey V. Kutsaev
2017-12-01
Full Text Available The development of high-gradient accelerating structures for low-β particles is the key for compact hadron linear accelerators. A particular example of such a machine is a hadron therapy linac, which is a promising alternative to cyclic machines, traditionally used for cancer treatment. Currently, the practical utilization of linear accelerators in radiation therapy is limited by the requirement to be under 50 m in length. A usable device for cancer therapy should produce 200–250 MeV protons and/or 400–450 MeV/u carbon ions, which sets the requirement of having 35 MV/m average “real-estate gradient” or gradient per unit of actual accelerator length, including different accelerating sections, focusing elements and beam transport lines, and at least 50 MV/m accelerating gradients in the high-energy section of the linac. Such high accelerating gradients for ion linacs have recently become feasible for operations at S-band frequencies. However, the reasonable application of traditional S-band structures is practically limited to β=v/c>0.4. However, the simulations show that for lower phase velocities, these structures have either high surface fields (>200 MV/m or low shunt impedances (<35 MΩ/m. At the same time, a significant (∼10% reduction in the linac length can be achieved by using the 50 MV/m structures starting from β∼0.3. To address this issue, we have designed a novel radio frequency structure where the beam is synchronous with the higher spatial harmonic of the electromagnetic field. In this paper, we discuss the principles of this approach, the related beam dynamics and especially the electromagnetic and thermomechanical designs of this novel structure. Besides the application to ion therapy, the technology described in this paper can be applied to future high gradient normal conducting ion linacs and high energy physics machines, such as a compact hadron collider. This approach preserves
The dominant mode of standing Alfven waves at the synchronous orbit
Cummins, W. D.; Countee, C.; Lyons, D.; Wiley, W., III
1975-01-01
Low-frequency oscillations of the earth's magnetic field recorded by a magnetometer on board ATS 1 have been examined for the 6-month interval between January and June 1968. Using evidence from OGO 5 and ATS 5 as well as the data from ATS 1, it is argued that the dominant mode at ATS 1 must be the fundamental rather than the second harmonic of a standing Alfven wave. It is concluded that these transverse oscillations are more accurately associated with magnetically disturbed days than with quiet days. From 14 instances when oscillations of distinctly different periods occurred during the same time interval at ATS 1, it is also concluded that higher harmonics can exist. The period ratio in seven of the 14 cases corresponds to the simultaneous occurrence of the second harmonic with the fundamental, and four other cases could be identified as the simultaneous occurrence of the fourth harmonic with the fundamental.
Three-dimensional simulations of harmonic radiation and harmonic lasing
Energy Technology Data Exchange (ETDEWEB)
Schmitt, M.J.; McVey, B.D.
1990-01-01
Characteristics of the harmonic emission from free-electron lasers (FELs) are examined in the spontaneous, coherent-spontaneous and stimulated emission regimes. The radiation at both odd and even harmonic frequencies is treated for electron beams with finite emittance and energy spread. In the spontaneous emission regime, the transverse radiation patterns including the transverse frequency dependences, are given. How this expression is modified to include energy spread and emittance is described. In the coherent-spontaneous emission and stimulated emission regimes, the interaction of the radiation fields with the electrons must be treated self-consistently. Here, a single-frequency distributed transverse source function for each electron is used in the harmonic version of the 3-D code FELEX to model the harmonic radiation. The code has recently been modified to simultaneously model the fundamental and harmonic interactions for multiple-pass oscillator simulations. These modifications facilitate the examination of FELs under various operating conditions. When the FEL is lasing at the fundamental, the evolution of the harmonic fields can be examined. This evolution is unique in the sense that the electron beam radiates at the harmonic frequencies in the presence of the harmonic radiation circulating in the cavity. As a result, enhancements of the harmonic emission can be observed. Finally, harmonic lasing can occur in cases where there is sufficient gain to overcome cavity losses and lasing at the fundamental can be suppressed. The characteristics and efficiency of these interactions are explored. 11 refs., 9 figs.
Directory of Open Access Journals (Sweden)
Tengfei Zhang
2015-12-01
Full Text Available With the rapid development of the micro-grid associated with new and clean energies, the smooth switching between grid-connected and islanded operation modes of the micro-grid is a key issue that needs to be addressed urgently. In traditional solutions, V/f (Voltage/frequency control is adopted for the master micro sources when the micro-grid works in islanded mode, while PQ (real and reactive power control is adopted when in grid-connected mode. However, when the two controllers switch when mode transfer occurs, transient oscillations usually occur and thereafter the dynamic response will be degraded. This paper considers an archetypical micro-grid with Wind-PV-ES (Wind, Photovoltaic and Energy Storage hybrid system, which forms the basis of our case study. The underlying reason for such transient oscillation is analyzed in this paper. Thereafter a modified control strategy for seamless mode transfer is designed and implemented. An improved PQ control method is designed by which the output of the PQ controller always synchronously tracks the output of the V/f controller for micro-grid switches from islanded mode to grid-connected; furthermore, a dq rotating coordinate synchronization based V/f control method is proposed for transition from grid-connected mode to islanded mode. Finally, experiments and analysis are undertaken on some basic and important operating cases; the results in our case study indicate that the modified control strategy is effective in dominating the micro-grid during mode transfer and thus yielding significantly better performances.
Harmonic generation in the generalized Sagdeev pseudopotential
Akbari-Moghanjoughi, M.
2017-09-01
In this paper, we study the nonlinear harmonic generation effect in different oscillator models. For weakly nonlinear systems, we use the generalized forced Korteweg de Vries Burgers (KdVB) and modified KdVB (mKdVB) models in order to classify three fundamentally different harmonic structures in a nonlinear dynamical system. The first is called the internal harmonic structure which exists due to the self oscillation of the system in the absence of dissipation effect and is shown to follow either relations of nf or (2n - 1)f depending on the symmetry of oscillator potential in which n is an integer number and f is the fundamental frequency which is exactly obtained for the Helmholtz oscillator. The second structure is the resonant harmonics which appears in the presence of damping and follows the harmonic structure nf0 in which f0 is the linear resonance frequency. Finally, the last harmonic structure appears in the presence of dissipation and external periodic forcing effects which we call the external harmonic pattern. It is shown that the external harmonic pattern, in which f1 is the driving frequency, always follows the nf1 rule regardless of the potential symmetry. We then extend our analysis to study the harmonic generation in the fully nonlinear generalized Sagdeev potential for real plasmas with isothermal and adiabatic ion fluids and investigate the effects of different plasma parameters such as the fractional ion temperature and normalized ion acoustic speed on all three kinds of harmonic generation.
High-power Kerr-lens mode-locked Yb:YAG thin-disk oscillator in the positive dispersion regime.
Pronin, O; Brons, J; Grasse, C; Pervak, V; Boehm, G; Amann, M-C; Apolonski, A; Kalashnikov, V L; Krausz, F
2012-09-01
We demonstrate a self-starting Kerr-lens mode-locked (KLM) Yb:YAG thin-disk oscillator operating in the regime of positive intracavity group-delay dispersion (GDD). It delivers 1.7 ps pulses at an average power of 17 W and a repetition rate of 40 MHz. Dispersive mirrors compress the pulses to a duration of 190 fs (assuming sech2 shape; Fourier limit: 150 fs) at an average power level of 11 W. To our knowledge, this is the first KLM thin-disk oscillator with positive GDD. Output powers of up to 30 W were achieved with an increased output coupler transmission and intracavity GDD. We demonstrate increase of the pulse energy with increasing positive intracavity GDD, limited by difficulties in initiating mode-locking.
Dyksik, Mateusz; Motyka, Marcin; Kurka, Marcin; Ryczko, Krzysztof; Misiewicz, Jan; Schade, Anne; Kamp, Martin; Höfling, Sven; Sęk, Grzegorz
2017-11-01
Two designs of active region for an interband cascade laser, based on double or triple GaInSb/InAs type II quantum wells (QWs), were compared with respect to passive mode-locked operation in the mid-infrared range around 4 µm. The layer structure and electron and hole wavefunctions under external electric field were engineered to allow controlling the optical transition oscillator strength and the resulting lifetimes. As a result, the investigated structures can mimic absorber-like and gain-like sections of a mode-locked device when properly polarized with opposite bias. A significantly larger oscillator strength tuning range for triple QWs was experimentally verified by Fourier-transform photoreflectance.
Hong, Xiaoping; Shen, Xinglai; Gong, Mali; Wang, Feng
2012-12-01
We report a continuous-wave, broadly tunable mid-infrared MgO:PPLN optical parametric oscillator pumped by a fiber amplifier. Using pump tuning with synchronized temperature optimization, we achieve the broadest mode-hop-free (MHF) tuning of idler light over 30 cm(-1). We further use this tunable mid-infrared laser to demonstrate high-resolution absorption spectroscopy of methane across the MHF tuning range.
Mahmutyazicioğlu, Kamran; Tanriverdi, H Alper; Ozdemir, Hüseyin; Barut, Aykut; Davşanci, Halit; Gündoğdu, Sadi
2005-02-01
In virgin policystic ovary syndrome (PCOS) patients transabdominal sonography is the preferential method of the pelvic examination. The purpose of this study was to determine ovarian morphology by the transabdominal route by pulse inversion harmonic imaging (PIHI) in virgin PCOS patients and to compare the diagnostic image quality with conventional B-mode ultrasonography (CBU). Fifty-two ovaries in 26 virgin patients were evaluated by the transabdominal approach. Each ovary was examined using both PIHI and CBU. The sharpness of the follicular cysts walls, degree of internal echo definitions of the follicle cysts and overall ovarian conspicuity was assessed subjectively, using 4 point scoring (0, being worst; 3, being best score). The number of countable follicles, the size of largest and smallest ovarian follicle and ovarian volumes were assessed quantitively by both techniques. The effect of body mass index (BMI) on qualitative and quantitative scoring was evaluated. The sharpness of the cyst wall and internal echo structure was significantly better with PIHI than with CBU (P ovaries.
Gupta, S.; Potters, M.G.; Ruffo, S.
2012-01-01
We study synchronization in a system of phase-only oscillators residing on the sites of a one-dimensional periodic lattice. The oscillators interact with a strength that decays as a power law of the separation along the lattice length and is normalized by a size-dependent constant. The exponent ? of
Shmelev, Gennady
2012-01-01
We calculate the current density in a semiconductor superlattice with parabolic miniband under crossed non-quantizing electric and magnetic fields. The Corbino disk geometry is considered. The current-voltage curve contains oscillations with period proportional to the magnetic field. The possibility is shown of the negative absolute conductivity. The Ampere-Gauss characteristics also contain overshoots under high enough electric fields. In all cases, the peaks smear with temperature rising.
Li, Ping-Xue; Yao, Yi-Fei; Chi, Jun-Jie; Hu, Hao-Wei; Zhang, Guang-Ju; Liang, Bo-Xing; Zhang, Meng-Meng; Ma, Chun-Mei; Su, Ning
2016-08-01
A 980-nm semiconductor saturable absorber mirror (SESAM) mode-locked Yb-doped phosphate fiber laser is demonstrated by using an all-fiber linear cavity configuration. Two different kinds of cavity lengths are introduced into the oscillator to obtain a robust and stable mode-locked seed source. When the cavity length is chosen to be 6 m, the oscillator generates an average output power of 3.5 mW and a pulse width of 76.27 ps with a repetition rate of 17.08 MHz. As the cavity length is optimized to short, 4.4-mW maximum output power and 61.15-ps pulse width are produced at a repetition rate of 20.96 MHz. The output spectrum is centered at 980 nm with a narrow spectral bandwidth of 0.13 nm. In the experiment, no undesired amplified spontaneous emission (ASE) nor harmful oscillation around 1030 nm is observed. Moreover, through a two-stage all-fiber-integrated amplifier, an output power of 740 mW is generated with a pulse width of 200 ps. Project supported by the National Natural Science Foundation of China (Grant No. 61205047).
Energy Technology Data Exchange (ETDEWEB)
Mahmutyazicioglu, Kamran; Tanriverdi, H. Alper; Oezdemir, Hueseyin; Barut, Aykut; Davsanci, Halit; Guendogdu, Sadi
2005-02-01
Objective: In virgin policystic ovary syndrome (PCOS) patients transabdominal sonography is the preferential method of the pelvic examination. The purpose of this study was to determine ovarian morphology by the transabdominal route by pulse inversion harmonic imaging (PIHI) in virgin PCOS patients and to compare the diagnostic image quality with conventional B-mode ultrasonography (CBU). Methods: Fifty-two ovaries in 26 virgin patients were evaluated by the transabdominal approach. Each ovary was examined using both PIHI and CBU. The sharpness of the follicular cysts walls, degree of internal echo definitions of the follicle cysts and overall ovarian conspicuity was assessed subjectively, using 4 point scoring (0, being worst; 3, being best score). The number of countable follicles, the size of largest and smallest ovarian follicle and ovarian volumes were assessed quantitively by both techniques. The effect of body mass index (BMI) on qualitative and quantitative scoring was evaluated. Results: The sharpness of the cyst wall and internal echo structure was significantly better with PIHI than with CBU (P < 0.001 P < 0.001 and P < 0.001, respectively). PIHI improved overall ovarian conspicuity in 41 (78.8%) of 52 examination. The number of countable follicles was significantly lower with CBU (P < 0.001). The maximum diameter of the largest follicle was larger with PIHI sonography to compared CBU (P < 0.001). Mean ovarian volume was significantly larger with CBU (P < 0.001). When data were analyzed separately according to BMI, number of non-diagnostic overall ovarian conspicuity scores with CBU was markedly high in obese patients (88% with CBU versus 3.8% with PIHI). On the other hand, mean number of countable follicles with CBU became much more lower in the obese group (P < 0.001). Conclusion: In virgin PCOS patients, when compared to transabdominal CBU, PIHI significantly improved the detection of ovarian follicles, especially in high BMI obese subjects, through
Song, Dong Hoon; In Hwang, Sung; Ko, Do-Kyeong
2011-03-01
We examined the soft-aperture Kerr-lens mode-locked femtosecond Ti:sapphire oscillator derived from an Herriott multi-pass cavity (HMPC). Additionally, a novel and simple configuration was provided to extend the cavity length, the HMPC consisting of notched, flat and curved (R = 4 m) mirrors by which beams were injected and extracted. To compensate for beams which failed to complete round trips, the configuration was designed and analyzed as a function of the output coupler position. Such an oscillator generated 21.5 nJ, 34 fs pulses at a repetition rate of approximately 13.5 MHz; the spectral bandwidth represented 20 nm, corresponding to a time-bandwidth product of 0.33, assuming a sech2 fit.
Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.
2012-01-01
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il
2017-05-15
The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.
On impulse excitation of the global poloidal modes in the magnetosphere
Directory of Open Access Journals (Sweden)
P. N. Mager
2006-10-01
Full Text Available Through the combined action of the field line curvature and finite plasma pressure in some regions of the magnetosphere (plasmapause, ring current there can exist global poloidal Alfvén modes standing both along field lines and across magnetic shells and propagating along azimuth. In this paper we investigate the spatio-temporal structure of such waves generated by an impulsive source. In general, the mode is the sum of radial harmonics whose structure is described by Hermitian polynomials. For the usually observed second harmonic structure along the background field, frequencies of these radial harmonics are very close to each other; therefore, the generated wave is almost a monochromatic oscillation. But mixing of the harmonics with different radial structure causes the evolution of the initially poloidal wave into the toroidal one. This casts some doubts upon the interpretation of observed high-m poloidal waves as global poloidal modes.
Lee, Dong-Hoon; Kim, Seung Kwan; Park, Seung-Nam; Park, Hee Su; Lee, Jae Yong; Choi, Sang-Kyung
2009-01-01
We report a continuous-wave (CW) optical parametric oscillator (OPO) based on a MgO-doped periodically poled LiNbO(3) (MgO:PPLN) crystal. The 532 nm pump generates coherent radiation that is tunable from 800 to 920 nm for the signal and from 1250 to 1580 nm for the idler, respectively. The OPO output power exhibits a slowly varying instability that we attribute to a thermal effect induced by the pump. This instability is truncated by means of a low-pass servo that includes a single-mode fiber that filters the beam into a single spatial mode. The resulting output characteristics are promising for radiometric applications in the near infrared including most fiber-optic communication bands.
Li, Jianfeng; Zhang, Zuxing; Sun, Zhongyuan; Luo, Hongyu; Liu, Yong; Yan, Zhijun; Mou, Chengbo; Zhang, Lin; Turitsyn, Sergei K
2014-04-07
A self-starting all-fiber passively mode-locked Tm(3+)-doped fiber laser based on nonlinear loop mirror (NOLM) is demonstrated. Stable soliton pulses centered at 2017.33 nm with 1.56 nm FWHM were produced at a repetition rate of 1.514 MHz with pulse duration of 2.8 ps and pulse energy of 83.8 pJ. As increased pump power, the oscillator can also operate at noise-like (NL) regime. Stable NL pulses with coherence spike width of 341 fs and pulse energy of up to 249.32 nJ was achieved at a center wavelength of 2017.24 nm with 21.33 nm FWHM. To the best of our knowledge, this is the first 2 µm region NOLM-based mode-locked fiber laser operating at two regimes with the highest single pulse energy for NL pulses.
Measuring Spherical Harmonic Coefficients on a Sphere
Energy Technology Data Exchange (ETDEWEB)
Pollaine, S; Haan, S W
2003-05-16
The eigenfunctions of Rayleigh-Taylor modes on a spherical capsule are the spherical harmonics Y{sub l,m} These can be measured by measuring the surface perturbations along great circles and fitting them to the first few modes by a procedure described in this article. For higher mode numbers, it is more convenient to average the Fourier power spectra along the great circles, and then transform them to spherical harmonic modes by an algorithm derived here.
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
theorem for a classical harmonic oscillator coupled linearly to a harmonic bath. Because of the coupling to the bath, the system becomes dissipative. We start from a Hamiltonian description for the system plus the harmonic heat bath and then the system is driven by an external agent for a time period of τ for a series. 666.
Schunck, N.; Dobaczewski, J.; Satuła, W.; Bączyk, P.; Dudek, J.; Gao, Y.; Konieczka, M.; Sato, K.; Shi, Y.; Wang, X. B.; Werner, T. R.
2017-07-01
We describe the new version (v2.73y) of the code HFODD which solves the nuclear Skyrme Hartree-Fock or Skyrme Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton-neutron mixing in the particle-hole channel for Skyrme functionals, (ii) the Gogny force in both particle-hole and particle-particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code HFBTHO, together with an enhanced interface between HFBTHO and HFODD, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.
Magnetostatic wave oscillator frequencies
Sethares, J. C.; Stiglitz, M. R.; Weinberg, I. J.
1981-03-01
The frequencies of magnetostatic wave (MSW) oscillators employing three principal modes of propagation, surface (MSSW), forward (MSFVW), and backward (MSBVW) volume waves, have been investigated. Previous (MSW) oscillator papers dealt with MSSW. Oscillators were fabricated using LPE-YIG MSW delay lines in a feedback loop of a 2-4 GHz amplifier. Wide and narrow band transducers were employed. Oscillator frequency as a function of biasing field is in agreement with a theoretical analysis. The analysis predicts frequency in terms of material parameters, biasing field, and transducer geometry. With wide band transducers a comb of frequencies is generated. Narrow band transducers for MSSW and MSFVW select a single mode; and MSBVW selects two modes. Spurious modes, attributed to instrumentation, are more than 20 dB below the main response, and bandwidths are less than 0.005 percent. No other spurious modes are observed. MSW oscillators produce clean electronically tunable signals and appear attractive in frequency agile systems.
The OPERA experiment. ν{sub μ}→ν{sub τ} oscillation discovered in appearance mode
Energy Technology Data Exchange (ETDEWEB)
Buettner, Benjamin [Universitaet Hamburg, Institut fuer Experimentalphysik (Germany); Collaboration: OPERA-Hamburg-Collaboration
2016-07-01
The primary goal of the OPERA long-baseline neutrino oscillation experiment is the first direct detection of ν{sub μ}→ν{sub τ} oscillations. The hybrid OPERA detector consists of a large-mass target made from lead and photo emulsions - providing micrometric resolution - and electronic detector parts for online readout. It is located in the LNGS underground laboratory, at a distance of 730 km from the SPS at CERN, where the CNGS ν{sub μ} beam is produced. The measurement of ν{sub τ} appearance relies on the detection of the decay of τ leptons which are created in ν{sub τ} charged current reactions. Data acquisition lasted from 2008 to 2012. With the collected data the OPERA experiment discovered ν{sub τ} appearance in the CNGS neutrino beam with a significance of 5.1 σ. This poster will give an overview about the OPERA experiment and the discovery of τ neutrino appearance in the CNGS neutrino beam.
Indian Academy of Sciences (India)
Harish-Chandra, Gelfand and several other mathematicians and physicists, group-theoretic harmonic analysis is a flourishing industry today paving the way to new developments in the con- text of noncompact Lie groups as well as quantum groups. Since B(n, z) = zn the expansion (3) suggests a link between Fourier series.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 10. Harmonic Analysis Fourier Series and Beyond. K R Parthasarathy. Book Review Volume 1 Issue 10 October 1996 pp 87-91. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/001/10/0087-0091 ...
Bian, Qi; Zhong, Qing-Shuang; Chang, Jin-Quan; Guo, Chuan; Bo, Yong; Zuo, Jun-Wei; Shen, Yu; Zong, Nan; Zhang, Shen-Jin; Yuan, Lei; Cui, Da-Fu; Peng, Qin-Jun; Chen, Hong-Bin; Xu, Zu-Yan
2017-06-01
We demonstrated a high-average-power, narrow-linewidth, quasi-continuous-wave diode-side-pumped 1319 nm Nd:YAG twisted-mode laser oscillator with a linearly polarized TEM00 mode. The resonator is based on a symmetrical convex-convex structure with a two-rod configuration for birefringence compensation, working in a thermally near-unstable cavity. With an optimum cavity length of 940 mm, a 39.4 W linear polarized 1319 nm laser is obtained with a good beam quality of M 2 = 1.21 and a linewidth of ~250 MHz, and the corresponding brightness is as high as 1.55 GW cm-2. The laser is operated at a repetition rate of 500 Hz and pulse duration of 150 µs. To the best of our knowledge, this is the highest output power 1319 nm laser with narrow-linewidth from diode-pumped Nd:YAG lasers, and is the first report on the twisted-mode laser operation at the 1.3 µm region.
A VHF Interleaved Self-Oscillating Resonant SEPIC Converter with Phase-Shift Burst-Mode Control
DEFF Research Database (Denmark)
Kovacevic, Milovan; Knott, Arnold; Andersen, Michael A. E.
2014-01-01
This paper presents design and implementation of the phase-shift burst-mode control method for interleaved selfoscillating resonant SEPIC converters for LED lighting applications. The proposed control method utilizes delays in the turn-on and turn-off of the power stage and control circuitry...
Liu, Yang; Wang, Chao; Luo, Daping; Yang, Chao; Li, Jiang; Ge, Lin; Pan, Yubai; Li, Wenxue
2017-12-01
We demonstrate the passively mode-locked laser performances of bulk Yb:YAG ceramic prepared by non-aqueous tape casting, which generates initial pulses in temporal width of 3 ps and spectrum width of 3 nm without intra-cavity dispersion management. The ceramic laser is further used as seeding oscillator in a fiber nonlinear amplification system, where ultrashort pulses in maximum output power of ∼100 W and pulse duration of 70 fs are achieved. Moreover, the laser spectrum is broadened to be ∼41 nm due to self-phase modulation effects in the gain fiber, overcoming the narrow spectrum limitations of ceramic materials. Our approach opens a new avenue for power-scaling and spectrum-expanding of femtosecond ceramic lasers.
Energy Technology Data Exchange (ETDEWEB)
Zhang, P. [Cockcroft Inst. Accel. Sci. Tech.; Baboi, N. [DESY; Eddy, N. [Fermilab; Fellenz, B. [Fermilab; Jones, R. M. [Cockcroft Inst. Accel. Sci. Tech.; Lorbeer, B. [DESY; Wamsat, T. [DESY; Wendt, M. [Fermilab
2012-08-01
Beam-excited higher order modes (HOM) in accelerating cavities contain transverse beam position information. Previous studies have narrowed down three modal options for beam position diagnostics in the third harmonic 3.9 GHz cavities at FLASH. Localized modes in the beam pipes at approximately 4.1 GHz and in the fifth cavity dipole band at approximately 9 GHz were found, that can provide a local measurement of the beam position. In contrast, propagating modes in the first and second dipole bands between 4.2 and 5.5 GHz can reach a better resolution. All the options were assessed with a specially designed test electronics built by Fermilab. The aim is to define a mode or spectral region suitable for the HOM electronics. Two data analysis techniques are used and compared in extracting beam position information from the dipole HOMs: direct linear regression and singular value decomposition. Current experiments suggest a resolution of 50 {\\mu}m accuracy in predicting local beam position using modes in the fifth dipole band, and a global resolution of 20 {\\mu}m over the complete module. Based on these results we decided to build a HOM electronics for the second dipole band and the fifth dipole band, so that we will have both high resolution measurements for the whole module, and localized measurements for individual cavity. The prototype electronics is being built by Fermilab and planned to be tested in FLASH by the end of 2012.
Energy Technology Data Exchange (ETDEWEB)
Zhang, P. [Manchester Univ. (United Kingdom); Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Baboi, N.; Lorbeer, B.; Wamsat, T. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Eddy, N.; Fellenz, B.; Wendt, M. [Fermi National Accelerator Lab., Batavia, IL (United States); Jones, R.M. [Manchester Univ. (United Kingdom); The Cockcroft Institute, Daresbury (United Kingdom)
2012-08-15
Beam-excited higher order modes (HOM) in accelerating cavities contain transverse beam position information. Previous studies have narrowed down three modal options for beam position diagnostics in the third harmonic 3.9 GHz cavities at FLASH. Localized modes in the beam pipes at approximately 4.1 GHz and in the fifth cavity dipole band at approximately 9 GHz were found, that can provide a local measurement of the beam position. In contrast, propagating modes in the first and second dipole bands between 4.2 and 5.5 GHz can reach a better resolution. All the options were assessed with a specially designed test electronics built by Fermilab. The aim is to de ne a mode or spectral region suitable for the HOM electronics. Two data analysis techniques are used and compared in extracting beam position information from the dipole HOMs: direct linear regression and singular value decomposition. Current experiments suggest a resolution of 50 m accuracy in predicting local beam position using modes in the fifth dipole band, and a global resolution of 20 m over the complete module. Based on these results we decided to build a HOM electronics for the second dipole band and the fifth dipole band, so that we will have both high resolution measurements for the whole module, and localized measurements for individual cavity. The prototype electronics is being built by Fermilab and planned to be tested in FLASH by the end of 2012.
Zhang, P; Eddy, N; Fellenz, B; Jones, R M; Lorbeer, B; Wamsat, T; Wendt, M
2012-01-01
Beam-excited higher order modes (HOM) in accelerating cavities contain transverse beam position information. Previous studies have narrowed down three modal options for beam position diagnostics in the third harmonic 3.9 GHz cavities at FLASH. Localized modes in the beam pipes at approximately 4.1 GHz and in the fifth cavity dipole band at approximately 9 GHz were found, that can provide a local measurement of the beam position. In contrast, propagating modes in the first and second dipole bands between 4.2 and 5.5 GHz can reach a better resolution. All the options were assessed with a specially designed test electronics built by Fermilab. The aim is to define a mode or spectral region suitable for the HOM electronics. Two data analysis techniques are used and compared in extracting beam position information from the dipole HOMs: direct linear regression and singular value decomposition. Current experiments suggest a resolution of 50 micron accuracy in predicting local beam position using modes in the fifth d...
Measurements of High-Degree Solar Oscillation Parameters
Bachmann, K. T.; Duvall, T. L., Jr.; Harvey, J. W.; Hill, F.
1994-12-01
We present results obtained from full-disk, 1000times 1024 pixel, Ca II intensity images of the Sun collected with the High-L Helioseismometer (HLH). Our measurement of p- and f-mode oscillation frequencies over the frequency range 1.8<=nu <=5.0 mHz and the spherical harmonic degree range 100<=l<=1200 from 22-25 June 1993 data represents an improvement over previous measurements. We are able to differentiate among the predictions of several solar models, thus constraining physical models of the solar convection zone. We also include recent splitting and frequency results from data collected during the entire month of June 1994. The purpose of the HLH research program is to measure high-degree solar oscillation parameters for the remainder of this decade in support of the Solar Oscillations Investigation - Michelson Doppler Imager collaboration, which is part of the Solar and Heliospheric Observatory, a joint ESA-NASA satellite mission.
Two-mode generalization of the Jaynes-Cummings and Anti-Jaynes-Cummings models
Choreño, E.; Ojeda-Guillén, D.; Salazar-Ramírez, M.; Granados, V. D.
2017-12-01
We introduce two generalizations of the Jaynes-Cummings (JC) model for two modes of oscillation. The first model is formed by two Jaynes-Cummings interactions, while the second model is written as a simultaneous Jaynes-Cummings and Anti-Jaynes-Cummings (AJC) interactions. We study some of its properties and obtain the energy spectrum and eigenfunctions of these models by using the tilting transformation and the Perelomov number coherent states of the two-dimensional harmonic oscillator. Moreover, as physical applications, we connect these new models with two important and novel problems: The relativistic non-degenerate parametric amplifier and the relativistic problem of two coupled oscillators.
Analytic stability criteria for edge MHD oscillations in high performance ELM free tokamak regimes
Brunetti, D.; Graves, J. P.; Lazzaro, E.; Mariani, A.; Nowak, S.; Cooper, W. A.; Wahlberg, C.
2018-01-01
A new dispersion relation, and associated stability criteria, is derived for low-n external kink and infernal modes, and is applied to modelling the stability properties of quiescent H-mode like regimes. The analysis, performed in toroidal geometry with large edge pressure gradients associated with a local flattening of the safety factor, includes a pedestal, sheared toroidal rotation and a vacuum region separating the plasma from an ideal metallic wall. The external kink-infernal modes found here exhibit similarities with experimentally observed edge harmonic oscillations.
Axisymmetric spheroidal modes of neutron stars magnetized with poloidal magnetic fields
Lee, Umin
2018-01-01
We calculate axisymmetric spheroidal modes of neutron stars magnetized with an axisymmetric poloidal magnetic field. We use polytropes of the indices n ∼ 1 as background equilibrium models of neutron stars where we ignore the deformation due to the magnetic fields. For a poloidal magnetic field, axisymmetric normal modes of non-rotating stars are decoupled into spheroidal modes and toroidal modes, and we can treat spheroidal modes separately from toroidal modes. For the surface field strength BS ranging from 1014 to 1016 G, we calculate axisymmetric spheroidal magnetic modes whose oscillation frequency is proportional to BS. The typical oscillation frequency of the magnetic modes is ˜ 0.01× √{GM/R^3} for BS ∼ 1015 G, where M and R are, respectively, the mass and radius of the star and G is the gravitational constant. For M = 1.4 M⊙ and R = 10 6cm, this frequency is ∼20 Hz, which may explain low-frequency quasi-periodic oscillations found for SGR 1806-204 and SGR 1900+14. We also find modes of frequency ≳ √{GM/R^3} corresponding to the radial fundamental and first harmonic modes. No unstable magnetic modes are found for axisymmetric spheroidal oscillations of magnetized stars.
Nonlinear Interactions of Multiple Linearly Unstable Thermoacoustic Modes
Directory of Open Access Journals (Sweden)
Jonas P. Moeck
2012-03-01
Full Text Available We investigate the dynamics of thermoacoustic systems with multiple linearly unstable modes. If a linear analysis reveals more than one mode with positive growth rate, nonlinear methods have to be used to determine the existence and stability of steady-state oscillations. One possible way to engage this problem is a first-order harmonic balance approach based on describing function representations for the flame response. In contrast to the case of a single unstable mode, the nonlinearity output to multiple sinusoidal components with different frequencies and amplitudes has to be known. Based on this approach, we present conditions for the existence and stability of single- or multi-mode steady-state oscillations. We apply this method to a thermoacoustic model system having two linearly unstable modes. By varying one of the system parameters, we find stable and unstable single-mode steady-states as well as unstable simultaneous oscillations. Associated with the stability of the single-mode limit cycles, we identify hysteresis in the oscillation type. Some related experimental observations are discussed.
Scleronomic Holonomic Constraints and Conservative Nonlinear Oscillators
Munoz, R.; Gonzalez-Garcia, G.; Izquierdo-De La Cruz, E.; Fernandez-Anaya, G.
2011-01-01
A bead sliding, under the sole influence of its own weight, on a rigid wire shaped in the fashion of a plane curve, will describe (generally anharmonic) oscillations around a local minimum. For given shapes, the bead will behave as a harmonic oscillator in the whole range, such as an unforced, undamped, Duffing oscillator, etc. We also present…
Effect of Sawtooth Oscillations on Energetic Ions
Energy Technology Data Exchange (ETDEWEB)
R.B. White; V.V. Lutsenko; Ya. I. Kolesnichenko; Yu. V. Yakovenko
1999-12-10
The work summarizes results of the authors' studies on the energetic ion transport induced by sawtooth oscillations in tokamaks. The main attention is paid to description of physical mechanisms responsible for the transport. In addition to overview, the work contains new material. The new results concern the resonant interaction of the particles and the electromagnetic field of the sawtooth crash. In particular, it is discovered that the dominant harmonic of the crash (m = n = 1) can lead to stochastic motion of particles having large orbit width (potatoes). Regular motion of potatoes and quasi-stagnation particles in the presence of an n = 1 mode is studied, and their characteristic displacements associated with quick switching on/off the mode are found.
Park, Barratt; Field, Robert W.
2014-06-01
Methods developed by J. K. G. Watson for calculation of Franck-Condon Factors in systems undergoing linear leftrightarrow bent electronic transitions in the harmonic normal mode basis have been extended to the acetylene tilde{A} ^1A_u--tilde{X} ^1Σ_g^+ transition in full dimension. Because the intensity of the overlap accumulates away from linear geometry, the Hamiltonian of the linear tilde{X} state may be approximately separated into 3 rotations and 3N-6 vibrations, resulting in a one-to-one correspondence between the normal modes in the linear and bent geometries. The calculated results reproduce experimental intensities quantitatively only at low quanta of vibrational excitation due to the exclusion of anharmonic effects. However, the qualitative results explain a number of observations that were previously not understood. A change of basis to local bending modes of the tilde{X} state has been performed to investigate Franck-Condon access to zero order bright states with extreme local bend excitation. These states are known to emerge above 12 quanta of bend excitation and are of interest because the local bending mode lies along the reaction coordinate in the acetylene rightleftharpoons vinylidene isomerization. The results indicate that the best strategy for reaching extreme local benders involves Stimulated Emission Pumping from tilde{A}-state levels with high excitation in ν_3' and ν_4', contrary to existing semi-classical arguments that ν_6' grants the best access to local bend states.
Experimental observation of a theoretically predicted nonlinear sleep spindle harmonic in human EEG.
Abeysuriya, R G; Rennie, C J; Robinson, P A; Kim, J W
2014-10-01
To investigate the properties of a sleep spindle harmonic oscillation previously predicted by a theoretical neural field model of the brain. Spindle oscillations were extracted from EEG data from nine subjects using an automated algorithm. The power and frequency of the spindle oscillation and the harmonic oscillation were compared across subjects. The bicoherence of the EEG was calculated to identify nonlinear coupling. All subjects displayed a spindle harmonic at almost exactly twice the frequency of the spindle. The power of the harmonic scaled nonlinearly with that of the spindle peak, consistent with model predictions. Bicoherence was observed at the spindle frequency, confirming the nonlinear origin of the harmonic oscillation. The properties of the sleep spindle harmonic were consistent with the theoretical modeling of the sleep spindle harmonic as a nonlinear phenomenon. Most models of sleep spindle generation are unable to produce a spindle harmonic oscillation, so the observation and theoretical explanation of the harmonic is a significant step in understanding the mechanisms of sleep spindle generation. Unlike seizures, sleep spindles produce nonlinear effects that can be observed in healthy controls, and unlike the alpha oscillation, there is no linearly generated harmonic that can obscure nonlinear effects. This makes the spindle harmonic a good candidate for future investigation of nonlinearity in the brain. Copyright © 2014 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.
Nuclear scissors modes and hidden angular momenta
Energy Technology Data Exchange (ETDEWEB)
Balbutsev, E. B., E-mail: balbuts@theor.jinr.ru; Molodtsova, I. V. [Joint Institute for Nuclear Research (Russian Federation); Schuck, P. [Université Paris-Sud, Institut de Physique Nucléaire, IN2P3–CNRS (France)
2017-01-15
The coupled dynamics of low-lying modes and various giant resonances are studied with the help of the Wigner Function Moments method generalized to take into account spin degrees of freedom and pair correlations simultaneously. The method is based on Time-Dependent Hartree–Fock–Bogoliubov equations. The model of the harmonic oscillator including spin–orbit potential plus quadrupole–quadrupole and spin–spin interactions is considered. New low-lying spin-dependent modes are analyzed. Special attention is paid to the scissors modes. A new source of nuclear magnetism, connected with counter-rotation of spins up and down around the symmetry axis (hidden angular momenta), is discovered. Its inclusion into the theory allows one to improve substantially the agreement with experimental data in the description of energies and transition probabilities of scissors modes.
Perturbative Semiclassical Trace Formulae for Harmonic Oscillators
DEFF Research Database (Denmark)
Møller-Andersen, Jakob; Ögren, Magnus
2015-01-01
U(D) to O(D) symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative (ħ → 0) trace formula. We then show how to apply the results to even-order polynomial potentials, possibly including mean-field terms. We have drawn...... the conclusion that the gross structure of the quantum spectrum is determined from only classical circular and diameter orbits for this class of systems....
Sobolev spaces associated to the harmonic oscillator
Indian Academy of Sciences (India)
Author Affiliations. B Bongioanni1 J L Torrea2. Departamento de Matemática, Facultad de Ingeniería Qímica, Universidad Nacional del Litoral, and Instituto de Matemática Aplicada del Litoral, Santa Fe (3000), Argentina; Departamento de Matemática, Facultad de Ciencias, Universidad Autónoma de Madrid, Spain ...
Improved Efficiency Type II Second Harmonic Generation
Barnes, Norman P.; Walsh, Brian M.; Reichle, Donald J., Jr.
2009-01-01
Second harmonic efficiency is limited by lateral and temporal separation of the ordinary and extraordinary components of the fundamental. A mode locked dual beam laser demonstrated these effects and a novel method to minimize them.
Kneis, Christian; Donelan, Brenda; Manek-Hönninger, Inka; Robin, Thierry; Cadier, Benoît; Eichhorn, Marc; Kieleck, Christelle
2016-06-01
A single-oscillator actively Q-switched mode-locked (QML) thulium-doped silica fiber laser is presented and used to pump a ZrF4-BaF2-LaF3-AlF3-NaF (ZBLAN) fiber for mid-infrared (mid-IR) supercontinuum (SC) generation. The fiber laser provided high-peak-power levels directly from the oscillator delivering single mode-locked pulse energies up to 48 μJ, being 2-4 orders of magnitude higher than conventional continuous wave mode-locked lasers. By pumping a ZBLAN fiber specially designed for high-output-power SC generation, 7.8 W have been achieved in all spectral bands with a spectrum extending to 4.2 μm.
Energy Technology Data Exchange (ETDEWEB)
Hoeye, Gudrun Kristine
1999-07-01
We have studied radial and nonradial oscillations in neutron stars, both in a general relativistic and non-relativistic frame, for several different equilibrium models. Different equations of state were combined, and our results show that it is possible to distinguish between the models based on their oscillation periods. We have particularly focused on the p-, f-, and g-modes. We find oscillation periods of II approx. 0.1 ms for the p-modes, II approx. 0.1 - 0.8 ms for the f-modes and II approx. 10 - 400 ms for the g-modes. For high-order (l (>{sub )} 4) f-modes we were also able to derive a formula that determines II{sub l+1} from II{sub l} and II{sub l-1} to an accuracy of 0.1%. Further, for the radial f-mode we find that the oscillation period goes to infinity as the maximum mass of the star is approached. Both p-, f-, and g-modes are sensitive to changes in the central baryon number density n{sub c}, while the g-modes are also sensitive to variations in the surface temperature. The g-modes are concentrated in the surface layer, while p- and f-modes can be found in all parts of the star. The effects of general relativity were studied, and we find that these are important at high central baryon number densities, especially for the p- and f-modes. General relativistic effects can therefore not be neglected when studying oscillations in neutron stars. We have further developed an improved Cowling approximation in the non-relativistic frame, which eliminates about half of the gap in the oscillation periods that results from use of the ordinary Cowling approximation. We suggest to develop an improved Cowling approximation also in the general relativistic frame. (Author)
Curvature, zero modes and quantum statistics
Energy Technology Data Exchange (ETDEWEB)
Calixto, M [Departamento de Matematica Aplicada y EstadIstica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de AstrofIsica de AndalucIa, Apartado Postal 3004, 18080 Granada (Spain)
2006-08-18
We explore an intriguing connection between the Fermi-Dirac and Bose-Einstein statistics and the thermal baths obtained from a vacuum radiation of coherent states of zero modes in a second quantized (many-particle) theory on the compact O(3) and noncompact O(2, 1) isometry subgroups of the de Sitter and anti-de Sitter spaces, respectively. The high frequency limit is retrieved as a (zero-curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the vacuum energy density and the cosmological constant problem. (letter to the editor)
Helson, Henry
2010-01-01
This second edition has been enlarged and considerably rewritten. Among the new topics are infinite product spaces with applications to probability, disintegration of measures on product spaces, positive definite functions on the line, and additional information about Weyl's theorems on equidistribution. Topics that have continued from the first edition include Minkowski's theorem, measures with bounded powers, idempotent measures, spectral sets of bounded functions and a theorem of Szego, and the Wiener Tauberian theorem. Readers of the book should have studied the Lebesgue integral, the elementary theory of analytic and harmonic functions, and the basic theory of Banach spaces. The treatment is classical and as simple as possible. This is an instructional book, not a treatise. Mathematics students interested in analysis will find here what they need to know about Fourier analysis. Physicists and others can use the book as a reference for more advanced topics.
Perez, R. Navarro; Schunck, N.; Lasseri, R.-D.; Zhang, C.; Sarich, J.
2017-11-01
We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. Program Files doi:http://dx.doi.org/10.17632/c5g2f92by3.1 Licensing provisions: GPL v3 Programming language: FORTRAN-95 Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013). Does the new version supersede the previous one: Yes Summary of revisions: 1. the Gogny force in both particle-hole and particle-particle channels was implemented; 2. the nuclear collective inertia at the perturbative cranking approximation was implemented; 3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments; 4. the regularization method of zero-range pairing forces was implemented; 5. the localization functions of the HFB solution were implemented; 6. a MPI interface for large-scale mass table calculations was implemented. Nature of problem:HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton
Kim, Baek-Min; Choi, Hyesun; Kim, Seong-Joong; Choi, Wookap
2017-02-01
Co-variability between the Southern Annular Mode (SAM) and the El Niño Southern Oscillation (ENSO) during the austral summer is examined, and it is found that there exists an apparent co-variability of a negative (positive) SAM during the mature period of El Niño (La Niña). However, this co-variability is largely controlled by the small number of strong ENSO cases. When strong ENSO cases are excluded, the correlation becomes non-significant. This behavior in the relationship between SAM and ENSO is supported by a series of general circulation model experiments with prescribed sea surface temperature boundary conditions that represent the incremental strengthening of El Niño (La Niña) conditions. The modeled Antarctic sub-polar jet exhibits similar behavior to that identified through observational analysis. Marked changes in both the magnitude and position of the sub-polar jet are largely controlled by particularly strong transient eddy forcing. Planetary wave forcing plays only a minor role in the co-variability, but it can explain in part the asymmetric response of the sub-polar jet between El Niño and La Niña.
Qiao, Junpeng; Zhao, Shengzhi; Yang, Kejian; Zhao, Jia; Li, Guiqiu; Li, Dechun; Li, Tao; Qiao, Wenchao; Chu, Hongwei; Luan, Chao
2017-07-01
In this paper, a sub-nanosecond KTiOPO4 (KTP)-based intracavity optical parametric oscillator (IOPO) pumped by a dual-loss modulated Q-switched and mode-locked (QML) laser with an acousto-optic modulator (AOM) and a Cr4+:YAG saturable absorber (Cr4+:YAG-SA) has been demonstrated. By changing the initial transmission of Cr4+:YAG-SA and the transmission of the output coupler at the signal wavelength, the signal pulse width compression can be realized. At an incident pump power of 8.3 W and an AOM repetition rate of 15 kHz, a single signal pulse underneath Q-switched envelope with the shortest pulse width of 220 ps was obtained. The experimental results reveal that this is a simple and effective way to obtain the sub-nanosecond OPO signal pulses. In addition, the related coupled rate equations have been set up and the simulation results agreed with the experimental results well.
Guo, Bin; Chen, Zhongsheng; Guo, Jinyun; Liu, Feng; Chen, Chuanfa; Liu, Kangli
2016-01-01
Changes in precipitation could have crucial influences on the regional water resources in arid regions such as Xinjiang. It is necessary to understand the intrinsic multi-scale variations of precipitation in different parts of Xinjiang in the context of climate change. In this study, based on precipitation data from 53 meteorological stations in Xinjiang during 1960–2012, we investigated the intrinsic multi-scale characteristics of precipitation variability using an adaptive method named ensemble empirical mode decomposition (EEMD). Obvious non-linear upward trends in precipitation were found in the north, south, east and the entire Xinjiang. Changes in precipitation in Xinjiang exhibited significant inter-annual scale (quasi-2 and quasi-6 years) and inter-decadal scale (quasi-12 and quasi-23 years). Moreover, the 2–3-year quasi-periodic fluctuation was dominant in regional precipitation and the inter-annual variation had a considerable effect on the regional-scale precipitation variation in Xinjiang. We also found that there were distinctive spatial differences in variation trends and turning points of precipitation in Xinjiang. The results of this study indicated that compared to traditional decomposition methods, the EEMD method, without using any a priori determined basis functions, could effectively extract the reliable multi-scale fluctuations and reveal the intrinsic oscillation properties of climate elements. PMID:27007388
Guo, Bin; Chen, Zhongsheng; Guo, Jinyun; Liu, Feng; Chen, Chuanfa; Liu, Kangli
2016-03-21
Changes in precipitation could have crucial influences on the regional water resources in arid regions such as Xinjiang. It is necessary to understand the intrinsic multi-scale variations of precipitation in different parts of Xinjiang in the context of climate change. In this study, based on precipitation data from 53 meteorological stations in Xinjiang during 1960-2012, we investigated the intrinsic multi-scale characteristics of precipitation variability using an adaptive method named ensemble empirical mode decomposition (EEMD). Obvious non-linear upward trends in precipitation were found in the north, south, east and the entire Xinjiang. Changes in precipitation in Xinjiang exhibited significant inter-annual scale (quasi-2 and quasi-6 years) and inter-decadal scale (quasi-12 and quasi-23 years). Moreover, the 2-3-year quasi-periodic fluctuation was dominant in regional precipitation and the inter-annual variation had a considerable effect on the regional-scale precipitation variation in Xinjiang. We also found that there were distinctive spatial differences in variation trends and turning points of precipitation in Xinjiang. The results of this study indicated that compared to traditional decomposition methods, the EEMD method, without using any a priori determined basis functions, could effectively extract the reliable multi-scale fluctuations and reveal the intrinsic oscillation properties of climate elements.
Brownian parametric oscillators
Zerbe, Christine; Jung, Peter; Hänggi, Peter
1994-05-01
We discuss the stochastic dynamics of dissipative, white-noise-driven Floquet oscillators, characterized by a time-periodic stiffness. Thus far, little attention has been paid to these exactly solvable nonstationary systems, although they carry a rich potential for several experimental applications. Here, we calculate and discuss the mean values and variances, as well as the correlation functions and the Floquet spectrum. As one main result, we find for certain parameter values that the fluctuations of the position coordinate are suppressed as compared to the equilibrium value of a harmonic oscillator (parametric squeezing).
Nonlinear MHD simulations of QH-mode DIII-D plasmas and implications for ITER high Q scenarios
Liu, F.; Huijsmans, G. T. A.; Loarte, A.; Garofalo, A. M.; Solomon, W. M.; Hoelzl, M.; Nkonga, B.; Pamela, S.; Becoulet, M.; Orain, F.; Van Vugt, D.
2018-01-01
In nonlinear MHD simulations of DIII-D QH-mode plasmas it has been found that low n kink/peeling modes (KPMs) are unstable and grow to a saturated kink-peeling mode. The features of the dominant saturated KPMs, which are localised toroidally by nonlinear coupling of harmonics, such as mode frequencies, density fluctuations and their effect on pedestal particle and energy transport, are in good agreement with the observations of the edge harmonic oscillation typically present in DIII-D QH-mode experiments. The nonlinear evolution of MHD modes including both kink-peeling modes and ballooning modes, is investigated through MHD simulations by varying the pedestal current and pressure relative to the initial conditions of DIII-D QH-mode plasma. The edge current and pressure at the pedestal are key parameters for the plasma either saturating to a QH-mode regime or a ballooning mode dominant regime. The influence of E × B flow and its shear on the QH-mode plasma has been investigated. E × B flow shear has a strong stabilisation effect on the medium to high-n modes but is destabilising for the n = 2 mode. The QH-mode extrapolation results of an ITER Q = 10 plasma show that the pedestal currents are large enough to destabilise n = 1–5 KPMs, leading to a stationary saturated kink-peeling mode.
Generation of Hydroacoustic Waves by an Oscillating Ice Block in Arctic Zones
Directory of Open Access Journals (Sweden)
Usama Kadri
2016-01-01
Full Text Available The time harmonic problem of propagating hydroacoustic waves generated in the ocean by a vertically oscillating ice block in arctic zones is discussed. The generated acoustic modes can result in orbital displacements of fluid parcels sufficiently high that may contribute to deep ocean currents and circulation. This mechanism adds to current efforts for explaining ocean circulation from a snowball earth Neoproterozoic Era to greenhouse earth arctic conditions and raises a challenge as the extent of ice blocks shrinks towards an ice-free sea. Surprisingly, unlike the free-surface setting, here it is found that the higher acoustic modes exhibit a larger contribution.
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we ...
Conformal symmetry of trapped Bose-Einstein condensates and massive Nambu-Goldstone modes
Ohashi, Keisuke; Fujimori, Toshiaki; Nitta, Muneto
2017-11-01
The Gross-Pitaevskii or nonlinear Schrödinger equation relevant to ultracold atomic gaseous Bose-Einstein condensates possesses a modified Schrödinger symmetry in two spatial dimensions, in the presence of a harmonic trapping potential, an (artificial) constant magnetic field (or rotation), and an (artificial) electric field of a quadratic electrostatic potential. We find that a variance and a center of a trapped gas with or without a vorticity can be regarded as massive Nambu-Goldstone (NG) modes associated with spontaneous breaking of the modified Schrödinger symmetry. We show that the Noether theorem for the modified Schrödinger symmetry gives universal equations of motion which describe exact time evolutions of the trapped gases such as a harmonic oscillation, a cyclotron motion, and a breathing oscillation with frequencies determined by the symmetry independent of the details of the system. We further construct an exact effective action for all the NG modes.
SEVENTH HARMONIC 20 GHz CO-GENERATOR
Energy Technology Data Exchange (ETDEWEB)
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.
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
The evolution of harmonic Indian musical drums: A mathematical perspective
Gaudet, Samuel; Gauthier, Claude; Léger, Sophie
2006-03-01
We explain using mathematics how harmonic musical drums were discovered by Indian artisans and musicians more than 2000 years ago. To this end, we introduce a harmonic error function which measures the quality of the harmonic relationship and degeneracy of the first modes of vibration of a centrally symmetric loaded membrane. We explain that although the tabla configuration found by the ancient Indians is the most natural one, other configurations exist and some are harmonically superior to the classical one.
Second and third harmonic waves excited by focused Gaussian beams.
Levy, Uri; Silberberg, Yaron
2015-10-19
Harmonic generation by tightly-focused Gaussian beams is finding important applications, primarily in nonlinear microscopy. It is often naively assumed that the nonlinear signal is generated predominantly in the focal region. However, the intensity of Gaussian-excited electromagnetic harmonic waves is sensitive to the excitation geometry and to the phase matching condition, and may depend on quite an extended region of the material away from the focal plane. Here we solve analytically the amplitude integral for second harmonic and third harmonic waves and study the generated harmonic intensities vs. focal-plane position within the material. We find that maximum intensity for positive wave-vector mismatch values, for both second harmonic and third harmonic waves, is achieved when the fundamental Gaussian is focused few Rayleigh lengths beyond the front surface. Harmonic-generation theory predicts strong intensity oscillations with thickness if the material is very thin. We reproduced these intensity oscillations in glass slabs pumped at 1550nm. From the oscillations of the 517nm third-harmonic waves with slab thickness we estimate the wave-vector mismatch in a Soda-lime glass as Δk(H)= -0.249μm(-1).
Directory of Open Access Journals (Sweden)
Aleksandra VASILJ
2010-01-01
Full Text Available Crucial problem of transport in the cities, as a source of pollution of the environment, are uncontrolled individual motorization, permanently increasing number of motor vehicles on the roads and streets that expels human primary need for walking.Reduced social area is also loaded with vibrations and increased sound pressure which often exceeds recommended 80 dB/A.Accent is on ecological problems caused by: polluted air, which comes from gas emissions (full of aerosol, metals, dust, soot, smoke, cutting and disappearance of green areas in order to provide space for transport, making huge amount of secondary waste (e. g. tyres, metal, used oil, liquids.To improve present sequences and reduce negative effects in the future it is necessary to take different measures: fiscal, administrative, educational, which will restrict use of individual, particularly car traffic. Same measures should be used to encourage users to use public transportation.Transport in the cities, with all weaknesses and comparative advantages, should be separately analyzed mode of road transport and also be an individual part in strategic documents.The most important questions that such strategy of transport in the cities should include are: regulation, privatization or other more efficient mode of organization in public transport of passengers, as well as urban elements of sustainable development of the urban areas and transport.
Gurram, Srikanth; Kuruvilla, A.; Singh, Rajpal; Bindra, K. S.
2017-06-01
We report studies on erbium:ytterbium doped fiber laser, that uses a commercially available off-the-shelf Er:Yb co-doped single mode fiber with small mode field diameter of 7 µm, which is compatible with single mode fibers used in most of the communication systems. In a FBG based laser oscillator configuration pumped at 976 nm, the single transverse mode fiber laser emitted more than 6.87 Watts of output power at 1550 nm with a conversion efficiency of ~32% over a narrow line width. The pump radiation is coupled into active fiber using free-space optics. To the best of our knowledge, this is the highest power reported in the 1.55 µm region by using commercially available off-the-shelf active fiber of small mode field diameter (~7 µm) in a simple laser oscillator configuration with 9×× nm pumping. We also observed the effect of weak secondary grating structure in FBGs on the spectral characteristics of EYDFLs and explained its significance for co-doped fiber lasers such as erbium-ytterbium fiber lasers.
DEFF Research Database (Denmark)
Verhoef, A.J.; Zhu, L.; Israelsen, Stine Møller
2015-01-01
, in contrast to dispersion compensation schemes used in previous demonstrations of all-polarization maintaining Yb-fiber oscillators. The performance of the saturable absorber mirror modelocked oscillator, that employs a free space scheme for coupling onto the saturable absorber mirror and output coupling...
Stefan, V. Alexander
2014-10-01
A novel method for alpha particle diagnostics is proposed. The theory of stimulated Raman scattering, SRS, of the fast wave and ion Bernstein mode, IBM, turbulence in multi-ion species plasmas, (Stefan University Press, La Jolla, CA, 2008). is utilized for the diagnostics of fast ions, (4)He (+2), in ITER plasmas. Nonlinear Landau damping of the IBM on fast ions near the plasma edge leads to the space-time changes in the turbulence level, (inverse alpha particle channeling). The space-time monitoring of the IBM turbulence via the SRS techniques may prove efficient for the real time study of the fast ion velocity distribution function, spatial distribution, and transport. Supported by Nikola Tesla Labs., La Jolla, CA 92037.
Directory of Open Access Journals (Sweden)
Piotr FOLĘGA
2014-03-01
Full Text Available The variety of types and sizes currently in production harmonic drive is a problem in their rational choice. Properly selected harmonic drive must meet certain requirements during operation, and achieve the anticipated service life. The paper discusses the problems associated with the selection of the harmonic drive. It also presents the algorithm correct choice of harmonic drive. The main objective of this study was to develop a computer program that allows the correct choice of harmonic drive by developed algorithm.
Bulovich, S. V.
2017-11-01
The structure of the gas flow in the vicinity of the open end of a tube for the oscillating gas flow caused by piston oscillations at the first resonance frequency at the other end of the tube has been determined by numerical integration of the Navier-Stokes equations using the ANSYS FLUENT program package. For the variant of the tube with an infinitely long flange and a sharp edge, the influence of the piston displacement amplitude on the gas flow rate in the tube is investigated, and the phases of gas inflow and outflow during the period of oscillation have been determined.
Kaur, Sukhdeep; Sharma, A. K.; Salih, Hyder A.
2009-04-01
Second harmonic generation of a right circularly polarized Gaussian electromagnetic beam in a magnetized plasma is investigated. The beam causes Ohmic heating of electrons and subsequent redistribution of the plasma, leading to self-defocusing. The radial density gradient, in conjunction with the oscillatory electron velocity, produces density oscillation at the wave frequency. The density oscillation beats with the oscillatory velocity to produce second harmonic current density, giving rise to resonant second harmonic radiation when the wave frequency is one-third of electron cyclotron frequency. The second harmonic field has azimuthal dependence as exp(iθ). The self-defocusing causes a reduction in the efficiency of harmonic generation.
Rosas-Ortiz, Oscar; Zelaya, Kevin
2018-01-01
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a mathematical procedure to satisfy the superposition principle. In this form the non-Hermitian oscillators can be studied in much the same way as in the Hermitian approaches. Two different nonlinear algebras generated by properly constructed ladder operators are found and the corresponding generalized coherent states are obtained. The non-Hermitian oscillators can be steered to the conventional one by the appropriate selection of parameters. In such limit, the generators of the nonlinear algebras converge to generalized ladder operators that would represent either intensity-dependent interactions or multi-photon processes if the oscillator is associated with single mode photon fields in nonlinear media.
Small Oscillations via Conservation of Energy
Troy, Tia; Reiner, Megan; Haugen, Andrew J.; Moore, Nathan T.
2017-01-01
The work describes an analogy-based small oscillations analysis of a standard static equilibrium lab problem. In addition to force analysis, a potential energy function for the system is developed, and by drawing out mathematical similarities to the simple harmonic oscillator, we are able to describe (and experimentally verify) the period of small…
Coherent ultrafast pulse synthesis between an optical parametric oscillator and a laser.
Sun, Jinghua; Reid, Derryck T
2009-03-15
We have demonstrated coherent pulse synthesis between the carrier-envelope, phase-locked, second-harmonic pulses from a synchronously pumped femtosecond optical parametric oscillator and those from its self-mode-locked Ti:sapphire pump laser. By using a single nonlinear crystal for parametric and second-harmonic generation, we maximized the common-mode rejection of environmental noise, obtaining a temporal overlap between the pulses with a precision of 30 as (1% of the optical period) in an observation time of 20 ms. Mutual coherence between the two parent pulses was verified optically by spectral interferometry, and synthesis was tested by measuring the autocorrelation of the combined pulses, with and without carrier-envelope phase locking.
Harmonic polynomials, hyperspherical harmonics, and atomic spectra
Avery, John Scales
2010-01-01
The properties of monomials, homogeneous polynomials and harmonic polynomials in d-dimensional spaces are discussed. The properties are shown to lead to formulas for the canonical decomposition of homogeneous polynomials and formulas for harmonic projection. Many important properties of spherical harmonics, Gegenbauer polynomials and hyperspherical harmonics follow from these formulas. Harmonic projection also provides alternative ways of treating angular momentum and generalised angular momentum. Several powerful theorems for angular integration and hyperangular integration can be derived in this way. These purely mathematical considerations have important physical applications because hyperspherical harmonics are related to Coulomb Sturmians through the Fock projection, and because both Sturmians and generalised Sturmians have shown themselves to be extremely useful in the quantum theory of atoms and molecules.
Entanglement between Collective Operators in a Linear Harmonic Chain
Kofler, Johannes; Vedral, Vlatko; Kim, Myungshik S.; Brukner, Caslav
2005-01-01
We investigate entanglement between collective operators of two blocks of oscillators in an infinite linear harmonic chain. These operators are defined as averages over local operators (individual oscillators) in the blocks. On the one hand, this approach of "physical blocks" meets realistic experimental conditions, where measurement apparatuses do not interact with single oscillators but rather with a whole bunch of them, i.e., where in contrast to usually studied "mathematical blocks" not e...
Small oscillations via conservation of energy
Troy, Tia; Reiner, Megan; Haugen, Andrew J.; Moore, Nathan T.
2017-11-01
The work describes an analogy-based small oscillations analysis of a standard static equilibrium lab problem. In addition to force analysis, a potential energy function for the system is developed, and by drawing out mathematical similarities to the simple harmonic oscillator, we are able to describe (and experimentally verify) the period of small oscillations about the static equilibrium state. The problem was developed and implemented in a standard University Physics course at Winona State University.
Quantum dissipative effect of one dimension coupled anharmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Sulaiman, A. [Badan Pengkajian dan Penerapan Teknologi, BPPT Bld. II (19thfloor), Jl. M.H. Thamrin 8, Jakarta 10340 (Indonesia); Indonesia Center for Theoretical and Mathematical Physics (ICTMP), Jl. Ganesha 10, Bandung 40132 (Indonesia); Zen, Freddy P. [Theoretical Physics Laboratory (THEPI), Department of Physics, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132 (Indonesia); Indonesia Center for Theoretical and Mathematical Physics (ICTMP), Jl. Ganesha 10, Bandung 40132 (Indonesia)
2015-04-16
Quantum dissipative effect of one dimension coupled anharmonic oscillator is investigated. The systems are two coupled harmonic oscillator with the different masses. The dissipative effect is studied based on the quantum state diffusion formalism. The result show that the anharmonic effect increase the amplitude but the lifetime of the oscillation depend on the damping coefficient and do not depend on the temperature.
Harmonics of circadian gene transcription in mammals.
Directory of Open Access Journals (Sweden)
Michael E Hughes
2009-04-01
Full Text Available The circadian clock is a molecular and cellular oscillator found in most mammalian tissues that regulates rhythmic physiology and behavior. Numerous investigations have addressed the contribution of circadian rhythmicity to cellular, organ, and organismal physiology. We recently developed a method to look at transcriptional oscillations with unprecedented precision and accuracy using high-density time sampling. Here, we report a comparison of oscillating transcription from mouse liver, NIH3T3, and U2OS cells. Several surprising observations resulted from this study, including a 100-fold difference in the number of cycling transcripts in autonomous cellular models of the oscillator versus tissues harvested from intact mice. Strikingly, we found two clusters of genes that cycle at the second and third harmonic of circadian rhythmicity in liver, but not cultured cells. Validation experiments show that 12-hour oscillatory transcripts occur in several other peripheral tissues as well including heart, kidney, and lungs. These harmonics are lost ex vivo, as well as under restricted feeding conditions. Taken in sum, these studies illustrate the importance of time sampling with respect to multiple testing, suggest caution in use of autonomous cellular models to study clock output, and demonstrate the existence of harmonics of circadian gene expression in the mouse.
Energetics and optimum motion of oscillating lifting surfaces. [energy losses of rigid wings
Ahmadi, A. R.; Widnall, S. E.
1983-01-01
Low-frequency, unsteady, lifting-line theory is used to characterize the energetics and optimum motion of an unswept rigid wing oscillating harmonically in an inviscid, incompressible flow. The energetics calculations account for the leading edge suction force, the power absorbed in the wing oscillations, and the energy loss rate produced by vortex shedding. Optimization is achieved by minimizing the average energy loss rate in relation to a given thrust, and a unique solution is found in the three dimensional case for low, reduced frequencies. The two-dimensional solution is nonunique, a condition which is examined in terms of the normal modes of the energy loss rate matrix. An invisible mode with a hydrodynamic efficiency of 100 pct is obtained in the two-dimensional case, causing the nonuniqueness of the solution by yielding no fixed positive thrust through perfect unsteady feathering.
Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions
Mustafa, M. T.
2012-01-01
For Riemannian manifolds $M$ and $N$ , admitting a submersion $\\varphi $ with compact fibres, we introduce the projection of a function via its decomposition intohorizontal and vertical components. By comparing the Laplacians on $M$ and $N$ , we determine conditions under which a harmonic function on $U={\\varphi }^{-1}(V)\\subset M$ projects down, via its horizontal component, to a harmonic function on $V\\subset N$ .
Heemink, Arnold; de Jong, B.; Prins, Harrie
1991-01-01
In this paper we describe a new approach to the harmonic analysis of the tide. For a number of reasons the harmonic constants are not really constant but vary slowly in time. Therefore, we introduce a narrow-band noise process to model the time-varying behaviour of these harmonic parameters.
Saio, Hideyuki; Kurtz, Donald W.; Murphy, Simon J.; Antoci, Victoria L.; Lee, Umin
2018-02-01
Asteroseismic inference from pressure modes (p modes) and buoyancy, or gravity, modes (g modes) is ubiquitous for stars across the Hertzsprung-Russell diagram. Until now, however, discussion of r modes (global Rossby waves) has been rare. Here we derive the expected frequency ranges of r modes in the observational frame by considering the visibility of these modes. We find that the frequencies of r modes of azimuthal order m appear as groups at slightly lower frequency than m times the rotation frequency. Comparing the visibility curves for r modes with Fourier amplitude spectra of Kepler light curves of upper main-sequence B, A, and F stars, we find that r modes are present in many γ Dor stars (as first discovered by Van Reeth et al.), spotted stars, and so-called heartbeat stars, which are highly eccentric binary stars. We also find a signature of r modes in a frequently bursting Be star observed by Kepler. In the amplitude spectra of moderately to rapidly rotating γ Dor stars, r-mode frequency groups appear at lower frequency than prograde g-mode frequency groups, while in the amplitude spectra of spotted early A to B stars, groups of symmetric (with respect to the equator) r-mode frequencies appear just below the frequency of a structured peak that we suggest represents an approximate stellar rotation rate. In many heartbeat stars, a group of frequencies can be fitted with symmetric m = 1 r modes, which can be used to obtain rotation frequencies of these stars.
Interaction of low- and high-frequency oscillations in resonant systems with distributed interaction
Bulgakov, S. A.; Vavriv, D. M.
1991-03-01
The oscillation dynamics of synchronized resonant oscillators with distributed interaction in the presence of LF modulation of the beam is analyzed. It is shown that the interaction of LF and HF oscillations can lead to the excitation of stochastic oscillations. Conditions and scenarios of the generation of such oscillations are established for oscillators with soft and hard oscillation-excitation modes.
Primer on coupling collective electronic oscillations to nuclei
Energy Technology Data Exchange (ETDEWEB)
Solem, J.C.; Biedenharn, L.C. Jr.
1987-07-01
On the basis of simple heuristic models, we show that atomic electrons can amplify fields observed at the nucleus, generate harmonics, and drive higher multipolarities. Considered is a model with the nucleus at the focus of a uniformly charged ellipsoid. It amplifies an oscillating external electric field and produces an oscillating electric-field gradient but no higher derivatives. The electric field has only odd harmonics and the electric-field gradient has only even harmonics. There is an optimum intensity for driving each harmonic. Commented on is the relevance of these results to the U/sup 235/ experiment and to the gamma-ray laser.
Long-period oscillations of active region patterns: least-squares mapping on second-order curves
Dumbadze, G.; Shergelashvili, B. M.; Kukhianidze, V.; Ramishvili, G.; Zaqarashvili, T. V.; Khodachenko, M.; Gurgenashvili, E.; Poedts, S.; De Causmaecker, P.
2017-01-01
Context. Active regions (ARs) are the main sources of variety in solar dynamic events. Automated detection and identification tools need to be developed for solar features for a deeper understanding of the solar cycle. Of particular interest here are the dynamical properties of the ARs, regardless of their internal structure and sunspot distribution. Aims: We studied the oscillatory dynamics of two ARs: NOAA 11327 and NOAA 11726 using two different methods of pattern recognition. Methods: We developed a novel method of automated AR border detection and compared it to an existing method for the proof-of-concept. The first method uses least-squares fitting on the smallest ellipse enclosing the AR, while the second method applies regression on the convex hull. Results: After processing the data, we found that the axes and the inclination angle of the ellipse and the convex hull oscillate in time. These oscillations are interpreted as the second harmonic of the standing long-period kink oscillations (with the node at the apex) of the magnetic flux tube connecting the two main sunspots of the ARs. We also found that the inclination angles oscillate with characteristic periods of 4.9 h in AR 11726 and 4.6 h in AR 11327. In addition, we discovered that the lengths of the pattern axes in the ARs oscillate with similar characteristic periods and these oscillations might be ascribed to standing global flute modes. Conclusions: In both ARs we have estimated the distribution of the phase speed magnitude along the magnetic tubes (along the two main spots) by interpreting the obtained oscillation of the inclination angle as the standing second harmonic kink mode. After comparing the obtained results for fast and slow kink modes, we conclude that both of these modes are good candidates to explain the observed oscillations of the AR inclination angles, as in the high plasma β regime the phase speeds of these modes are comparable and on the order of the Alfvén speed. Based on the
Mitigation of Voltage and Current Harmonics in Grid-Connected Microgrids
DEFF Research Database (Denmark)
Savaghebi, Mehdi; Guerrero, Josep M.; Jalilian, Alireza
2012-01-01
coupling (PCC), voltage compensation mode is activated in order to provide a high voltage quality at PCC. Otherwise, grid current harmonics are mitigated (current compensation mode) in order to avoid excessive harmonic supply by the grid. In both modes, harmonic compensation is achieved through proper......In this paper, a control approach is proposed for selective compensation of main voltage and current harmonics in grid-connected microgrids. Two modes of compensation are considered, i.e. voltage and current compensation modes. In the case that sensitive loads are connected to the point of common...... control of distributed generators (DGs) interface converters. The compensation effort of each harmonic is shared considering the corresponding current harmonic supplied by the DGs. The control system of each DG comprises harmonic compensator, power controllers, voltage and current controllers and virtual...
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.
Hyperchaotic system with unstable oscillators
DEFF Research Database (Denmark)
Murali, K.; Tamasevicius, A.; Mykolaitis, G.
2000-01-01
A simple electronic system exhibiting hyperchaotic behaviour is described. The system includes two nonlinearly coupled 2nd order unstable oscillators, each composed of an LC resonance loop and an amplifier. The system is investigated by means of numerical integration of appropriate differential...... equations, PSPICE simulations and hardware experiments. The Lyapunov exponents are presented to confirm hyperchaotic mode of the oscillations....
Non normal modal analysis of oscillations in boiling water reactors
Energy Technology Data Exchange (ETDEWEB)
Suarez-Antola, Roberto, E-mail: roberto.suarez@miem.gub.uy [Ministerio de Industria, Energia y Mineria (MIEM), Montevideo (Uruguay); Flores-Godoy, Jose-Job, E-mail: job.flores@ibero.mx [Universidad Iberoamericana (UIA), Mexico, DF (Mexico). Dept. de Fisica Y Matematicas
2013-07-01
The first objective of the present work is to construct a simple reduced order model for BWR stability analysis, combining a two nodes nodal model of the thermal hydraulics with a two modes modal model of the neutronics. Two coupled non-linear integral-differential equations are obtained, in terms of one global (in phase) and one local (out of phase) power amplitude, with direct and cross feedback reactivities given as functions of thermal hydraulics core variables (void fractions and temperatures). The second objective is to apply the effective life time approximation to further simplify the nonlinear equations. Linear approximations for the equations of the amplitudes of the global and regional modes are derived. The linearized equation for the amplitude of the global mode corresponds to a decoupled and damped harmonic oscillator. An analytical closed form formula for the damping coefficient, as a function of the parameters space of the BWR, is obtained. The coefficient changes its sign (with the corresponding modification in the decay ratio) when a stability boundary is crossed. This produces a supercritical Hopf bifurcation, with the steady state power of the reactor as the bifurcation parameter. However, the linearized equation for the amplitude of the regional mode corresponds always to an over-damped and always coupled (with the amplitude of the global mode) harmonic oscillator, for every set of possible values of core parameters (including the steady state power of the reactor) in the framework of the present mathematical model. The equation for the above mentioned over damped linear oscillator is closely connected with a non-normal operator. Due to this connection, there could be a significant transient growth of some solutions of the linear equation. This behavior allows a significant shrinking of the basin of attraction of the equilibrium state. The third objective is to apply the above approach to partially study the stability of the regional mode and
Jones, R. T.
1976-01-01
For acoustic tests the violin is driven laterally at the bridge by a small speaker of the type commonly found in pocket transistor radios. An audio oscillator excites the tone which is picked up by a sound level meter. Gross patterns of vibration modes are obtained by the Chladni method.
High harmonic phase in molecular nitrogen
Energy Technology Data Exchange (ETDEWEB)
McFarland, Brian K.
2009-10-17
Electronic structure in atoms and molecules modulates the amplitude and phase of high harmonic generation (HHG). We report measurements of the high harmonic spectral amplitude and phase in N{sub 2}. The phase is measured interferometrically by beating the N{sub 2} harmonics with those of an Ar reference oscillator in a gas mixture. A rapid phase shift of 0.2{pi} is observed in the vicinity of the HHG spectral minimum, where a shift of {pi} had been presumed [J. Itatani et al., Nature 432, 867 (2004)]. We compare the phase measurements to a simulation of the HHG recombination step in N{sub 2} that is based on a simple interference model. The results of the simulation suggest that modifications beyond the simple interference model are needed to explain HHG spectra in molecules.
Nonlinear (Anharmonic Casimir Oscillator
Directory of Open Access Journals (Sweden)
Habibollah Razmi
2011-01-01
Full Text Available We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an nonlinear (anharmonic Casimir oscillator. Generally, the equation of motion of this nonlinear micromechanical Casimir oscillator has no exact solvable (analytical solution and the turning point(s of the system has (have no fixed position(s; however, for particular values of the stiffness of the micro spring and at appropriately well-chosen distance scales and conditions, there is (are approximately sinusoidal solution(s for the problem (the variable turning points are collected in a very small interval of positions. This, as a simple and elementary plan, may be useful in controlling the Casimir stiction problem in micromechanical devices.
A Passive Harmonic Tag for Humidity Sensing
Antonio Lazaro; Ramon Villarino; David Girbau
2014-01-01
This paper describes a passive harmonic tag for radio frequency identification (RFID) and wireless sensor applications. The tag uses a dual polarized UHF patch antenna as an input antenna. One of the outputs is connected to a frequency doubler, which consists of a Schottky diode with its output connected to a patch tuned at twice the input frequency. The other output of the input antenna feeds a DC power harvested converter that drives an oscillator which modulates its output signal by contro...
Aeroelastic Computations of a Compressor Stage Using the Harmonic Balance Method
Reddy, T. S. R.
2010-01-01
The aeroelastic characteristics of a compressor stage were analyzed using a computational fluid dynamic (CFD) solver that uses the harmonic balance method to solve the governing equations. The three dimensional solver models the unsteady flow field due to blade vibration using the Reynolds-Averaged Navier-Stokes equations. The formulation enables the study of the effect of blade row interaction through the inclusion of coupling modes between blade rows. It also enables the study of nonlinear effects of high amplitude blade vibration by the inclusion of higher harmonics of the fundamental blade vibration frequency. In the present work, the solver is applied to study in detail the aeroelastic characteristics of a transonic compressor stage. Various parameters were included in the study: number of coupling modes, blade row axial spacing, and operating speeds. Only the first vibration mode is considered with amplitude of oscillation in the linear range. Both aeroelastic stability (flutter) of rotor blade and unsteady loading on the stator are calculated. The study showed that for the stage considered, the rotor aerodynamic damping is not influenced by the presence of the stator even when the axial spacing is reduced by nearly 25 percent. However, the study showed that blade row interaction effects become important for the unsteady loading on the stator when the axial spacing is reduced by the same amount.
Decay of oscillating universes
Mithani, Audrey Todhunter
2016-08-01
It has been suggested by Ellis et al that the universe could be eternal in the past, without beginning. In their model, the "emergent universe'' exists forever in the past, in an "eternal'' phase before inflation begins. We will show that in general, such an "eternal'' phase is not possible, because of an instability due to quantum tunneling. One candidate model, the "simple harmonic universe'' has been shown by Graham et al to be perturbatively stable; we find that it is unstable with respect to quantum tunneling. We also investigate the stability of a distinct oscillating model in loop quantum cosmology with respect to small perturbations and to quantum collapse. We find that the model has perturbatively stable and unstable solutions, with both types of solutions occupying significant regions of the parameter space. All solutions are unstable with respect to collapse by quantum tunneling to zero size. In addition, we investigate the effect of vacuum corrections, due to the trace anomaly and the Casimir effect, on the stability of an oscillating universe with respect to decay by tunneling to the singularity. We find that these corrections do not generally stabilize an oscillating universe. Finally, we determine the decay rate of the oscillating universe. Although the wave function of the universe lacks explicit time dependence in canonical quantum cosmology, time evolution may be present implicitly through the semiclassical superspace variables, which themselves depend on time in classical dynamics. Here, we apply this approach to the simple harmonic universe, by extending the model to include a massless, minimally coupled scalar field φ which has little effect on the dynamics but can play the role of a "clock''.
Scleronomic holonomic constraints and conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Munoz, R; Gonzalez-Garcia, G; Izquierdo-De La Cruz, E Izquierdo-De La [Universidad Autonoma de la Ciudad de Mexico, Centro Historico, Fray Servando Teresa de Mier 92, Col Centro, Del Cuauhtemoc, Mexico DF, CP 06080 (Mexico); Fernandez-Anaya, G, E-mail: rodrigo.munoz@uacm.edu.mx, E-mail: gggharper@gmail.com, E-mail: erickidc@gmail.com, E-mail: guillermo.fernandez@uia.mx [Universidad Iberoamericana, Departamento de Fisica y Matematicas, Prolongacon Paseo de de la Reforma 880, Col Lomas de Santa Fe, Del Alvaro Obregn, Mexico DF, CP 01219 (Mexico)
2011-05-15
A bead sliding, under the sole influence of its own weight, on a rigid wire shaped in the fashion of a plane curve, will describe (generally anharmonic) oscillations around a local minimum. For given shapes, the bead will behave as a harmonic oscillator in the whole range, such as an unforced, undamped, Duffing oscillator, etc. We also present cases in which the effective potential acting on the bead is not analytical around a minimum. The small oscillation approximation cannot be applied to such pathological cases. Nonetheless, these latter instances are studied with other standard techniques.
Detecting harmonic signals in a noisy time-series: the z-domain Autoregressive (AR-z) spectrum
Ding, Hao; Chao, Benjamin F.
2015-06-01
We develop a new method referred to as the AR-z spectrum for detecting harmonic signals with exponential decay/growth contained in a noisy time-series by extending the autoregressive (AR) method of Chao & Gilbert. The method consists of (i) `blindly' forcing one 2nd-order AR fit to the signal content in the frequency domain for any chosen frequency whether or not there is truly a signal; (ii) finding the corresponding AR (complex-conjugate pair of) poles in the complex z-domain; (iii) converting the pole locations into the corresponding complex frequencies of the harmonic signals via the Prony's relation and (iv) constructing the Lorentzian power spectrum in the z-domain, conceptually constituting the analytical continuation of the spectrum from the (real) frequency domain to the complex z-domain, where a true harmonic signal is manifested as a Lorentzian peak. The AR-z spectrum can be further enhanced by forming the product spectrum from multiple records as available. We apply the AR-z spectral method to detect and to estimate the complex frequencies of the Earth's normal-modes of free oscillation using superconducting gravimeter records after recent large earthquakes. Specifically we show examples of detection and precise estimation of the frequencies and Q values of the split singlets of the spheroidal modes 0S2, 2S1, 1S2 and 0S0, and report the mode couplings manifested by the gravimeter recording of the toroidal modes 0T2, 0T3 and 0T4. The AR-z spectrum proves to be highly sensitive for harmonic signal of decaying sinusoids in comparison to the conventional Fourier-based spectrum, particularly when the signal in question is weak and where high spectral resolution is desired.
harmonics mitigation on industrial loads using series and parallel
African Journals Online (AJOL)
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system efficiency and provide great energy saving, their vulnerability to harmonics ... wave. Typical examples of harmonics sources include fluorescent lighting, computer switch mode power supplies, static var compensators, variable frequency motor drives, dc-dc converters, inverters, chillers etc. [13]. When considering ...
Intense Harmonic Emissions Observed in Saturn's Ionosphere
Sulaiman, A. H.; Kurth, W. S.; Persoon, A. M.; Menietti, J. D.; Farrell, W. M.; Ye, S.-Y.; Hospodarsky, G. B.; Gurnett, D. A.; Hadid, L. Z.
2017-12-01
The Cassini spacecraft's first Grand Finale orbit was carried out in April 2017. This set of 22 orbits had an inclination of 63° with a periapsis grazing Saturn's ionosphere, thus providing unprecedented coverage and proximity to the planet. Cassini's Radio and Plasma Wave Science instrument repeatedly detected intense electrostatic waves and their harmonics near closest approach in the dayside equatorial topside ionosphere. The fundamental modes were found to both scale and trend best with the H+ plasma or lower hybrid frequencies, depending on the plasma composition considered. The fine-structured harmonics are unlike previous observations, which scale with cyclotron frequencies. We explore their generation mechanism and show strong evidence of their association with whistler mode waves, consistent with theory. The possibility of Cassini's presence in the ionosphere influencing the resonance and harmonics is discussed. Given their link to the lower hybrid frequency, these emissions may offer clues to constraining Saturn's ionospheric properties.
Second harmonic generation in resonant optical structures
Energy Technology Data Exchange (ETDEWEB)
Eichenfield, Matt; Moore, Jeremy; Friedmann, Thomas A.; Olsson, Roy H.; Wiwi, Michael; Padilla, Camille; Douglas, James Kenneth; Hattar, Khalid Mikhiel
2018-01-09
An optical second-harmonic generator (or spontaneous parametric down-converter) includes a microresonator formed of a nonlinear optical medium. The microresonator supports at least two modes that can be phase matched at different frequencies so that light can be converted between them: A first resonant mode having substantially radial polarization and a second resonant mode having substantially vertical polarization. The first and second modes have the same radial order. The thickness of the nonlinear medium is less than one-half the pump wavelength within the medium.
Periodic motions and resonances of impact oscillators
Dyskin, Arcady V.; Pasternak, Elena; Pelinovsky, Efim
2012-06-01
Bilinear oscillators - the oscillators whose springs have different stiffnesses in compression and tension - model a wide range of phenomena. A limiting case of bilinear oscillator with infinite stiffness in compression - the impact oscillator - is studied here. We investigate a special set of impact times - the eigenset, which corresponds to the solution of the homogeneous equation, i.e. the oscillator without the driving force. We found that this set and its subsets are stable with respect to variation of initial conditions. Furthermore, amongst all periodic sets of impact times with the period commensurate with the period of driving force, the eigenset is the only one which can support resonances, in particular the multi-'harmonic' resonances. Other resonances should produce non-periodic sets of impact times. This funding indicates that the usual simplifying assumption [e.g., S.W. Shaw, P.J. Holmes, A periodically forced piecewise linear oscillator, Journal of Sound and Vibration 90 (1983) 129-155] that the times between impacts are commensurate with the period of the driving force does not always hold. We showed that for the first sub-'harmonic resonance' - the resonance achieved on a half frequency of the main resonance - the set of impact times is asymptotically close to the eigenset. The envelope of the oscillations in this resonance increases as a square root of time, opposite to the linear increase characteristic of multi-'harmonic' resonances.
Espinosa, Ismael; Gonzalez, Hortensia; Quiza, Jorge; Gonazalez, J. Jesus; Arroyo, Ruben; Lara, Ritaluz
1995-01-01
Oscillation of electrical activity has been found in many nervous systems, from invertebrates to vertebrates including man. There exists experimental evidence of very simple circuits with the capability of oscillation. Neurons with intrinsic oscillation have been found and also neural circuits where oscillation is a property of the network. These two types of oscillations coexist in many instances. It is nowadays hypothesized that behind synchronization and oscillation there is a system of coupled oscillators responsible for activities that range from locomotion and feature binding in vision to control of sleep and circadian rhythms. The huge knowledge that has been acquired on oscillators from the times of Lord Rayleigh has made the simulation of neural oscillators a very active endeavor. This has been enhanced with more recent physiological findings about small neural circuits by means of intracellular and extracellular recordings as well as imaging methods. The future of this interdisciplinary field looks very promising; some researchers are going into quantum mechanics with the idea of trying to provide a quantum description of the brain. In this work we describe some simulations using neuron models by means of which we form simple neural networks that have the capability of oscillation. We analyze the oscillatory activity with root locus method, cross-correlation histograms, and phase planes. In the more complicated neural network models there is the possibility of chaotic oscillatory activity and we study that by means of Lyapunov exponents. The companion paper shows an example of that kind.
Hidden symmetries of deformed oscillators
Directory of Open Access Journals (Sweden)
Sergey Krivonos
2017-11-01
Full Text Available We associate with each simple Lie algebra a system of second-order differential equations invariant under a non-compact real form of the corresponding Lie group. In the limit of a contraction to a Schrödinger algebra, these equations reduce to a system of ordinary harmonic oscillators. We provide two clarifying examples of such deformed oscillators: one system invariant under SO(2,3 transformations, and another system featuring G2(2 symmetry. The construction of invariant actions requires adding semi-dynamical degrees of freedom; we illustrate the algorithm with the two examples mentioned.
Energy Technology Data Exchange (ETDEWEB)
Maccari, A. [Istituto Tecnico `G. Cardano`, Monterotondo, Rome (Italy)
1996-08-01
The most important characteristics of the non-local oscillator, an oscillator subjected to an additional non-local force, are extensively studied by means of a new asymptotic perturbation method that is able to furnish an approximate solution of weakly non-linear differential equations. The resulting motion is doubly periodic, because a second little frequency appears, in addition to the fundamental harmonic frequency. Comparison with the numerical solution obtained by the Runge-Kitta method confirms the validity of the asymptotic perturbation method and its importance for the study of non-linear dynamical systems.
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
Soft-x-ray harmonic comb from relativistic electron spikes.
Pirozhkov, A S; Kando, M; Esirkepov, T Zh; Gallegos, P; Ahmed, H; Ragozin, E N; Faenov, A Ya; Pikuz, T A; Kawachi, T; Sagisaka, A; Koga, J K; Coury, M; Green, J; Foster, P; Brenner, C; Dromey, B; Symes, D R; Mori, M; Kawase, K; Kameshima, T; Fukuda, Y; Chen, L; Daito, I; Ogura, K; Hayashi, Y; Kotaki, H; Kiriyama, H; Okada, H; Nishimori, N; Imazono, T; Kondo, K; Kimura, T; Tajima, T; Daido, H; Rajeev, P; McKenna, P; Borghesi, M; Neely, D; Kato, Y; Bulanov, S V
2012-03-30
We demonstrate a new high-order harmonic generation mechanism reaching the "water window" spectral region in experiments with multiterawatt femtosecond lasers irradiating gas jets. A few hundred harmonic orders are resolved, giving μJ/sr pulses. Harmonics are collectively emitted by an oscillating electron spike formed at the joint of the boundaries of a cavity and bow wave created by a relativistically self-focusing laser in underdense plasma. The spike sharpness and stability are explained by catastrophe theory. The mechanism is corroborated by particle-in-cell simulations.
The electronic system for mechanical oscillation parameters registration
Directory of Open Access Journals (Sweden)
Bulavin L. A.
2008-08-01
Full Text Available On the basis of the 8-bit microcontroller Microchip PIC16F630 the digital electronic device for harmonic oscillation parameters registration was developed. The device features are simple electric circuit and high operating speed (response time is less than 10 microseconds. The relevant software for the computer-controlled recording of harmonic oscillation parameters was designed. The device can be used as a part of the experimental setup for consistent fluids rheological parameters measurements.
Discretized representations of harmonic variables by bilateral Jacobi operators
Directory of Open Access Journals (Sweden)
Andreas Ruffing
2000-01-01
Full Text Available Starting from a discrete Heisenberg algebra we solve several representation problems for a discretized quantum oscillator in a weighted sequence space. The Schrödinger operator for a discrete harmonic oscillator is derived. The representation problem for a q-oscillator algebra is studied in detail. The main result of the article is the fact that the energy representation for the discretized momentum operator can be interpreted as follows: It allows to calculate quantum properties of a large number of non-interacting harmonic oscillators at the same time. The results can be directly related to current research on squeezed laser states in quantum optics. They reveal and confirm the observation that discrete versions of continuum Schrodinger operators allow more structural freedom than their continuum analogs do.
Damping of Collective Oscillations in a Box Trap
Proukakis, Nick; Lee, Kean Loon; Zaremba, Eugene; Turzak, Patrik; Eigen, Chris; Gaunt, Alex; Smith, Rob; Hadzibabic, Zoran; Navon, Nir
2017-04-01
We model numerically the lowest-lying collective mode of a Bose gas in a box trap excited by a kick in the potential, as in a recent experiment. Our analysis is performed at finite temperatures (below the critical region), based on the so-called ``ZNG'' model, in which the condensate is described by a dissipative Gross-Pitaevskii equation which is itself self-consistently coupled to a dynamical thermal cloud described by a quantum Boltzmann equation `` a model which has proven most successful in describing damping observed in harmonic traps. For typical parameters probed far from the hydrodynamic region, we find a single oscillation - whose frequency agrees well with experiments - with the thermal cloud rapidly damping out higher frequency modes primarily through self-consistent dynamical mean-field coupling. Our results are confirmed by an independent analysis with the stochastic projected Gross-Pitaevskii equation. Intuitively, we find damping in a box trap to depend much more weakly on temperature than in harmonic traps, in broad agreement with experimental data. EPSRC; NSERC; ERC; Royal Society.
Oscillations of a polarizable vacuum
Directory of Open Access Journals (Sweden)
James G. Gilson
1991-01-01
Full Text Available A classical basis for one-dimensional Schrödinger quantum theory is constructed from simple vacuum polarization harmonic oscillators within standard stochastic theory. The model is constructed on a two-dimensional phase configuration surface with phase velocity vectors that have a speed of light zitterbewegung behaviour character. The system supplies a natural Hermitian scalar product describing probability density which is derived from angular momentum considerations. The generality of the model which is extensive is discussed.
Direct harmonic voltage control strategy for shunt active power filter
DEFF Research Database (Denmark)
Munir, Hafiz Mudassir; Zou, JianXiao; Xie, Chuan
2017-01-01
Shunt active power filters (S-APF) are highly popular ways for harmonic compensation due to the high performance and simplicity of installation. S-APF is commonly controlled in current control mode with load harmonic current detection, which is not quite suitable for the distributed power...... generation system (DPGS) where the nonlinear loads are highly dispersed. Local harmonic voltage detection based Resistive-APF (R-APF) seems more suitable to be applied in the DPGS, however, R-APF suffers from poor compensation performance and difficulty of parameter tuning. In this paper, a direct harmonic...
Solar atmosphere wave dynamics generated by solar global oscillating eigenmodes
Griffiths, M. K.; Fedun, V.; Erdélyi, R.; Zheng, R.
2018-01-01
The solar atmosphere exhibits a diverse range of wave phenomena, where one of the earliest discovered was the five-minute global acoustic oscillation, also referred to as the p-mode. The analysis of wave propagation in the solar atmosphere may be used as a diagnostic tool to estimate accurately the physical characteristics of the Sun's atmospheric layers. In this paper, we investigate the dynamics and upward propagation of waves which are generated by the solar global eigenmodes. We report on a series of hydrodynamic simulations of a realistically stratified model of the solar atmosphere representing its lower region from the photosphere to low corona. With the objective of modelling atmospheric perturbations, propagating from the photosphere into the chromosphere, transition region and low corona, generated by the photospheric global oscillations the simulations use photospheric drivers mimicking the solar p-modes. The drivers are spatially structured harmonics across the computational box parallel to the solar surface. The drivers perturb the atmosphere at 0.5 Mm above the bottom boundary of the model and are placed coincident with the location of the temperature minimum. A combination of the VALIIIC and McWhirter solar atmospheres are used as the background equilibrium model. We report how synthetic photospheric oscillations may manifest in a magnetic field free model of the quiet Sun. To carry out the simulations, we employed the magnetohydrodynamics code, SMAUG (Sheffield MHD Accelerated Using GPUs). Our results show that the amount of energy propagating into the solar atmosphere is consistent with a model of solar global oscillations described by Taroyan and Erdélyi (2008) using the Klein-Gordon equation. The computed results indicate a power law which is compared to observations reported by Ireland et al. (2015) using data from the Solar Dynamics Observatory/Atmospheric Imaging Assembly.
Pintér, Balázs; Erdélyi, R.
2018-01-01
Solar fundamental (f) acoustic mode oscillations are investigated analytically in a magnetohydrodynamic (MHD) model. The model consists of three layers in planar geometry, representing the solar interior, the magnetic atmosphere, and a transitional layer sandwiched between them. Since we focus on the fundamental mode here, we assume the plasma is incompressible. A horizontal, canopy-like, magnetic field is introduced to the atmosphere, in which degenerated slow MHD waves can exist. The global (f-mode) oscillations can couple to local atmospheric Alfvén waves, resulting, e.g., in a frequency shift of the oscillations. The dispersion relation of the global oscillation mode is derived, and is solved analytically for the thin-transitional layer approximation and for the weak-field approximation. Analytical formulae are also provided for the frequency shifts due to the presence of a thin transitional layer and a weak atmospheric magnetic field. The analytical results generally indicate that, compared to the fundamental value (ω =√{ gk }), the mode frequency is reduced by the presence of an atmosphere by a few per cent. A thin transitional layer reduces the eigen-frequencies further by about an additional hundred microhertz. Finally, a weak atmospheric magnetic field can slightly, by a few percent, increase the frequency of the eigen-mode. Stronger magnetic fields, however, can increase the f-mode frequency by even up to ten per cent, which cannot be seen in observed data. The presence of a magnetic atmosphere in the three-layer model also introduces non-permitted propagation windows in the frequency spectrum; here, f-mode oscillations cannot exist with certain values of the harmonic degree. The eigen-frequencies can be sensitive to the background physical parameters, such as an atmospheric density scale-height or the rate of the plasma density drop at the photosphere. Such information, if ever observed with high-resolution instrumentation and inverted, could help to
Simulating Nonlinear Oscillations of Viscoelastically Damped Mechanical Systems
Directory of Open Access Journals (Sweden)
M. D. Monsia
2014-12-01
Full Text Available The aim of this work is to propose a mathematical model in terms of an exact analytical solution that may be used in numerical simulation and prediction of oscillatory dynamics of a one-dimensional viscoelastic system experiencing large deformations response. The model is represented with the use of a mechanical oscillator consisting of an inertial body attached to a nonlinear viscoelastic spring. As a result, a second-order first-degree Painlevé equation has been obtained as a law, governing the nonlinear oscillatory dynamics of the viscoelastic system. Analytical resolution of the evolution equation predicts the existence of three solutions and hence three damping modes of free vibration well known in dynamics of viscoelastically damped oscillating systems. Following the specific values of damping strength, over-damped, critically-damped and under-damped solutions have been obtained. It is observed that the rate of decay is not only governed by the damping degree but, also by the magnitude of the stiffness nonlinearity controlling parameter. Computational simulations demonstrated that numerical solutions match analytical results very well. It is found that the developed mathematical model includes a nonlinear extension of the classical damped linear harmonic oscillator and incorporates the Lambert nonlinear oscillatory equation with well-known solutions as special case. Finally, the three damped responses of the current mathematical model devoted for representing mechanical systems undergoing large deformations and viscoelastic behavior are found to be asymptotically stable.
Indian Academy of Sciences (India)
processes at the cellular level like the glycolytic pathway, peroxi- dase-catalysed reaction or the biosynthesis of certain proteins. A systematic study of oscillating chemical reactions is of consider- able interest, since these oscillating reactions can be used as prototype examples of the behaviours possible in reactions gov-.
BEAM OPTIMIZATION STUDY FOR AN X-RAY FEL OSCILLATOR AT THE LCLS-II
Energy Technology Data Exchange (ETDEWEB)
Qin, Weilun; Huang, S.; Liu, K.X.; Huang, Z; Ding, Y.; Maxwell, T.J.; Kim, K.-J.
2016-06-01
The 4 GeV LCLS-II superconducting linac with high repetition beam rate enables the possibility to drive an X-Ray FEL oscillator at harmonic frequencies *. Compared to the regular LCLS-II machine setup, the oscillator mode requires a much longer bunch length with a relatively lower current. Also a flat longitudinal phase space distribution is critical to maintain the FEL gain since the X-ray cavity has extremely narrow bandwidth. In this paper, we study the longitudinal phase space optimization including shaping the initial beam from the injector and optimizing the bunch compressor and dechirper parameters. We obtain a bunch with a flat energy chirp over 400 fs in the core part with current above 100 A. The optimization was based on LiTrack and Elegant simulations using LCLS-II beam parameters.
Multiscale low-frequency circulation modes in the global atmosphere
Lau, K.-M.; Sheu, P.-J.; Kang, I.-S.
1994-01-01
In this paper, fundamental multiscale circulation modes in the global atmosphere are identified with the objective of providing better understanding of atmospheric low-frequency variabilities over a wide range of spatial and temporal scales. With the use of a combination of rotated principal component technique, singular spectrum analysis, and phase space portraits, three categories of basic multiscale modes in the atmosphere are found. The first is the interannual-mode (IAM), which is dominated by time scales longer than a year and can be attributed to heating and circulation anomalies associated with the coupled tropical ocean-atmosphere, in particular the El Nino-Southern Oscillation. The second is a set of tropical intraseasonal modes consisting of three separate multiscale patterns (ISO-1, -2, -3) related to tropical heating that can be identified with the different phases of the Madden-Julian Oscillation (MJO), including its teleconnection to the extratropics. The ISO spatial and temporal patterns suggest that the extratropical wave train in the North Pacific and North America is related to heating over the Maritime Continent and that the evolution of the MJO around the equator may require forcing from the extratropics spawning convection over the Indian Ocean. The third category represents extratropical intraseasonal oscillations arising from internal dynamics of the basic-state circulation. In the Northern Hemisphere, there are two distinct circulation modes with multiple frequencies in this category: the Pacific/North America (PNA) and the North Atlantic/Eurasia (NAE). In the Southern Hemisphere, two phase-locked modes (PSA-1 and PSA-2) are found depicting an eastward propagating wave train from eastern Australia, via the Pacific South America to the South Atlantic. The extratropical modes exhibit temporal characteristics such as phase locking and harmonic oscillations possibly associated with quadratically nonlinear dynamical systems. Additionally, the
Oscillations of a single Abrikosov vortex in hard type-II superconductors
Rusakov, V. F.; Chabanenko, V. V.; Nabiałek, A.; Chumak, O. M.
2017-06-01
During the last decade, detection and manipulation of single vortex lines in bulk superconductors have been achieved experimentally. Electrodynamic response of pinned vortices in the high-frequency range is instrumental in studying specific aspects of their behavior. The present paper reviews the state of the art in studies of the oscillations of a single Abrikosov vortex in type II superconductors. The equations for free and forced oscillations of a single elastic vortex line are analyzed taking into account different forces affecting its motion: pinning, elasticity, viscosity and the Lorenz force. The equations also account for the inertial properties of a vortex due to various mechanisms of massiveness. The nature and magnitude of the vortex effective mass caused by some of the mechanisms are discussed in the paper. The roles of each force and inertia in the free oscillation spectrum are thoroughly analyzed. For the De Gennes and Matricon mode (at about a megahertz) with parabolic dispersion and the pinning force taken into account, there is an activation threshold. Taking into account the effective vortex mass in the equation of motion leads to the occurrence of a high-frequency mode (at about a terahertz) in the oscillation spectrum which is also of the activation nature. Estimations of the characteristic frequencies for these modes are given for two common superconductors, NbTi and anisotropic YBaCuO. The paper also presents the features of the resonant behavior of an elastic massive vortex line arising under an external uniform harmonic driving force that decays into the bulk of the sample, taking into account all the above forces. The frequency and temperature dependences of the energy absorption by a vortex line are analyzed. Maximum absorption in the low-frequency mode corresponds to the threshold frequency, while that in the high-frequency mode corresponds to the vortex cyclotron frequency. Vortex manipulation experiments and vortex dynamics simulation
Bounce-harmonic Landau Damping of Plasma Waves
Anderegg, Francois
2015-11-01
We present measurement of plasma wave damping, spanning the temperature regimes of direct Landau damping, bounce-harmonic Landau damping, inter-species drag damping, and viscous damping. Direct Landau damping is dominant at high temperatures, but becomes negligible as v harmonics damping, controlled by an applied ``squeeze'' potential, which generates harmonics in the wave potential and in the particle dynamics. A particle moving in z experiences a non-sinusoidal mode potential caused by the squeeze, producing high spatial harmonics with lower phase velocity. These harmonics are Landau damped even when the mode phase velocity vph is large compared to the thermal velocity v , since the nth harmonic is resonant with a particle bouncing at velocity vb =vph / n . Here we increase the bounce harmonics through applied squeeze potential; but some harmonics are always present in finite length systems. For our centered squeeze geometry, theory shows that only odd harmonics are generated, and predicts the Landau damping rate from vph / n . Experimentally, the squeeze potential increases the wave damping and reduces its frequency. The frequency shift occurs because the squeeze potential reduces the number of particle where the mode velocity is the largest, therefore reducing the mode frequency. We observe an increase in the damping proportional to Vs2,and a frequency reduction proportional to Vs , in quantitative agreement with theory. Wave-coherent laser induced fluorescence allows direct observation of bounce resonances on the particle distribution, here predominantly at vph / 3 . A clear increase of the bounce harmonics is visible on the particle distribution when the squeeze potential is applied. Supported by NSF Grant PHY-1414570, and DOE Grants DE-SC0002451 and DE-SC0008693.
The oscillator model for dissipative QED in an inhomogeneous dielectric
van Wonderen, A. J.; Suttorp, L. G.
2004-11-01
The Ullersma model for the damped harmonic oscillator is coupled to the quantized electromagnetic field. All material parameters and interaction strengths are allowed to depend on position. The ensuing Hamiltonian is expressed in terms of canonical fields, and diagonalized by performing a normal-mode expansion. The commutation relations of the diagonalizing operators are in agreement with the canonical commutation relations. For the proof we replace all sums of normal modes by complex integrals with the help of the residue theorem. The same technique helps us to explicitly calculate the quantum evolution of all canonical and electromagnetic fields. We identify the dielectric constant and the Green function of the wave equation for the electric field. Both functions are meromorphic in the complex frequency plane. The solution of the extended Ullersma model is in keeping with well-known phenomenological rules for setting up quantum electrodynamics in an absorptive and spatially inhomogeneous dielectric. To establish this fundamental justification, we subject the reservoir of independent harmonic oscillators to a continuum limit. The resonant frequencies of the reservoir are smeared out over the real axis. Consequently, the poles of both the dielectric constant and the Green function unite to form a branch cut. Performing an analytic continuation beyond this branch cut, we find that the long-time behaviour of the quantized electric field is completely determined by the sources of the reservoir. Through a Riemann-Lebesgue argument we demonstrate that the field itself tends to zero, whereas its quantum fluctuations stay alive. We argue that the last feature may have important consequences for application of entanglement and related processes in quantum devices.
Erratum to “Ultra-Broadband Photonic Harmonic Mixer Based on Optical Comb Generation”
DEFF Research Database (Denmark)
Zhao, Ying; Pang, Xiaodan; Deng, Lei
2012-01-01
We propose a novel photonic harmonic mixer operating at frequencies up to the millimeter-wave (MMW) band. By combining a broadband fiber-wireless signal with highorder harmonics of a fundamental local oscillator in an optical frequency comb generator, frequency down-conversion can be implemented ...
A Spectrum Sensing Technique for Cognitive Radios in the Presence of Harmonic Images
Moseley, N.A.; Klumperink, Eric A.M.; Nauta, Bram
2008-01-01
Abstract—Harmonic downmixing is an important effect that must be taken into account when performing sensitive spectrum sensing using direct-conversion receivers. When the local oscillator waveform contains harmonics of the fundamental frequency, the quadrature mixer in the receiver will downconvert
Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM
Kfir Kuchuk; Uri Sivan
2015-01-01
Summary The nonlinear interaction between an AFM tip and a sample gives rise to oscillations of the cantilever at integral multiples (harmonics) of the fundamental resonance frequency. The higher order harmonics have long been recognized to hold invaluable information on short range interactions but their utilization has thus far been relatively limited due to theoretical and experimental complexities. In particular, existing approximations of the interaction force in terms of higher harmonic...
Guo, Jianguang; Budarz, Timo; Ward, Joshua M; Prohofsky, Earl W
2010-10-01
Self-consistent normal mode analysis (SCNMA) is applied to heme c type cytochrome f to study temperature-dependent protein motion. Classical normal mode analysis assumes harmonic behavior and the protein mean-square displacement has a linear dependence on temperature. This is only consistent with low-temperature experimental results. To connect the protein vibrational motions between low and physiological temperatures, we have incorporated a fitted set of anharmonic potentials into SCNMA. In addition, quantum harmonic-oscillator theory has been used to calculate the displacement distribution for individual vibrational modes. We find that the modes involving soft bonds exhibit significant non-Gaussian dynamics at physiological temperature, which suggests that it may be the cause of the non-Gaussian behavior of the protein motions probed by elastic incoherent neutron scattering. The combined theory displays a dynamical transition caused by the softening of few "torsional" modes in the low-frequency regime ( 0.6 ps). These modes change from Gaussian to a classical distribution upon heating. Our theory provides an alternative way to understand the microscopic origin of the protein dynamical transition.
Wang, Jing; Liu, Nianqiao; Song, Peng; Zhang, Haikun
2016-11-01
The rate-equation-based model for the Q-switched mode-locking (QML) intra-cavity OPO (IOPO) is developed, which includes the behavior of the fundamental laser. The intensity fluctuation mechanism of the fundamental laser is first introduced into the dynamics of a mode-locking OPO. In the derived model, the OPO nonlinear conversion is considered as a loss for the fundamental laser and thus the QML signal profile originates from the QML fundamental laser. The rate equations are solved by a digital computer for the case of an IOPO pumped by an electro-optic (EO) Q-switched self-mode-locking fundamental laser. The simulated results for the temporal shape with 20 kHz EO repetition and 11.25 W pump power, the signal average power, the Q-switched pulsewidth and the Q-switched pulse energy are obtained from the rate equations. The signal trace and output power from an EO QML Nd3+: GdVO4/KTA IOPO are experimentally measured. The theoretical values from the rate equations agree with the experimental results well. The developed model explains the behavior, which is helpful to system optimization.
Geometric phases, evolution loops and generalized oscillator potentials
Fernandez, David J.
1995-01-01
The geometric phases for dynamical processes where the evolution operator becomes the identity (evolution loops) are studied. The case of time-independent Hamiltonians with equally spaced energy levels is considered; special emphasis is made on the potentials having the same spectrum as the harmonic oscillator potential (the generalized oscillator potentials) and their recently found coherent states.
Dynamics of 'quantumness' measures in the decohering harmonic ...
Indian Academy of Sciences (India)
2016-07-26
Jul 26, 2016 ... Abstract. We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given ...
Exact complex integrals in two dimensions for shifted harmonic ...
Indian Academy of Sciences (India)
We use rationalization method to study two-dimensional complex dynamical systems (shifted harmonic oscillator in complex plane) on the extended comples phase space (ECPS). The role and scope of the derived invatiants in the context of various physical problems are high-lighted.
Manipulating single enzymes by an external harmonic force
DEFF Research Database (Denmark)
Lomholt, Michael A; Urbakh, Michael; Metzler, Ralf
2007-01-01
We study a Michaelis-Menten reaction for a single two-state enzyme molecule, whose transition rates between the two conformations are modulated by an harmonically oscillating external force. In particular, we obtain a range of optimal driving frequencies for changing the conformation of the enzym...
Model of stochastic self-oscillation in Gunn diode oscillators
Energy Technology Data Exchange (ETDEWEB)
Bocharov, E.P.; Korostelev, G.N.; Khripunov, M.V.
1987-07-01
The applicability of the two-mode nonlinear model of decay stochasticity for explanation of the transition from monochromatic self-oscillation to developed stochasticity in the Gunn diode oscillator is demonstrated. Numerical realizations of the basic regimes corresponding to various cases of consideration of the weak nonlinearity of the falling portion of the current-voltage characteristic are presented. A comparative analysis of calculation results of time realizations and experimentally observed oscillograms of stochastic regimes is performed.
Long period oscillations in sunspots
Chorley, N.; Hnat, B.; Nakariakov, V. M.; Inglis, A. R.; Bakunina, I. A.
2010-04-01
Long period oscillations of the gyroresonant emission from sunspot atmospheres are studied. Time series data generated from the sequences of images obtained by the Nobeyama Radioheliograph operating at a frequency of 17 GHz for three sunspots have been analysed and are found to contain significant periods in the range of several tens of minutes. Wavelet analysis shows that these periods are persistent throughout the observation periods. The presence of the oscillations is confirmed by several methods (periodogram, wavelets, Fisher randomisation and empirical mode decomposition). Spatial analysis using the techniques of period, power, correlation and time lag mapping reveals regions of enhanced oscillatory power in the umbral regions. Also seen are two regions of coherent oscillation of about 25 pixels in size, that oscillate in anti-phase with each other. Possible interpretation of the observed periodicities is discussed, in terms of the shallow sunspot model and the leakage of the solar g-modes.
W.H. van Boom (Willem)
2009-01-01
textabstractThis paper presents a review of the literature on comparative tort law and economics. It pays special attention to the economics arguments against and in favour of harmonization of tort law in Europe.
Chen, Shigao; Kinnick, Randall R; Greenleaf, James F; Fatemi, Mostafa
2007-07-01
Vibro-acoustography is an imaging method that uses the radiation force of two interfering ultrasound beams of slightly different frequency to probe an object. An image is made using the acoustic emission resulted from the object vibration at the difference frequency. In this paper, the feasibility of imaging objects at twice the difference frequency (harmonic acoustic emission) is studied. Several possible origins of harmonic acoustic emission are explored. As an example, it is shown that microbubbles close to resonance can produce significant harmonic acoustic emission due to its high nonlinearity. Experiments demonstrate that, compared to the fundamental acoustic emission, harmonic acoustic emission greatly improves the contrast between microbubbles and other objects in vibro-acoustography (an improvement of 17-23 dB in these experiments). Applications of this technique include imaging the nonlinearity of the object and selective detection of microbubbles for perfusion imaging. The impact of microbubble destruction during the imaging process also is discussed.
Harmonic Tracking of Acoustic Radiation Force Induced Displacements
Doherty, Joshua R.; Dahl, Jeremy J.; Trahey, Gregg E.
2014-01-01
Ultrasound-based elasticity imaging methods rely upon accurate estimates of tissue deformation to characterize the mechanical properties of soft tissues. These methods are corrupted by clutter, which can bias and/or increase variance in displacement estimates. Harmonic imaging methods are routinely used for clutter suppression and improved image quality in conventional B-mode ultrasound, but have not been utilized in ultrasound-based elasticity imaging methods. We introduce a novel, fully-sampled pulse inversion harmonic method for tracking tissue displacements that corrects the loss in temporal sampling frequency associated with conventional pulse inversion techniques. The method is implemented with Acoustic Radiation Force Impulse (ARFI) imaging to monitor the displacements induced by an impulsive acoustic radiation force excitation. Custom pulse sequences were implemented on a diagnostic ultrasound scanner to collect spatially-matched fundamental and harmonic information within a single acquisition. B-mode and ARFI images created from fundamental data collected at 4 MHz and 8 MHz are compared with 8 MHz harmonic images created using a bandpass filter approach and the fully sampled pulse inversion method. In homogeneous, tissue-mimicking phantoms, where no visible clutter was observed, there was little difference in the axial displacements, estimated jitter, and normalized cross-correlation among the fundamental and harmonic tracking methods. The similarity of the lower and higher frequency methods suggests that any improvement due to the increased frequency of the harmonic components is negligible. The harmonic tracking methods demonstrated a marked improvement in B-mode and ARFI image quality of in vivo carotid arteries. Improved feature detection and decreased variance in estimated displacements were observed in the arterial walls of harmonic ARFI images, especially in the pulse inversion harmonic ARFI images. Within the lumen, the harmonic tracking methods
Harmonic tracking of acoustic radiation force-induced displacements.
Doherty, Joshua R; Dahl, Jeremy J; Trahey, Gregg E
2013-11-01
Ultrasound-based elasticity imaging methods rely upon accurate estimates of tissue deformation to characterize the mechanical properties of soft tissues. These methods are corrupted by clutter, which can bias and/or increase variance in displacement estimates. Harmonic imaging methods are routinely used for clutter suppression and improved image quality in conventional B-mode ultrasound, but have not been utilized in ultrasound-based elasticity imaging methods. We introduce a novel, fully-sampled pulse-inversion harmonic method for tracking tissue displacements that corrects the loss in temporal sampling frequency associated with conventional pulse-inversion techniques. The method is implemented with acoustic radiation force impulse (ARFI) imaging to monitor the displacements induced by an impulsive acoustic radiation force excitation. Custom pulse sequences were implemented on a diagnostic ultrasound scanner to collect spatially-matched fundamental and harmonic information within a single acquisition. B-mode and ARFI images created from fundamental data collected at 4 MHz and 8 MHz are compared with 8-MHz harmonic images created using a band-pass filter approach and the fully sampled pulse-inversion method. In homogeneous, tissue-mimicking phantoms, where no visible clutter was observed, there was little difference in the axial displacements, estimated jitter, and normalized cross-correlation among the fundamental and harmonic tracking methods. The similarity of the lower- and higher-frequency methods suggests that any improvement resulting from the increased frequency of the harmonic components is negligible. The harmonic tracking methods demonstrated a marked improvement in B-mode and ARFI image quality of in vivo carotid arteries. Improved feature detection and decreased variance in estimated displacements were observed in the arterial walls of harmonic ARFI images, especially in the pulse-inversion harmonic ARFI images. Within the lumen, the harmonic tracking
Energy Technology Data Exchange (ETDEWEB)
Arik, M. (Istanbul Technical Univ. (Turkey). Dept. of Mathematics Bogazici Univ., Istanbul (Turkey). Dept. of Physics); Demircan, E.; Turgut, T. (Texas Univ., Austin, TX (United States). Dept. of Physics); Ekinci, L.; Mungan, M. (Bogazici Univ., Istanbul (Turkey). Dept. of Physics)
1992-07-01
We discuss the properties of oscillators whose spectrum is given by a generalized Fibonacci sequence. The properties include: Invariance under the unitary quantum group, generalized angular momentum, coherent states and difference calculus, relativistic interpretation. (orig.).
Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach
Energy Technology Data Exchange (ETDEWEB)
Toutounji, Mohamad, E-mail: Mtoutounji@uaeu.ac.ae
2015-02-15
This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.
Entanglement of higher-derivative oscillators in holographic systems
Energy Technology Data Exchange (ETDEWEB)
Dimov, Hristo, E-mail: h_dimov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Mladenov, Stefan, E-mail: smladenov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Rashkov, Radoslav C., E-mail: rash@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstr. 8–10, 1040 Vienna (Austria); Vetsov, Tsvetan, E-mail: vetsov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria)
2017-05-15
We study the quantum entanglement of coupled Pais–Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of N coupled Pais–Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. We also make remarks on the appearance of instabilities of higher-derivative oscillators in the context of AdS/CFT correspondence. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.