Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps

ERIC Educational Resources Information Center

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…

Damping of coupled harmonic oscillators

NASA Astrophysics Data System (ADS)

Dolfo, Gilles; Vigué, Jacques

2018-03-01

When two harmonic oscillators are coupled in the presence of damping, their dynamics exhibit two very different regimes depending on the relative magnitude of the coupling and damping terms At resonance, when the coupling has its largest effect, if the coupling dominates the damping, there is a periodic exchange of energy between the two oscillators while, in the opposite case, the energy transfer from one oscillator to the other one is irreversible. We prove that the border between these two regimes goes through an exceptional point and we briefly explain what is an exceptional point. The present paper is written for undergraduate students, with some knowledge in classical mechanics, but it may also be of interest for graduate students.

KvN mechanics approach to the time-dependent frequency harmonic oscillator.

PubMed

Ramos-Prieto, Irán; Urzúa-Pineda, Alejandro R; Soto-Eguibar, Francisco; Moya-Cessa, Héctor M

2018-05-30

Using the Ermakov-Lewis invariants appearing in KvN mechanics, the time-dependent frequency harmonic oscillator is studied. The analysis builds upon the operational dynamical model, from which it is possible to infer quantum or classical dynamics; thus, the mathematical structure governing the evolution will be the same in both cases. The Liouville operator associated with the time-dependent frequency harmonic oscillator can be transformed using an Ermakov-Lewis invariant, which is also time dependent and commutes with itself at any time. Finally, because the solution of the Ermakov equation is involved in the evolution of the classical state vector, we explore some analytical and numerical solutions.

Exact solution of a quantum forced time-dependent harmonic oscillator

NASA Technical Reports Server (NTRS)

Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN

1992-01-01

The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.

Free fall and harmonic oscillations: analyzing trampoline jumps

NASA Astrophysics Data System (ADS)

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 obtained in terms of maximum normalized force from the trampoline and the harmonic frequency. A simple expression is obtained for the ratio between air-time and harmonic period, and the maximum g-factor. The results are compared to experimental results, including accelerometer data showing 7g during bounces on a small trampoline in an amusement park play area. Similar results are obtained on a larger garden trampoline, and even larger accelerations have been measured for gymnastic trampolines.

Harmonic and Anharmonic Behaviour of a Simple Oscillator

ERIC Educational Resources Information Center

O'Shea, Michael J.

2009-01-01

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

Wideband tunable 140 GHz second-harmonic InP-TED oscillator

NASA Astrophysics Data System (ADS)

Rydberg, A.; Kollberg, E.

1986-07-01

A second-harmonic InP-TED oscillator, with an output power of more than 3 dBm at 144 GHz and tunable over a 10 percent frequency range, has been developed. The design incorporates two waveguide resonators. One resonator determines the fundamental frequency of oscillation and the other optimizes the second-harmonic output power.

Predicting chaos in memristive oscillator via harmonic balance method.

PubMed

Wang, Xin; Li, Chuandong; Huang, Tingwen; Duan, Shukai

2012-12-01

This paper studies the possible chaotic behaviors in a memristive oscillator with cubic nonlinearities via harmonic balance method which is also called the method of describing function. This method was proposed to detect chaos in classical Chua's circuit. We first transform the considered memristive oscillator system into Lur'e model and present the prediction of the existence of chaotic behaviors. To ensure the prediction result is correct, the distortion index is also measured. Numerical simulations are presented to show the effectiveness of theoretical results.

Driven damped harmonic oscillator resonance with an Arduino

NASA Astrophysics Data System (ADS)

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.

Entanglement dynamics in short- and long-range harmonic oscillators

NASA Astrophysics Data System (ADS)

Nezhadhaghighi, M. Ghasemi; Rajabpour, M. A.

2014-11-01

We study the time evolution of the entanglement entropy in the short- and long-range-coupled harmonic oscillators that have well-defined continuum limit field theories. We first introduce a method to calculate the entanglement evolution in generic coupled harmonic oscillators after quantum quench. Then we study the entanglement evolution after quantum quench in harmonic systems in which the couplings decay effectively as 1 /rd +α with the distance r . After quenching the mass from a nonzero value to zero we calculate numerically the time evolution of von Neumann and Rényi entropies. We show that for 1 <α <2 we have a linear growth of entanglement and then saturation independent of the initial state. For 0 <α <1 depending on the initial state we can have logarithmic growth or just fluctuation of entanglement. We also calculate the mutual information dynamics of two separated individual harmonic oscillators. Our findings suggest that in our system there is no particular connection between having a linear growth of entanglement after quantum quench and having a maximum group velocity or generalized Lieb-Robinson bound.

Controllability in tunable chains of coupled harmonic oscillators

NASA Astrophysics Data System (ADS)

Buchmann, L. F.; Mølmer, K.; Petrosyan, D.

2018-04-01

We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N -1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach any desired Gaussian state requires at most 3 N (N -1 )/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides.

Covariant harmonic oscillators: 1973 revisited

NASA Technical Reports Server (NTRS)

Noz, M. E.

1993-01-01

Using the relativistic harmonic oscillator, a physical basis is given to the phenomenological wave function of Yukawa which is covariant and normalizable. It is shown that this wave function can be interpreted in terms of the unitary irreducible representations of the Poincare group. The transformation properties of these covariant wave functions are also demonstrated.

Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

PubMed

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

Relativistic harmonic oscillator revisited

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bars, Itzhak

2009-02-15

The familiar Fock space commonly used to describe the relativistic harmonic oscillator, for example, as part of string theory, is insufficient to describe all the states of the relativistic oscillator. We find that there are three different vacua leading to three disconnected Fock sectors, all constructed with the same creation-annihilation operators. These have different spacetime geometric properties as well as different algebraic symmetry properties or different quantum numbers. Two of these Fock spaces include negative norm ghosts (as in string theory), while the third one is completely free of ghosts. We discuss a gauge symmetry in a worldline theory approachmore » that supplies appropriate constraints to remove all the ghosts from all Fock sectors of the single oscillator. The resulting ghost-free quantum spectrum in d+1 dimensions is then classified in unitary representations of the Lorentz group SO(d,1). Moreover, all states of the single oscillator put together make up a single infinite dimensional unitary representation of a hidden global symmetry SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these new results in string theory and other areas of physics and mathematics are briefly mentioned.« less

The Coupled Harmonic Oscillator: Not Just for Seniors Anymore.

ERIC Educational Resources Information Center

Preyer, Norris W.

1996-01-01

Presents experiments that use Microcomputer Based Laboratory (MBL) techniques to enable freshmen physics students to investigate complex systems, such as nonlinear oscillators or coupled harmonic oscillators, at a level appropriate for an independent project. (JRH)

A harmonic oscillator having “volleyball damping”

NASA Astrophysics Data System (ADS)

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.

Predicting charmonium and bottomonium spectra with a quark harmonic oscillator.

PubMed

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

1986-11-01

We present a simple application of the three-dimensional harmonic oscillator which should provide a very nice particle physics example to be presented in introductory undergraduate quantum mechanics course. The idea is to use the nonrelativistic quark model to calculate the spin-averaged mass levels of the charmonium and bottomonium spectra.

A Look at Damped Harmonic Oscillators through the Phase Plane

ERIC Educational Resources Information Center

Daneshbod, Yousef; Latulippe, Joe

2011-01-01

Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the…

West Coast Swing Dancing as a Driven Harmonic Oscillator Model

NASA Astrophysics Data System (ADS)

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.

Optimal control of a harmonic oscillator: Economic interpretations

NASA Astrophysics Data System (ADS)

Janová, Jitka; Hampel, David

2013-10-01

Optimal control is a popular technique for modelling and solving the dynamic decision problems in economics. A standard interpretation of the criteria function and Lagrange multipliers in the profit maximization problem is well known. On a particular example, we aim to a deeper understanding of the possible economic interpretations of further mathematical and solution features of the optimal control problem: we focus on the solution of the optimal control problem for harmonic oscillator serving as a model for Phillips business cycle. We discuss the economic interpretations of arising mathematical objects with respect to well known reasoning for these in other problems.

Quantum harmonic oscillator in a thermal bath

NASA Technical Reports Server (NTRS)

Zhang, Yuhong

1993-01-01

The influence functional path-integral treatment of quantum Brownian motion is briefly reviewed. A newly derived exact master equation of a quantum harmonic oscillator coupled to a general environment at arbitrary temperature is discussed. It is applied to the problem of loss of quantum coherence.

Harmonic and anharmonic oscillations investigated by using a microcomputer-based Atwood's machine

NASA Astrophysics Data System (ADS)

Pecori, Barbara; Torzo, Giacomo; Sconza, Andrea

1999-03-01

We describe how the Atwood's machine, interfaced to a personal computer through a rotary encoder, is suited for investigating harmonic and anharmonic oscillations, exploiting the buoyancy force acting on a body immersed in water. We report experimental studies of oscillators produced by driving forces of the type F=-kxn with n=1,2,3, and F=-k sgn(x). Finally we suggest how this apparatus can be used for showing to the students a macroscopic model of interatomic forces.

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

NASA Astrophysics Data System (ADS)

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.

The harmonic oscillator and the position dependent mass Schroedinger equation: isospectral partners and factorization operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morales, J.; Ovando, G.; Pena, J. J.

2010-12-23

One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potentialmore » as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.« less

Teaching from a Microgravity Environment: Harmonic Oscillator and Pendulum

NASA Astrophysics Data System (ADS)

Benge, Raymond; Young, Charlotte; Davis, Shirley; Worley, Alan; Smith, Linda; Gell, Amber

2009-04-01

This presentation reports on an educational experiment flown in January 2009 as part of NASA's Microgravity University program. The experiment flown was an investigation into the properties of harmonic oscillators in reduced gravity. Harmonic oscillators are studied in every introductory physics class. The equation for the period of a harmonic oscillator does not include the acceleration due to gravity, so the period should be independent of gravity. However, the equation for the period of a pendulum does include the acceleration due to gravity, so the period of a pendulum should appear longer under reduced gravity (such as lunar or Martian gravity) and shorter under hyper-gravity. These environments can be simulated aboard an aircraft. Video of the experiments being performed aboard the aircraft is to be used in introductory physics classes. Students will be able to record information from watching the experiment performed aboard the aircraft in a similar manner to how they collect data in the laboratory. They can then determine if the experiment matches theory. Video and an experimental procedure are being prepared based upon this flight, and these materials will be available for download by faculty anywhere with access to the internet who wish to use the experiment in their own classrooms.

The Study of Damped Harmonic Oscillations Using an Electronic Counter

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

Coherent control of acoustic vibrations in metal nanoparticles and thin films with sequences of femtosecond pulses: Harmonic-oscillator model

NASA Astrophysics Data System (ADS)

Zheltikov, A. M.

2002-08-01

A harmonic oscillator model is used to demonstrate the possibility of coherent control of acoustic vibrations of metal nanoparticles and thin films with sequences of femtosecond laser pulses. When the interval between the pulses in such a sequence is chosen equal to the oscillation period of the expansion mode of a nanoscale system, the relevant acoustic vibrations can be excited in a resonant and selective way. Sequences of femtosecond pulses with picosecond time intervals between the pulses are shown to be ideally suited for a resonant excitation and coherent control of acoustic modes of silver nanoparticles.

The One-Dimensional Damped Forced Harmonic Oscillator Revisited

ERIC Educational Resources Information Center

Flores-Hidalgo, G.; Barone, F. A.

2011-01-01

In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.

Harmonic oscillator in quantum rotational spectra: Molecules and nuclei

NASA Technical Reports Server (NTRS)

Pavlichenkov, Igor M.

1995-01-01

The mapping of a rotational dynamics on a harmonic oscillator is considered. The method used for studying the stabilization of the rigid top rotation around the intermediate moment of inertial axix by orbiting particle is described.

Microwave Imaging Reflectometry for the study of Edge Harmonic Oscillations on DIII-D [Microwave Imaging Reflectometry (MIR) for the study of Edge Harmonic Oscillations (EHOs) on DIII-D

DOE PAGES

Ren, X.; Chen, M.; Chen, X.; ...

2015-10-23

Quiescent H-mode (QH) is an ELM free mode of operation in which edge-localized harmonic oscillations (EHOs) are believed to enhance particle transport, thereby stabilizing ELMs and preventing damage to the divertor and plasma facing components. Microwave Imaging Reflectometer (MIR) enabling direct comparison between the measured and simulated 2D images of density fluctuations near the edge can determine the 2D structure of density oscillation which can help to explain the physics behind EHO modes. MIR data sometimes indicates a counter-propagation between higher (n>1) and dominant (n=1) harmonics of coherent EHOs in the steep gradient regions of the pedestal. To preclude diagnosticmore » artifacts, we have performed forward modeling that includes possible optical misalignments to show that offsets between transmitting and receiving antennas do not account for this feature. We have also simulated the non-uniform rotation of the EHO structure, which induces multiple harmonics that are properly characterized in the synthetic diagnostic. Excluding these possible explanations for the data, the counter-propagation observed in MIR data, which is not corroborated by external Mirnov coil array measurements, may be due to subtleties of the eigenmode structure, such as an inversion radius consistent with a magnetic island. Similar effects are observed in analysis of internal ECE-Imaging and BES data. Furthermore, the identification of a non-ideal structure motivates further exploration of nonlinear models of this instability.« less

Oscillator Seeding of a High Gain Harmonic Generation FEL in a Radiator-First Configuration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gandhi, P.; Wurtele, J.; Penn, G.

2012-05-20

A longitudinally coherent X-ray pulse from a high repetition rate free electron laser (FEL) is desired for a wide variety of experimental applications. However, generating such a pulse with a repetition rate greater than 1 MHz is a significant challenge. The desired high repetition rate sources, primarily high harmonic generation with intense lasers in gases or plasmas, do not exist now, and, for the multi-MHz bunch trains that superconducting accelerators can potentially produce, are likely not feasible with current technology. In this paper, we propose to place an oscillator downstream of a radiator. The oscillator generates radiation that is usedmore » as a seed for a high gain harmonic generation (HGHG) FEL which is upstream of the oscillator. For the first few pulses the oscillator builds up power and, until power is built up, the radiator has no HGHG seed. As power in the oscillator saturates, the HGHG is seeded and power is produced. The dynamics and stability of this radiator-first scheme is explored analytically and numerically. A single-pass map is derived using a semi-analytic model for FEL gain and saturation. Iteration of the map is shown to be in good agreement with simulations. A numerical example is presented for a soft X-ray FEL.« less

Information measures of a deformed harmonic oscillator in a static electric field

NASA Astrophysics Data System (ADS)

Nascimento, J. P. G.; Ferreira, F. A. P.; Aguiar, V.; Guedes, I.; Costa Filho, Raimundo N.

2018-06-01

The Shannon entropy and the Fischer information are calculated for an harmonic oscillator in the presence of an applied electric field (ε) in a space with metrics given by gxx-1/2 = 1 + γx. For that metric the harmonic oscillator can be mapped into a Morse potential in an Euclidean space. For ε = 0, the ground state energy decreases when γ increases. However, for certain values of ε the energy decrease can be canceled out. The dependence of the uncertainties, the entropy, and the information on the parameters γ and ε are shown.

Sampled-data synchronisation of coupled harmonic oscillators with communication and input delays subject to controller failure

NASA Astrophysics Data System (ADS)

Zhao, Liyun; Zhou, Jin; Wu, Quanjun

2016-01-01

This paper considers the sampled-data synchronisation problems of coupled harmonic oscillators with communication and input delays subject to controller failure. A synchronisation protocol is proposed for such oscillator systems over directed network topology, and then some general algebraic criteria on exponential convergence for the proposed protocol are established. The main features of the present investigation include: (1) both the communication and input delays are simultaneously addressed, and the directed network topology is firstly considered and (2) the effects of time delays on synchronisation performance are theoretically and numerically investigated. It is shown that in the absence of communication delays, coupled harmonic oscillators can achieve synchronisation oscillatory motion. Whereas if communication delays are nonzero at infinite multiple sampled-data instants, its synchronisation (or consensus) state is zero. This conclusion can be used as an effective control strategy to stabilise coupled harmonic oscillators in practical applications. Furthermore, it is interesting to find that increasing either communication or input delays will enhance the synchronisation performance of coupled harmonic oscillators. Subsequently, numerical examples illustrate and visualise theoretical results.

The Adiabatic Invariant of the n-Degree-of-Freedom Harmonic Oscillator

ERIC Educational Resources Information Center

Devaud, M.; Leroy, V.; Bacri, J.-C.; Hocquet, T.

2008-01-01

In this graduate-level theoretical paper, we propose a general derivation of the adiabatic invariant of the n-degree-of-freedom harmonic oscillator, available whichever the physical nature of the oscillator and of the parametrical excitation it undergoes. This derivation is founded on the use of the classical Glauber variables and ends up with…

Symmetry algebra of a generalized anisotropic harmonic oscillator

NASA Technical Reports Server (NTRS)

Castanos, O.; Lopez-Pena, R.

1993-01-01

It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.

Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams

NASA Technical Reports Server (NTRS)

Steely, Sidney L.

1993-01-01

The similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite-Gaussian laser beams is illustrated. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite-Gaussian laser beams. The classical limits of a corresponding two-dimensional harmonic oscillator provide a definition of the spot size of Hermite-Gaussian laser beams. The classical limits of the harmonic oscillator provide integration limits for the photon probability densities of the laser beam modes to determine the fraction of photons detected therein. Mathematica is used to integrate the probability densities for large-order beam modes and to illustrate the functional similarities. The probabilities of detecting photons within the classical limits of Hermite-Gaussian laser beams asymptotically approach unity in the limit of large-order modes, in agreement with the Correspondence Principle. The classical limits for large-order modes include all of the nodes for Hermite Gaussian laser beams; Sturm's theorem provides a direct proof.

Non-unique monopole oscillations of harmonically confined Yukawa systems

NASA Astrophysics Data System (ADS)

Ducatman, Samuel; Henning, Christian; Kaehlert, Hanno; Bonitz, Michael

2008-11-01

Recently it was shown that the Breathing Mode (BM), the mode of uniform radial expansion and contraction, which is well known from harmonically confined Coulomb systems [1], does not exist in general for other systems [2]. As a consequence the monopole oscillation (MO), the radial collective excitation, is not unique, but there are several MO with different frequencies. Within this work we show simulation results of those monopole oscillations of 2-dimensional harmonically confined Yukawa systems, which are known from, e.g., dusty plasma crystals [3,4]. We present the corresponding spectrum of the particle motion, including analysis of the frequencies found, and compare with theoretical investigations.[1] D.H.E. Dubin and J.P. Schiffer, Phys. Rev. E 53, 5249 (1996)[2] C. Henning at al., accepted for publication in Phys. Rev. Lett. (2008)[3] A. Melzer et al., Phys. Rev. Lett. 87, 115002 (2001)[4] M. Bonitz et al., Phys. Rev. Lett. 96, 075001 (2006)

Evidence for Harmonic Content and Frequency Evolution of Oscillations During the Rising Phase of X-ray Bursts From 4U 1636-536

NASA Technical Reports Server (NTRS)

Bgattacharyya, Sudip; Strohmayer, E.

2005-01-01

We report on a study of the evolution of burst oscillation properties during the rising phase of X-ray bursts from 4U 1636-536 observed with the proportional counter array (PCA) on board the Rossi X-Ray Timing Explorer (RXTE) . We present evidence for significant harmonic structure of burst oscillation pulses during the early rising phases of bursts. This is the first such detection in burst rise oscillations, and is very important for constraining neutron star structure parameters and the equation of state models of matter at the core of a neutron star. The detection of harmonic content only during the initial portions of the burst rise is consistent with the theoretical expectation that with time the thermonuclear burning region becomes larger, and hence the fundamental and harmonic amplitudes both diminish. We also find, for the first time from this source, strong evidence of oscillation frequency increase during the burst rise. The timing behavior of harmonic content, amplitude, and frequency of burst rise oscillations may be important in understanding the spreading of thermonuclear flames under the extreme physical conditions on neutron star surfaces.

Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, E-mail: xbataxel@gmail.com; Wang, Jie, E-mail: wangjie@iun.edu

2015-07-15

We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system.

Noncanonical harmonic and anharmonic oscillator in high-energy physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jannussis, A.; Vavougios, D.

1986-09-01

We study the eigenvalues of the noncanonical harmonic and anharmonic oscillator, by using different values of the elementary length l corresponding to typical cross sections for the strong interactions. There is evidence for a correlation between the energies of elementary particles (mesons, baryons, resonances) and the energy eigenvalues of the noncanonical theory.

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

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 formore » 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.« less

Entanglement prethermalization in an interaction quench between two harmonic oscillators.

PubMed

Ikeda, Tatsuhiko N; Mori, Takashi; Kaminishi, Eriko; Ueda, Masahito

2017-02-01

Entanglement prethermalization (EP) refers to a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble exactly describes the total system if we take into account nonlocal conserved quantities that act nontrivially on both subsystems. In the presence of a symmetry-breaking perturbation, the relaxation dynamics of the system exhibits a quasi-stationary EP plateau and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.

A method of solving simple harmonic oscillator Schroedinger equation

NASA Technical Reports Server (NTRS)

Maury, Juan Carlos F.

1995-01-01

A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.

Analysis of biochemical phase shift oscillators by a harmonic balancing technique.

PubMed

Rapp, P

1976-11-25

The use of harmonic balancing techniques for theoretically investigating a large class of biochemical phase shift oscillators is outlined and the accuracy of this approximate technique for large dimension nonlinear chemical systems is considered. It is concluded that for the equations under study these techniques can be successfully employed to both find periodic solutions and to indicate those cases which can not oscillate. The technique is a general one and it is possible to state a step by step procedure for its application. It has a substantial advantage in producing results which are immediately valid for arbitrary dimension. As the accuracy of the method increases with dimension, it complements classical small dimension methods. The results obtained by harmonic balancing analysis are compared with those obtained by studying the local stability properties of the singular points of the differential equation. A general theorem is derived which identifies those special cases where the results of first order harmonic balancing are identical to those of local stability analysis, and a necessary condition for this equivalence is derived. As a concrete example, the n-dimensional Goodwin oscillator is considered where p, the Hill coefficient of the feedback metabolite, is equal to three and four. It is shown that for p = 3 or 4 and n less than or equal to 4 the approximation indicates that it is impossible to construct a set of physically permissible reaction constants such that the system possesses a periodic solution. However for n greater than or equal to 5 it is always possible to find a large domain in the reaction constant space giving stable oscillations. A means of constructing such a parameter set is given. The results obtained here are compared with previously derived results for p = 1 and p = 2.

Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators

PubMed Central

Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong

2016-01-01

Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO. PMID:26961962

The `Miracle' of Applicability? The Curious Case of the Simple Harmonic Oscillator

NASA Astrophysics Data System (ADS)

Bangu, Sorin; Moir, Robert H. C.

2018-05-01

The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner's famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of the Wigner problem.

Sonic horizon formation for oscillating Bose-Einstein condensates in isotropic harmonic potential

PubMed Central

Wang, Ying; Zhou, Yu; Zhou, Shuyu

2016-01-01

We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study. PMID:27922129

The `Miracle' of Applicability? The Curious Case of the Simple Harmonic Oscillator

NASA Astrophysics Data System (ADS)

Bangu, Sorin; Moir, Robert H. C.

2018-03-01

The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner's famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of the Wigner problem.

Action-angle variables for the harmonic oscillator: Ambiguity spin × duplication spin

NASA Astrophysics Data System (ADS)

de Oliveira, César R.; Malta, Coraci P.

1984-07-01

The difficulties of obtaining for the harmonic oscillator a well-defined unitary transformation to action-angle variables were overcome by M. Moshinsky and T. H. Seligman ( Ann. Phys. (N.Y.)114 (1978), 243) through the introduction of a spinlike variable (ambiguity spin) from a classical point of view. The difficulty of defining a unitary phase operator for the harmonic oscillator was overcome by Roger G. Newton ( Ann. Phys. (N.Y.)124 (1980), 324) also through the introduction of a spinlike variable (named duplication spin by us) but within a quantum framework. Here the relation between the ambiguity spin and the duplication spin is investigated by introducing these two types of spins in the canonical transformation to action-angle variables. In this way both well-defined unitary transformation and phase operators were obtained.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Menikoff, Ralph

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.

Confined One Dimensional Harmonic Oscillator as a Two-Mode System

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gueorguiev, V G; Rau, A P; Draayer, J P

2005-07-11

The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two limits has a characteristic spectral structure describing the two different excitation modes of the system. Near each of these limits, one can use perturbation theory to achieve an accurate description of the eigenstates. Away from the exact limits, however, one has to carry out a matrix diagonalization because the basis-state mixing that occurs is typically too large to be reproduced in anymore » other way. An alternative to casting the problem in terms of one or the other basis set consists of using an ''oblique'' basis that uses both sets. Through a study of this alternative in this one-dimensional problem, we are able to illustrate practical solutions and infer the applicability of the concept for more complex systems, such as in the study of complex nuclei where oblique-basis calculations have been successful.« less

Novel Approach for Solving the Equation of Motion of a Simple Harmonic Oscillator. Classroom Notes

ERIC Educational Resources Information Center

Gauthier, N.

2004-01-01

An elementary method, based on the use of complex variables, is proposed for solving the equation of motion of a simple harmonic oscillator. The method is first applied to the equation of motion for an undamped oscillator and it is then extended to the more important case of a damped oscillator. It is finally shown that the method can readily be…

Modeling Bloch oscillations in nanoscale Josephson junctions.

PubMed

Vora, Heli; Kautz, R L; Nam, S W; Aumentado, J

2017-08-01

Bloch oscillations in nanoscale Josephson junctions with a Coulomb charging energy comparable to the Josephson coupling energy are explored within the context of a model previously considered by Geigenmüller and Schön that includes Zener tunneling and treats quasiparticle tunneling as an explicit shot-noise process. The dynamics of the junction quasicharge are investigated numerically using both Monte Carlo and ensemble approaches to calculate voltage-current characteristics in the presence of microwaves. We examine in detail the origin of harmonic and subharmonic Bloch steps at dc biases I = ( n/m )2 ef induced by microwaves of frequency f and consider the optimum parameters for the observation of harmonic ( m = 1) steps. We also demonstrate that the GS model allows a detailed semiquantitative fit to experimental voltage-current characteristics previously obtained at the Chalmers University of Technology, confirming and strengthening the interpretation of the observed microwave-induced steps in terms of Bloch oscillations.

Modeling Bloch oscillations in nanoscale Josephson junctions

PubMed Central

Vora, Heli; Kautz, R. L.; Nam, S. W.; Aumentado, J.

2018-01-01

Bloch oscillations in nanoscale Josephson junctions with a Coulomb charging energy comparable to the Josephson coupling energy are explored within the context of a model previously considered by Geigenmüller and Schön that includes Zener tunneling and treats quasiparticle tunneling as an explicit shot-noise process. The dynamics of the junction quasicharge are investigated numerically using both Monte Carlo and ensemble approaches to calculate voltage-current characteristics in the presence of microwaves. We examine in detail the origin of harmonic and subharmonic Bloch steps at dc biases I = (n/m)2ef induced by microwaves of frequency f and consider the optimum parameters for the observation of harmonic (m = 1) steps. We also demonstrate that the GS model allows a detailed semiquantitative fit to experimental voltage-current characteristics previously obtained at the Chalmers University of Technology, confirming and strengthening the interpretation of the observed microwave-induced steps in terms of Bloch oscillations. PMID:29577106

Coherent states for the relativistic harmonic oscillator

NASA Technical Reports Server (NTRS)

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.

A multi-harmonic generalized energy balance method for studying autonomous oscillations of nonlinear conservative systems

NASA Astrophysics Data System (ADS)

Balaji, Nidish Narayanaa; Krishna, I. R. Praveen; Padmanabhan, C.

2018-05-01

The Harmonic Balance Method (HBM) is a frequency-domain based approximation approach used for obtaining the steady state periodic behavior of forced dynamical systems. Intrinsically these systems are non-autonomous and the method offers many computational advantages over time-domain methods when the fundamental period of oscillation is known (generally fixed as the forcing period itself or a corresponding sub-harmonic if such behavior is expected). In the current study, a modified approach, based on He's Energy Balance Method (EBM), is applied to obtain the periodic solutions of conservative systems. It is shown that by this approach, periodic solutions of conservative systems on iso-energy manifolds in the phase space can be obtained very efficiently. The energy level provides the additional constraint on the HBM formulation, which enables the determination of the period of the solutions. The method is applied to the linear harmonic oscillator, a couple of nonlinear oscillators, the elastic pendulum and the Henon-Heiles system. The approach is used to trace the bifurcations of the periodic solutions of the last two, being 2 degree-of-freedom systems demonstrating very rich dynamical behavior. In the process, the advantages offered by the current formulation of the energy balance is brought out. A harmonic perturbation approach is used to evaluate the stability of the solutions for the bifurcation diagram.

Making chaotic behavior in a damped linear harmonic oscillator

NASA Astrophysics Data System (ADS)

Konishi, Keiji

2001-06-01

The present Letter proposes a simple control method which makes chaotic behavior in a damped linear harmonic oscillator. This method is a modified scheme proposed in paper by Wang and Chen (IEEE CAS-I 47 (2000) 410) which presents an anti-control method for making chaotic behavior in discrete-time linear systems. We provide a systematic procedure to design parameters and sampling period of a feedback controller. Furthermore, we show that our method works well on numerical simulations.

A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vignat, C.; Lamberti, P. W.

2009-10-15

Recently, Carinena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positivemore » curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.« less

Multivariable harmonic balance analysis of the neuronal oscillator for leech swimming.

PubMed

Chen, Zhiyong; Zheng, Min; Friesen, W Otto; Iwasaki, Tetsuya

2008-12-01

Biological systems, and particularly neuronal circuits, embody a very high level of complexity. Mathematical modeling is therefore essential for understanding how large sets of neurons with complex multiple interconnections work as a functional system. With the increase in computing power, it is now possible to numerically integrate a model with many variables to simulate behavior. However, such analysis can be time-consuming and may not reveal the mechanisms underlying the observed phenomena. An alternative, complementary approach is mathematical analysis, which can demonstrate direct and explicit relationships between a property of interest and system parameters. This paper introduces a mathematical tool for analyzing neuronal oscillator circuits based on multivariable harmonic balance (MHB). The tool is applied to a model of the central pattern generator (CPG) for leech swimming, which comprises a chain of weakly coupled segmental oscillators. The results demonstrate the effectiveness of the MHB method and provide analytical explanations for some CPG properties. In particular, the intersegmental phase lag is estimated to be the sum of a nominal value and a perturbation, where the former depends on the structure and span of the neuronal connections and the latter is roughly proportional to the period gradient, communication delay, and the reciprocal of the intersegmental coupling strength.

Use of an untuned cavity for absolute power measurements of the harmonics above 100 GHz from an IMPATT oscillator

NASA Astrophysics Data System (ADS)

Llewellyn-Jones, D. T.; Knight, R. J.; Gebbie, H. A.

1980-07-01

A new technique of measuring absolute power exploiting an untuned cavity and Fourier spectroscopy has been used to examine the power spectrum of the harmonics and other overtones produced by a 95 GHz IMPATT oscillator. The conditions which favor the production of a rich harmonic spectrum are not those which maximize the fundamental power. Under some conditions of mismatch at the fundamental frequency it is possible to produce over 200 microW of harmonic power in the 100-200 GHz region comparable with the fundamental power from the oscillator.

Harmonic oscillator representation in the theory of scattering and nuclear reactions

NASA Technical Reports Server (NTRS)

Smirnov, Yuri F.; Shirokov, A. M.; Lurie, Yuri, A.; Zaitsev, S. A.

1995-01-01

The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.

Cycle-Averaged Phase-Space States for the Harmonic and the Morse Oscillators, and the Corresponding Uncertainty Relations

ERIC Educational Resources Information Center

Nicolaides, Cleanthes A.; Constantoudis, Vasilios

2009-01-01

In Planck's model of the harmonic oscillator (HO) a century ago, both the energy and the phase space were quantized according to epsilon[subscript n] = nhv, n = 0, 1, 2..., and [double integral]dp[subscript x] dx = h. By referring to just these two relations, we show how the adoption of "cycle-averaged phase-space states" (CAPSSs) leads to the…

A finite difference method for the solution of the transonic flow around harmonically oscillating wings

NASA Technical Reports Server (NTRS)

Ehlers, E. F.

1974-01-01

A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.

Solution of the Quantum Harmonic Oscillator Plus a Delta-Function Potential at the Origin: The "Oddness" of Its Even-Parity Solutions

ERIC Educational Resources Information Center

Viana-Gomes, J.; Peres, N. M. R.

2011-01-01

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…

ABC of ladder operators for rationally extended quantum harmonic oscillator systems

NASA Astrophysics Data System (ADS)

Cariñena, José F.; Plyushchay, Mikhail S.

2017-07-01

The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler transformations by which such systems can be generated from the quantum harmonic oscillator. Any REQHO system is characterized by the number of separated states in its spectrum, the number of ‘valence bands’ in which the separated states are organized, and by the total number of the missing energy levels and their position. All these peculiarities of a REQHO system are shown to be detected and reflected by a trinity (A^+/- , B^+/- , C^+/-) of the basic (primary) lowering and raising ladder operators related between themselves by certain algebraic identities with coefficients polynomially-dependent on the Hamiltonian. We show that all the secondary, higher-order ladder operators are obtainable by a composition of the basic ladder operators of the trinity which form the set of the spectrum-generating operators. Each trinity, in turn, can be constructed from the intertwining operators of the two complementary minimal schemes of the Darboux-Crum-Krein-Adler transformations.

Improving Density Functionals with Quantum Harmonic Oscillators

NASA Astrophysics Data System (ADS)

Tkatchenko, Alexandre

2013-03-01

Density functional theory (DFT) is the most widely used and successful approach for electronic structure calculations. However, one of the pressing challenges for DFT is developing efficient functionals that can accurately capture the omnipresent long-range electron correlations, which determine the structure and stability of many molecules and materials. Here we show that, under certain conditions, the problem of computing the long-range correlation energy of interacting electrons can be mapped to a system of coupled quantum harmonic oscillators (QHOs). The proposed model allows us to synergistically combine concepts from DFT, quantum chemistry, and the widely discussed random-phase approximation for the correlation energy. In the dipole limit, the interaction energy for a system of coupled QHOs can be calculated exactly, thereby leading to an efficient and accurate model for the many-body dispersion energy of complex molecules and materials. The studied examples include intermolecular binding energies, the conformational hierarchy of DNA structures, the geometry and stability of molecular crystals, and supramolecular host-guest complexes (A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012); R. A. DiStasio Jr., A. von Lilienfeld, A. Tkatchenko, PNAS 109, 14791 (2012); A. Tkatchenko, D. Alfe, K. S. Kim, J. Chem. Theory and Comp. (2012), doi: 10.1021/ct300711r; A. Tkatchenko, A. Ambrosetti, R. A. DiStasio Jr., arXiv:1210.8343v1).

An analogue of the Berry phase for simple harmonic oscillators

NASA Astrophysics Data System (ADS)

Suslov, S. K.

2013-03-01

We evaluate a variant of Berry's phase for a ‘missing’ family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables (in a natural way). Instead, it is obtained by the action of the maximal kinematical invariance group on the standard solutions. A simple closed formula for the phase (in terms of elementary functions) is found here by integration with the help of a computer algebra system.

Chaos, ergodic convergence, and fractal instability for a thermostated canonical harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.; Isbister, Dennis J.

2001-02-01

The authors thermostat a qp harmonic oscillator using the two additional control variables ζ and ξ to simulate Gibbs' canonical distribution. In contrast to the motion of purely Hamiltonian systems, the thermostated oscillator motion is completely ergodic, covering the full four-dimensional \\{q,p,ζ,ξ\\} phase space. The local Lyapunov spectrum (instantaneous growth rates of a comoving corotating phase-space hypersphere) exhibits singularities like those found earlier for Hamiltonian chaos, reinforcing the notion that chaos requires kinetic-as opposed to statistical-study, both at and away from equilibrium. The exponent singularities appear to have a fractal character.

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

NASA Astrophysics Data System (ADS)

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.

A contribution to the design of wideband tunable second harmonic mode millimeter-wave InP-TED oscillators above 110 GHz

NASA Astrophysics Data System (ADS)

Rydberg, Anders

1990-03-01

Second harmonic InP-TED oscillators are investigated for frequencies above 110 GHz using different mounts and TED's. It is found that state of the art output powers, comparable to Schottky-varactor multipliers, of more than 2 mW can be generated above 190 GHz by reducing the capsule parasitics. Output power up to 216 GHz are observed. The tuning range above 110 GHz is found to be more than 40 percent. Using theoretical waveguide models the tuning behavior of the oscillators is also investigated.

Harmonic Bloch and dipole oscillations and their transition in elliptical optical waveguide arrays

NASA Astrophysics Data System (ADS)

Chan, Yun San; Zheng, Ming Jie; Yu, Kin Wah

2011-03-01

We have studied harmonic oscillations in an elliptical optical waveguide array in which the couplings between neighboring waveguides are varied in accord with a Kac matrix so that the propagation constant eigenvalues can take equally spaced values. As a result, the long-living optical Bloch oscillation (BO) and dipole oscillation (DO) are obtained. Moreover, when a linear gradient in the propagation constant is applied, we achieve a switching from DO to BO and vice versa by ramping up or down the gradient profile]. The various optical oscillations as well as their switching are investigated by field evolution analysis and confirmed by Hamiltonian optics. The equally spaced eigenvalues in the propagation constant allow viable applications in transmitting images, switching and routing of optical signals. Work supported by the General Research Fund of the Hong Kong SAR Government.

Harmonic oscillations of laminae in non-Newtonian fluids: A lattice Boltzmann-Immersed Boundary approach

NASA Astrophysics Data System (ADS)

De Rosis, Alessandro

2014-11-01

In this paper, the fluid dynamics induced by a rigid lamina undergoing harmonic oscillations in a non-Newtonian calm fluid is investigated. The fluid is modelled through the lattice Boltzmann method and the flow is assumed to be nearly incompressible. An iterative viscosity-correction based procedure is proposed to properly account for the non-Newtonian fluid feature and its accuracy is evaluated. In order to handle the mutual interaction between the lamina and the encompassing fluid, the Immersed Boundary method is adopted. A numerical campaign is performed. In particular, the effect of the non-Newtonian feature is highlighted by investigating the fluid forces acting on a harmonically oscillating lamina for different values of the Reynolds number. The findings prove that the non-Newtonian feature can drastically influence the behaviour of the fluid and, as a consequence, the forces acting upon the lamina. Several considerations are carried out on the time history of the drag coefficient and the results are used to compute the added mass through the hydrodynamic function. Moreover, the computational cost involved in the numerical simulations is discussed. Finally, two applications concerning water resources are investigated: the flow through an obstructed channel and the particle sedimentation. Present findings highlight a strong coupling between the body shape, the Reynolds number, and the flow behaviour index.

A Daily Oscillation in the Fundamental Frequency and Amplitude of Harmonic Syllables of Zebra Finch Song

PubMed Central

Wood, William E.; Osseward, Peter J.; Roseberry, Thomas K.; Perkel, David J.

2013-01-01

Complex motor skills are more difficult to perform at certain points in the day (for example, shortly after waking), but the daily trajectory of motor-skill error is more difficult to predict. By undertaking a quantitative analysis of the fundamental frequency (FF) and amplitude of hundreds of zebra finch syllables per animal per day, we find that zebra finch song follows a previously undescribed daily oscillation. The FF and amplitude of harmonic syllables rises across the morning, reaching a peak near mid-day, and then falls again in the late afternoon until sleep. This oscillation, although somewhat variable, is consistent across days and across animals and does not require serotonin, as animals with serotonergic lesions maintained daily oscillations. We hypothesize that this oscillation is driven by underlying physiological factors which could be shared with other taxa. Song production in zebra finches is a model system for studying complex learned behavior because of the ease of gathering comprehensive behavioral data and the tractability of the underlying neural circuitry. The daily oscillation that we describe promises to reveal new insights into how time of day affects the ability to accomplish a variety of complex learned motor skills. PMID:24312654

Use of videos for students to see the effect of changing gravity on harmonic oscillators

NASA Astrophysics Data System (ADS)

Benge, Raymond; Young, Charlotte; Worley, Alan; Davis, Shirley; Smith, Linda; Gell, Amber

2010-03-01

In introductory physics classes, students are introduced to harmonic oscillators such as masses on springs and the simple pendulum. In derivation of the equations describing these systems, the term ``g'' for the acceleration due to gravity cancels in the equation for the period of a mass oscillating on a spring, but it remains in the equation for the period of a pendulum. Frequently there is a homework problem asking how the system described would behave on the Moon, Mars, etc. Students have to have faith in the equations. In January, 2009, a team of community college faculty flew an experiment aboard an aircraft in conjunction with NASA's Microgravity University program. The experiment flown was a study in harmonic oscillator and pendulum behavior under various gravity situations. The aircraft simulated zero gravity, Martian, Lunar, and hypergravity conditions. The experiments were video recorded for students to study the behavior of the systems in varying gravity conditions. These videos are now available on the internet for anyone to use in introductory physics classes.

Dynamics of entanglement and uncertainty relation in coupled harmonic oscillator system: exact results

NASA Astrophysics Data System (ADS)

Park, DaeKil

2018-06-01

The dynamics of entanglement and uncertainty relation is explored by solving the time-dependent Schrödinger equation for coupled harmonic oscillator system analytically when the angular frequencies and coupling constant are arbitrarily time dependent. We derive the spectral and Schmidt decompositions for vacuum solution. Using the decompositions, we derive the analytical expressions for von Neumann and Rényi entropies. Making use of Wigner distribution function defined in phase space, we derive the time dependence of position-momentum uncertainty relations. To show the dynamics of entanglement and uncertainty relation graphically, we introduce two toy models and one realistic quenched model. While the dynamics can be conjectured by simple consideration in the toy models, the dynamics in the realistic quenched model is somewhat different from that in the toy models. In particular, the dynamics of entanglement exhibits similar pattern to dynamics of uncertainty parameter in the realistic quenched model.

Double simple-harmonic-oscillator formulation of the thermal equilibrium of a fluid interacting with a coherent source of phonons

NASA Technical Reports Server (NTRS)

Defacio, B.; Vannevel, Alan; Brander, O.

1993-01-01

A formulation is given for a collection of phonons (sound) in a fluid at a non-zero temperature which uses the simple harmonic oscillator twice; one to give a stochastic thermal 'noise' process and the other which generates a coherent Glauber state of phonons. Simple thermodynamic observables are calculated and the acoustic two point function, 'contrast' is presented. The role of 'coherence' in an equilibrium system is clarified by these results and the simple harmonic oscillator is a key structure in both the formulation and the calculations.

Stochastic and superharmonic stochastic resonances of a confined overdamped harmonic oscillator

NASA Astrophysics Data System (ADS)

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.

Harmonic uniflow engine

DOEpatents

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.

High efficiency and output power from second- and third-harmonic millimeter-wave InP-TED oscillators at frequencies above 170 GHz

NASA Astrophysics Data System (ADS)

Rydberg, Anders

1990-10-01

InP TED (transferred electron device) oscillators have been experimentally investigated for frequencies between 170 and 279 GHz. It has been found that output powers of more than 7 and 0.2 mW are possible at 180 and 272 GHz using second- and third-harmonic mode operation, respectively. Conversion efficiencies of more than 13 percent and 0.3 percent between fundamental and second harmonic and fundamental and third harmonic, respectively, have been found. The conversion efficiencies are comparable to GaAs TEDs. The output powers, conversion efficiencies, and tuning ranges (more than 22 percent) are the largest reported for InP TEDs at these frequencies. The output power at third harmonic was sufficient for supplying a superconducting mixer with local oscillator power.

Using Monte Carlo ray tracing simulations to model the quantum harmonic oscillator modes observed in uranium nitride

NASA Astrophysics Data System (ADS)

Lin, J. Y. Y.; Aczel, A. A.; Abernathy, D. L.; Nagler, S. E.; Buyers, W. J. L.; Granroth, G. E.

2014-04-01

Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of-flight chopper spectrometers [A. A. Aczel et al., Nat. Commun. 3, 1124 (2012), 10.1038/ncomms2117]. These modes are well described by three-dimensional isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states, and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature-dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T dependence of the scattering from these modes is strongly influenced by the uranium lattice.

Using Monte Carlo ray tracing simulations to model the quantum harmonic oscillator modes observed in uranium nitride

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, J. Y. Y.; Aczel, Adam A; Abernathy, Douglas L

2014-01-01

Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of- flight chopper spectrometers [A.A. Aczel et al, Nature Communications 3, 1124 (2012)]. These modes are well described by 3D isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accountingmore » for the nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states (PDOS), and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T-dependence of the scattering from these modes is strongly influenced by the uranium lattice.« less

Elementary derivation of the quantum propagator for the harmonic oscillator

NASA Astrophysics Data System (ADS)

Shao, Jiushu

2016-10-01

Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.

Spontaneous decoherence of coupled harmonic oscillators confined in a ring

NASA Astrophysics Data System (ADS)

Gong, ZhiRui; Zhang, ZhenWei; Xu, DaZhi; Zhao, Nan; Sun, ChangPu

2018-04-01

We study the spontaneous decoherence of coupled harmonic oscillators confined in a ring container, where the nearest-neighbor harmonic potentials are taken into consideration. Without any external symmetry-breaking field or surrounding environment, the quantum superposition state prepared in the relative degrees of freedom gradually loses its quantum coherence spontaneously. This spontaneous decoherence is interpreted by the gauge couplings between the center-of-mass and the relative degrees of freedoms, which actually originate from the symmetries of the ring geometry and the corresponding nontrivial boundary conditions. In particular, such spontaneous decoherence does not occur at all at the thermodynamic limit because the nontrivial boundary conditions become the trivial Born-von Karman boundary conditions when the perimeter of the ring container tends to infinity. Our investigation shows that a thermal macroscopic object with certain symmetries has a chance for its quantum properties to degrade even without applying an external symmetry-breaking field or surrounding environment.

Arbitrary-quantum-state preparation of a harmonic oscillator via optimal control

NASA Astrophysics Data System (ADS)

Rojan, Katharina; Reich, Daniel M.; Dotsenko, Igor; Raimond, Jean-Michel; Koch, Christiane P.; Morigi, Giovanna

2014-08-01

The efficient initialization of a quantum system is a prerequisite for quantum technological applications. Here we show that several classes of quantum states of a harmonic oscillator can be efficiently prepared by means of a Jaynes-Cummings interaction with a single two-level system. This is achieved by suitably tailoring external fields which drive the dipole and/or the oscillator. The time-dependent dynamics that leads to the target state is identified by means of optimal control theory (OCT) based on Krotov's method. Infidelities below 10-4 can be reached for the parameters of the experiment of Raimond, Haroche, Brune and co-workers, where the oscillator is a mode of a high-Q microwave cavity and the dipole is a Rydberg transition of an atom. For this specific situation we analyze the limitations on the fidelity due to parameter fluctuations and identify robust dynamics based on pulses found using ensemble OCT. Our analysis can be extended to quantum-state preparation of continuous-variable systems in other platforms, such as trapped ions and circuit QED.

Quantization with maximally degenerate Poisson brackets: the harmonic oscillator!

NASA Astrophysics Data System (ADS)

Nutku, Yavuz

2003-07-01

Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these degenerate Poisson brackets are brought to the form of Heisenberg's equations. We propose a definition for constructing quantum operators for classical functions, which enables us to turn the maximally degenerate Poisson brackets into operators. They pose a set of eigenvalue problems for a new state vector. The requirement of the single-valuedness of this eigenfunction leads to quantization. The example of the harmonic oscillator is used to illustrate this general procedure for quantizing a class of maximally super-integrable systems.

Symmetries of the quantum damped harmonic oscillator

NASA Astrophysics Data System (ADS)

Guerrero, J.; López-Ruiz, F. F.; Aldaya, V.; Cossío, F.

2012-11-01

For the non-conservative Caldirola-Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg-Weyl algebra can be found. The inclusion of the standard time evolution generator (which is not a symmetry) as a symmetry in this algebra, in a unitary manner, requires a non-trivial extension of this basic algebra and hence of the physical system itself. Surprisingly, this extension leads directly to the so-called Bateman dual system, which now includes a new particle acting as an energy reservoir. In addition, the Caldirola-Kanai dissipative system can be retrieved by imposing constraints. The algebra of symmetries of the dual system is presented, as well as a quantization that implies, in particular, a first-order Schrödinger equation. As opposed to other approaches, where it is claimed that the spectrum of the Bateman Hamiltonian is complex and discrete, we obtain that it is real and continuous, with infinite degeneracy in all regimes.

A quantum anharmonic oscillator model for the stock market

NASA Astrophysics Data System (ADS)

Gao, Tingting; Chen, Yu

2017-02-01

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

A Back-to-Front Derivation: The Equal Spacing of Quantum Levels Is a Proof of Simple Harmonic Oscillator Physics

ERIC Educational Resources Information Center

Andrews, David L.; Romero, Luciana C. Davila

2009-01-01

The dynamical behaviour of simple harmonic motion can be found in numerous natural phenomena. Within the quantum realm of atomic, molecular and optical systems, two main features are associated with harmonic oscillations: a finite ground-state energy and equally spaced quantum energy levels. Here it is shown that there is in fact a one-to-one…

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

NASA Astrophysics Data System (ADS)

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.

Coupled harmonic oscillators and their quantum entanglement.

PubMed

Makarov, Dmitry N

2018-04-01

A system of two coupled quantum harmonic oscillators with the Hamiltonian H[over ̂]=1/2(1/m_{1}p[over ̂]_{1}^{2}+1/m_{2}p[over ̂]_{2}^{2}+Ax_{1}^{2}+Bx_{2}^{2}+Cx_{1}x_{2}) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H[over ̂]Ψ=iℏ∂Ψ/∂t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.

Coupled harmonic oscillators and their quantum entanglement

NASA Astrophysics Data System (ADS)

Makarov, Dmitry N.

2018-04-01

A system of two coupled quantum harmonic oscillators with the Hamiltonian H ̂=1/2 (1/m1p̂1 2+1/m2p̂2 2+A x12+B x22+C x1x2) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H ̂Ψ =i ℏ ∂/Ψ ∂ t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.

Modelling vertical human walking forces using self-sustained oscillator

NASA Astrophysics Data System (ADS)

Kumar, Prakash; Kumar, Anil; Racic, Vitomir; Erlicher, Silvano

2018-01-01

This paper proposes a model of a self-sustained oscillator which can generate reliably the vertical contact force between the feet of a healthy pedestrian and the supporting flat rigid surface. The model is motivated by the self-sustained nature of the walking process, i.e. a pedestrian generates the required inner energy to sustain its repetitive body motion. The derived model is a fusion of the well-known Rayleigh, Van der Pol and Duffing oscillators. Some additional nonlinear terms are added to produce both the odd and even harmonics observed in the experimentally measured force data. The model parameters were derived from force records due to twelve pedestrians walking on an instrumented treadmill at ten speeds using a linear least square technique. The stability analysis was performed using the energy balance method and perturbation method. The results obtained from the model show a good agreement with the experimental results.

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

NASA Astrophysics Data System (ADS)

Wang, Yang; Song, Hai-Ying; Liu, H. Y.; Liu, Shi-Bing

2017-07-01

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.

Refined Weyl Law for Homogeneous Perturbations of the Harmonic Oscillator

NASA Astrophysics Data System (ADS)

Doll, Moritz; Gannot, Oran; Wunsch, Jared

2018-02-01

Let H denote the harmonic oscillator Hamiltonian on R}^d,} perturbed by an isotropic pseudodifferential operator of order 1. We consider the Schrödinger propagator {U(t)=e^{-itH},} and find that while sing-supp Tr U(t) \\subset 2 π Z as in the unperturbed case, there exists a large class of perturbations in dimensions {d ≥ 2 for which the singularities of {Tr U(t)} at nonzero multiples of {2 π} are weaker than the singularity at t = 0. The remainder term in the Weyl law is of order {o(λ^{d-1})} , improving in these cases the {o(λ^{d-1})} remainder previously established by Helffer-Robert.

Continuous-Wave Operation of a 460-GHz Second Harmonic Gyrotron Oscillator

PubMed Central

Hornstein, Melissa K.; Bajaj, Vikram S.; Griffin, Robert G.; Temkin, Richard J.

2007-01-01

We report the regulated continuous-wave (CW) operation of a second harmonic gyrotron oscillator at output power levels of over 8 W (12.4 kV and 135 mA beam voltage and current) in the TE0,6,1 mode near 460 GHz. The gyrotron also operates in the second harmonic TE2,6,1 mode at 456 GHz and in the TE2,3,1 fundamental mode at 233 GHz. CW operation was demonstrated for a one-hour period in the TE0,6,1 mode with better than 1% power stability, where the power was regulated using feedback control. Nonlinear simulations of the gyrotron operation agree with the experimentally measured output power and radio-frequency (RF) efficiency when cavity ohmic losses are included in the analysis. The output radiation pattern was measured using a pyroelectric camera and is highly Gaussian, with an ellipticity of 4%. The 460-GHz gyrotron will serve as a millimeter-wave source for sensitivity-enhanced nuclear magnetic resonance (dynamic nuclear polarization) experiments at a magnetic field of 16.4 T. PMID:17710187

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

DOE PAGES

Chen, Xi; Burrell, K. H.; Osborne, T. H.; ...

2017-06-14

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 collisionalitymore » $$\

Evidence for new resonances in the K-barN system: A prima facie case for the even-wave harmonic-oscillator model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamath, S.G.

1978-10-01

Arguments are presented to show that the new resonance parameters obtained by Alston-Garnjost et al. in a recent analysis of the K-barN system from 365 to 1320 MeV/c provide a prima facie case for the even-wave harmonic-oscillator theory of baryonic states in the framework of SU(6)/sub W/ x O(3). A new quantum classification of the ..lambda.. states belonging to the (70,1/sup -/) is also proposed.

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

NASA Astrophysics Data System (ADS)

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.

Generation of a tunable environment for electrical oscillator systems.

PubMed

León-Montiel, R de J; Svozilík, J; Torres, Juan P

2014-07-01

Many physical, chemical, and biological systems can be modeled by means of random-frequency harmonic oscillator systems. Even though the noise-free evolution of harmonic oscillator systems can be easily implemented, the way to experimentally introduce, and control, noise effects due to a surrounding environment remains a subject of lively interest. Here, we experimentally demonstrate a setup that provides a unique tool to generate a fully tunable environment for classical electrical oscillator systems. We illustrate the operation of the setup by implementing the case of a damped random-frequency harmonic oscillator. The high degree of tunability and control of our scheme is demonstrated by gradually modifying the statistics of the oscillator's frequency fluctuations. This tunable system can readily be used to experimentally study interesting noise effects, such as noise-induced transitions in systems driven by multiplicative noise, and noise-induced transport, a phenomenon that takes place in quantum and classical coupled oscillator networks.

Spin current and second harmonic generation in non-collinear magnetic systems: the hydrodynamic model

NASA Astrophysics Data System (ADS)

Karashtin, E. A.; Fraerman, A. A.

2018-04-01

We report a theoretical study of the second harmonic generation in a noncollinearly magnetized conductive medium with equilibrium spin current. The hydrodynamic model is used to unravel the mechanism of a novel effect of the double frequency signal generation that is attributed to the spin current. According to our calculations, this second harmonic response appears due to the ‘non-adiabatic’ spin polarization of the conduction electrons induced by the oscillations in the non-uniform magnetization forced by the electric field of the electromagnetic wave. Together with the linear velocity response this leads to the generation of the double frequency spin current. This spin current is converted to the electric current via the inverse spin Hall effect, and the double-frequency electric current emits the second harmonic radiation. Possible experiment for detection of the new second harmonic effect is proposed.

𝒩 = 2 supersymmetric Pais-Uhlenbeck oscillator

NASA Astrophysics Data System (ADS)

Masterov, Ivan

2015-06-01

We construct an 𝒩 = 2 supersymmetric extension of the Pais-Uhlenbeck oscillator for distinct frequencies of oscillation. A link to a set of decoupled 𝒩 = 2 supersymmetric harmonic oscillators with alternating sign in the Hamiltonian is introduced. Symmetries of the model are discussed in detail. The investigation of a quantum counterpart of the constructed model shows that the corresponding Fock space contains negative norm states and the energy spectrum of the system is unbounded from below.

Quantum Dynamics of Multi Harmonic Oscillators Described by Time Variant Conic Hamiltonian and their Use in Contemporary Sciences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Demiralp, Metin

This work focuses on the dynamics of a system of quantum multi harmonic oscillators whose Hamiltonian is conic in positions and momenta with time variant coefficients. While it is simple, this system is useful for modeling the dynamics of a number of systems in contemporary sciences where the equations governing spatial or temporal changes are described by sets of ODEs. The dynamical causal models used readily in neuroscience can be indirectly described by these systems. In this work, we want to show that it is possible to describe these systems using quantum wave function type entities and expectations if themore » dynamic of the system is related to a set of ODEs.« less

Addendum to "An update on the classical and quantum harmonic oscillators on the sphere and the hyperbolic plane in polar coordinates" [Phys. Lett. A 379 (26-27) (2015) 1589-1593

NASA Astrophysics Data System (ADS)

Quesne, C.

2016-02-01

The classical and quantum solutions of a nonlinear model describing harmonic oscillators on the sphere and the hyperbolic plane, derived in polar coordinates in a recent paper (Quesne, 2015) [1], are extended by the inclusion of an isotonic term.

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

NASA Astrophysics Data System (ADS)

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.

Local Gram-Schmidt and covariant Lyapunov vectors and exponents for three harmonic oscillator problems

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.

2012-02-01

We compare the Gram-Schmidt and covariant phase-space-basis-vector descriptions for three time-reversible harmonic oscillator problems, in two, three, and four phase-space dimensions respectively. The two-dimensional problem can be solved analytically. The three-dimensional and four-dimensional problems studied here are simultaneously chaotic, time-reversible, and dissipative. Our treatment is intended to be pedagogical, for use in an updated version of our book on Time Reversibility, Computer Simulation, and Chaos. Comments are very welcome.

Entanglement of a class of non-Gaussian states in disordered harmonic oscillator systems

NASA Astrophysics Data System (ADS)

Abdul-Rahman, Houssam

2018-03-01

For disordered harmonic oscillator systems over the d-dimensional lattice, we consider the problem of finding the bipartite entanglement of the uniform ensemble of the energy eigenstates associated with a particular number of modes. Such an ensemble defines a class of mixed, non-Gaussian entangled states that are labeled, by the energy of the system, in an increasing order. We develop a novel approach to find the exact logarithmic negativity of this class of states. We also prove entanglement bounds and demonstrate that the low energy states follow an area law.

Harmonic engine

DOEpatents

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.

Computer model for harmonic ultrasound imaging.

PubMed

Li, Y; Zagzebski, J A

2000-01-01

Harmonic ultrasound imaging has received great attention from ultrasound scanner manufacturers and researchers. In this paper, we present a computer model that can generate realistic harmonic images. In this model, the incident ultrasound is modeled after the "KZK" equation, and the echo signal is modeled using linear propagation theory because the echo signal is much weaker than the incident pulse. Both time domain and frequency domain numerical solutions to the "KZK" equation were studied. Realistic harmonic images of spherical lesion phantoms were generated for scans by a circular transducer. This model can be a very useful tool for studying the harmonic buildup and dissipation processes in a nonlinear medium, and it can be used to investigate a wide variety of topics related to B-mode harmonic imaging.

Computer model for harmonic ultrasound imaging.

PubMed

Li, Y; Zagzebski, J A

2000-01-01

Harmonic ultrasound imaging has received great attention from ultrasound scanner manufacturers and researchers. Here, the authors present a computer model that can generate realistic harmonic images. In this model, the incident ultrasound is modeled after the "KZK" equation, and the echo signal is modeled using linear propagation theory because the echo signal is much weaker than the incident pulse. Both time domain and frequency domain numerical solutions to the "KZK" equation were studied. Realistic harmonic images of spherical lesion phantoms were generated for scans by a circular transducer. This model can be a very useful tool for studying the harmonic buildup and dissipation processes in a nonlinear medium, and it can be used to investigate a wide variety of topics related to B-mode harmonic imaging.

Harmonic oscillators and resonance series generated by a periodic unstable classical orbit

NASA Technical Reports Server (NTRS)

Kazansky, A. K.; Ostrovsky, Valentin N.

1995-01-01

The presence of an unstable periodic classical orbit allows one to introduce the decay time as a purely classical magnitude: inverse of the Lyapunov index which characterizes the orbit instability. The Uncertainty Relation gives the corresponding resonance width which is proportional to the Planck constant. The more elaborate analysis is based on the parabolic equation method where the problem is effectively reduced to the multidimensional harmonic oscillator with the time-dependent frequency. The resonances form series in the complex energy plane which is equidistant in the direction perpendicular to the real axis. The applications of the general approach to various problems in atomic physics are briefly exposed.

Quantum entanglement of a harmonic oscillator with an electromagnetic field.

PubMed

Makarov, Dmitry N

2018-05-29

At present, there are many methods for obtaining quantum entanglement of particles with an electromagnetic field. Most methods have a low probability of quantum entanglement and not an exact theoretical apparatus based on an approximate solution of the Schrodinger equation. There is a need for new methods for obtaining quantum-entangled particles and mathematically accurate studies of such methods. In this paper, a quantum harmonic oscillator (for example, an electron in a magnetic field) interacting with a quantized electromagnetic field is considered. Based on the exact solution of the Schrodinger equation for this system, it is shown that for certain parameters there can be a large quantum entanglement between the electron and the electromagnetic field. Quantum entanglement is analyzed on the basis of a mathematically exact expression for the Schmidt modes and the Von Neumann entropy.

Harmonic engine

DOEpatents

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.

A novel model of interaction between high frequency electromagnetic non-ionizing fields and microtubules viewed as coupled two-degrees of freedom harmonic oscillators.

PubMed

Caligiuri, Luigi Maxmilian

2015-01-01

The question regarding the potential biological and adverse health effects of non-ionizing electromagnetic fields on living organisms is of primary importance in biophysics and medicine. Despite the several experimental evidences showing such occurrence in a wide frequency range from extremely low frequency to microwaves, a definitive theoretical model able to explain a possible mechanism of interaction between electromagnetic fields and living matter, especially in the case of weak and very weak intensities, is still missing. In this paper it has been suggested a possible mechanism of interaction involving the resonant absorption of electromagnetic radiation by microtubules. To this aim these have been modeled as non-dissipative forced harmonic oscillators characterized by two coupled "macroscopic" degrees of freedom, respectively describing longitudinal and transversal vibrations induced by the electromagnetic field. We have shown that the proposed model, although at a preliminary stage, is able to explain the ability of even weak electromagnetic radiating electromagnetic fields to transfer high quantities of energy to living systems by means of a resonant mechanism, so capable to easily damage microtubules structure.

A neural network model of harmonic detection

NASA Astrophysics Data System (ADS)

Lewis, Clifford F.

2003-04-01

Harmonic detection theories postulate that a virtual pitch is perceived when a sufficient number of harmonics is present. The harmonics need not be consecutive, but higher harmonics contribute less than lower harmonics [J. Raatgever and F. A. Bilsen, in Auditory Physiology and Perception, edited by Y. Cazals, K. Horner, and L. Demany (Pergamon, Oxford, 1992), pp. 215-222 M. K. McBeath and J. F. Wayand, Abstracts of the Psychonom. Soc. 3, 55 (1998)]. A neural network model is presented that has the potential to simulate this operation. Harmonics are first passed through a bank of rounded exponential filters with lateral inhibition. The results are used as inputs for an autoassociator neural network. The model is trained using harmonic data for symphonic musical instruments, in order to test whether it can self-organize by learning associations between co-occurring harmonics. It is shown that the trained model can complete the pattern for missing-fundamental sounds. The Performance of the model in harmonic detection will be compared with experimental results for humans.

The Duffin-Kemmer-Petiau oscillator

NASA Technical Reports Server (NTRS)

Nedjadi, Youcef; Barrett, Roger

1995-01-01

In view of current interest in relativistic spin-one systems and the recent work on the Dirac Oscillator, we introduce the Duffin-Kemmer-Petiau (DKP) equation obtained by using an external potential linear in r. Since, in the non-relativistic limit, the spin 1 representation leads to a harmonic oscillator with a spin-orbit coupling of the Thomas form, we call the equation the DKP oscillator. This oscillator is a relativistic generalization of the quantum harmonic oscillator for scalar and vector bosons. We show that it conserves total angular momentum and that it is exactly solvable. We calculate and discuss the eigenspectrum of the DKP oscillator in the spin 1 representation.

Revisiting an old concept: the coupled oscillator model for VCD. Part 1: the generalised coupled oscillator mechanism and its intrinsic connection to the strength of VCD signals.

PubMed

Nicu, Valentin Paul

2016-08-03

Motivated by the renewed interest in the coupled oscillator (CO) model for VCD, in this work a generalised coupled oscillator (GCO) expression is derived by introducing the concept of a coupled oscillator origin. Unlike the standard CO expression, the GCO expression is exact within the harmonic approximation. Using two illustrative example molecules, the theoretical concepts introduced here are demonstrated by performing a GCO decomposition of the rotational strengths computed using DFT. This analysis shows that: (1) the contributions to the rotational strengths that are normally neglected in the standard CO model can be comparable to or larger than the CO contribution, and (2) the GCO mechanism introduced here can affect the VCD intensities of all types of modes in symmetric and asymmetric molecules.

Second- and third-harmonic generation in metal-based structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scalora, M.; Akozbek, N.; Bloemer, M. J.

We present a theoretical approach to the study of second- and third-harmonic generation from metallic structures and nanocavities filled with a nonlinear material in the ultrashort pulse regime. We model the metal as a two-component medium, using the hydrodynamic model to describe free electrons and Lorentz oscillators to account for core electron contributions to both the linear dielectric constant and harmonic generation. The active nonlinear medium that may fill a metallic nanocavity, or be positioned between metallic layers in a stack, is also modeled using Lorentz oscillators and surface phenomena due to symmetry breaking are taken into account. We studymore » the effects of incident TE- and TM-polarized fields and show that a simple reexamination of the basic equations reveals additional, exploitable dynamical features of nonlinear frequency conversion in plasmonic nanostructures.« less

A position-dependent mass harmonic oscillator and deformed space

NASA Astrophysics Data System (ADS)

da Costa, Bruno G.; Borges, Ernesto P.

2018-04-01

We consider canonically conjugated generalized space and linear momentum operators x^ q and p^ q in quantum mechanics, associated with a generalized translation operator which produces infinitesimal deformed displacements controlled by a deformation parameter q. A canonical transformation (x ^ ,p ^ ) →(x^ q,p^ q ) leads the Hamiltonian of a position-dependent mass particle in usual space to another Hamiltonian of a particle with constant mass in a conservative force field of the deformed space. The equation of motion for the classical phase space (x, p) may be expressed in terms of the deformed (dual) q-derivative. We revisit the problem of a q-deformed oscillator in both classical and quantum formalisms. Particularly, this canonical transformation leads a particle with position-dependent mass in a harmonic potential to a particle with constant mass in a Morse potential. The trajectories in phase spaces (x, p) and (xq, pq) are analyzed for different values of the deformation parameter. Finally, we compare the results of the problem in classical and quantum formalisms through the principle of correspondence and the WKB approximation.

Protective measurement of the wave function of a single squeezed harmonic-oscillator state

NASA Astrophysics Data System (ADS)

Alter, Orly; Yamamoto, Yoshihisa

1996-05-01

A scheme for the "protective measurement"

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

NASA Astrophysics Data System (ADS)

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.

PubMed

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.

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

PubMed

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.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noguera, Norman, E-mail: norman.noguera@ucr.ac.cr; Rózga, Krzysztof, E-mail: krzysztof.rozga@upr.edu

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 ofmore » a slightly more general potential than the one for harmonic oscillator.« less

Investigation of Student Reasoning about Harmonic Motions

NASA Astrophysics Data System (ADS)

Tongnopparat, N.; Poonyawatpornkul, J.; Wattanakasiwich, P.

This study aimed to investigate student reasoning about harmonic oscillations. We conducted a semi-structured interview based on three situations of harmonic motions—(1) a mass attaching to spring and horizontally oscillating without damping, (2) the same situation but vertically oscillating and (3) a mass attaching to spring and oscillating in viscous liquid. Forty-five second-year students taking a vibrations and wave course at Chiang Mai University, Thailand participated in a fifteen-minute interview, which was video-recorded. The videos were transcribed and analyzed by three physics instructors. As results, we found that most students had misconceptions about angular frequency and energy mostly in the second and third situations.

Simulation of 100-300 GHz solid-state harmonic sources

NASA Technical Reports Server (NTRS)

Zybura, Michael F.; Jones, J. Robert; Jones, Stephen H.; Tait, Gregory B.

1995-01-01

Accurate and efficient simulations of the large-signal time-dependent characteristics of second-harmonic Transferred Electron Oscillators (TEO's) and Heterostructure Barrier Varactor (HBV) frequency triplers have been obtained. This is accomplished by using a novel and efficient harmonic-balance circuit analysis technique which facilitates the integration of physics-based hydrodynamic device simulators. The integrated hydrodynamic device/harmonic-balance circuit simulators allow TEO and HBV circuits to be co-designed from both a device and a circuit point of view. Comparisons have been made with published experimental data for both TEO's and HBV's. For TEO's, excellent correlation has been obtained at 140 GHz and 188 GHz in second-harmonic operation. Excellent correlation has also been obtained for HBV frequency triplers operating near 200 GHz. For HBV's, both a lumped quasi-static equivalent circuit model and the hydrodynamic device simulator have been linked to the harmonic-balance circuit simulator. This comparison illustrates the importance of representing active devices with physics-based numerical device models rather than analytical device models.

Synthesizing Virtual Oscillators to Control Islanded Inverters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Brian B.; Sinha, Mohit; Ainsworth, Nathan G.

Virtual oscillator control (VOC) is a decentralized control strategy for islanded microgrids where inverters are regulated to emulate the dynamics of weakly nonlinear oscillators. Compared to droop control, which is only well defined in sinusoidal steady state, VOC is a time-domain controller that enables interconnected inverters to stabilize arbitrary initial conditions to a synchronized sinusoidal limit cycle. However, the nonlinear oscillators that are elemental to VOC cannot be designed with conventional linear-control design methods. We address this challenge by applying averaging- and perturbation-based nonlinear analysis methods to extract the sinusoidal steady-state and harmonic behavior of such oscillators. The averaged modelsmore » reveal conclusive links between real- and reactive-power outputs and the terminal-voltage dynamics. Similarly, the perturbation methods aid in quantifying higher order harmonics. The resultant models are then leveraged to formulate a design procedure for VOC such that the inverter satisfies standard ac performance specifications related to voltage regulation, frequency regulation, dynamic response, and harmonic content. Experimental results for a single-phase 750 VA, 120 V laboratory prototype demonstrate the validity of the design approach. They also demonstrate that droop laws are, in fact, embedded within the equilibria of the nonlinear-oscillator dynamics. This establishes the backward compatibility of VOC in that, while acting on time-domain waveforms, it subsumes droop control in sinusoidal steady state.« less

High efficiency fourth-harmonic generation from nanosecond fiber master oscillator power amplifier

NASA Astrophysics Data System (ADS)

Mu, Xiaodong; Steinvurzel, Paul; Rose, Todd S.; Lotshaw, William T.; Beck, Steven M.; Clemmons, James H.

2016-03-01

We demonstrate high power, deep ultraviolet (DUV) conversion to 266 nm through frequency quadrupling of a nanosecond pulse width 1064 nm fiber master oscillator power amplifier (MOPA). The MOPA system uses an Yb-doped double-clad polarization-maintaining large mode area tapered fiber as the final gain stage to generate 0.5-mJ, 10 W, 1.7- ns single mode pulses at a repetition rate of 20 kHz with measured spectral bandwidth of 10.6 GHz (40 pm), and beam qualities of Mx 2=1.07 and My 2=1.03, respectively. Using LBO and BBO crystals for the second-harmonic generation (SHG) and fourth-harmonic generation (FHG), we have achieved 375 μJ (7.5 W) and 92.5 μJ (1.85 W) at wavelengths of 532 nm and 266 nm, respectively. To the best of our knowledge these are the highest narrowband infrared, green and UV pulse energies obtained to date from a fully spliced fiber amplifier. We also demonstrate high efficiency SHG and FHG with walk-off compensated (WOC) crystal pairs and tightly focused pump beam. An SHG efficiency of 75%, FHG efficiency of 47%, and an overall efficiency of 35% from 1064 nm to 266 nm are obtained.

Rotational Shear Effects on Edge Harmonic Oscillations in DIII-D Quiescent H-mode Discharges

NASA Astrophysics Data System (ADS)

Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, Wm.; Tobias, B. J.; Yan, Z.

2015-11-01

In quiescent H-mode (QH) regime, the edge harmonic oscillations (EHO) play an important role in avoiding the transient ELM power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n <= 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended MHD code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-I and MIR diagnostics, as well as the kink/peeling mode properties of the ideal MHD code ELITE. The numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by the toroidal rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that the low-n EHO can be destabilized in principle with rotation in both directions. These modeling results are consistent with experimental observations of the EHO and support the proposed theory of the EHO as a rotational shear driven kink/peeling mode.

Decaying and decayless transverse oscillations of a coronal loop

NASA Astrophysics Data System (ADS)

Nisticò, G.; Nakariakov, V. M.; Verwichte, E.

2013-04-01

Aims: We investigate kink oscillations of loops observed in an active region with the Atmospheric Imaging Assembly (AIA) instrument on board the Solar Dynamics Observatory (SDO) spacecraft before and after a flare. Methods: The oscillations were depicted and analysed with time-distance maps, extracted from the cuts taken parallel or perpendicular to the loop axis. Moving loops were followed in time with steadily moving slits. The period of oscillations and its time variation were determined by best-fitting harmonic functions. Results: We show that before and well after the occurrence of the flare, the loops experience low-amplitude decayless oscillations. The flare and the coronal mass ejection associated to it trigger large-amplitude oscillations that decay exponentially in time. The periods of the kink oscillations in both regimes (about 240 s) are similar. An empirical model of the phenomenon in terms of a damped linear oscillator excited by a continuous low-amplitude harmonic driver and by an impulsive high-amplitude driver is found to be consistent with the observations. Two movies are available in electronic form at http://www.aanda.org

Data-adaptive harmonic spectra and multilayer Stuart-Landau models

NASA Astrophysics Data System (ADS)

Chekroun, Mickaël D.; Kondrashov, Dmitri

2017-09-01

Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure. The corresponding eigenvalues can be grouped per Fourier frequency and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey, furthermore, a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum. The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coefficients stacked by Fourier frequency which can be efficiently modeled—provided the decay of temporal correlations is sufficiently well-resolved—within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators. Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence.

Development and applications of algorithms for calculating the transonic flow about harmonically oscillating wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Weatherill, W. H.; Yip, E. L.

1984-01-01

A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.

MODEL HARMONIZATION POTENTIAL AND BENEFITS

EPA Science Inventory

The IPCS Harmonization Project, which is currently ongoing under the auspices of the WHO, in the context of chemical risk assessment or exposure modeling, does not imply global standardization. Instead, harmonization is thought of as an effort to strive for consistency among appr...

Multichannel high-order harmonic generation from solids

NASA Astrophysics Data System (ADS)

Du, Tao-Yuan; Tang, Dong; Huang, Xiao-Huan; Bian, Xue-Bin

2018-04-01

We studied the ultrafast dynamics of high-order harmonic generation (HHG) from solids numerically. It is found that a superposition of Bloch oscillation in the same band and Zenner tunneling to its neighboring conduction band (i.e., Bloch-Zener oscillation effect) play significant roles in HHG when the Bloch electrons cross the boundary of the first Brillouin zone. It increases the number of the harmonic emission channels. These multichannel signals extend the cutoff energy of the plateau in the HHG spectra and enhance both the intra- and interband contributions. The interference of different channels makes the structure of the HHG spectra complex. The multichannel dynamics in the monochromatic and two-color laser fields are demonstrated in a periodic potential model and single-crystal MgO, respectively. It provides an alternative way to control the ultrafast electron dynamics and HHG emission processes in solids.

Generalized power-spectrum Larmor formula for an extended charged particle embedded in a harmonic oscillator

NASA Astrophysics Data System (ADS)

Marengo, Edwin A.; Khodja, Mohamed R.

2006-09-01

The nonrelativistic Larmor radiation formula, giving the power radiated by an accelerated charged point particle, is generalized for a spatially extended particle in the context of the classical charged harmonic oscillator. The particle is modeled as a spherically symmetric rigid charge distribution that possesses both translational and spinning degrees of freedom. The power spectrum obtained exhibits a structure that depends on the form factor of the particle, but reduces, in the limit of an infinitesimally small particle and for the charge distributions considered, to Larmor’s familiar result. It is found that for finite-duration small-enough accelerations as well as perpetual uniform accelerations the power spectrum of the spatially extended particle reduces to that of a point particle. It is also found that when the acceleration is violent or the size parameter of the particle is very large compared to the wavelength of the emitted radiation the power spectrum is highly suppressed. Possible applications are discussed.

Quantization and instability of the damped harmonic oscillator subject to a time-dependent force

NASA Astrophysics Data System (ADS)

Majima, H.; Suzuki, A.

2011-12-01

We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity ( -γẋ) and a time-dependent external force ( K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman's system, which is described by the Lagrangian: ℒ=mẋẏ-U(x+{1}/{2}y)+U(x-{1}/{2}y)+{γ}/{2}(xẏ-yẋ)-xK(t)+yK(t), which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting U(x±y/2)={1}/{2}k( specifically for a dual extended damped-amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman's Hamiltonian ℋ. The Heisenberg equations of motion utilizing the quantized Hamiltonian ℋ̂ surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped-amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force.

Bound state solution of Dirac equation for 3D harmonics oscillator plus trigonometric scarf noncentral potential using SUSY QM approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cari, C., E-mail: carinln@yahoo.com; Suparmi, A., E-mail: carinln@yahoo.com

2014-09-30

Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.

Data-adaptive harmonic analysis and prediction of sea level change in North Atlantic region

NASA Astrophysics Data System (ADS)

Kondrashov, D. A.; Chekroun, M.

2017-12-01

This study aims to characterize North Atlantic sea level variability across the temporal and spatial scales. We apply recently developed data-adaptive Harmonic Decomposition (DAH) and Multilayer Stuart-Landau Models (MSLM) stochastic modeling techniques [Chekroun and Kondrashov, 2017] to monthly 1993-2017 dataset of Combined TOPEX/Poseidon, Jason-1 and Jason-2/OSTM altimetry fields over North Atlantic region. The key numerical feature of the DAH relies on the eigendecomposition of a matrix constructed from time-lagged spatial cross-correlations. In particular, eigenmodes form an orthogonal set of oscillating data-adaptive harmonic modes (DAHMs) that come in pairs and in exact phase quadrature for a given temporal frequency. Furthermore, the pairs of data-adaptive harmonic coefficients (DAHCs), obtained by projecting the dataset onto associated DAHMs, can be very efficiently modeled by a universal parametric family of simple nonlinear stochastic models - coupled Stuart-Landau oscillators stacked per frequency, and synchronized across different frequencies by the stochastic forcing. Despite the short record of altimetry dataset, developed DAH-MSLM model provides for skillful prediction of key dynamical and statistical features of sea level variability. References M. D. Chekroun and D. Kondrashov, Data-adaptive harmonic spectra and multilayer Stuart-Landau models. HAL preprint, 2017, https://hal.archives-ouvertes.fr/hal-01537797

Alternative descriptions of wave and particle aspects of the harmonic oscillator

NASA Technical Reports Server (NTRS)

Schuch, Dieter

1993-01-01

The dynamical properties of the wave and particle aspects of the harmonic oscillator can be studied with the help of the time-dependent Schroedinger equation (SE). Especially the time-dependence of maximum and width of Gaussian wave packet solutions allow to show the evolution and connections of those two complementary aspects. The investigation of the relations between the equations describing wave and particle aspects leads to an alternative description of the considered systems. This can be achieved by means of a Newtonian equation for a complex variable in connection with a conservation law for a nonclassical angular momentum-type quantity. With the help of this complex variable, it is also possible to develop a Hamiltonian formalism for the wave aspect contained in the SE, which allows to describe the dynamics of the position and momentum uncertainties. In this case the Hamiltonian function is equivalent to the difference between the mean value of the Hamiltonian operator and the classical Hamiltonian function.

A model for internal oscillations in geysers, with application to Old Faithful (Yellowstone, USA)

NASA Astrophysics Data System (ADS)

Rudolph, Maxwell L.; Sohn, Robert A.

2017-09-01

We present a mechanical model for internal oscillations in geysers with "bubble trap" configurations, where ascending gas or vapor becomes trapped beneath the roof of a cavity that is laterally offset from the eruption conduit. We consider two cases, one in which the trapped gas behaves as an isothermal ideal gas, and one where it is treated as isenthalpic steam. In both cases the system behaves as a damped, harmonic oscillator with a resonant frequency that is sensitive to the conduit geometries and fluid volumes. We use the model to predict internal oscillation frequencies for Old Faithful geyser, in Yellowstone, USA, using conduit geometry constraints from the literature, and find that the frequencies predicted by the model are consistent with observations ( 1 Hz). We show that systematic frequency increases during the recharge cycle, when the fluid volume of the system is increasing due to recharge, are consistent with either a decrease in the amount (both volume and mass) of trapped gas or vapor, a decrease in the eruption conduit area, or a combination of both.

Photonic harmonic up-converter based on a self-oscillating optical frequency comb using a DP-DPMZM

NASA Astrophysics Data System (ADS)

Xiao, Xuedi; Li, Shangyuan; Xie, Zhengyang; Peng, Shaowen; Wu, Dexin; Xue, Xiaoxiao; Zheng, Xiaoping; Zhou, Bingkun

2018-04-01

A photonic harmonic up-converter based on a self-oscillating optical frequency comb (OFC) utilizing an integrated dual-polarization dual-parallel Mach-Zehnder Modulator (DP-DPMZM) is proposed and experimentally demonstrated. One DPMZM is used to generate the optoelectronic oscillator (OEO)-based OFC, and the rest one is used to generate the optical-modulated intermediate frequency (IF) signal. Beating these two signals, the up-converted signals at different bands would be obtained. As the OFC is generated based on the OEO loop, phase noise can be very low, ensuring good phase noise properties of the up-converted signals. Moreover, frequency spacing between the combs is dependent on oscillating frequency of the OEO, which can be as large as tens of gigahertz. Thus IF signals with large bandwidth can be up-converted to RF bands without aliasing. Experimentally, the 2.5 GHz IF signal is simultaneously up-converted to 13.3, 24.1, and 34.9 GHz by a self-oscillating 7-line OFC spacing at 10.8 GHz. Owing to good phase noise property of the OEO, the up-converted signals at 13.3 and 24.1 GHz maintain the phase noise of the IF signal from 1 KHz to 100 KHz offset. The results show that the converter is promising for multi-band radar and satellite navigation applications.

Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Xi; Burrell, Keith H.; Ferraro, Nathaniel M.

In the quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHO) play an important role in avoiding transient edge localized mode (ELM) power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n ≤ 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended MHD code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-Imaging and microwave imaging reflectometer (MIR) diagnostics, as well as the kink/peeling mode properties found by the ideal MHD code ELITE.more » Numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by the rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that EHO can be destabilized in principle with rotation in either direction. Furthermore, the modeling results are consistent with observations of the EHO, support the proposed theory of the EHO as a rotational shear driven kink/peeling mode, and improve our understanding and confidence in creating and sustaining QH-mode in present and future devices.« less

Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges

DOE PAGES

Chen, Xi; Burrell, Keith H.; Ferraro, Nathaniel M.; ...

2016-06-21

In the quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHO) play an important role in avoiding transient edge localized mode (ELM) power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n ≤ 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended MHD code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-Imaging and microwave imaging reflectometer (MIR) diagnostics, as well as the kink/peeling mode properties found by the ideal MHD code ELITE.more » Numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by the rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that EHO can be destabilized in principle with rotation in either direction. Furthermore, the modeling results are consistent with observations of the EHO, support the proposed theory of the EHO as a rotational shear driven kink/peeling mode, and improve our understanding and confidence in creating and sustaining QH-mode in present and future devices.« less

Representation of the five- and six-dimensional harmonic oscillators in a u(5) ⊃ so(5) ⊃ so(3) basis

NASA Astrophysics Data System (ADS)

Rowe, D. J.

1994-06-01

The duality that exists between the two subgroups SU(1,1) and O(5) of Sp(5,R) to construct basis states for the five-dimensional harmonic oscillator which simultaneously reduce the Sp(5,R)⊇U(5)⊇O(5)⊇SO(3) and Sp(5,R)⊇ SU(1,1)⊇U(1) subgroup chains is used. It is shown that the vector-coherent-state wave functions of the fundamental five-dimensional SO(5) irrep [1,0] realize the traceless bosons introduced by Lohe and Hurst to classify the irreps of the orthogonal groups and employed in Chacon, Moshinsky, and Sharp's construction of a basis for the five-dimensional harmonic oscillator. Moreover, it is shown that VCS theory provides a simple mechanism for constructing matrix elements of the traceless boson operators. These matrix elements are used to extend the VCS representations of SO(5) in an SO(3) basis, given in a previous paper, to irreps of U(5) in an SO(5)⊇ SO(3) basis. The extension to U(6)⊇U(5)⊇SO(5)⊇SO(3) is also given.

The Influence of Second Harmonic Phase and Amplitude Variation in Cyclically Pitching Wings

NASA Astrophysics Data System (ADS)

Culler, Ethan; Farnsworth, John

2017-11-01

From wind tunnel testing of a cyber-physical wing model, it has been found that the pitch trajectory for stall flutter is described by an array of higher harmonic frequencies with decaying energy content. These frequencies distort the stall flutter motion from that of a pure sinusoidal oscillation in pitch and can have a significant effect on the resulting force production. In order to understand how these higher harmonic frequencies contribute to the overall pitching moment characteristics of a wing in stall flutter, a rigid finite span wing model, with aspect ratio four, was pitched in the wind tunnel. The prescribed motion of the pitch cycle was varied by changing the amplitude ratio and phase of the second harmonic of the oscillation frequency. The second harmonic represents the second highest energy mode in the pitching cycle spectra. Pitching moment and planar particle image velocimetry data was collected. From these pitching trajectories, a significant dependence of pitching moment on both the phase and amplitude of the prescribed waveforms was found. Specifically, for the same amplitude ratio, variations in the phase produced changes of approximately 30 percent in the phase averaged pitching moment.

Modeling nonlinearities in MEMS oscillators.

PubMed

Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A

2013-08-01

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.

Assessment of pulmonary arterial compliance evaluated using harmonic oscillator kinematics

PubMed Central

Hayabuchi, Yasunobu; Ono, Akemi; Homma, Yukako; Kagami, Shoji

2017-01-01

We hypothesized that KPA, a harmonic oscillator kinematics-derived spring constant parameter of the pulmonary artery pressure (PAP) profile, reflects PA compliance in pediatric patients. In this prospective study of 33 children (age range = 0.5–20 years) with various cardiac diseases, we assessed the novel parameter designated as KPA calculated using the pressure phase plane and the equation KPA = (dP/dt_max)2/([Pmax – Pmin])/2)2, where dP/dt_max is the peak derivative of PAP, and Pmax – Pmin is the difference between the minimum and maximum PAP. PA compliance was also calculated using two conventional methods: systolic PA compliance (sPAC) was expressed as the stroke volume/Pmax – Pmin; and diastolic PA compliance (dPAC) was determined according to a two-element Windkessel model of PA diastolic pressure decay. In addition, data were recorded during abdominal compression to determine the influence of preload on KPA. A significant correlation was observed between KPA and sPAC (r = 0.52, P = 0.0018), but not dPAC. Significant correlations were also seen with the time constant (τ) of diastolic PAP (r = −0.51, P = 0.0026) and the pulmonary vascular resistance index (r = −0.39, P = 0.0242). No significant difference in KPA was seen between before and after abdominal compression. KPA had a higher intraclass correlation coefficient than other compliance and resistance parameters for both intra-observer and inter-observer variability (0.998 and 0.997, respectively). These results suggest that KPA can provide insight into the underlying mechanisms and facilitate the quantification of PA compliance. PMID:28621582

Assessment of pulmonary arterial compliance evaluated using harmonic oscillator kinematics.

PubMed

Hayabuchi, Yasunobu; Ono, Akemi; Homma, Yukako; Kagami, Shoji

2017-01-01

We hypothesized that K PA , a harmonic oscillator kinematics-derived spring constant parameter of the pulmonary artery pressure (PAP) profile, reflects PA compliance in pediatric patients. In this prospective study of 33 children (age range = 0.5-20 years) with various cardiac diseases, we assessed the novel parameter designated as K PA calculated using the pressure phase plane and the equation K PA  = (dP/dt_max) 2 /([Pmax - Pmin])/2) 2 , where dP/dt_max is the peak derivative of PAP, and Pmax - Pmin is the difference between the minimum and maximum PAP. PA compliance was also calculated using two conventional methods: systolic PA compliance (sPAC) was expressed as the stroke volume/Pmax - Pmin; and diastolic PA compliance (dPAC) was determined according to a two-element Windkessel model of PA diastolic pressure decay. In addition, data were recorded during abdominal compression to determine the influence of preload on K PA . A significant correlation was observed between K PA and sPAC (r = 0.52, P = 0.0018), but not dPAC. Significant correlations were also seen with the time constant (τ) of diastolic PAP (r = -0.51, P = 0.0026) and the pulmonary vascular resistance index (r = -0.39, P = 0.0242). No significant difference in K PA was seen between before and after abdominal compression. K PA had a higher intraclass correlation coefficient than other compliance and resistance parameters for both intra-observer and inter-observer variability (0.998 and 0.997, respectively). These results suggest that K PA can provide insight into the underlying mechanisms and facilitate the quantification of PA compliance.

Tunable Soft X-Ray Oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wurtele, Jonathan; Gandhi, Punut; Gu, X-W

A concept for a tunable soft x-ray free electron laser (FEL) photon source is presented and studied numerically. The concept is based on echo-enabled harmonic generation (EEHG), wherein two modulator-chicane sections impose high harmonic structure with much greater efficacy as compared to conventional high harmonic FELs that use only one modulator-chicane section. The idea proposed here is to replace the external laser power sources in the EEHG modulators with FEL oscillators, and to combine the bunching of the beam with the production of radiation. Tunability is accomplished by adjusting the magnetic chicanes while the two oscillators remain at a fixedmore » frequency. This scheme eliminates the need to develop coherent sources with the requisite power, pulse length, and stability requirements by exploiting the MHz bunch repetition rates of FEL continuous wave (CW) sources driven by superconducting (SC) linacs. We present time-dependent GINGER simulation results for an EEHG scheme with an oscillator modulator at 43 nm employing 50percent reflective dielectric mirrors and a second modulator employing an external, 215-nm drive laser. Peak output of order 300 MW is obtained at 2.7 nm, corresponding to the 80th harmonic of 215 nm. An alternative single-cavity echo-oscillator scheme based on a 13.4 nm oscillator is investigated with time-independent simulations that a 180-MW peak power at final wavelength of 1.12 nm. Three alternate configurations that use separate bunches to produce the radiation for EEHG microbunching are also presented. Our results show that oscillator-based soft x-ray FELs driven by CWSC linacs are extremely attractive because of their potential to produce tunable radiation at high average power together with excellent longitudinal coherence and narrow spectral bandwidth.« less

Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges

NASA Astrophysics Data System (ADS)

Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, W. M.; Tobias, B. J.; Yan, Z.

2016-07-01

In the quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHOs) play an important role in avoiding transient edge localized mode (ELM) power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n  ⩽  5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended magentoohydrodynamics (MHD) code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-Imaging and microwave imaging reflectometer (MIR) diagnostics, as well as the kink/peeling mode properties found by the ideal MHD code ELITE. Numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by rotation and/or rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that EHOs can be destabilized in principle with rotation in either direction. The modeling results are consistent with observations of EHO, support the proposed theory of the EHO as a low-n kink/peeling mode destabilized by edge E  ×  B rotational shear, and improve our understanding and confidence in creating and sustaining QH-mode in present and future devices.

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

NASA Astrophysics Data System (ADS)

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

2014-02-01

Ultrafast charge transport in strongly biased semiconductors is at the heart of high-speed electronics, electro-optics and fundamental solid-state physics. Intense light pulses in the terahertz spectral range have opened fascinating vistas. Because terahertz 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 terahertz amplitudes, reaching atomic field strengths. We exploit controlled (multi-)terahertz waveforms with peak fields of 72 MV cm-1 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 terahertz-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 intraband dynamics. Our results pave the way towards all-coherent terahertz-rate electronics.

A novel method for determining the phase-noise behavior of resonator-oscillators

NASA Astrophysics Data System (ADS)

Hoffmann, Michael H. W.

2005-05-01

A novel approach to the theory of phase-noise in resonator-oscillators will be given that is based on a combination of a large-signal-small-signal method, harmonic balance, and a modified Rice-model of signals plus noise. The method will be explained using a simple example. Since the type of oscillator under consideration not only de-attenuates eigen-oscillations but also noise in the spectral vicinity of the eigen-frequency, a signal is generated that is quasi-harmonic, and that might be described by means of a pseudo-Fourier-series expansion. Due to the specific description of the internal noise-sources, it is possible to use a time-domain description that at the same time reveals information about the spectral components of the signal. By comparison of these components, the spectrum of the oscillation might be determined. Relations between the spectrum of internal noise sources and the generated oscillator-signal will be recognized. The novel method will thus enable the designer to predict the phase-noise behavior of a specific oscillator-design.

Matrix eigenvalue method for free-oscillations modelling of spherical elastic bodies

NASA Astrophysics Data System (ADS)

Zábranová, E.; Hanyk, L.; Matyska, C.

2017-11-01

Deformations and changes of the gravitational potential of pre-stressed self-gravitating elastic bodies caused by free oscillations are described by means of the momentum and Poisson equations and the constitutive relation. For spherically symmetric bodies, the equations and boundary conditions are transformed into ordinary differential equations of the second order by the spherical harmonic decomposition and further discretized by highly accurate pseudospectral difference schemes on Chebyshev grids; we pay special attention to the conditions at the centre of the models. We thus obtain a series of matrix eigenvalue problems for eigenfrequencies and eigenfunctions of the free oscillations. Accuracy of the presented numerical approach is tested by means of the Rayleigh quotients calculated for the eigenfrequencies up to 500 mHz. Both the modal frequencies and eigenfunctions are benchmarked against the output from the Mineos software package based on shooting methods. The presented technique is a promising alternative to widely used methods because it is stable and with a good capability up to high frequencies.

A model for the harmonic of compressional Pc 5 waves

NASA Technical Reports Server (NTRS)

Takahashi, K.; Zanetti, L. J.; Potemra, T. A.; Acuna, M. H.

1987-01-01

Compressional Pc 5 magnetic waves in the magnetosphere are a unique phenomenon showing a nonsinusoidal waveform in spite of a well-defined period. Although the waveform can be Fourier-decomposed into the fundamental and the second harmonics, the phase between the two is kept constant from event to event, implying that the waveform is not the result of a chance superposition of two magnetospheric eigenmodes. A phenomenological explanation to this waveform is offered using a field-line configuration model that is a modified version of a previously proposed antisymmetric standing wave. In this model, the location of the equatorial node of field-line displacement is assumed to oscillate with the wave, with a peak-to-peak amplitude greater than 10 percent of the wavelength of the standing wave. The predicted waveform at various magnetic latitudes is found to be in excellent agreement with an observation taken near the magnetic equator by the Active Magnetospheric Particle Tracer Explorers/Charge Composition Explorer spacecraft.

A model for the harmonic of compressional Pc 5 waves

NASA Astrophysics Data System (ADS)

Takahashi, K.; Zanetti, L. J.; Potemra, T. A.; Acuna, M. H.

1987-04-01

Compressional Pc 5 magnetic waves in the magnetosphere are a unique phenomenon showing a nonsinusoidal waveform in spite of a well-defined period. Although the waveform can be Fourier-decomposed into the fundamental and the second harmonics, the phase between the two is kept constant from event to event, implying that the waveform is not the result of a chance superposition of two magnetospheric eigenmodes. A phenomenological explanation to this waveform is offered using a field-line configuration model that is a modified version of a previously proposed antisymmetric standing wave. In this model, the location of the equatorial node of field-line displacement is assumed to oscillate with the wave, with a peak-to-peak amplitude greater than 10 percent of the wavelength of the standing wave. The predicted waveform at various magnetic latitudes is found to be in excellent agreement with an observation taken near the magnetic equator by the Active Magnetospheric Particle Tracer Explorers/Charge Composition Explorer spacecraft.

Spherical harmonic analysis of a model-generated climatology

NASA Technical Reports Server (NTRS)

Christidis, Z. D.; Spar, J.

1981-01-01

Monthly mean fields of 850 mb temperature (T850), 500 mb geopotential height (G500) and sea level pressure (SLP) were generated in the course of a five-year climate simulation run with a global general circulation model. Both the model-generated climatology and an observed climatology were subjected to spherical harmonic analysis, with separate analyses of the globe and the Northern Hemisphere. Comparison of the dominant harmonics of the two climatologies indicates that more than 95% of the area-weighted spatial variance of G500 and more than 90% of that of T850 are explained by fewer than three components, and that the model adequately simulates these large-scale characteristics. On the other hand, as many as 25 harmonics are needed to explain 95% of the observed variance of SLP, and the model simulation of this field is much less satisfactory. The model climatology is also evaluated in terms of the annual cycles of the dominant harmonics.

Mixed quantum-classical simulation of the hydride transfer reaction catalyzed by dihydrofolate reductase based on a mapped system-harmonic bath model

NASA Astrophysics Data System (ADS)

Xu, Yang; Song, Kai; Shi, Qiang

2018-03-01

The hydride transfer reaction catalyzed by dihydrofolate reductase is studied using a recently developed mixed quantum-classical method to investigate the nuclear quantum effects on the reaction. Molecular dynamics simulation is first performed based on a two-state empirical valence bond potential to map the atomistic model to an effective double-well potential coupled to a harmonic bath. In the mixed quantum-classical simulation, the hydride degree of freedom is quantized, and the effective harmonic oscillator modes are treated classically. It is shown that the hydride transfer reaction rate using the mapped effective double-well/harmonic-bath model is dominated by the contribution from the ground vibrational state. Further comparison with the adiabatic reaction rate constant based on the Kramers theory confirms that the reaction is primarily vibrationally adiabatic, which agrees well with the high transmission coefficients found in previous theoretical studies. The calculated kinetic isotope effect is also consistent with the experimental and recent theoretical results.

Relaxation oscillation suppression in continuous-wave intracavity optical parametric oscillators.

PubMed

Stothard, David J M; Dunn, Malcolm H

2010-01-18

We report a solution to the long standing problem of the occurrence of spontaneous and long-lived bursts of relaxation oscillations which occur when a continuous-wave optical parametric oscillator is operated within the cavity of the parent pump-laser. By placing a second nonlinear crystal within the pump-wave cavity for the purpose of second-harmonic-generation of the pump-wave the additional nonlinear loss thereby arising due to up-conversion effectively suppresses the relaxation oscillations with very little reduction in down-converted power.

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

NASA Astrophysics Data System (ADS)

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

Human brain networks function in connectome-specific harmonic waves.

PubMed

Atasoy, Selen; Donnelly, Isaac; Pearson, Joel

2016-01-21

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

Physical realization of the Glauber quantum oscillator.

PubMed

Gentilini, Silvia; Braidotti, Maria Chiara; Marcucci, Giulia; DelRe, Eugenio; Conti, Claudio

2015-11-02

More than thirty years ago Glauber suggested that the link between the reversible microscopic and the irreversible macroscopic world can be formulated in physical terms through an inverted harmonic oscillator describing quantum amplifiers. Further theoretical studies have shown that the paradigm for irreversibility is indeed the reversed harmonic oscillator. As outlined by Glauber, providing experimental evidence of these idealized physical systems could open the way to a variety of fundamental studies, for example to simulate irreversible quantum dynamics and explain the arrow of time. However, supporting experimental evidence of reversed quantized oscillators is lacking. We report the direct observation of exploding n = 0 and n = 2 discrete states and Γ0 and Γ2 quantized decay rates of a reversed harmonic oscillator generated by an optical photothermal nonlinearity. Our results give experimental validation to the main prediction of irreversible quantum mechanics, that is, the existence of states with quantized decay rates. Our results also provide a novel perspective to optical shock-waves, potentially useful for applications as lasers, optical amplifiers, white-light and X-ray generation.

Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom

NASA Astrophysics Data System (ADS)

Plenio, M. B.; Hartley, J.; Eisert, J.

2004-03-01

We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest-neighbour interactions. For a one-dimensional chain, we provide compact analytical solutions and approximations to the dynamical evolution of the entanglement between spatially separated oscillators. Key properties such as the speed of entanglement propagation, the maximum amount of transferred entanglement and the efficiency for the entanglement transfer are computed. For harmonic oscillators coupled by springs, corresponding to a phonon model, we observe a non-monotonic transfer efficiency in the initially prepared amount of entanglement, i.e. an intermediate amount of initial entanglement is transferred with the highest efficiency. In contrast, within the framework of the rotating-wave approximation (as appropriate, e.g. in quantum optical settings) one finds a monotonic behaviour. We also study geometrical configurations that are analogous to quantum optical devices (such as beamsplitters and interferometers) and observe characteristic differences when initially thermal or squeezed states are entering these devices. We show that these devices may be switched on and off by changing the properties of an individual oscillator. They may therefore be used as building blocks of large fixed and pre-fabricated but programmable structures in which quantum information is manipulated through propagation. We discuss briefly possible experimental realizations of systems of interacting harmonic oscillators in which these effects may be confirmed experimentally.

Theoretical and experimental investigation of millimeter-wave TED's in cross-waveguide oscillators

NASA Astrophysics Data System (ADS)

Rydberg, A.

1985-07-01

Theoretical and experimental investigations of millimeterwave GaAs second harmonic transferred electron device (TED) oscillators using separate circuits for frequency and power optimization, are described. The theory predicts the oscillation frequency with less than 2 percent error for the second harmonic. Apart from the 2d and 3d, a 4th harmonic from the TED was observed up to 130 GHz.

LETTER TO THE EDITOR: Exact energy distribution function in a time-dependent harmonic oscillator

NASA Astrophysics Data System (ADS)

Robnik, Marko; Romanovski, Valery G.; Stöckmann, Hans-Jürgen

2006-09-01

Following a recent work by Robnik and Romanovski (2006 J. Phys. A: Math. Gen. 39 L35, 2006 Open Syst. Inf. Dyn. 13 197-222), we derive an explicit formula for the universal distribution function of the final energies in a time-dependent 1D harmonic oscillator, whose functional form does not depend on the details of the frequency ω(t) and is closely related to the conservation of the adiabatic invariant. The normalized distribution function is P(x) = \\pi^{-1} (2\\mu^2 - x^2)^{-\\frac{1}{2}} , where x=E_1- \\skew3\\bar{E}_1 ; E1 is the final energy, \\skew3\\bar{E}_1 is its average value and µ2 is the variance of E1. \\skew3\\bar{E}_1 and µ2 can be calculated exactly using the WKB approach to all orders.

Quantum damped oscillator I: Dissipation and resonances

NASA Astrophysics Data System (ADS)

Chruściński, Dariusz; Jurkowski, Jacek

2006-04-01

Quantization of a damped harmonic oscillator leads to so called Bateman’s dual system. The corresponding Bateman’s Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states which are responsible for the irreversible quantum dynamics of a damped harmonic oscillator.

Forecasting of Machined Surface Waviness on the Basis of Self-oscillations Analysis

NASA Astrophysics Data System (ADS)

Belov, E. B.; Leonov, S. L.; Markov, A. M.; Sitnikov, A. A.; Khomenko, V. A.

2017-01-01

The paper states a problem of providing quality of geometrical characteristics of machined surfaces, which makes it necessary to forecast the occurrence and amount of oscillations appearing in the course of mechanical treatment. Objectives and tasks of the research are formulated. Sources of oscillation onset are defined: these are coordinate connections and nonlinear dependence of cutting force on the cutting velocity. A mathematical model of forecasting steady-state self-oscillations is investigated. The equation of the cutter tip motion is a system of two second-order nonlinear differential equations. The paper shows an algorithm describing a harmonic linearization method which allows for a significant reduction of the calculation time. In order to do that it is necessary to determine the amplitude of oscillations, frequency and a steady component of the first harmonic. Software which allows obtaining data on surface waviness parameters is described. The paper studies an example of the use of the developed model in semi-finished lathe machining of the shaft made from steel 40H which is a part of the BelAZ wheel electric actuator unit. Recommendations on eliminating self-oscillations in the process of shaft cutting and defect correction of the surface waviness are given.

Location identification of closed crack based on Duffing oscillator transient transition

NASA Astrophysics Data System (ADS)

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.

Modeling spike-wave discharges by a complex network of neuronal oscillators.

PubMed

Medvedeva, Tatiana M; Sysoeva, Marina V; van Luijtelaar, Gilles; Sysoev, Ilya V

2018-02-01

The organization of neural networks and the mechanisms, which generate the highly stereotypical for absence epilepsy spike-wave discharges (SWDs) is heavily debated. Here we describe such a model which can both reproduce the characteristics of SWDs and dynamics of coupling between brain regions, relying mainly on properties of hierarchically organized networks of a large number of neuronal oscillators. We used a two level mesoscale model. The first level consists of three structures: the nervus trigeminus serving as an input, the thalamus and the somatosensory cortex; the second level of a group of nearby situated neurons belonging to one of three modeled structures. The model reproduces the main features of the transition from normal to epileptiformic activity and its spontaneous abortion: an increase in the oscillation amplitude, the emergence of the main frequency and its higher harmonics, and the ability to generate trains of seizures. The model was stable with respect to variations in the structure of couplings and to scaling. The analyzes of the interactions between model structures from their time series using Granger causality method showed that the model reproduced the preictal coupling increase detected previously from experimental data. SWDs can be generated by changes in network organization. It is proposed that a specific pathological architecture of couplings in the brain is necessary to allow the transition from normal to epileptiformic activity, next to by others modeled and reported factors referring to complex, intrinsic, and synaptic mechanisms. Copyright © 2017 Elsevier Ltd. All rights reserved.

Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems

NASA Technical Reports Server (NTRS)

Isar, Aurelian

1995-01-01

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

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

PubMed

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

2018-06-01

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.

On harmonic oscillators and their Kemmer relativistic forms

NASA Technical Reports Server (NTRS)

Debergh, Nathalie; Beckers, Jules

1993-01-01

It is shown that Dirac (Kemmer) equations are intimately connected with (para)supercharges coming from (para)supersymmetric quantum mechanics, a nonrelativistic theory. The dimensions of the irreducible representations of Clifford (Kemmer) algebras play a fundamental role in such an analysis. These considerations are illustrated through oscillator like interactions, leading to (para)relativistic oscillators.

Muonic molecular ions p p μ and p d μ driven by superintense VUV laser pulses: Postexcitation muonic and nuclear oscillations and high-order harmonic generation

NASA Astrophysics Data System (ADS)

Paramonov, Guennaddi K.; Saalfrank, Peter

2018-05-01

The non-Born-Oppenheimer quantum dynamics of p p μ and p d μ molecular ions excited by ultrashort, superintense VUV laser pulses polarized along the molecular axis (z ) is studied by the numerical solution of the time-dependent Schrödinger equation within a three-dimensional (3D) model, including the internuclear distance R and muon coordinates z and ρ , a transversal degree of freedom. It is shown that in both p p μ and p d μ , muons approximately follow the applied laser field out of phase. After the end of the laser pulse, expectation values , <ρ > , and demonstrate "post-laser-pulse" oscillations in both p p μ and p d μ . In the case of p d μ , the post-laser-pulse oscillations of and appear as shaped "echo pulses." Power spectra, which are related to high-order harmonic generation (HHG), generated due to muonic and nuclear motion are calculated in the acceleration form. For p d μ it is found that there exists a unique characteristic frequency ωoscp d μ representing both frequencies of post-laser-pulse muonic oscillations and the frequency of nuclear vibrations, which manifest themselves by very sharp maxima in the corresponding power spectra of p d μ . The homonuclear p p μ ion does not possess such a unique characteristic frequency. The "exact" dynamics and power, and HHG spectra of the 3D model are compared with a Born-Oppenheimer, fixed-nuclei model featuring interesting differences: postpulse oscillations are absent and HHG spectra are affected indirectly or directly by nuclear motion.

Hydroelastic Oscillations of a Circular Plate, Resting on Winkler Foundation

NASA Astrophysics Data System (ADS)

Kondratov, D. V.; Mogilevich, L. I.; Popov, V. S.; Popova, A. A.

2018-01-01

The forced hydroelastic oscillations of a circular plate resting on elastic foundation are investigated. The oscillations are caused by a stamp vibration under interaction with a plate through a thin layer of viscous incompressible liquid. The axis-symmetric problem for the regime of the steady-state harmonic oscillations is considered. On the basis of hydroelasticity problem solution the laws of plate deflection and pressure in the liquid are found. The functions of the amplitudes deflection distribution and liquid pressure along the plate are constructed. The presented mathematical model provides for investigating viscous liquid layer interaction dynamics with a circular plate resting on an elastic foundation. The above-mentioned model makes it possible to define the plate oscillations resonance frequencies and the corresponding amplitudes of deflection and liquid pressure, as well.

A Harmonic Motion Experiment

ERIC Educational Resources Information Center

Gluck, P.; Krakower, Zeev

2010-01-01

We present a unit comprising theory, simulation and experiment for a body oscillating on a vertical spring, in which the simultaneous use of a force probe and an ultrasonic range finder enables one to explore quantitatively and understand many aspects of simple and damped harmonic motions. (Contains 14 figures.)

Investigating the influence of sea level oscillations in the Danish Straits on the Baltic Sea dynamics

NASA Astrophysics Data System (ADS)

Tikhonova, Natalia; Gusev, Anatoly; Diansky, Nikolay; Zakharchuk, Evgeny

2016-04-01

In this research, we study the influence of dynamic processes in the Danish Straits on the sea surface height (SSH) oscillations in the Baltic Sea. For this purpose, we use the model of marine and oceanic circulation INMOM (Institute of Numerical Mathematics Ocean Model). The simulations were carried out for the period 2009-2010, and the coastal station data were used for verification of SSH modelling quality. Comparison of the simulated data with the ones measured in the coastal points showed us that the model does not describe SSH variability in different areas of the Baltic Sea well enough, so in the following simulation series the in situ SSH data of the coastal measurements were assimilated at the open boundary in the Danish Straits. The results of the new simulation showed us that this approach significantly increases the SSH simulation quality in all areas of the sea, where the comparison was made. In particular, the correlation coefficients between the simulated and measured SSH data increased from 0.21-0.73 to 0.81-0.90. On the basis of these results, it has been suggested that the Baltic Sea SSH variability is largely determined by the influence of the dynamic processes in the Danish Straits, which can be represented as a superposition of oscillations of different space-time scales. These oscillations can either be generated in the straits themselves, or propagate from the North Sea. For verification of this hypothesis and assessment of the oscillation propagation distance in the Baltic Sea, the following experiment was performed. At the open boundary in the Danish Straits, the six harmonics were set with the following parameters: the periods are 1.5, 3.0, 6.0, 13.5, 40.5, and 121.5 days, and the amplitude for all the harmonics is 50 cm. The results showed us that the prescribed harmonic oscillations at the open boundary propagate into all areas of the sea without changing the frequency, but with decreasing amplitude. The decrease in amplitude is not

Modeling Wave Driven Non-linear Flow Oscillations: The Terrestrial QBO and a Solar Analog

NASA Technical Reports Server (NTRS)

Mayr, Hans G.; Bhartia, P. K. (Technical Monitor)

2001-01-01

The Quasi Biennial Oscillation (QBO) of the zonal circulation observed in the terrestrial atmosphere at low latitudes is driven by wave mean flow interaction as was demonstrated first by Lindzen and Holton (1968), shown in a laboratory experiment by Plumb and McEwan (1978), and modeled by others (e.g., Plumb, Dunkerton). Although influenced by the seasonal cycle of solar forcing, the QBO, in principle, represents a nonlinear flow oscillation that can be maintained by a steady source of upward propagating waves. The wave driven non-linearity is of third or odd order in the flow velocity, which regenerates the fundamental harmonic itself to keep the oscillation going - the fluid dynamical analog of the displacement mechanism in the mechanical clock. Applying Hines' Doppler Spread Parameterization (DSP) for gravity waves (GW), we discuss with a global-scale spectral model numerical experiments that elucidate some properties of the QBO and its possible effects on the climatology of the atmosphere. Depending on the period of the QBO, wave filtering can cause interaction with the seasonal variations to produce pronounced oscillations with beat periods around 10 years. Since the seasonal cycle and its variability influence the period of the QBO, it may also be a potent conduit of solar activity variations to lower altitudes. Analogous to the terrestrial QBO, we propose that a flow oscillation may account for the 22-year periodicity of the solar magnetic cycle, potentially answering Dicke (1978) who asked, "Is there a chronometer hidden deep inside the Sun?" The oscillation would occur below the convection region, where gravity waves can propagate. Employing a simplified, analytic model, Hines' DSP is applied to estimate the flow oscillation. Depending on the adopted horizontal wavelengths of GW's, wave amplitudes less than 10 m/s can be made to produce oscillating zonal flows of about 20 m/s that should be large enough to generate a significant oscillation in the magnetic

Excitation of H+2 with one-cycle laser pulses: shaped post-laser-field electronic oscillations, generation of higher- and lower-order harmonics

NASA Astrophysics Data System (ADS)

Paramonov, Guennaddi K.; Kühn, Oliver; Bandrauk, André D.

2017-08-01

Non-Born-Oppenheimer quantum dynamics of H+2 excited by shaped one-cycle laser pulses linearly polarised along the molecular axis have been studied by the numerical solution of the time-dependent Schrödinger equation within a three-dimensional model, including the internuclear separation, R, and the electron coordinates z and ρ. Laser carrier frequencies corresponding to the wavelengths λl = 25 nm through λl = 400 nm were used and the amplitudes of the pulses were chosen such that the energy of H+2 was close to its dissociation threshold at the end of any laser pulse applied. It is shown that there exists a characteristic oscillation frequency ωosc ≃ 0.2265 au (corresponding to the period of τosc ≃ 0.671 fs and the wavelength of λosc ≃ 201 nm) that manifests itself as a 'carrier' frequency of temporally shaped oscillations of the time-dependent expectation values ⟨z ⟩ and ⟨∂V/∂z ⟩ that emerge at the ends of the laser pulses and exist on a timescale of at least 50 fs. Time-dependent expectation values ⟨ρ⟩ and ⟨∂V /∂ρ⟩ of the optically passive degree of freedom, ρ, demonstrate post-laser-field oscillations at two basic frequencies ωρ1 ≈ ωosc and ωρ2 ≈ 2ωosc. Power spectra associated with the electronic motion show higher- and lower-order harmonics with respect to the driving field.

Analysis of graphic representation ability in oscillation phenomena

NASA Astrophysics Data System (ADS)

Dewi, A. R. C.; Putra, N. M. D.; Susilo

2018-03-01

This study aims to investigates how the ability of students to representation graphs of linear function and harmonic function in understanding of oscillation phenomena. Method of this research used mix methods with concurrent embedded design. The subjects were 35 students of class X MIA 3 SMA 1 Bae Kudus. Data collection through giving essays and interviews that lead to the ability to read and draw graphs in material of Hooke's law and oscillation characteristics. The results of study showed that most of the students had difficulty in drawing graph of linear function and harmonic function of deviation with time. Students’ difficulties in drawing the graph of linear function is the difficulty of analyzing the variable data needed in graph making, confusing the placement of variable data on the coordinate axis, the difficulty of determining the scale interval on each coordinate, and the variation of how to connect the dots forming the graph. Students’ difficulties in representing the graph of harmonic function is to determine the time interval of sine harmonic function, the difficulty to determine the initial deviation point of the drawing, the difficulty of finding the deviation equation of the case of oscillation characteristics and the confusion to different among the maximum deviation (amplitude) with the length of the spring caused the load.Complexity of the characteristic attributes of the oscillation phenomena graphs, students tend to show less well the ability of graphical representation of harmonic functions than the performance of the graphical representation of linear functions.

Scleronomic Holonomic Constraints and Conservative Nonlinear Oscillators

ERIC Educational Resources Information Center

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…

An Oscillating System with Sliding Friction

ERIC Educational Resources Information Center

Kamela, Martin

2007-01-01

Both harmonic oscillations and friction are the types of concepts in freshman physics that are readily applicable to the "real world" and as such, most students find these ideas interesting. Damped oscillations are usually presented with resistance proportional to velocity, which has the advantage of a relatively straightforward mathematical…

An Empirical Polarizable Force Field Based on the Classical Drude Oscillator Model: Development History and Recent Applications

PubMed Central

2016-01-01

Molecular mechanics force fields that explicitly account for induced polarization represent the next generation of physical models for molecular dynamics simulations. Several methods exist for modeling induced polarization, and here we review the classical Drude oscillator model, in which electronic degrees of freedom are modeled by charged particles attached to the nuclei of their core atoms by harmonic springs. We describe the latest developments in Drude force field parametrization and application, primarily in the last 15 years. Emphasis is placed on the Drude-2013 polarizable force field for proteins, DNA, lipids, and carbohydrates. We discuss its parametrization protocol, development history, and recent simulations of biologically interesting systems, highlighting specific studies in which induced polarization plays a critical role in reproducing experimental observables and understanding physical behavior. As the Drude oscillator model is computationally tractable and available in a wide range of simulation packages, it is anticipated that use of these more complex physical models will lead to new and important discoveries of the physical forces driving a range of chemical and biological phenomena. PMID:26815602

Exploiting bistable oscillator subharmonics for magnified broadband vibration energy harvesting

NASA Astrophysics Data System (ADS)

Huguet, Thomas; Badel, Adrien; Lallart, Mickaël

2017-10-01

Recent research on primary battery alternatives for supplying autonomous wireless devices has recently highlighted the advantages of nonlinear oscillators' dynamics and more particularly bistable oscillators' behavior for ambient vibration harvesting. The key property of bistable oscillators compared to linear ones is their enhanced operational frequency bandwidth under harmonic excitation, potentially leading to a better adaptation to the environment. However, the classical frequency response characterization of such devices does not reveal all the possible dynamic behaviors offered by bistable oscillators. Thus, subharmonic motions are experimentally investigated in this letter, and their energy harvesting potential as well as their ability to enhance the bistable generator bandwidth is evaluated. The results obtained with a generator integrating buckled beams for the bistability feature show that, in addition to the commonly considered harmonic behavior, subharmonics allow widening of the useful operating frequency band of the bistable microgenerator by 180% compared to the sole exploitation of the first harmonic motion.

Mathematical Modeling of an Oscillating Droplet

NASA Technical Reports Server (NTRS)

Berry, S.; Hyers, R. W.; Racz, L. M.; Abedian, B.; Rose, M. Franklin (Technical Monitor)

2000-01-01

Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is performed by electromagnetic levitation. The natural oscillation frequency of the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k-epsilon turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity.

High-Speed Video Analysis of Damped Harmonic Motion

ERIC Educational Resources Information Center

Poonyawatpornkul, J.; Wattanakasiwich, P.

2013-01-01

In this paper, we acquire and analyse high-speed videos of a spring-mass system oscillating in glycerin at different temperatures. Three cases of damped harmonic oscillation are investigated and analysed by using high-speed video at a rate of 120 frames s[superscript -1] and Tracker Video Analysis (Tracker) software. We present empirical data for…

Symmetry properties of second harmonics generated by antisymmetric Lamb waves

NASA Astrophysics Data System (ADS)

Zhu, Wujun; Xiang, Yanxun; Liu, Chang-Jun; Deng, Mingxi; Xuan, Fu-Zhen

2018-03-01

Symmetry properties of second harmonics generated by antisymmetric primary Lamb waves are systematically studied in this work. In theory, the acoustic field of second harmonic Lamb waves is obtained by using the perturbation approximation and normal modal method, and the energy flux transfer from the primary Lamb waves to second harmonics is mainly explored. Symmetry analyses indicate that either the symmetric or antisymmetric Lamb waves can merely generate the symmetric second harmonics. Finite element simulations are performed on the nonlinear Lamb wave propagation of the antisymmetric A0 mode in the low frequency region. The signals of the second harmonics and the symmetric second harmonic s0 mode are found to be exactly equivalent in the time domain. The relative acoustic nonlinearity parameter A2/A12 oscillates with the propagation distance, and the oscillation amplitude and spatial period are well consistent with the theoretical prediction of the A0-s0 mode pair, which means that only the second harmonic s0 mode is generated by the antisymmetric primary A0 mode. Experiments are further conducted to examine the cumulative generation of symmetric second harmonics for the antisymmetric-symmetric mode pair A3-s6. Results show that A2/A12 increases linearly with the propagation distance, which means that the symmetric second harmonic s6 mode is generated cumulatively by the antisymmetric primary A3 mode. The present investigation systematically corroborates the proposed theory that only symmetric second harmonics can be generated accompanying the propagation of antisymmetric primary Lamb waves in a plate.

Exploring harmonization between integrated assessment and capacity expansion models

NASA Astrophysics Data System (ADS)

Iyer, G.; Brown, M.; Cohen, S.; Macknick, J.; Patel, P.; Wise, M. A.; Horing, J.

2017-12-01

Forward-looking quantitative models of the electric sector are extensively used to provide science-based strategic decision support to national, international and private-sector entities. Given that these models are used to inform a wide-range of stakeholders and influence policy decisions, it is vital to examine how the models' underlying data and structure influence their outcomes. We conduct several experiments harmonizing key model characteristics between ReEDS—an electric sector only model, and GCAM—an integrated assessment model—to understand how different degrees of harmonization impact model outcomes. ReEDS has high spatial, temporal, and process detail but lacks electricity demand elasticity and endogenous representations of other economic sectors, while GCAM has internally consistent representations of energy (including the electric sector), agriculture, and land-use systems but relatively aggregate representations of the factors influencing electric sector investments . We vary the degree of harmonization in electricity demand, fuel prices, technology costs and performance, and variable renewable energy resource characteristics. We then identify the prominent sources of divergence in key outputs (electricity capacity, generation, and price) across the models and study how the convergence between models can be improved with permutations of harmonized characteristics. The remaining inconsistencies help to establish how differences in the models' underlying data, construction, perspective, and methodology play into each model's outcome. There are three broad contributions of this work. First, our study provides a framework to link models with similar scope but different resolutions. Second, our work provides insight into how the harmonization of assumptions contributes to a unified and robust portrayal of the US electricity sector under various potential futures. Finally, our study enhances the understanding of the influence of structural uncertainty

Small Oscillations via Conservation of Energy

ERIC Educational Resources Information Center

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…

Data harmonization and model performance

NASA Astrophysics Data System (ADS)

The Joint Committee on Urban Storm Drainage of the International Association for Hydraulic Research (IAHR) and International Association on Water Pollution Research and Control (IAWPRC) was formed in 1982. The current committee members are (no more than two from a country): B. C. Yen, Chairman (USA); P. Harremoes, Vice Chairman (Denmark); R. K. Price, Secretary (UK); P. J. Colyer (UK), M. Desbordes (France), W. C. Huber (USA), K. Krauth (FRG), A. Sjoberg (Sweden), and T. Sueishi (Japan).The IAHR/IAWPRC Joint Committee is forming a Task Group on Data Harmonization and Model Performance. One objective is to promote international urban drainage data harmonization for easy data and information exchange. Another objective is to publicize available models and data internationally. Comments and suggestions concerning the formation and charge of the Task Group are welcome and should be sent to: B. C. Yen, Dept. of Civil Engineering, Univ. of Illinois, 208 N. Romine St., Urbana, IL 61801.

Extended-MHD Studies of Flow-Profile Effects on Edge Harmonic Oscillations in QH-mode Discharges

NASA Astrophysics Data System (ADS)

King, J. R.; Burrell, K. H.; Garofalo, A. M.; Jenkins, T. G.; Kruger, S. E.; Snyder, P. B.

2012-10-01

It is desirable to have an ITER H-mode regime that is quiescent to edge-localized modes (ELMs). ELMs deposit large, localized, impulsive, surface heat loads that can damage the divertor. One such quiescent regime with edge harmonic oscillations (EHO) is observed on DIII-D, JET, JT-60U, and ASDEX-U [1]. The physical mechanisms of EHO are not fully understood, but linear MHD calculations suggest EHO may be a saturated kink-peeling mode partially driven by flow-profile shear [2]. We present preliminary EHO computations using the extended-MHD NIMROD code. The model incorporates first-order FLR effects and parallel heat flows. Using reconstructed DIII-D profiles from discharges with EHO, we scan the ExB and polodial flow profiles and compute linear stability. The aim is to ascertain the role of the ExB flow shear, as motivated by experimental results [3], and to compare with theoretical predictions where the growth rate is enhanced at intermediate wavenumbers and cut-off at large wavenumbers by diamagnetic effects [4]. Initial nonlinear computations exploring the EHO saturation mechanism are presented.[4pt] [1] Phys. Plasmas, v19, p056117, 2012 (and refs. within).[0pt] [2] Nucl. Fusion, v47, p961, 2007.[0pt] [3] Nucl. Fusion, v51, p083018, 2011.[0pt] [4] Phys. Plasmas v10, p4405, 2003.

Developing Antimatter Containment Technology: Modeling Charged Particle Oscillations in a Penning-Malmberg Trap

NASA Technical Reports Server (NTRS)

Chakrabarti, S.; Martin, J. J.; Pearson, J. B.; Lewis, R. A.

2003-01-01

The NASA MSFC Propulsion Research Center (PRC) is conducting a research activity examining the storage of low energy antiprotons. The High Performance Antiproton Trap (HiPAT) is an electromagnetic system (Penning-Malmberg design) consisting of a 4 Tesla superconductor, a high voltage confinement electrode system, and an ultra high vacuum test section; designed with an ultimate goal of maintaining charged particles with a half-life of 18 days. Currently, this system is being experimentally evaluated using normal matter ions which are cheap to produce and relatively easy to handle and provide a good indication of overall trap behavior, with the exception of assessing annihilation losses. Computational particle-in-cell plasma modeling using the XOOPIC code is supplementing the experiments. Differing electrode voltage configurations are employed to contain charged particles, typically using flat, modified flat and harmonic potential wells. Ion cloud oscillation frequencies are obtained experimentally by amplification of signals induced on the electrodes by the particle motions. XOOPIC simulations show that for given electrode voltage configurations, the calculated charged particle oscillation frequencies are close to experimental measurements. As a two-dimensional axisymmetric code, XOOPIC cannot model azimuthal plasma variations, such as those induced by radio-frequency (RF) modulation of the central quadrupole electrode in experiments designed to enhance ion cloud containment. However, XOOPIC can model analytically varying electric potential boundary conditions and particle velocity initial conditions. Application of these conditions produces ion cloud axial and radial oscillation frequency modes of interest in achieving the goal of optimizing HiPAT for reliable containment of antiprotons.

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

DOE PAGES

Gan, K. F.; Ahn, J. -W.; Gray, T. K.; ...

2017-10-26

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 (more » $${{\\lambda}_{\\operatorname{int}}}$$ ) 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. Finally, experimental result of the counter current rotation of strike points splitting is consistent with the counter-current EHO.« less

Responses to applied forces and the Jarzynski equality in classical oscillator systems coupled to finite baths: an exactly solvable nondissipative nonergodic model.

PubMed

Hasegawa, Hideo

2011-07-01

Responses of small open oscillator systems to applied external forces have been studied with the use of an exactly solvable classical Caldeira-Leggett model in which a harmonic oscillator (system) is coupled to finite N-body oscillators (bath) with an identical frequency (ω(n) = ω(o) for n = 1 to N). We have derived exact expressions for positions, momenta, and energy of the system in nonequilibrium states and for work performed by applied forces. A detailed study has been made on an analytical method for canonical averages of physical quantities over the initial equilibrium state, which is much superior to numerical averages commonly adopted in simulations of small systems. The calculated energy of the system which is strongly coupled to a finite bath is fluctuating but nondissipative. It has been shown that the Jarzynski equality is valid in nondissipative nonergodic open oscillator systems regardless of the rate of applied ramp force.

Robust Sub-harmonic Mixer at 340 GHz Using Intrinsic Resonances of Hammer-Head Filter and Improved Diode Model

NASA Astrophysics Data System (ADS)

Wang, Cheng; He, Yue; Lu, Bin; Jiang, Jun; Miao, Li; Deng, Xian-Jin; Xiong, Yong-zhong; Zhang, Jian

2017-11-01

This paper presents a sub-harmonic mixer at 340 GHz based on anti-parallel Schottky diodes (SBDs). Intrinsic resonances in low-pass hammer-head filter have been adopted to enhance the isolation for different harmonic components, while greatly minimizing the transmission loss. The application of new DC grounding structure, impedance matching structure, and suspended micro-strip mitigates the negative influences of fabrication errors from metal cavity, quartz substrate, and micro-assembly. An improved lumped element equivalent circuit model of SBDs guarantees the accuracy of simulation, which takes current-voltage (I/V) behavior, capacitance-voltage (C/V) behavior, carrier velocity saturation, DC series resistor, plasma resonance, skin effect, and four kinds of noise generation mechanisms into consideration thoroughly. The measurement indicates that with local oscillating signal of 2 mW, the lowest double sideband conversion loss is 5.5 dB at 339 GHz; the corresponding DSB noise temperature is 757 K. The 3 dB bandwidth of conversion loss is 50 GHz from 317 to 367 GHz.

The study of two-dimensional oscillations using a smartphone acceleration sensor: example of Lissajous curves

NASA Astrophysics Data System (ADS)

Tuset-Sanchis, Luis; Castro-Palacio, Juan C.; Gómez-Tejedor, José A.; Manjón, Francisco J.; Monsoriu, Juan A.

2015-08-01

A smartphone acceleration sensor is used to study two-dimensional harmonic oscillations. The data recorded by the free android application, Accelerometer Toy, is used to determine the periods of oscillation by graphical analysis. Different patterns of the Lissajous curves resulting from the superposition of harmonic motions are illustrated for three experiments. This work introduces an example of how two-dimensional oscillations can be easily studied with a smartphone acceleration sensor.

Analysing harmonic motions with an iPhone’s magnetometer

NASA Astrophysics Data System (ADS)

Yavuz, Ahmet; Kağan Temiz, Burak

2016-05-01

In this paper, we propose an experiment for analysing harmonic motion using an iPhone’s (or iPad’s) magnetometer. This experiment consists of the detection of magnetic field variations obtained from an iPhone’s magnetometer sensor. A graph of harmonic motion is directly displayed on the iPhone’s screen using the Sensor Kinetics application. Data from this application was analysed with Eureqa software to establish the equation of the harmonic motion. Analyses show that the use of an iPhone’s magnetometer to analyse harmonic motion is a practical and effective method for small oscillations and frequencies less than 15-20 Hz.

The Study of Two-Dimensional Oscillations Using a Smartphone Acceleration Sensor: Example of Lissajous Curves

ERIC Educational Resources Information Center

Tuset-Sanchis, Luis; Castro-Palacio, Juan C.; Gómez-Tejedor, José A.; Manjón, Francisco J.; Monsoriu, Juan A.

2015-01-01

A smartphone acceleration sensor is used to study two-dimensional harmonic oscillations. The data recorded by the free android application, Accelerometer Toy, is used to determine the periods of oscillation by graphical analysis. Different patterns of the Lissajous curves resulting from the superposition of harmonic motions are illustrated for…

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

PubMed

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.

Decay-less kink oscillations in coronal loops

NASA Astrophysics Data System (ADS)

Anfinogentov, S.; Nisticò, G.; Nakariakov, V. M.

2013-12-01

Context. Kink oscillations of coronal loops in an off-limb active region are detected with the Imaging Assembly Array (AIA) instruments of the Solar Dynamics Observatory (SDO) at 171 Å. Aims: We aim to measure periods and amplitudes of kink oscillations of different loops and to determinate the evolution of the oscillation phase along the oscillating loop. Methods: Oscillating coronal loops were visually identified in the field of view of SDO/AIA and STEREO/EUVI-A: the loop length was derived by three-dimensional analysis. Several slits were taken along the loops to assemble time-distance maps. We identified oscillatory patterns and retrieved periods and amplitudes of the oscillations. We applied the cross-correlation technique to estimate the phase shift between oscillations at different segments of oscillating loops. Results: We found that all analysed loops show low-amplitude undamped transverse oscillations. Oscillation periods of loops in the same active region range from 2.5 to 11 min, and are different for different loops. The displacement amplitude is lower than 1 Mm. The oscillation phase is constant along each analysed loop. The spatial structure of the phase of the oscillations corresponds to the fundamental standing kink mode. We conclude that the observed behaviour is consistent with the empirical model in terms of a damped harmonic resonator affected by a non-resonant continuously operating external force. A movie is available in electronic form at http://www.aanda.org

A unified lense-thirring precession model for optical and X-ray quasi-periodic oscillations in black hole binaries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Veledina, Alexandra; Poutanen, Juri; Ingram, Adam, E-mail: alexandra.veledina@oulu.fi, E-mail: juri.poutanen@oulu.fi

2013-12-01

Recent observations of accreting black holes reveal the presence of quasi-periodic oscillations (QPO) in the optical power density spectra. The corresponding oscillation periods match those found in X-rays, implying a common origin. Among the numerous suggested X-ray QPO mechanisms, some may also work in the optical. However, their relevance to the broadband—optical through X-ray—spectral properties have not been investigated. For the first time, we discuss the QPO mechanism in the context of the self-consistent spectral model. We propose that the QPOs are produced by Lense-Thirring precession of the hot accretion flow, whose outer parts radiate in optical wavelengths. At themore » same time, its innermost parts are emitting X-rays, which explains the observed connection of QPO periods. We predict that the X-ray and optical QPOs should be either in phase or shifted by half a period, depending on the observer position. We investigate the QPO harmonic content and find that the variability amplitudes at the fundamental frequency are larger in the optical, while the X-rays are expected to have strong harmonics. We then discuss the QPO spectral dependence and compare the expectations to the existing data.« less

Computational-Model-Based Analysis of Context Effects on Harmonic Expectancy.

PubMed

Morimoto, Satoshi; Remijn, Gerard B; Nakajima, Yoshitaka

2016-01-01

Expectancy for an upcoming musical chord, harmonic expectancy, is supposedly based on automatic activation of tonal knowledge. Since previous studies implicitly relied on interpretations based on Western music theory, the underlying computational processes involved in harmonic expectancy and how it relates to tonality need further clarification. In particular, short chord sequences which cannot lead to unique keys are difficult to interpret in music theory. In this study, we examined effects of preceding chords on harmonic expectancy from a computational perspective, using stochastic modeling. We conducted a behavioral experiment, in which participants listened to short chord sequences and evaluated the subjective relatedness of the last chord to the preceding ones. Based on these judgments, we built stochastic models of the computational process underlying harmonic expectancy. Following this, we compared the explanatory power of the models. Our results imply that, even when listening to short chord sequences, internally constructed and updated tonal assumptions determine the expectancy of the upcoming chord.

Computational-Model-Based Analysis of Context Effects on Harmonic Expectancy

PubMed Central

Morimoto, Satoshi; Remijn, Gerard B.; Nakajima, Yoshitaka

2016-01-01

Expectancy for an upcoming musical chord, harmonic expectancy, is supposedly based on automatic activation of tonal knowledge. Since previous studies implicitly relied on interpretations based on Western music theory, the underlying computational processes involved in harmonic expectancy and how it relates to tonality need further clarification. In particular, short chord sequences which cannot lead to unique keys are difficult to interpret in music theory. In this study, we examined effects of preceding chords on harmonic expectancy from a computational perspective, using stochastic modeling. We conducted a behavioral experiment, in which participants listened to short chord sequences and evaluated the subjective relatedness of the last chord to the preceding ones. Based on these judgments, we built stochastic models of the computational process underlying harmonic expectancy. Following this, we compared the explanatory power of the models. Our results imply that, even when listening to short chord sequences, internally constructed and updated tonal assumptions determine the expectancy of the upcoming chord. PMID:27003807

Polymerization and oscillation stuttering in a filamentous model of the subcellular Min oscillation

NASA Astrophysics Data System (ADS)

Rutenberg, Andrew; Sengupta, Supratim; Sain, Anirban; Derr, Julien

2011-03-01

We present a computational model of the E. coli Min oscillation that involves polymerization of MinD filaments followed by depolymerization stimulated by filament-end zones of MinE. Our stochastic model is fully three-dimensional, and tracks the diffusion and interactions of every MinD and MinE molecule. We recover self-organized Min oscillations. We investigate the experimental phenomenon of oscillation stuttering, which we relate to the disruption of MinE tip-binding at the filament scale.

Computational modeling of the cell-autonomous mammalian circadian oscillator.

PubMed

Podkolodnaya, Olga A; Tverdokhleb, Natalya N; Podkolodnyy, Nikolay L

2017-02-24

This review summarizes various mathematical models of cell-autonomous mammalian circadian clock. We present the basics necessary for understanding of the cell-autonomous mammalian circadian oscillator, modern experimental data essential for its reconstruction and some special problems related to the validation of mathematical circadian oscillator models. This work compares existing mathematical models of circadian oscillator and the results of the computational studies of the oscillating systems. Finally, we discuss applications of the mathematical models of mammalian circadian oscillator for solving specific problems in circadian rhythm biology.

One-Dimensional Harmonic Model for Biomolecules

PubMed Central

Krizan, John E.

1973-01-01

Following in spirit a paper by Rosen, we propose a one-dimensional harmonic model for biomolecules. Energy bands with gaps of the order of semi-conductor gaps are found. The method is discussed for general symmetric and periodic potential functions. PMID:4709518

Quantized discrete space oscillators

NASA Technical Reports Server (NTRS)

Uzes, C. A.; Kapuscik, Edward

1993-01-01

A quasi-canonical sequence of finite dimensional quantizations was found which has canonical quantization as its limit. In order to demonstrate its practical utility and its numerical convergence, this formalism is applied to the eigenvalue and 'eigenfunction' problem of several harmonic and anharmonic oscillators.

A compact D-band monolithic APDP-based sub-harmonic mixer

NASA Astrophysics Data System (ADS)

Zhang, Shengzhou; Sun, Lingling; Wang, Xiang; Wen, Jincai; Liu, Jun

2017-11-01

The paper presents a compact D-band monolithic sub-harmonic mixer (SHM) with 3 μm planar hyperabrupt schottky-varactor diodes offered by 70 nm GaAs mHEMT technology. According to empirical equivalent-circuit models, a wide-band large signal equivalent circuit model of the diode is proposed. Based on the extracted model, the mixer is implemented and optimized with a shunt-mounted anti-parallel diode pair (APDP) to fulfill the sub-harmonic mixing mechanism. Furthermore, a modified asymmetric three-transmission-line coupler is devised to achieve high-level coupling and minimize the chip size. The measured results show that the conversion gain varies between -13.9 dB and -17.5 dB from 110 GHz to 145 GHz, with a local oscillator (LO) power level of 14 dBm and an intermediate frequency (IF) of 1 GHz. The total chip size including probe GSG pads is 0.57 × 0.68mm2. In conclusion, the mixer exhibits outstanding figure-of-merits.

Fundamental and subharmonic excitation for an oscillator with several tunneling diodes in series

NASA Technical Reports Server (NTRS)

Boric-Lubecke, Olga; Pan, Dee-Son; Itoh, Tatsuo

1995-01-01

Connecting several tunneling diodes in series shows promise as a method for increasing the output power of these devices as millimeter-wave oscillators. However, due to the negative differential resistance (NDR) region in the dc I-V curve of a single tunneling diode, a circuit using several devices connected in series, and biased simultaneously in the NDR region, is dc unstable. Because of this instability, an oscillator with several tunneling diodes in series has a demanding excitation condition. Excitation using an externally applied RF signal is one approach to solving this problem. This is experimentally demonstrated using an RF source, both with frequency close to as well as with frequency considerably lower than the oscillation frequency. Excitation by an RF (radio frequency) source with a frequency as low as one sixth of the oscillation frequency was demonstrated in a proof-of-principle experiment at 2 GHz, for an oscillator with two tunnel diodes connected in series. Strong harmonics of the oscillation signal were generated as a result of the highly nonlinear dc I-V curve of the tunnel diode and a large signal oscillator design. Third harmonic output power comparable to that of the fundamental was observed in one oscillator circuit. If submillimeter wave resonant-tunneling diodes (RTD's) are used instead of tunnel diodes, this harmonic output may be useful for generating signals at frequencies well into the terahertz range.

Non-linear Min protein interactions generate harmonics that signal mid-cell division in Escherichia coli

PubMed Central

Walsh, James C.; Angstmann, Christopher N.; Duggin, Iain G.

2017-01-01

The Min protein system creates a dynamic spatial pattern in Escherichia coli cells where the proteins MinD and MinE oscillate from pole to pole. MinD positions MinC, an inhibitor of FtsZ ring formation, contributing to the mid-cell localization of cell division. In this paper, Fourier analysis is used to decompose experimental and model MinD spatial distributions into time-dependent harmonic components. In both experiment and model, the second harmonic component is responsible for producing a mid-cell minimum in MinD concentration. The features of this harmonic are robust in both experiment and model. Fourier analysis reveals a close correspondence between the time-dependent behaviour of the harmonic components in the experimental data and model. Given this, each molecular species in the model was analysed individually. This analysis revealed that membrane-bound MinD dimer shows the mid-cell minimum with the highest contrast when averaged over time, carrying the strongest signal for positioning the cell division ring. This concurs with previous data showing that the MinD dimer binds to MinC inhibiting FtsZ ring formation. These results show that non-linear interactions of Min proteins are essential for producing the mid-cell positioning signal via the generation of second-order harmonic components in the time-dependent spatial protein distribution. PMID:29040283

Physical modeling with orthotropic material based on harmonic fields.

PubMed

Liao, Sheng-Hui; Zou, Bei-Ji; Geng, Jian-Ping; Wang, Jin-Xiao; Ding, Xi

2012-11-01

Although it is well known that human bone tissues have obvious orthotropic material properties, most works in the physical modeling field adopted oversimplified isotropic or approximated transversely isotropic elasticity due to the simplicity. This paper presents a convenient methodology based on harmonic fields, to construct volumetric finite element mesh integrated with complete orthotropic material. The basic idea is taking advantage of the fact that the longitudinal axis direction indicated by the shape configuration of most bone tissues is compatible with the trajectory of the maximum material stiffness. First, surface harmonic fields of the longitudinal axis direction for individual bone models were generated, whose scalar distribution pattern tends to conform very well to the object shape. The scalar iso-contours were extracted and sampled adaptively to construct volumetric meshes of high quality. Following, the surface harmonic fields were expanded over the whole volumetric domain to create longitudinal and radial volumetric harmonic fields, from which the gradient vector fields were calculated and employed as the orthotropic principal axes vector fields. Contrastive finite element analyses demonstrated that elastic orthotropy has significant effect on simulating stresses and strains, including the value as well as distribution pattern, which underlines the relevance of our orthotropic modeling scheme. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

A Computer Model for Soda Bottle Oscillations: "The Bottelator".

ERIC Educational Resources Information Center

Soltzberg, Leonard J.; And Others

1997-01-01

Presents a model to explain the behavior of oscillatory phenomena found in the soda bottle oscillator. Describes recording the oscillations, and the design of the model based on the qualitative explanation of the oscillations. Illustrates a variety of physiochemical concepts including far-from-equilibrium oscillations, feedback, solubility and…

Exploratory investigation of sound pressure level in the wake of an oscillating airfoil in the vicinity of stall

NASA Technical Reports Server (NTRS)

Gray, R. B.; Pierce, G. A.

1972-01-01

Wind tunnel tests were performed on two oscillating two-dimensional lifting surfaces. The first of these models had an NACA 0012 airfoil section while the second simulated the classical flat plate. Both of these models had a mean angle of attack of 12 degrees while being oscillated in pitch about their midchord with a double amplitude of 6 degrees. Wake surveys of sound pressure level were made over a frequency range from 16 to 32 Hz and at various free stream velocities up to 100 ft/sec. The sound pressure level spectrum indicated significant peaks in sound intensity at the oscillation frequency and its first harmonic near the wake of both models. From a comparison of these data with that of a sound level meter, it is concluded that most of the sound intensity is contained within these peaks and no appreciable peaks occur at higher harmonics. It is concluded that within the wake the sound intensity is largely pseudosound while at one chord length outside the wake, it is largely true vortex sound. For both the airfoil and flat plate the peaks appear to be more strongly dependent upon the airspeed than on the oscillation frequency. Therefore reduced frequency does not appear to be a significant parameter in the generation of wake sound intensity.

Direct measurement of density oscillation induced by a radio-frequency wave.

PubMed

Yamada, T; Ejiri, A; Shimada, Y; Oosako, T; Tsujimura, J; Takase, Y; Kasahara, H

2007-08-01

An O-mode reflectometer at a frequency of 25.85 GHz was applied to plasmas heated by the high harmonic fast wave (21 MHz) in the TST-2 spherical tokamak. An oscillation in the phase of the reflected microwave in the rf range was observed directly for the first time. In TST-2, the rf (250 kW) induced density oscillation depends mainly on the poloidal rf electric field, which is estimated to be about 0.2 kV/m rms by the reflectometer measurement. Sideband peaks separated in frequency by ion cyclotron harmonics from 21 MHz, and peaks at ion cyclotron harmonics which are suggested to be quasimodes generated by parametric decay, were detected.

Spatially resolved observation of the fundamental and second harmonic standing kink modes using SDO/AIA

NASA Astrophysics Data System (ADS)

Pascoe, D. J.; Goddard, C. R.; Nakariakov, V. M.

2016-09-01

Aims: We consider a coronal loop kink oscillation observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) which demonstrates two strong spectral components. The period of the lower frequency component being approximately twice that of the shorter frequency component suggests the presence of harmonics. Methods: We examine the presence of two longitudinal harmonics by investigating the spatial dependence of the loop oscillation. The time-dependent displacement of the loop is measured at 15 locations along the loop axis. For each position the displacement is fitted as the sum of two damped sinusoids, having periods P1 and P2, and a damping time τ. The shorter period component exhibits anti-phase oscillations in the loop legs. Results: We interpret the observation in terms of the first (global or fundamental) and second longitudinal harmonics of the standing kink mode. The strong excitation of the second harmonic appears connected to the preceding coronal mass ejection (CME) which displaced one of the loop legs. The oscillation parameters found are P1 = 5.00±0.62 min, P2 = 2.20±0.23 min, P1/ 2P2 = 1.15±0.22, and τ/P = 3.35 ± 1.45. A movie associated to Fig. 5 is available in electronic form at http://www.aanda.org

Extracting harmonic signal from a chaotic background with local linear model

NASA Astrophysics Data System (ADS)

Li, Chenlong; Su, Liyun

2017-02-01

In this paper, the problems of blind detection and estimation of harmonic signal in strong chaotic background are analyzed, and new methods by using local linear (LL) model are put forward. The LL model has been exhaustively researched and successfully applied for fitting and forecasting chaotic signal in many chaotic fields. We enlarge the modeling capacity substantially. Firstly, we can predict the short-term chaotic signal and obtain the fitting error based on the LL model. Then we detect the frequencies from the fitting error by periodogram, a property on the fitting error is proposed which has not been addressed before, and this property ensures that the detected frequencies are similar to that of harmonic signal. Secondly, we establish a two-layer LL model to estimate the determinate harmonic signal in strong chaotic background. To estimate this simply and effectively, we develop an efficient backfitting algorithm to select and optimize the parameters that are hard to be exhaustively searched for. In the method, based on sensitivity to initial value of chaos motion, the minimum fitting error criterion is used as the objective function to get the estimation of the parameters of the two-layer LL model. Simulation shows that the two-layer LL model and its estimation technique have appreciable flexibility to model the determinate harmonic signal in different chaotic backgrounds (Lorenz, Henon and Mackey-Glass (M-G) equations). Specifically, the harmonic signal can be extracted well with low SNR and the developed background algorithm satisfies the condition of convergence in repeated 3-5 times.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Sampled-data-based consensus and containment control of multiple harmonic oscillators: A motion-planning approach

NASA Astrophysics Data System (ADS)

Liu, Yongfang; Zhao, Yu; Chen, Guanrong

2016-11-01

This paper studies the distributed consensus and containment problems for a group of harmonic oscillators with a directed communication topology. First, for consensus without a leader, a class of distributed consensus protocols is designed by using motion planning and Pontryagin's principle. The proposed protocol only requires relative information measurements at the sampling instants, without requiring information exchange over the sampled interval. By using stability theory and the properties of stochastic matrices, it is proved that the distributed consensus problem can be solved in the motion planning framework. Second, for the case with multiple leaders, a class of distributed containment protocols is developed for followers such that their positions and velocities can ultimately converge to the convex hull formed by those of the leaders. Compared with the existing consensus algorithms, a remarkable advantage of the proposed sampled-data-based protocols is that the sampling periods, communication topologies and control gains are all decoupled and can be separately designed, which relaxes many restrictions in controllers design. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.

Advanced light source master oscillator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lo, C.C.; Taylor, B.; Baptiste, K.

1989-03-01

The Master Oscillator of the Advanced Light Source operates at a frequency of 499.654 MHz which is the 328th harmonic of the storage ring. The oscillator is capable of providing up to a maximum of {plus minus} 500 KHz frequency deviation for various experimental purposes. Provisions for external signal injection as well as using an external signal source have been designed into the unit. A power distribution system has also been included to provide signals for various parts of the ALS machine and user requirements. The Master Oscillator is made up with modules housed in a Euro chassis. 4 refs.,more » 7 figs.« less

Irregular-regular-irregular mixed mode oscillations in a glow discharge plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Sabuj, E-mail: sabuj.ghosh@saha.ac.in; Shaw, Pankaj Kumar, E-mail: pankaj.shaw@saha.ac.in; Saha, Debajyoti, E-mail: debajyoti.saha@saha.ac.in

2015-05-15

Floating potential fluctuations of a glow discharge plasma are found to exhibit different kinds of mixed mode oscillations. Power spectrum analysis reveals that with change in the nature of the mixed mode oscillation (MMO), there occurs a transfer of power between the different harmonics and subharmonics. The variation in the chaoticity of different types of mmo was observed with the study of Lyapunov exponents. Estimates of correlation dimension and the Hurst exponent suggest that these MMOs are of low dimensional nature with an anti persistent character. Numerical modeling also reflects the experimentally found transitions between the different MMOs.

Numerical modeling of Harmonic Imaging and Pulse Inversion fields

NASA Astrophysics Data System (ADS)

Humphrey, Victor F.; Duncan, Tracy M.; Duck, Francis

2003-10-01

Tissue Harmonic Imaging (THI) and Pulse Inversion (PI) Harmonic Imaging exploit the harmonics generated as a result of nonlinear propagation through tissue to improve the performance of imaging systems. A 3D finite difference model, that solves the KZK equation in the frequency domain, is used to investigate the finite amplitude fields produced by rectangular transducers driven with short pulses and their inverses, in water and homogeneous tissue. This enables the characteristic of the fields and the effective PI field to be calculated. The suppression of the fundamental field in PI is monitored, and the suppression of side lobes and a reduction in the effective beamwidth for each field are calculated. In addition, the differences between the pulse and inverse pulse spectra resulting from the use of very short pulses are noted, and the differences in the location of the fundamental and second harmonic spectral peaks observed.

Building Mathematical Models of Simple Harmonic and Damped Motion.

ERIC Educational Resources Information Center

Edwards, Thomas

1995-01-01

By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

Calculations of wall shear stress in harmonically oscillated turbulent pipe flow using a low-Reynolds-number {kappa}-{epsilon} model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ismael, J.O.; Cotton, M.A.

1996-03-01

The low-Reynolds-number {kappa}-{epsilon} turbulence model of Launder and Sharma is applied to the calculation of wall shear stress in spatially fully-developed turbulent pipe flow oscillated at small amplitudes. It is believed that the present study represents the first systematic evaluation of the turbulence closure under consideration over a wide range of frequency. Model results are well correlated in terms of the parameter {omega}{sup +} = {omega}{nu}/{bar U}{sub {tau}}{sup 2} at high frequencies, whereas at low frequencies there is an additional Reynolds number dependence. Comparison is made with the experimental data of Finnicum and Hanratty.

Light atom quantum oscillations in UC and US

DOE PAGES

Yiu, Yuen; Aczel, Adam A.; Granroth, Garrett E.; ...

2016-01-19

High energy vibrational scattering in the binary systems UC and US is measured using time-of-flight inelastic neutron scattering. A clear set of well-defined peaks equally separated in energy is observed in UC, corresponding to harmonic oscillations of the light C atoms in a cage of heavy U atoms. The scattering is much weaker in US and only a few oscillator peaks are visible. We show how the difference between the materials can be understood by considering the neutron scattering lengths and masses of the lighter atoms. Monte Carlo ray tracing is used to simulate the scattering, with near quantitative agreementmore » with the data in UC, and some differences with US. The possibility of observing anharmonicity and anisotropy in the potentials of the light atoms is investigated in UC. Lastly, the observed data is well accounted for by considering each light atom as a single atom isotropic quantum harmonic oscillator.« less

Nonlinearity induced synchronization enhancement in mechanical oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Czaplewski, David A.; Lopez, Omar; Guest, Jeffrey R.

An autonomous oscillator synchronizes to an external harmonic force only when the forcing frequency lies within a certain interval, known as the synchronization range, around the oscillator's natural frequency. Under ordinary conditions, the width of the synchronization range decreases when the oscillation amplitude grows, which constrains synchronized motion of micro- and nano-mechanical resonators to narrow frequency and amplitude bounds. The present invention shows that nonlinearity in the oscillator can be exploited to manifest a regime where the synchronization range increases with an increasing oscillation amplitude. The present invention shows that nonlinearities in specific configurations of oscillator systems, as described herein,more » are the key determinants of the effect. The present invention presents a new configuration and operation regime that enhances the synchronization of micro- and nano-mechanical oscillators by capitalizing on their intrinsic nonlinear dynamics.« less

An Enhanced GINGERSimulation Code with Harmonic Emission and HDF5IO Capabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fawley, William M.

GINGER [1] is an axisymmetric, polychromatic (r-z-t) FEL simulation code originally developed in the mid-1980's to model the performance of single-pass amplifiers. Over the past 15 years GINGER's capabilities have been extended to include more complicated configurations such as undulators with drift spaces, dispersive sections, and vacuum chamber wakefield effects; multi-pass oscillators; and multi-stage harmonic cascades. Its coding base has been tuned to permit running effectively on platforms ranging from desktop PC's to massively parallel processors such as the IBM-SP. Recently, we have made significant changes to GINGER by replacing the original predictor-corrector field solver with a new direct implicitmore » algorithm, adding harmonic emission capability, and switching to the HDF5 IO library [2] for output diagnostics. In this paper, we discuss some details regarding these changes and also present simulation results for LCLS SASE emission at {lambda} = 0.15 nm and higher harmonics.« less

The effect of shot noise on the start up of the fundamental and harmonics in free-electron lasers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Freund, H. P.; Miner, W. H. Jr.; Giannessi, L.

2008-12-15

The problem of radiation start up in free-electron lasers (FELs) is important in the simulation of virtually all FEL configurations including oscillators and amplifiers in both seeded master oscillator power amplifier (MOPA) and self-amplified spontaneous emission (SASE) modes. Both oscillators and SASE FELs start up from spontaneous emission due to shot noise on the electron beam, which arises from the random fluctuations in the phase distribution of the electrons. The injected power in a MOPA is usually large enough to overwhelm the shot noise. However, this noise must be treated correctly in order to model the initial start up ofmore » the harmonics. In this paper, we discuss and compare two different shot noise models that are implemented in both one-dimensional wiggler-averaged (PERSEO) and non-wiggler-averaged (MEDUSA1D) simulation codes, and a three-dimensional non-wiggler-averaged (MEDUSA) formulation. These models are compared for examples describing both SASE and MOPA configurations in one dimension, in steady-state, and time-dependent simulations. Remarkable agreement is found between PERSEO and MEDUSA1D for the evolution of the fundamental and harmonics. In addition, three-dimensional correction factors have been included in the MEDUSA1D and PERSEO, which show reasonable agreement with MEDUSA for a sample MOPA in steady-state and time-dependent simulations.« less

Kerr-like behaviour of second harmonic generation in the far-off resonant regime

NASA Astrophysics Data System (ADS)

Peřinová, Vlasta; Lukš, Antonín; Křepelka, Jaromír; Leoński, Wiesław; Peřina, Jan

2018-05-01

We separate the Kerr-like behaviour of the second-harmonic generation in the far-off resonant regime from the oscillations caused by the time-dependence of the interaction energy. To this purpose, we consider the approximation obtained from the exact dynamics by the method of small rotations. The Floquet-type decomposition of the approximate dynamics comprises the Kerr-like dynamics and oscillations of the same order of magnitude as those assumed for the exact dynamics of the second-harmonic generation. We have found that a superposition of two states of concentrated quantum phase arises in the fundamental mode in the second-harmonic generation in the far-off resonant limit at a later time than a superposition of two coherent states in the corresponding Kerr medium and the difference is larger for higher initial coherent amplitudes. The quantum phase fluctuation is higher for the same initial coherent amplitudes in the fundamental mode in the second-harmonic generation in the far-off resonant limit than in the corresponding Kerr medium and the difference is larger for higher initial coherent amplitudes.

Coupled oscillators and Feynman's three papers

NASA Astrophysics Data System (ADS)

Kim, Y. S.

2007-05-01

According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the "rest of the universe" contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators.

Memcapacitor model and its application in chaotic oscillator with memristor.

PubMed

Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching

2017-01-01

Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.

Chemical event chain model of coupled genetic oscillators.

PubMed

Jörg, David J; Morelli, Luis G; Jülicher, Frank

2018-03-01

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Chemical event chain model of coupled genetic oscillators

NASA Astrophysics Data System (ADS)

Jörg, David J.; Morelli, Luis G.; Jülicher, Frank

2018-03-01

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Steady-state visual evoked potential (SSVEP)-based communication: impact of harmonic frequency components

NASA Astrophysics Data System (ADS)

Müller-Putz, Gernot R.; Scherer, Reinhold; Brauneis, Christian; Pfurtscheller, Gert

2005-12-01

Brain-computer interfaces (BCIs) can be realized on the basis of steady-state evoked potentials (SSEPs). These types of brain signals resulting from repetitive stimulation have the same fundamental frequency as the stimulation but also include higher harmonics. This study investigated how the classification accuracy of a 4-class BCI system can be improved by incorporating visually evoked harmonic oscillations. The current study revealed that the use of three SSVEP harmonics yielded a significantly higher classification accuracy than was the case for one or two harmonics. During feedback experiments, the five subjects investigated reached a classification accuracy between 42.5% and 94.4%.

Steady-state visual evoked potential (SSVEP)-based communication: impact of harmonic frequency components.

PubMed

Müller-Putz, Gernot R; Scherer, Reinhold; Brauneis, Christian; Pfurtscheller, Gert

2005-12-01

Brain-computer interfaces (BCIs) can be realized on the basis of steady-state evoked potentials (SSEPs). These types of brain signals resulting from repetitive stimulation have the same fundamental frequency as the stimulation but also include higher harmonics. This study investigated how the classification accuracy of a 4-class BCI system can be improved by incorporating visually evoked harmonic oscillations. The current study revealed that the use of three SSVEP harmonics yielded a significantly higher classification accuracy than was the case for one or two harmonics. During feedback experiments, the five subjects investigated reached a classification accuracy between 42.5% and 94.4%.

Parameters of oscillation generation regions in open star cluster models

NASA Astrophysics Data System (ADS)

Danilov, V. M.; Putkov, S. I.

2017-07-01

We determine the masses and radii of central regions of open star cluster (OCL) models with small or zero entropy production and estimate the masses of oscillation generation regions in clustermodels based on the data of the phase-space coordinates of stars. The radii of such regions are close to the core radii of the OCL models. We develop a new method for estimating the total OCL masses based on the cluster core mass, the cluster and cluster core radii, and radial distribution of stars. This method yields estimates of dynamical masses of Pleiades, Praesepe, and M67, which agree well with the estimates of the total masses of the corresponding clusters based on proper motions and spectroscopic data for cluster stars.We construct the spectra and dispersion curves of the oscillations of the field of azimuthal velocities v φ in OCL models. Weak, low-amplitude unstable oscillations of v φ develop in cluster models near the cluster core boundary, and weak damped oscillations of v φ often develop at frequencies close to the frequencies of more powerful oscillations, which may reduce the non-stationarity degree in OCL models. We determine the number and parameters of such oscillations near the cores boundaries of cluster models. Such oscillations points to the possible role that gradient instability near the core of cluster models plays in the decrease of the mass of the oscillation generation regions and production of entropy in the cores of OCL models with massive extended cores.

On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

NASA Astrophysics Data System (ADS)

BOERTJENS, G. J.; VAN HORSSEN, W. T.

2000-08-01

In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.

Asymmetries of solar oscillation line profiles

NASA Technical Reports Server (NTRS)

Duvall, T. L., Jr.; Jefferies, S. M.; Harvey, J. W.; Osaki, Y.; Pomerantz, M. A.

1993-01-01

Asymmetries of the power spectral line profiles of solar global p-modes are detected in full-disk intensity observations of the Ca II K Fraunhofer line. The asymmetry is a strong function of temporal frequency being strongest at the lowest frequencies observed and vanishing near the peak of the power distribution. The variation with spherical harmonic degree is small. The asymmetry is interpreted in terms of a model in which the solar oscillation cavity is compared to a Fabry-Perot interferometer with the source slightly outside the cavity. A phase difference between an outward direct wave and a corresponding inward wave that passes through the cavity gives rise to the asymmetry. The asymmetry is different in velocity and intensity observations. Neglecting the asymmetry when modeling the power spectrum can lead to systematic errors in the measurement of mode frequencies of as much as 10 exp -4 of the mode frequency. The present observations and interpretation locate the source of the oscillations to be approximately 60 km beneath the photosphere, the shallowest position suggested to date.

Experimental evidence for dynamic friction on rock fractures from frequency-dependent nonlinear hysteresis and harmonic generation

NASA Astrophysics Data System (ADS)

Saltiel, Seth; Bonner, Brian P.; Mittal, Tushar; Delbridge, Brent; Ajo-Franklin, Jonathan B.

2017-07-01

Frictional properties affect the propagation of high-amplitude seismic waves across rock fractures and faults. Laboratory evidence suggests that these properties can be measured in active seismic surveys, potentially offering a route to characterizing friction in situ. We present experimental results from a subresonance torsional modulus and attenuation apparatus that utilizes micron-scale sinusoidal oscillations to probe the nonlinear stress-strain relation at a range of strain amplitudes and rates. Nonlinear effects are further quantified using harmonic distortion; however, time series data best illuminate underlying physical processes. The low-frequency stress-strain hysteretic loops show stiffening at the sinusoid's static ends, but stiffening is reduced above a threshold frequency. This shape is determined by harmonic generation in the strain; the stress signal has no harmonics, confirming that the fractured sample is the source of the nonlinearity. These qualitative observations suggest the presence of rate-dependent friction and are consistent between fractures in three different rock types. We propose that static friction at the low strain rate part of the cycle, when given sufficient "healing" time at low oscillation frequencies, causes this stiffening cusp shape in the hysteresis loop. While rate-and-state friction is commonly used to represent dynamic friction, it cannot capture static friction or negative slip velocities. So we implement another dynamic friction model, based on the work of Dahl, which describes this process and produces similar results. Since the two models have a similar form, parameterizations of field data could constraint fault model inputs, such as specific location velocity strengthening or weakening properties.

Higher harmonics generation in relativistic electron beam with virtual cathode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kurkin, S. A., E-mail: KurkinSA@gmail.com; Badarin, A. A.; Koronovskii, A. A.

2014-09-15

The study of the microwave generation regimes with intense higher harmonics taking place in a high-power vircator consisting of a relativistic electron beam with a virtual cathode has been made. The characteristics of these regimes, in particular, the typical spectra and their variations with the change of the system parameters (beam current, the induction of external magnetic field) as well as physical processes occurring in the system have been analyzed by means of 3D electromagnetic simulation. It has been shown that the system under study demonstrates the tendency to the sufficient growth of the amplitudes of higher harmonics in themore » spectrum of current oscillations in the VC region with the increase of beam current. The obtained results allow us to consider virtual cathode oscillators as promising high power mmw-to-THz sources.« less

Seizure Dynamics of Coupled Oscillators with Epileptor Field Model

NASA Astrophysics Data System (ADS)

Zhang, Honghui; Xiao, Pengcheng

The focus of this paper is to investigate the dynamics of seizure activities by using the Epileptor coupled model. Based on the coexistence of seizure-like event (SLE), refractory status epilepticus (RSE), depolarization block (DB), and normal state, we first study the dynamical behaviors of two coupled oscillators in different activity states with Epileptor model by linking them with slow permittivity coupling. Our research has found that when one oscillator in normal states is coupled with any oscillator in SLE, RSE or DB states, these two oscillators can both evolve into SLE states under appropriate coupling strength. And then these two SLE oscillators can perform epileptiform synchronization or epileptiform anti-synchronization. Meanwhile, SLE can be depressed when considering the fast electrical or chemical coupling in Epileptor model. Additionally, a two-dimensional reduced model is also given to show the effect of coupling number on seizures. Those results can help to understand the dynamical mechanism of the initiation, maintenance, propagation and termination of seizures in focal epilepsy.

A Method for Harmonic Sources Detection based on Harmonic Distortion Power Rate

NASA Astrophysics Data System (ADS)

Lin, Ruixing; Xu, Lin; Zheng, Xian

2018-03-01

Harmonic sources detection at the point of common coupling is an essential step for harmonic contribution determination and harmonic mitigation. The harmonic distortion power rate index is proposed for harmonic source location based on IEEE Std 1459-2010 in the paper. The method only based on harmonic distortion power is not suitable when the background harmonic is large. To solve this problem, a threshold is determined by the prior information, when the harmonic distortion power is larger than the threshold, the customer side is considered as the main harmonic source, otherwise, the utility side is. A simple model of public power system was built in MATLAB/Simulink and field test results of typical harmonic loads verified the effectiveness of proposed method.

Efficient forward second-harmonic generation from planar archimedean nanospirals

DOE PAGES

Davidson, II, Roderick B.; Ziegler, Jed I.; Vargas, Guillermo; ...

2015-05-01

Here, the enhanced electric field at plasmonic resonances in nanoscale antennas can lead to efficient harmonic generation, especially when the plasmonic geometry is asymmetric on either inter-particle or intra-particle levels. The planar Archimedean nanospiral offers a unique geometrical asymmetry for second-harmonic generation (SHG) because the SHG results neither from arranging centrosymmetric nanoparticles in asymmetric groupings, nor from non-centrosymmetric nanoparticles that retain a local axis of symmetry. Here, we report forward SHG from planar arrays of Archimedean nanospirals using 15 fs pulses from a Ti:sapphire oscillator tuned to 800 nm wavelength.

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

NASA Astrophysics Data System (ADS)

Marquette, Ian; Quesne, Christiane

2016-05-01

The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent PIV, 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 Xm1,m2,…,mk 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.

Region Spherical Harmonic Magnetic Modeling from Near-Surface and Satellite-Altitude Anomlaies

NASA Technical Reports Server (NTRS)

Kim, Hyung Rae; von Frese, Ralph R. B.; Taylor, Patrick T.

2013-01-01

The compiled near-surface data and satellite crustal magnetic measured data are modeled with a regionally concentrated spherical harmonic presentation technique over Australia and Antarctica. Global crustal magnetic anomaly studies have used a spherical harmonic analysis to represent the Earth's magnetic crustal field. This global approach, however is best applied where the data are uniformly distributed over the entire Earth. Satellite observations generally meet this requirement, but unequally distributed data cannot be easily adapted in global modeling. Even for the satellite observations, due to the errors spread over the globe, data smoothing is inevitable in the global spherical harmonic presentations. In addition, global high-resolution modeling requires a great number of global spherical harmonic coefficients for the regional presentation of crustal magnetic anomalies, whereas a lesser number of localized spherical coefficients will satisfy. We compared methods in both global and regional approaches and for a case where the errors were propagated outside the region of interest. For observations from the upcoming Swarm constellation, the regional modeling will allow the production a lesser number of spherical coefficients that are relevant to the region of interest

Model of resonant high harmonic generation in multi-electron systems

NASA Astrophysics Data System (ADS)

Redkin, P. V.; Ganeev, R. A.

2017-09-01

We extend the 4-step analytical model of resonant enhancement of high harmonic generation to the systems possessing resonant transitions of inner-shell electrons. Resonant enhancement is explained by lasing without inversion in a three-level system of ground, excited and shifted resonant states, which are coupled to the fundamental field and its high harmonics. The role of inelastic scattering is studied by simulation of an excited state’s population dynamics. It is shown that maximal gain is achieved when the energy shift between the excited state and resonant state is close to the energy of the fundamental photon. To prove the concept we demonstrate the enhancement of harmonics in the In plasma using different pumps.

On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator

ERIC Educational Resources Information Center

Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru

2009-01-01

The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.

Homodyne detection of short-range Doppler radar using a forced oscillator model

NASA Astrophysics Data System (ADS)

Kittipute, Kunanon; Saratayon, Peerayudh; Srisook, Suthasin; Wardkein, Paramote

2017-03-01

This article presents the homodyne detection in a self-oscillation system, which represented by a short-range radar (SRR) circuit, that is analysed using a multi-time forced oscillator (MTFO) model. The MTFO model is based on a forced oscillation perspective with the signal and system theory, a second-order differential equation, and the multiple time variable technique. This model can also apply to analyse the homodyne phenomenon in a difference kind of the oscillation system under same method such as the self-oscillation system, and the natural oscillation system with external forced. In a free oscillation system, which forced by the external source is represented by a pendulum with an oscillating support experiment, and a modified Colpitts oscillator circuit in the UHF band with input as a Doppler signal is a representative of self-oscillation system. The MTFO model is verified with the experimental result, which well in line with the theoretical analysis.

Homodyne detection of short-range Doppler radar using a forced oscillator model

PubMed Central

Kittipute, Kunanon; Saratayon, Peerayudh; Srisook, Suthasin; Wardkein, Paramote

2017-01-01

This article presents the homodyne detection in a self-oscillation system, which represented by a short-range radar (SRR) circuit, that is analysed using a multi-time forced oscillator (MTFO) model. The MTFO model is based on a forced oscillation perspective with the signal and system theory, a second-order differential equation, and the multiple time variable technique. This model can also apply to analyse the homodyne phenomenon in a difference kind of the oscillation system under same method such as the self-oscillation system, and the natural oscillation system with external forced. In a free oscillation system, which forced by the external source is represented by a pendulum with an oscillating support experiment, and a modified Colpitts oscillator circuit in the UHF band with input as a Doppler signal is a representative of self-oscillation system. The MTFO model is verified with the experimental result, which well in line with the theoretical analysis. PMID:28252000

Teaching Oscillations by a Model of Nanoresonator

ERIC Educational Resources Information Center

Lindell, A.; Viiri, J.

2009-01-01

Nanoscience offers fascinating opportunities for science education as it links the achievements of modern technology to traditional models of science. In this article we present a nanotechnology orientated lesson on oscillations, suitable for physics courses at high schools and universities. The focus of the lesson is in forced oscillations on a…

Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations

PubMed Central

Kurihara, Eru; Hay, Todd A.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2011-01-01

Interaction between acoustically driven or laser-generated bubbles causes the bubble surfaces to deform. Dynamical equations describing the motion of two translating, nominally spherical bubbles undergoing small shape oscillations in a viscous liquid are derived using Lagrangian mechanics. Deformation of the bubble surfaces is taken into account by including quadrupole and octupole perturbations in the spherical-harmonic expansion of the boundary conditions on the bubbles. Quadratic terms in the quadrupole and octupole amplitudes are retained, and surface tension and shear viscosity are included in a consistent manner. A set of eight coupled second-order ordinary differential equations is obtained. Simulation results, obtained by numerical integration of the model equations, exhibit qualitative agreement with experimental observations by predicting the formation of liquid jets. Simulations also suggest that bubble-bubble interactions act to enhance surface mode instability. PMID:22088009

Thermal dephasing in second-harmonic generation of an amplified copper-vapor laser beam in beta barium borate.

PubMed

Prakash, Om; Dixit, Sudhir Kumar; Bhatnagar, Rajiva

2005-03-20

The conversion efficiency in second-harmonic generation of an amplified beam in a master-oscillator power amplifier copper-vapor laser (CVL) is lower than that of the oscillator beam alone. This lower efficiency is often vaguely attributed to wave-front degradation in the amplifier. We investigate the role of wave-front degradation and thermal dephasing in the second-harmonic generation of a CVL from a beta-barium borate crystal. Choosing two beams with constant intrapulse divergence, one from a generalized diffraction filtered resonator master oscillator alone and other obtained by amplifying oscillator by use of a power amplifier, we show that at low flux levels the decrease in efficiency is due to wave-front degradation. At a fundamental power above the critical power for thermal dephasing, the decrease is due to increased UV absorption and consequent thermal dephasing. Thermal dephasing is higher for the beam with the lower coherence width.

The NASA/MSFC global reference atmospheric model: MOD 3 (with spherical harmonic wind model)

NASA Technical Reports Server (NTRS)

Justus, C. G.; Fletcher, G. R.; Gramling, F. E.; Pace, W. B.

1980-01-01

Improvements to the global reference atmospheric model are described. The basic model includes monthly mean values of pressure, density, temperature, and geostrophic winds, as well as quasi-biennial and small and large scale random perturbations. A spherical harmonic wind model for the 25 to 90 km height range is included. Below 25 km and above 90 km, the GRAM program uses the geostrophic wind equations and pressure data to compute the mean wind. In the altitudes where the geostrophic wind relations are used, an interpolation scheme is employed for estimating winds at low latitudes where the geostrophic wind relations being to mesh down. Several sample wind profiles are given, as computed by the spherical harmonic model. User and programmer manuals are presented.

Truncation of Spherical Harmonic Series and its Influence on Gravity Field Modelling

NASA Astrophysics Data System (ADS)

Fecher, T.; Gruber, T.; Rummel, R.

2009-04-01

Least-squares adjustment is a very common and effective tool for the calculation of global gravity field models in terms of spherical harmonic series. However, since the gravity field is a continuous field function its optimal representation by a finite series of spherical harmonics is connected with a set of fundamental problems. Particularly worth mentioning here are cut off errors and aliasing effects. These problems stem from the truncation of the spherical harmonic series and from the fact that the spherical harmonic coefficients cannot be determined independently of each other within the adjustment process in case of discrete observations. The latter is shown by the non-diagonal variance-covariance matrices of gravity field solutions. Sneeuw described in 1994 that the off-diagonal matrix elements - at least if data are equally weighted - are the result of a loss of orthogonality of Legendre polynomials on regular grids. The poster addresses questions arising from the truncation of spherical harmonic series in spherical harmonic analysis and synthesis. Such questions are: (1) How does the high frequency data content (outside the parameter space) affect the estimated spherical harmonic coefficients; (2) Where to truncate the spherical harmonic series in the adjustment process in order to avoid high frequency leakage?; (3) Given a set of spherical harmonic coefficients resulting from an adjustment, what is the effect of using only a truncated version of it?

Fractional Relativistic Yamaleev Oscillator Model and Its Dynamical Behaviors

NASA Astrophysics Data System (ADS)

Luo, Shao-Kai; He, Jin-Man; Xu, Yan-Li; Zhang, Xiao-Tian

2016-07-01

In the paper we construct a new kind of fractional dynamical model, i.e. the fractional relativistic Yamaleev oscillator model, and explore its dynamical behaviors. We will find that the fractional relativistic Yamaleev oscillator model possesses Lie algebraic structure and satisfies generalized Poisson conservation law. We will also give the Poisson conserved quantities of the model. Further, the relation between conserved quantities and integral invariants of the model is studied and it is proved that, by using the Poisson conserved quantities, we can construct integral invariants of the model. Finally, the stability of the manifold of equilibrium states of the fractional relativistic Yamaleev oscillator model is studied. The paper provides a general method, i.e. fractional generalized Hamiltonian method, for constructing a family of fractional dynamical models of an actual dynamical system.

Bloch oscillations as generators of polarons in a 1D crystal

NASA Astrophysics Data System (ADS)

Nazareno, H. N.; Brito, P. E. de

2016-08-01

The main purpose of this work is to characterize the kind of propagation/localization of carriers in a one-dimensional crystalline structure along the tight-binding model while the electron-phonon interaction is taken into account through a deformation potential and the system is under the action of a dc electric field. The lattice was treated in the classical formalism of harmonic vibrations. A remarkable effect is obtained due to the presence of the electric field. On one side the particle performs Bloch oscillations and at the same time it interacts with the lattice and as a result at each turning point of its trajectory phonons are generated that carry with them a fraction of the electronic wave packet, it is the polaron formation. This way the Bloch oscillations pump polarons into the system. We explain why the polaron is formed at returning points of the oscillations.

Rotational-oscillational motions of the nonrigid Earth about the center of mass

NASA Astrophysics Data System (ADS)

Bondarenko, V. V.; Perepelkin, V. V.

2009-10-01

We use the model of a nearly axisymmetric viscoelastic rigid body to study perturbed rotational-oscillational motions of the Earth's pole. We point out that the Chandler component of oscillations is of celestial-mechanics nature and is caused by the gravitational-tidal actions of the Sun and the Moon. We analyze the pole oscillation excitation mechanism at a frequency close to the Chandler frequency and show that the undamped pole oscillations are caused by the resonance harmonic of the external perturbation at a frequency close to the free nutation frequency. We discuss whether it is possible to solve the problem of constructing a short-term forecast of the pole motion on the basis of a polynomial filter obtained by the least-squares method without taking into account small-scale oscillations caused by wide-band random factors of arbitrary physical nature. In the present paper, we perform numerical simulation of tidal inhomogeneities in the Earth's axial rotation. Attention is mainly paid to the analysis of day length variations on short time intervals with periods less than or equal to one year (interannual oscillations) and to their forecast.

Ferromagnetic mass fixed on a spring and subjected to an electromagnet powered by self-sustained oscillators

NASA Astrophysics Data System (ADS)

Abobda, L. T.; Woafo, P.

2014-12-01

The study of a ferromagnetic mass, fixed on a spring and subjected to an electromagnet powered by a Van der Pol (VDP) oscillator and by a Hindmarsh-Rose (HR) oscillator is performed, to serve as an electromechanical devices, but also to mimic the action of a natural pacemaker and nerves on a cardiac assist device or artificial heart. The excitation with the VDP oscillator shows in the mechanical part the transition from harmonic, periodic, biperiodic up to bursting oscillations, high displacement without pull-in instability in the free dynamics regime. Under DC plus square wave excitation, there is a coexistence of the bursting oscillations of the free dynamics and the one of the modulated dynamics. Considering the action of a HR oscillator, it is found transition from spikes, bursting oscillations, relaxation spikes, multiperiodic and sinusoidal oscillations under DC or DC plus square wave excitation. These electrical behaviors are transferred to the mechanical part which can then adopt spiking or bursting dynamics as the HR oscillator. For this electromechanical model, the VDP oscillator is more efficient than the HR oscillator to induce pulsatile pumping function with higher amplitude and to react to external influences without pull-in.

Minimal models of electric potential oscillations in non-excitable membranes.

PubMed

Perdomo, Guillermo; Hernández, Julio A

2010-01-01

Sustained oscillations in the membrane potential have been observed in a variety of cellular and subcellular systems, including several types of non-excitable cells and mitochondria. For the plasma membrane, these electrical oscillations have frequently been related to oscillations in intracellular calcium. For the inner mitochondrial membrane, in several cases the electrical oscillations have been attributed to modifications in calcium dynamics. As an alternative, some authors have suggested that the sustained oscillations in the mitochondrial membrane potential induced by some metabolic intermediates depends on the direct effect of internal protons on proton conductance. Most theoretical models developed to interpret oscillations in the membrane potential integrate several transport and biochemical processes. Here we evaluate whether three simple dynamic models may constitute plausible representations of electric oscillations in non-excitable membranes. The basic mechanism considered in the derivation of the models is based upon evidence obtained by Hattori et al. for mitochondria and assumes that an ionic species (i.e., the proton) is transported via passive and active transport systems between an external and an internal compartment and that the ion affects the kinetic properties of transport by feedback regulation. The membrane potential is incorporated via its effects on kinetic properties. The dynamic properties of two of the models enable us to conclude that they may represent alternatives enabling description of the generation of electrical oscillations in membranes that depend on the transport of a single ionic species.

Modeling complex tone perception: grouping harmonics with combination-sensitive neurons.

PubMed

Medvedev, Andrei V; Chiao, Faye; Kanwal, Jagmeet S

2002-06-01

Perception of complex communication sounds is a major function of the auditory system. To create a coherent precept of these sounds the auditory system may instantaneously group or bind multiple harmonics within complex sounds. This perception strategy simplifies further processing of complex sounds and facilitates their meaningful integration with other sensory inputs. Based on experimental data and a realistic model, we propose that associative learning of combinations of harmonic frequencies and nonlinear facilitation of responses to those combinations, also referred to as "combination-sensitivity," are important for spectral grouping. For our model, we simulated combination sensitivity using Hebbian and associative types of synaptic plasticity in auditory neurons. We also provided a parallel tonotopic input that converges and diverges within the network. Neurons in higher-order layers of the network exhibited an emergent property of multifrequency tuning that is consistent with experimental findings. Furthermore, this network had the capacity to "recognize" the pitch or fundamental frequency of a harmonic tone complex even when the fundamental frequency itself was missing.

Chaos in generically coupled phase oscillator networks with nonpairwise interactions.

PubMed

Bick, Christian; Ashwin, Peter; Rodrigues, Ana

2016-09-01

The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling-including three and four-way interactions of the oscillator phases-that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.

Chaos in generically coupled phase oscillator networks with nonpairwise interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bick, Christian; Ashwin, Peter; Rodrigues, Ana

The Kuramoto–Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling—including three and four-way interactions of the oscillator phases—that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamicsmore » in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.« less

A harmonic analysis method for unsteady transonic flow and its application to the flutter of airfoils

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Weatherill, W. H.

1982-01-01

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. A study is presented of the shock motion associated with an oscillating airfoil and its representation by the harmonic procedure. The effects of the shock motion and the resulting pressure pulse are shown to be included in the harmonic pressure distributions and the corresponding generalized forces. Analytical and experimental pressure distributions for the NACA 64A010 airfoil are compared for Mach numbers of 0.75, 0.80 and 0.842. A typical section, two-degree-of-freedom flutter analysis of a NACA 64A010 airfoil is performed. The results show a sharp transonic bucket in one case and abrupt changes in instability modes.

Privacy-Preserving Predictive Modeling: Harmonization of Contextual Embeddings From Different Sources.

PubMed

Huang, Yingxiang; Lee, Junghye; Wang, Shuang; Sun, Jimeng; Liu, Hongfang; Jiang, Xiaoqian

2018-05-16

Data sharing has been a big challenge in biomedical informatics because of privacy concerns. Contextual embedding models have demonstrated a very strong representative capability to describe medical concepts (and their context), and they have shown promise as an alternative way to support deep-learning applications without the need to disclose original data. However, contextual embedding models acquired from individual hospitals cannot be directly combined because their embedding spaces are different, and naive pooling renders combined embeddings useless. The aim of this study was to present a novel approach to address these issues and to promote sharing representation without sharing data. Without sacrificing privacy, we also aimed to build a global model from representations learned from local private data and synchronize information from multiple sources. We propose a methodology that harmonizes different local contextual embeddings into a global model. We used Word2Vec to generate contextual embeddings from each source and Procrustes to fuse different vector models into one common space by using a list of corresponding pairs as anchor points. We performed prediction analysis with harmonized embeddings. We used sequential medical events extracted from the Medical Information Mart for Intensive Care III database to evaluate the proposed methodology in predicting the next likely diagnosis of a new patient using either structured data or unstructured data. Under different experimental scenarios, we confirmed that the global model built from harmonized local models achieves a more accurate prediction than local models and global models built from naive pooling. Such aggregation of local models using our unique harmonization can serve as the proxy for a global model, combining information from a wide range of institutions and information sources. It allows information unique to a certain hospital to become available to other sites, increasing the fluidity of

Periodically poled potassium niobate for second-harmonic generation at 463 nm.

PubMed

Meyn, J P; Klein, M E; Woll, D; Wallenstein, R; Rytz, D

1999-08-15

We report on the fabrication and characterization of quasi-phase-matched potassium niobate crystals for second-harmonic generation. Periodic 30-mum -pitch antiparallel ferroelectric domains are fabricated by means of poling in an electrical field. Both birefrigence and periodic phase shift of the generated second harmonic contribute to phase matching when the d(31) nonlinear optical tensor element is used. 3.8 mW of second-harmonic radiation at 463 nm is generated by frequency doubling of the output of master-oscillator power-amplifier diode laser in a 5-mm-long crystal. The measured effective nonlinear coefficient is 3.7pm/V. The measured spectral acceptance bandwidth of 0.25 nm corresponds to the theoretical value.

Forced oscillations of cracked beam under the stochastic cyclic loading

NASA Astrophysics Data System (ADS)

Matsko, I.; Javors'kyj, I.; Yuzefovych, R.; Zakrzewski, Z.

2018-05-01

An analysis of forced oscillations of cracked beam using statistical methods for periodically correlated random processes is presented. The oscillation realizations are obtained on the basis of numerical solutions of differential equations of the second order, for the case when applied force is described by a sum of harmonic and stationary random process. It is established that due to crack appearance forced oscillations acquire properties of second-order periodical non-stationarity. It is shown that in a super-resonance regime covariance and spectral characteristics, which describe non-stationary structure of forced oscillations, are more sensitive to crack growth than the characteristics of the oscillation's deterministic part. Using diagnostic indicators formed on their basis allows the detection of small cracks.

Experimental study of the oscillation of spheres in an acoustic levitator.

PubMed

Andrade, Marco A B; Pérez, Nicolás; Adamowski, Julio C

2014-10-01

The spontaneous oscillation of solid spheres in a single-axis acoustic levitator is experimentally investigated by using a high speed camera to record the position of the levitated sphere as a function of time. The oscillations in the axial and radial directions are systematically studied by changing the sphere density and the acoustic pressure amplitude. In order to interpret the experimental results, a simple model based on a spring-mass system is applied in the analysis of the sphere oscillatory behavior. This model requires the knowledge of the acoustic pressure distribution, which was obtained numerically by using a linear finite element method (FEM). Additionally, the linear acoustic pressure distribution obtained by FEM was compared with that measured with a laser Doppler vibrometer. The comparison between numerical and experimental pressure distributions shows good agreement for low values of pressure amplitude. When the pressure amplitude is increased, the acoustic pressure distribution becomes nonlinear, producing harmonics of the fundamental frequency. The experimental results of the spheres oscillations for low pressure amplitudes are consistent with the results predicted by the simple model based on a spring-mass system.

Understanding photoluminescence of metal nanostructures based on an oscillator model.

PubMed

Cheng, Yuqing; Zhang, Weidong; Zhao, Jingyi; Wen, Te; Hu, Aiqin; Gong, Qihuang; Lu, Guowei

2018-08-03

Scattering and absorption properties of metal nanostructures have been well understood based on the classic oscillator theory. Here, we demonstrate that photoluminescence of metal nanostructures can also be explained based on a classic model. The model shows that inelastic radiation of an oscillator resembles its resonance band after external excitation, and is related to the photoluminescence from metallic nanostructures. The understanding based on the classic oscillator model is in agreement with that predicted by a quantum electromagnetic cavity model. Moreover, by correlating a two-temperature model and the electron distributions, we demonstrate that both one-photon and two-photon luminescence of the metal nanostructures undergo the same mechanism. Furthermore, the model explains most of the emission characteristics of the metallic nanostructures, such as quantum yield, spectral shape, excitation polarization and power dependence. The model based on an oscillator provides an intuitive description of the photoluminescence process and may enable rapid optimization and exploration of the plasmonic properties.

Modeling Tight Junction Dynamics and Oscillations

PubMed Central

Kassab, Fuad; Marques, Ricardo Paulino; Lacaz-Vieira, Francisco

2002-01-01

Tight junction (TJ) permeability responds to changes of extracellular Ca2+ concentration. This can be gauged through changes of the transepithelial electrical conductance (G) determined in the absence of apical Na+. The early events of TJ dynamics were evaluated by the fast Ca2+ switch assay (FCSA) (Lacaz-Vieira, 2000), which consists of opening the TJs by removing basal calcium (Ca2+ bl) and closing by returning Ca2+ bl to normal values. Oscillations of TJ permeability were observed when Ca2+ bl is removed in the presence of apical calcium (Ca2+ ap) and were interpreted as resulting from oscillations of a feedback control loop which involves: (a) a sensor (the Ca2+ binding sites of zonula adhaerens), (b) a control unit (the cell signaling machinery), and (c) an effector (the TJs). A mathematical model to explain the dynamical behavior of the TJs and oscillations was developed. The extracellular route (ER), which comprises the paracellular space in series with the submucosal interstitial fluid, was modeled as a continuous aqueous medium having the TJ as a controlled barrier located at its apical end. The ER was approximated as a linear array of cells. The most apical cell is separated from the apical solution by the TJ and this cell bears the Ca2+ binding sites of zonula adhaerens that control the TJs. According to the model, the control unit receives information from the Ca2+ binding sites and delivers a signal that regulates the TJ barrier. Ca2+ moves along the ER according to one-dimensional diffusion following Fick's second law. Across the TJ, Ca2+ diffusion follows Fick's first law. Our first approach was to simulate the experimental results in a semiquantitative way. The model tested against experiment results performed in the frog urinary bladder adequately predicts the responses obtained in different experimental conditions, such as: (a) TJ opening and closing in a FCSA, (b) opening by the presence of apical Ca2+ and attainment of a new steady-state, (c

The radio-frequency fluctuation effect on the floating harmonic method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Jaewon; Kim, Kyung-Hyun; Kim, Dong-Hwan

2016-08-15

The radio-frequency (RF) plasma diagnostics with an electrical probe facing a challenge, because the RF fluctuation oscillates the plasma potential and distorts the current-voltage (I-V) curve. As Langmuir probe is widely used in plasma diagnostics, many researchers have been studying the effect of RF fluctuation on probe and compensation methods. On the other hand, there have not been enough studies on the fluctuation effect on the floating harmonic method. Therefore, we investigated the impact of RF fluctuation on the floating harmonic method theoretically and experimentally. When the electrons are in ideal Maxwellian distribution, the floating potential is negatively shifted bymore » the RF fluctuation, but the fluctuation does not distort I-V curve around the floating potential. However, in practical plasmas, the I-V curve and their harmonic components are distorted. This RF fluctuation effect becomes more significant in a low density plasma with a high impedance sheath. The second harmonic current decreases with the RF fluctuation while the first harmonic current is merely affected. Therefore, the electron temperatures measured with the floating harmonic method under low density plasma with uncompensated probe are overestimated than the results obtained with the compensated probe.« less

Transients in the synchronization of asymmetrically coupled oscillator arrays

NASA Astrophysics Data System (ADS)

Cantos, C. E.; Hammond, D. K.; Veerman, J. J. P.

2016-09-01

We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a certain parameter regime Ω. As corollaries we show that minimizing the transients requires considering non-symmetric coupling, and that within Ω the computed linear growth in N of the transients is independent of (reasonable) boundary conditions.

Undamped transverse oscillations of coronal loops as a self-oscillatory process

NASA Astrophysics Data System (ADS)

Nakariakov, V. M.; Anfinogentov, S. A.; Nisticò, G.; Lee, D.-H.

2016-06-01

Context. Standing transverse oscillations of coronal loops are observed to operate in two regimes: rapidly decaying, large amplitude oscillations and undamped small amplitude oscillations. In the latter regime the damping should be compensated by energy supply, which allows the loop to perform almost monochromatic oscillations with almost constant amplitude and phase. Different loops oscillate with different periods. The oscillation amplitude does not show dependence on the loop length or the oscillation period. Aims: We aim to develop a low-dimensional model explaining the undamped kink oscillations as a self-oscillatory process caused by the effect of negative friction. The source of energy is an external quasi-steady flow, for example, supergranulation motions near the loop footpoints or external flows in the corona. Methods: We demonstrate that the interaction of a quasi-steady flow with a loop can be described by a Rayleigh oscillator equation that is a non-linear ordinary differential equation, with the damping and resonant terms determined empirically. Results: Small-amplitude self-oscillatory solutions to the Rayleigh oscillator equation are harmonic signals of constant amplitude, which is consistent with the observed properties of undamped kink oscillations. The period of self-oscillations is determined by the frequency of the kink mode. The damping by dissipation and mode conversion is compensated by the continuous energy deposition at the frequency of the natural oscillation. Conclusions: We propose that undamped kink oscillations of coronal loops may be caused by the interaction of the loops with quasi-steady flows, and hence are self-oscillations, which is analogous to producing a tune by moving a bow across a violin string.

Resonance-modulated wavelength scaling of high-order-harmonic generation from H2+

NASA Astrophysics Data System (ADS)

Wang, Baoning; He, Lixin; Wang, Feng; Yuan, Hua; Zhu, Xiaosong; Lan, Pengfei; Lu, Peixiang

2018-01-01

Wavelength scaling of high-order harmonic generation (HHG) in a non-Born-Oppenheimer treatment of H2+ is investigated by numerical simulations of the time-dependent Schrödinger equation. The results show that the decrease in the wavelength-dependent HHG yield is reduced compared to that in the fixed-nucleus approximation. This slower wavelength scaling is related to the charge-resonance-enhanced ionization effect, which considerably increases the ionization rate at longer driving laser wavelengths due to the relatively larger nuclear separation. In addition, we find an oscillation structure in the wavelength scaling of HHG from H2+. Upon decreasing the laser intensity or increasing the nuclear mass, the oscillation structure will shift towards a longer wavelength of the laser pulse. These results permit the generation of an efficient harmonic spectrum in the midinfrared regime by manipulating the nuclear dynamics of molecules.

Analysis of variability in the burst oscillations of the accreting millisecond pulsar XTE J1814-338

NASA Technical Reports Server (NTRS)

Watts, Anna L.; Strohmayer, Tod E.; Markwardt, Craig B.

2005-01-01

The accreting millisecond pulsar XTE J1814-338 exhibits oscillations at the known spin frequency during Type I X-ray bursts. The properties of the burst oscillations reflect the nature of the thermal asymmetry on the stellar surface. We present an analysis of the variability of the burst oscillations of this source, focusing on three characteristics: fractional amplitude, harmonic content and frequency. Fractional amplitude and harmonic content constrain the size, shape and position of the emitting region, whilst variations in frequency indicate motion of the emitting region on the neutron star surface. We examine both long-term variability over the course of the outburst, and short-term variability during the bursts. For most of the bursts, fractional amplitude is consistent with that of the accretion pulsations, implying a low degree of fuel spread. There is however a population of bursts whose fractional amplitudes are substantially lower, implying a higher degree of fuel spread, possibly forced by the explosive burning front of a precursor burst. For the first harmonic, substantial differences between the burst and accretion pulsations suggest that hotspot geometry is not the only mechanism giving rise to harmonic content in the latter. Fractional amplitude variability during the bursts is low; we can only rule out the hypothesis that the fractional amplitude remains constant at the l(sigma) level for bursts that do not exhibit photospheric radius expansion (PRE). There are no significant variations in frequency in any of the bursts except for the one burst that exhibits PRE. This burst exhibits a highly significant but small (= 0.1Hz) drop in frequency in the burst rise. The timescale of the frequency shift is slower than simple burning layer expansion models predict, suggesting that other mechanisms may be at work.

Observations of decay-less low-amplitude kink oscillations of EUV coronal loops

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe; Nakariakov, Valery; Anfinogentov, Sergey

The high spatial and temporal resolution observations at Extreme Ultra-Violet (EUV) wavelengths from the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) reveal new features in kink oscillations of coronal loops. We show that, in addition to the well-known rapidly decaying oscillations, a new type of kink waves is present, characterized by low-amplitude and undamped oscillations, that we define as decay-less. Typical periods range from 2.5 to 12 min in both regimes and are different for different loops, increasing with the loop length. Estimates of the loop lengths are supported by three dimensional reconstruction of the loop geometry. The amplitude for the decay-less regime is about 1 Mm, close to the spatial resolution of the AIA instruments. The oscillation phase, measured by the cross-correlation method, is found to be constant along each analysed loop, and the spatial structure of the phase of the oscillations corresponds to the fundamental standing kink mode. We show that the observed behaviours are consistent with the empirical model of a damped linear oscillator excited by a continuous low-amplitude harmonic driver, in addition to an eventual impulsive high-amplitude driver. The observed life-time of the oscillations is likely to be determined by the observational conditions rather than any physical damping. However, the balance between the driving and damping is a necessary ingredient of this model. The properties of this type of transverse oscillations make them interesting object of study in the framework of resonant absorption theory and coronal heating process.

Harmonic generation in metallic, GaAs-filled nanocavities in the enhanced transmission regime at visible and UV wavelengths.

PubMed

Vincenti, M A; de Ceglia, D; Roppo, V; Scalora, M

2011-01-31

We have conducted a theoretical study of harmonic generation from a silver grating having slits filled with GaAs. By working in the enhanced transmission regime, and by exploiting phase-locking between the pump and its harmonics, we guarantee strong field localization and enhanced harmonic generation under conditions of high absorption at visible and UV wavelengths. Silver is treated using the hydrodynamic model, which includes Coulomb and Lorentz forces, convection, electron gas pressure, plus bulk χ(3) contributions. For GaAs we use nonlinear Lorentz oscillators, with characteristic χ(2) and χ(3) and nonlinear sources that arise from symmetry breaking and Lorentz forces. We find that: (i) electron pressure in the metal contributes to linear and nonlinear processes by shifting/reshaping the band structure; (ii) TE- and TM-polarized harmonics can be generated efficiently; (iii) the χ(2) tensor of GaAs couples TE- and TM-polarized harmonics that create phase-locked pump photons having polarization orthogonal compared to incident pump photons; (iv) Fabry-Perot resonances yield more efficient harmonic generation compared to plasmonic transmission peaks, where most of the light propagates along external metal surfaces with little penetration inside its volume. We predict conversion efficiencies that range from 10(-6) for second harmonic generation to 10(-3) for the third harmonic signal, when pump power is 2 GW/cm2.

Optimal Control of the Parametric Oscillator

ERIC Educational Resources Information Center

Andresen, B.; Hoffmann, K. H.; Nulton, J.; Tsirlin, A.; Salamon, P.

2011-01-01

We present a solution to the minimum time control problem for a classical harmonic oscillator to reach a target energy E[subscript T] from a given initial state (q[subscript i], p[subscript i]) by controlling its frequency [omega], [omega][subscript min] less than or equal to [omega] less than or equal to [omega][subscript max]. A brief synopsis…

Spherical harmonic modelling to ultra-high degree of Bouguer and isostatic anomalies

NASA Astrophysics Data System (ADS)

Balmino, G.; Vales, N.; Bonvalot, S.; Briais, A.

2012-07-01

The availability of high-resolution global digital elevation data sets has raised a growing interest in the feasibility of obtaining their spherical harmonic representation at matching resolution, and from there in the modelling of induced gravity perturbations. We have therefore estimated spherical Bouguer and Airy isostatic anomalies whose spherical harmonic models are derived from the Earth's topography harmonic expansion. These spherical anomalies differ from the classical planar ones and may be used in the context of new applications. We succeeded in meeting a number of challenges to build spherical harmonic models with no theoretical limitation on the resolution. A specific algorithm was developed to enable the computation of associated Legendre functions to any degree and order. It was successfully tested up to degree 32,400. All analyses and syntheses were performed, in 64 bits arithmetic and with semi-empirical control of the significant terms to prevent from calculus underflows and overflows, according to IEEE limitations, also in preserving the speed of a specific regular grid processing scheme. Finally, the continuation from the reference ellipsoid's surface to the Earth's surface was performed by high-order Taylor expansion with all grids of required partial derivatives being computed in parallel. The main application was the production of a 1' × 1' equiangular global Bouguer anomaly grid which was computed by spherical harmonic analysis of the Earth's topography-bathymetry ETOPO1 data set up to degree and order 10,800, taking into account the precise boundaries and densities of major lakes and inner seas, with their own altitude, polar caps with bedrock information, and land areas below sea level. The harmonic coefficients for each entity were derived by analyzing the corresponding ETOPO1 part, and free surface data when required, at one arc minute resolution. The following approximations were made: the land, ocean and ice cap gravity spherical

Umbral oscillations and penumbral waves in H alpha. [in sunspots

NASA Technical Reports Server (NTRS)

Moore, R. L.; Tang, F.

1975-01-01

Examples are presented of umbral oscillations observed on Big Bear H-alpha filtergram movies, and the relation between umbral oscillations and running penumbral waves occurring in the same sunspot is investigated. Umbral oscillations near the center of the umbra are probably physically independent of the penumbral waves because the period of these umbral oscillations (150 sec) is shorter than the penumbral wave period (270 sec), but not a harmonic. Dark puffs emerge from the edge of the umbra and move outward across the penumbra, and have the same period as the running penumbral waves. These dark puffs are interpreted to be the extension of chromospheric umbral oscillations at the edge of the umbra. It is suggested that the dark puffs and the running penumbral waves have a common source: photospheric oscillations just inside the umbra.

The shifted harmonic approximation and asymptotic SU(2) and SU(1,1) Clebsch-Gordan coefficients

NASA Astrophysics Data System (ADS)

Rowe, D. J.; de Guise, Hubert

2010-12-01

Clebsch-Gordan coefficients of SU(2) and SU(1,1) are defined as eigenfunctions of a linear operator acting on the tensor product of the Hilbert spaces for two irreps of these groups. The shifted harmonic approximation is then used to solve these equations in asymptotic limits in which these eigenfunctions approach harmonic oscillator wavefunctions and thereby derive asymptotic expressions for these Clebsch-Gordan coefficients.

An oscillating dynamic model of collective cells in a monolayer

NASA Astrophysics Data System (ADS)

Lin, Shao-Zhen; Xue, Shi-Lei; Li, Bo; Feng, Xi-Qiao

2018-03-01

Periodic oscillations of collective cells occur in the morphogenesis and organogenesis of various tissues and organs. In this paper, an oscillating cytodynamic model is presented by integrating the chemomechanical interplay between the RhoA effector signaling pathway and cell deformation. We show that both an isolated cell and a cell aggregate can undergo spontaneous oscillations as a result of Hopf bifurcation, upon which the system evolves into a limit cycle of chemomechanical oscillations. The dynamic characteristics are tailored by the mechanical properties of cells (e.g., elasticity, contractility, and intercellular tension) and the chemical reactions involved in the RhoA effector signaling pathway. External forces are found to modulate the oscillation intensity of collective cells in the monolayer and to polarize their oscillations along the direction of external tension. The proposed cytodynamic model can recapitulate the prominent features of cell oscillations observed in a variety of experiments, including both isolated cells (e.g., spreading mouse embryonic fibroblasts, migrating amoeboid cells, and suspending 3T3 fibroblasts) and multicellular systems (e.g., Drosophila embryogenesis and oogenesis).

Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

NASA Technical Reports Server (NTRS)

Bogdan, V. M.; Bond, V. B.

1980-01-01

The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

Hypothesis driven single cell dual oscillator mathematical model of circadian rhythms

PubMed Central

S, Shiju

2017-01-01

Molecular mechanisms responsible for 24 h circadian oscillations, entrainment to external cues, encoding of day length and the time-of-day effects have been well studied experimentally. However, it is still debated from the molecular network point of view whether each cell in suprachiasmatic nuclei harbors two molecular oscillators, where one tracks dawn and the other tracks dusk activities. A single cell dual morning and evening oscillator was proposed by Daan et al., based on the molecular network that has two sets of similar non-redundant per1/cry1 and per2/cry2 circadian genes and each can independently maintain their endogenous oscillations. Understanding of dual oscillator dynamics in a single cell at molecular level may provide insight about the circadian mechanisms that encodes day length variations and its response to external zeitgebers. We present here a realistic dual oscillator model of circadian rhythms based on the series of hypotheses proposed by Daan et al., in which they conjectured that the circadian genes per1/cry1 track dawn while per2/cry2 tracks dusk and they together constitute the morning and evening oscillators (dual oscillator). Their hypothesis also provides explanations about the encoding of day length in terms of molecular mechanisms of per/cry expression. We frame a minimal mathematical model with the assumption that per1 acts a morning oscillator and per2 acts as an evening oscillator and to support and interpret this assumption we fit the model to the experimental data of per1/per2 circadian temporal dynamics, phase response curves (PRC's), and entrainment phenomena under various light-dark conditions. We also capture different patterns of splitting phenomena by coupling two single cell dual oscillators with neuropeptides vasoactive intestinal polypeptide (VIP) and arginine vasopressin (AVP) as the coupling agents and provide interpretation for the occurrence of splitting in terms of ME oscillators, though they are not required to

Hypothesis driven single cell dual oscillator mathematical model of circadian rhythms.

PubMed

S, Shiju; Sriram, K

2017-01-01

Molecular mechanisms responsible for 24 h circadian oscillations, entrainment to external cues, encoding of day length and the time-of-day effects have been well studied experimentally. However, it is still debated from the molecular network point of view whether each cell in suprachiasmatic nuclei harbors two molecular oscillators, where one tracks dawn and the other tracks dusk activities. A single cell dual morning and evening oscillator was proposed by Daan et al., based on the molecular network that has two sets of similar non-redundant per1/cry1 and per2/cry2 circadian genes and each can independently maintain their endogenous oscillations. Understanding of dual oscillator dynamics in a single cell at molecular level may provide insight about the circadian mechanisms that encodes day length variations and its response to external zeitgebers. We present here a realistic dual oscillator model of circadian rhythms based on the series of hypotheses proposed by Daan et al., in which they conjectured that the circadian genes per1/cry1 track dawn while per2/cry2 tracks dusk and they together constitute the morning and evening oscillators (dual oscillator). Their hypothesis also provides explanations about the encoding of day length in terms of molecular mechanisms of per/cry expression. We frame a minimal mathematical model with the assumption that per1 acts a morning oscillator and per2 acts as an evening oscillator and to support and interpret this assumption we fit the model to the experimental data of per1/per2 circadian temporal dynamics, phase response curves (PRC's), and entrainment phenomena under various light-dark conditions. We also capture different patterns of splitting phenomena by coupling two single cell dual oscillators with neuropeptides vasoactive intestinal polypeptide (VIP) and arginine vasopressin (AVP) as the coupling agents and provide interpretation for the occurrence of splitting in terms of ME oscillators, though they are not required to

Spherical harmonic analysis of a synoptic climatology generated with a global general circulation model

NASA Technical Reports Server (NTRS)

Christidis, Z. D.; Spar, J.

1980-01-01

Spherical harmonic analysis was used to analyze the observed climatological (C) fields of temperature at 850 mb, geopotential height at 500 mb, and sea level pressure. The spherical harmonic method was also applied to the corresponding "model climatological" fields (M) generated by a general circulation model, the "GISS climate model." The climate model was initialized with observed data for the first of December 1976 at 00. GMT and allowed to generate five years of meteorological history. Monthly means of the above fields for the five years were computed and subjected to spherical harmonic analysis. It was found from the comparison of the spectral components of both sets, M and C, that the climate model generated reasonable 500 mb geopotential heights. The model temperature field at 850 mb exhibited a generally correct structure. However, the meridional temperature gradient was overestimated and overheating of the continents was observed in summer.

Duffing revisited: phase-shift control and internal resonance in self-sustained oscillators

NASA Astrophysics Data System (ADS)

Arroyo, Sebastián I.; Zanette, Damián H.

2016-01-01

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, have intrinsic significance to the field of nonlinear 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, and provide analytical approximate expressions for the time dependence of the oscillation amplitude and frequency during transients. 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 when the resonance takes place, and present preliminary experimental results that illustrate the phenomenon. This synchronization process has been proposed to counteract the undesirable frequency-amplitude interdependence in nonlinear time-keeping micromechanical devices. Supplementary material in the form of one pdf file and one gif file available from the Journal web page at http://dx.doi.org/10.1140/epjb/e2015-60517-3

Inducing and destruction of chimeras and chimera-like states by an external harmonic force

NASA Astrophysics Data System (ADS)

Shepelev, I. A.; Vadivasova, T. E.

2018-03-01

We study the phenomena of chimera destruction and inducing of chimera-like states in an ensemble of nonlocally coupled chaotic Rössler oscillators under an external harmonic force. The localized harmonic influence can lead to both destruction and changing of the spatial topology of chimeras. At the same time this influence can cause the emergence of stable chimera-like states (induced chimeras) for the regime of partial coherent chaos. Induced chimeras are also observed for the global influence. We show the possibility of controlling the chimera-like state topology by varying the parameters of localized external harmonic influence.

A self-contained quantum harmonic engine

NASA Astrophysics Data System (ADS)

Reid, B.; Pigeon, S.; Antezza, M.; De Chiara, G.

2017-12-01

We propose a system made of three quantum harmonic oscillators as a compact quantum engine for producing mechanical work. The three oscillators play respectively the role of the hot bath, the working medium and the cold bath. The working medium performs an Otto cycle during which its frequency is changed and it is sequentially coupled to each of the two other oscillators. As the two environments are finite, the lifetime of the machine is finite and after a number of cycles it stops working and needs to be reset. Remarkably, we show that this machine can extract more than 90% of the available energy during 70 cycles. Differently from usually investigated infinite-reservoir configurations, this machine allows the protection of induced quantum correlations and we analyse the entanglement and quantum discord generated during the strokes. Interestingly, we show that high work generation is always accompanied by large quantum correlations. Our predictions can be useful for energy management at the nanoscale, and can be relevant for experiments with trapped ions and experiments with light in integrated optical circuits.

Oscillations in a simple climate-vegetation model

NASA Astrophysics Data System (ADS)

Rombouts, J.; Ghil, M.

2015-05-01

We formulate and analyze a simple dynamical systems model for climate-vegetation interaction. The planet we consider consists of a large ocean and a land surface on which vegetation can grow. The temperature affects vegetation growth on land and the amount of sea ice on the ocean. Conversely, vegetation and sea ice change the albedo of the planet, which in turn changes its energy balance and hence the temperature evolution. Our highly idealized, conceptual model is governed by two nonlinear, coupled ordinary differential equations, one for global temperature, the other for vegetation cover. The model exhibits either bistability between a vegetated and a desert state or oscillatory behavior. The oscillations arise through a Hopf bifurcation off the vegetated state, when the death rate of vegetation is low enough. These oscillations are anharmonic and exhibit a sawtooth shape that is characteristic of relaxation oscillations, as well as suggestive of the sharp deglaciations of the Quaternary. Our model's behavior can be compared, on the one hand, with the bistability of even simpler, Daisyworld-style climate-vegetation models. On the other hand, it can be integrated into the hierarchy of models trying to simulate and explain oscillatory behavior in the climate system. Rigorous mathematical results are obtained that link the nature of the feedbacks with the nature and the stability of the solutions. The relevance of model results to climate variability on various timescales is discussed.

Oscillations in a simple climate-vegetation model

NASA Astrophysics Data System (ADS)

Rombouts, J.; Ghil, M.

2015-02-01

We formulate and analyze a simple dynamical systems model for climate-vegetation interaction. The planet we consider consists of a large ocean and a land surface on which vegetation can grow. The temperature affects vegetation growth on land and the amount of sea ice on the ocean. Conversely, vegetation and sea ice change the albedo of the planet, which in turn changes its energy balance and hence the temperature evolution. Our highly idealized, conceptual model is governed by two nonlinear, coupled ordinary differential equations, one for global temperature, the other for vegetation cover. The model exhibits either bistability between a vegetated and a desert state or oscillatory behavior. The oscillations arise through a Hopf bifurcation off the vegetated state, when the death rate of vegetation is low enough. These oscillations are anharmonic and exhibit a sawtooth shape that is characteristic of relaxation oscillations, as well as suggestive of the sharp deglaciations of the Quaternary. Our model's behavior can be compared, on the one hand, with the bistability of even simpler, Daisyworld-style climate-vegetation models. On the other hand, it can be integrated into the hierarchy of models trying to simulate and explain oscillatory behavior in the climate system. Rigorous mathematical results are obtained that link the nature of the feedbacks with the nature and the stability of the solutions. The relevance of model results to climate variability on various time scales is discussed.

Pole movement in electronic and optoelectronic oscillators

NASA Astrophysics Data System (ADS)

Chatterjee, S.; Pal, S.; Biswas, B. N.

2013-12-01

An RLC circuit with poles on the left half of the complex frequency plane is capable of executing transient oscillations. During this period, energy conversion from potential to kinetic and from kinetic to potential continuously goes on, until the stored energy is lost in dissipation through the resistance. On the other hand, in an electronic or opto-electronic oscillator with an embedded RLC circuit, the poles are forcibly placed on the right-half plane (RHP) and as far as practicable away from the imaginary axis in order to help the growth of oscillation as quickly as possible. And ultimately, it is imagined that, like the case of an ideal linear harmonic oscillator, the poles are frozen on the imaginary axis so that the oscillation neither grows nor decays. The authors feel that this act of holding the poles right on the imaginary axis is a theoretical conjecture in a soft or hard self-excited oscillator. In this article, a detailed discussion on pole movement in an electronic and opto-electronic oscillator is carried out from the basic concept. A new analytical method for estimating the time-dependent part of the pole is introduced here.

Near-threshold harmonics from a femtosecond enhancement cavity-based EUV source: effects of multiple quantum pathways on spatial profile and yield.

PubMed

Hammond, T J; Mills, Arthur K; Jones, David J

2011-12-05

We investigate the photon flux and far-field spatial profiles for near-threshold harmonics produced with a 66 MHz femtosecond enhancement cavity-based EUV source operating in the tight-focus regime. The effects of multiple quantum pathways in the far-field spatial profile and harmonic yield show a strong dependence on gas jet dynamics, particularly nozzle diameter and position. This simple system, consisting of only a 700 mW Ti:Sapphire oscillator and an enhancement cavity produces harmonics up to 20 eV with an estimated 30-100 μW of power (intracavity) and > 1μW (measured) of power spectrally-resolved and out-coupled from the cavity. While this power is already suitable for applications, a quantum mechanical model of the system indicates substantial improvements should be possible with technical upgrades.

Synchronization of chaotic and nonchaotic oscillators: Application to bipolar disorder

NASA Astrophysics Data System (ADS)

Nono Dueyou Buckjohn, C.; Siewe Siewe, M.; Tchawoua, C.; Kofane, T. C.

2010-08-01

In this Letter, we use a synchronization scheme on two bipolar disorder models consisting of a strong nonlinear system with multiplicative excitation and a nonlinear oscillator without parametric harmonic forcing. The stability condition following our control function is analytically demonstrated using the Lyapunov theory and Routh-Hurwitz criteria, we then have the condition for the existence of a feedback gain matrix. A convenient demonstration of the accuracy of the method is complemented by the numerical simulations from which we illustrate the synchronized dynamics between the two non-identical bipolar disorder patients.

Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators.

PubMed

Hong, Hyunsuk; Strogatz, Steven H

2011-02-04

We consider a generalization of the Kuramoto model in which the oscillators are coupled to the mean field with random signs. Oscillators with positive coupling are "conformists"; they are attracted to the mean field and tend to synchronize with it. Oscillators with negative coupling are "contrarians"; they are repelled by the mean field and prefer a phase diametrically opposed to it. The model is simple and exactly solvable, yet some of its behavior is surprising. Along with the stationary states one might have expected (a desynchronized state, and a partially-synchronized state, with conformists and contrarians locked in antiphase), it also displays a traveling wave, in which the mean field oscillates at a frequency different from the population's mean natural frequency.

On Discontinuous Piecewise Linear Models for Memristor Oscillators

NASA Astrophysics Data System (ADS)

Amador, Andrés; Freire, Emilio; Ponce, Enrique; Ros, Javier

2017-06-01

In this paper, we provide for the first time rigorous mathematical results regarding the rich dynamics of piecewise linear memristor oscillators. In particular, for each nonlinear oscillator given in [Itoh & Chua, 2008], we show the existence of an infinite family of invariant manifolds and that the dynamics on such manifolds can be modeled without resorting to discontinuous models. Our approach provides topologically equivalent continuous models with one dimension less but with one extra parameter associated to the initial conditions. It is possible to justify the periodic behavior exhibited by three-dimensional memristor oscillators, by taking advantage of known results for planar continuous piecewise linear systems. The analysis developed not only confirms the numerical results contained in previous works [Messias et al., 2010; Scarabello & Messias, 2014] but also goes much further by showing the existence of closed surfaces in the state space which are foliated by periodic orbits. The important role of initial conditions that justify the infinite number of periodic orbits exhibited by these models, is stressed. The possibility of unsuspected bistable regimes under specific configurations of parameters is also emphasized.

NONLINEAR OPTICS PHENOMENA: Second harmonic generation from DF laser radiation in ZnGeP2

NASA Astrophysics Data System (ADS)

Andreev, Yu M.; Velikanov, S. D.; Yerutin, A. S.; Zapol'skiĭ, A. F.; Konkin, D. V.; Mishkin, S. N.; Smirnov, S. V.; Frolov, Yu N.; Shchurov, V. V.

1992-11-01

We have succeeded in generating the second harmonic of the radiation from a DF laser for the first time, using single crystals of ZnGeP2. For crystals with lengths of 10.1 and 13.6 mm, the overall external efficiencies of the entire oscillator system were 4 and 6.2%. The internal efficiencies of second-harmonic generation in the crystals were 7.6 and 11.8%, respectively.

Time delay in the Kuramoto model of coupled-phase oscillators

NASA Astrophysics Data System (ADS)

Yeung, Man Kit Stephen

1999-10-01

The Kuramoto model is a mean-field model of coupled phase oscillators with distributed natural frequencies. It was proposed to study collective synchronization in large systems of nonlinear oscillators. Here we generalize this model to allow time-delayed interactions. Despite the delay, synchronization is still possible. We derive exact stability conditions for the incoherent state, and for synchronized states and clustering states in the special case of noiseless identical oscillators. We also study the bifurcations of these states. We find that the incoherent state loses stability in a Hopf bifurcation. In the absence of noise, this leads to partial synchrony, where some oscillators are entrained to a common frequency. New phenomena caused by the delay include multistability among synchronization, incoherence, and clustering; and unsteady solutions with time-dependent order parameters. The experimental implications of the model are discussed for populations of chirping crickets, where the finite speed of sound causes communication delays, and for physical systems such as coupled phase- locked loops, lasers, and communication satellites.

Maintenance and suppression of chaos by weak harmonic perturbations: a unified view.

PubMed

Chacón, R

2001-02-26

General results concerning maintenance or enhancement of chaos are presented for dissipative systems subjected to two harmonic perturbations (one chaos inducing and the other chaos enhancing). The connection with previous results on chaos suppression is also discussed in a general setting. It is demonstrated that, in general, a second harmonic perturbation can reliably play an enhancer or inhibitor role by solely adjusting its initial phase. Numerical results indicate that general theoretical findings concerning periodic chaos-inducing perturbations also work for aperiodic chaos-inducing perturbations, and in arrays of identical chaotic coupled oscillators.

A simple model of intraseasonal oscillations

NASA Astrophysics Data System (ADS)

Fuchs, Željka; Raymond, David J.

2017-06-01

The intraseasonal oscillations and in particular the MJO have been and still remain a "holy grail" of today's atmospheric science research. Why does the MJO propagate eastward? What makes it unstable? What is the scaling for the MJO, i.e., why does it prefer long wavelengths or planetary wave numbers 1-3? What is the westward moving component of the intraseasonal oscillation? Though linear WISHE has long been discounted as a plausible model for intraseasonal oscillations and the MJO, the version we have developed explains many of the observed features of those phenomena, in particular, the preference for large zonal scale. In this model version, the moisture budget and the increase of precipitation with tropospheric humidity lead to a "moisture mode." The destabilization of the large-scale moisture mode occurs via WISHE only and there is no need to postulate large-scale radiatively induced instability or negative effective gross moist stability. Our WISHE-moisture theory leads to a large-scale unstable eastward propagating mode in n = -1 case and a large-scale unstable westward propagating mode in n = 1 case. We suggest that the n = -1 case might be connected to the MJO and the observed westward moving disturbance to the observed equatorial Rossby mode.

Frictional-faulting model for harmonic tremor before Redoubt Volcano eruptions

NASA Astrophysics Data System (ADS)

Dmitrieva, Ksenia; Hotovec-Ellis, Alicia J.; Prejean, Stephanie; Dunham, Eric M.

2013-08-01

Seismic unrest, indicative of subsurface magma transport and pressure changes within fluid-filled cracks and conduits, often precedes volcanic eruptions. An intriguing form of volcano seismicity is harmonic tremor, that is, sustained vibrations in the range of 0.5-5Hz. Many source processes can generate harmonic tremor. Harmonic tremor in the 2009 eruption of Redoubt Volcano, Alaska, has been linked to repeating earthquakes of magnitudes around 0.5-1.5 that occur a few kilometres beneath the vent. Before many explosions in that eruption, these small earthquakes occurred in such rapid succession--up to 30 events per second--that distinct seismic wave arrivals blurred into continuous, high-frequency tremor. Tremor abruptly ceased about 30 s before the explosions. Here we introduce a frictional-faulting model to evaluate the credibility and implications of this tremor mechanism. We find that the fault stressing rates rise to values ten orders of magnitude higher than in typical tectonic settings. At that point, inertial effects stabilize fault sliding and the earthquakes cease. Our model of the Redoubt Volcano observations implies that the onset of volcanic explosions is preceded by active deformation and extreme stressing within a localized region of the volcano conduit, at a depth of several kilometres.

Frictional-faulting model for harmonic tremor before Redoubt Volcano eruptions

USGS Publications Warehouse

Dmitrieva, Ksenia; Hotovec-Ellis, Alicia J.; Prejean, Stephanie G.; Dunham, Eric M.

2013-01-01

Seismic unrest, indicative of subsurface magma transport and pressure changes within fluid-filled cracks and conduits, often precedes volcanic eruptions. An intriguing form of volcano seismicity is harmonic tremor, that is, sustained vibrations in the range of 0.5–5 Hz. Many source processes can generate harmonic tremor. Harmonic tremor in the 2009 eruption of Redoubt Volcano, Alaska, has been linked to repeating earthquakes of magnitudes around 0.5–1.5 that occur a few kilometres beneath the vent. Before many explosions in that eruption, these small earthquakes occurred in such rapid succession—up to 30 events per second—that distinct seismic wave arrivals blurred into continuous, high-frequency tremor. Tremor abruptly ceased about 30 s before the explosions. Here we introduce a frictional-faulting model to evaluate the credibility and implications of this tremor mechanism. We find that the fault stressing rates rise to values ten orders of magnitude higher than in typical tectonic settings. At that point, inertial effects stabilize fault sliding and the earthquakes cease. Our model of the Redoubt Volcano observations implies that the onset of volcanic explosions is preceded by active deformation and extreme stressing within a localized region of the volcano conduit, at a depth of several kilometres.

Method of Harmonic Balance in Full-Scale-Model Tests of Electrical Devices

NASA Astrophysics Data System (ADS)

Gorbatenko, N. I.; Lankin, A. M.; Lankin, M. V.

2017-01-01

Methods for determining the weber-ampere characteristics of electrical devices, one of which is based on solution of direct problem of harmonic balance and the other on solution of inverse problem of harmonic balance by the method of full-scale-model tests, are suggested. The mathematical model of the device is constructed using the describing function and simplex optimization methods. The presented results of experimental applications of the method show its efficiency. The advantage of the method is the possibility of application for nondestructive inspection of electrical devices in the processes of their production and operation.

Synchronization of multi-phase oscillators: an Axelrod-inspired model

NASA Astrophysics Data System (ADS)

Kuperman, M. N.; Zanette, D. H.

2009-07-01

Inspired by Axelrod’s model of culture dissemination, we introduce and analyze a model for a population of coupled oscillators where different levels of synchronization can be assimilated to different degrees of cultural organization. The state of each oscillator is represented by a set of phases, and the interaction - which occurs between homologous phases - is weighted by a decreasing function of the distance between individual states. Both ordered arrays and random networks are considered. We find that the transition between synchronization and incoherent behaviour is mediated by a clustering regime with rich organizational structure, where any two oscillators can be synchronized in some of their phases, while their remain unsynchronized in the others.

Isgur-Karl model revisited

DOE Office of Scientific and Technical Information (OSTI.GOV)

Galeta, Leonardo; Pirjol, Dan; Schat, Carlos

2009-12-01

We show how to match the Isgur-Karl model to the spin-flavor quark operator expansion used in the 1/N{sub c} studies of the nonstrange negative parity L=1 excited baryons. Using the transformation properties of states and interactions under the permutation group S{sub 3} we are able to express the operator coefficients as overlap integrals, without making any assumption on the spatial dependence of the quark wave functions. The general mass operator leads to parameter free mass relations and constraints on the mixing angles that are valid beyond the usual harmonic oscillator approximation. The Isgur-Karl model with harmonic oscillator wave functions providesmore » a simple counterexample that demonstrates explicitly that the alternative operator basis for the 1/N{sub c} expansion for excited baryons recently proposed by Matagne and Stancu is incomplete.« less

Supersonic flow past oscillating airfoils including nonlinear thickness effects

NASA Technical Reports Server (NTRS)

Van Dyke, Milton D

1954-01-01

A solution to second order in thickness is derived for harmonically oscillating two-dimensional airfoils in supersonic flow. For slow oscillations of an arbitrary profile, the result is found as a series including the third power of frequency. For arbitrary frequencies, the method of solution for any specific profile is indicated, and the explicit solution derived for a single wedge. Nonlinear thickness effects are found generally to reduce the torsional damping, and so enlarge the range of Mach numbers within which torsional instability is possible.

On the spring and mass of the Dirac oscillator

NASA Technical Reports Server (NTRS)

Crawford, James P.

1993-01-01

The Dirac oscillator is a relativistic generalization of the quantum harmonic oscillator. In particular, the square of the Hamiltonian for the Dirac oscillator yields the Klein-Gordon equation with a potential of the form: (ar(sub 2) + b(L x S)), where a and b are constants. To obtain the Dirac oscillator, a 'minimal substitution' is made in the Dirac equation, where the ordinary derivative is replaced with a covariant derivative. However, an unusual feature of the covariant derivative in this case is that the potential is a non-trivial element of the Clifford algebra. A theory which naturally gives rise to gage potentials which are non-trivial elements of the Clifford algebra is that based on local automorphism invariance. An exact solution of the automorphism gage field equations which reproduces both the potential term and the mass term of the Dirac oscillator is presented.

Phase computations and phase models for discrete molecular oscillators.

PubMed

Suvak, Onder; Demir, Alper

2012-06-11

Biochemical oscillators perform crucial functions in cells, e.g., they set up circadian clocks. The dynamical behavior of oscillators is best described and analyzed in terms of the scalar quantity, phase. A rigorous and useful definition for phase is based on the so-called isochrons of oscillators. Phase computation techniques for continuous oscillators that are based on isochrons have been used for characterizing the behavior of various types of oscillators under the influence of perturbations such as noise. In this article, we extend the applicability of these phase computation methods to biochemical oscillators as discrete molecular systems, upon the information obtained from a continuous-state approximation of such oscillators. In particular, we describe techniques for computing the instantaneous phase of discrete, molecular oscillators for stochastic simulation algorithm generated sample paths. We comment on the accuracies and derive certain measures for assessing the feasibilities of the proposed phase computation methods. Phase computation experiments on the sample paths of well-known biological oscillators validate our analyses. The impact of noise that arises from the discrete and random nature of the mechanisms that make up molecular oscillators can be characterized based on the phase computation techniques proposed in this article. The concept of isochrons is the natural choice upon which the phase notion of oscillators can be founded. The isochron-theoretic phase computation methods that we propose can be applied to discrete molecular oscillators of any dimension, provided that the oscillatory behavior observed in discrete-state does not vanish in a continuous-state approximation. Analysis of the full versatility of phase noise phenomena in molecular oscillators will be possible if a proper phase model theory is developed, without resorting to such approximations.

Realization of a new concept for visible frequency division: phase locking of harmonic and sum frequencies.

PubMed

Telle, H R; Meschede, D; Hänsch, T W

1990-05-15

We explore and demonstrate the feasibility of an optical-frequency-to-radio-frequency division method that is based on visible or near-infrared laser oscillators only. Comparing harmonic and sum frequencies, we generate the arithmetic average of two visible frequencies. Cascading n stages provides difference-frequency division by 2(n). For a demonstration we have phase locked the second harmonic and the sum frequency of two independent diode lasers.

Automated analysis of biological oscillator models using mode decomposition.

PubMed

Konopka, Tomasz

2011-04-01

Oscillating signals produced by biological systems have shapes, described by their Fourier spectra, that can potentially reveal the mechanisms that generate them. Extracting this information from measured signals is interesting for the validation of theoretical models, discovery and classification of interaction types, and for optimal experiment design. An automated workflow is described for the analysis of oscillating signals. A software package is developed to match signal shapes to hundreds of a priori viable model structures defined by a class of first-order differential equations. The package computes parameter values for each model by exploiting the mode decomposition of oscillating signals and formulating the matching problem in terms of systems of simultaneous polynomial equations. On the basis of the computed parameter values, the software returns a list of models consistent with the data. In validation tests with synthetic datasets, it not only shortlists those model structures used to generate the data but also shows that excellent fits can sometimes be achieved with alternative equations. The listing of all consistent equations is indicative of how further invalidation might be achieved with additional information. When applied to data from a microarray experiment on mice, the procedure finds several candidate model structures to describe interactions related to the circadian rhythm. This shows that experimental data on oscillators is indeed rich in information about gene regulation mechanisms. The software package is available at http://babylone.ulb.ac.be/autoosc/.

The role of the Southern Hemisphere semiannual oscillation in the development of a precursor to central and eastern Pacific Southern Oscillation warm events

NASA Astrophysics Data System (ADS)

Meehl, Gerald A.; van Loon, Harry; Arblaster, Julie M.

2017-07-01

The semiannual oscillation (SAO) is a twice-yearly northward movement (in May-June-July (MJJ) and November-December-January (NDJ)) of the circumpolar trough of sea level pressure (SLP) in the Southern Hemisphere with effects throughout the troposphere. During MJJ the second harmonic of SLP, describing the SAO, has low values of SLP north of 50°S in the subtropical South Pacific, while the first harmonic, which is dominant over the Australian sector, increases to its peak. This once-a-year peak in negative SLP gradients (decreasing to the east) between Australia and the ocean to its east extends to the equatorial Pacific. Southern Oscillation warm events since 1950, with an intensification of this seasonal cycle, have larger-amplitude SST anomalies in the eastern equatorial Pacific in MJJ and during the following mature phase in NDJ. Weak amplification of the seasonal cycle in MJJ tends to be followed by larger-amplitude SST anomalies in the central equatorial Pacific during NDJ.

A Parametric Oscillator Experiment for Undergraduates

NASA Astrophysics Data System (ADS)

Huff, Alison; Thompson, Johnathon; Pate, Jacob; Kim, Hannah; Chiao, Raymond; Sharping, Jay

We describe an upper-division undergraduate-level analytic mechanics experiment or classroom demonstration of a weakly-damped pendulum driven into parametric resonance. Students can derive the equations of motion from first principles and extract key oscillator features, such as quality factor and parametric gain, from experimental data. The apparatus is compact, portable and easily constructed from inexpensive components. Motion control and data acquisition are accomplished using an Arduino micro-controller incorporating a servo motor, laser sensor, and data logger. We record the passage time of the pendulum through its equilibrium position and obtain the maximum speed per oscillation as a function of time. As examples of the interesting physics which the experiment reveals, we present contour plots depicting the energy of the system as functions of driven frequency and modulation depth. We observe the transition to steady state oscillation and compare the experimental oscillation threshold with theoretical expectations. A thorough understanding of this hands-on laboratory exercise provides a foundation for current research in quantum information and opto-mechanics, where damped harmonic motion, quality factor, and parametric amplification are central.

Oscillation characteristics of endodontic files: numerical model and its validation.

PubMed

Verhaagen, Bram; Lea, Simon C; de Bruin, Gerrit J; van der Sluis, Luc W M; Walmsley, A Damien; Versluis, Michel

2012-11-01

During a root canal treatment, an antimicrobial fluid is injected into the root canal to eradicate all bacteria from the root canal system. Agitation of the fluid using an ultrasonically vibrating miniature file results in a significant improvement in the cleaning efficacy over conventional syringe irrigation. Numerical analysis of the oscillation characteristics of the file, modeled as a tapered, driven rod, shows a sinusoidal wave pattern with an increase in amplitude and decrease in wavelength toward the free end of the file. Measurements of the file oscillation with a scanning laser vibrometer show good agreement with the numerical simulation. The numerical model of endodontic file oscillation has the potential for predicting the oscillation pattern and fracture likeliness of various file types and the acoustic streaming they induce during passive ultrasonic irrigation.

Long-term operation of surface high-harmonic generation from relativistic oscillating mirrors using a spooling tape

DOE PAGES

Bierbach, Jana; Yeung, Mark; Eckner, Erich; ...

2015-05-01

Surface high-harmonic generation in the relativistic regime is demonstrated as a source of extreme ultra-violet (XUV) pulses with extended operation time. Relativistic high-harmonic generation is driven by a frequency-doubled high-power Ti:Sapphire laser focused to a peak intensity of 3·1019 W/cm2 onto spooling tapes. We demonstrate continuous operation over up to one hour runtime at a repetition rate of 1 Hz. Harmonic spectra ranging from 20 eV to 70 eV (62 nm to 18 nm) were consecutively recorded by an XUV spectrometer. An average XUV pulse energy in the µJ range is measured. With the presented setup, relativistic surface high-harmonic generationmore » becomes a powerful source of coherent XUV pulses that might enable applications in, e.g. attosecond laser physics and the seeding of free-electron lasers, when the laser issues causing 80-% pulse energy fluctuations are overcome.« less

A flight investigation of oscillating air forces: Equipment and technique

NASA Technical Reports Server (NTRS)

Reed, W. H., III

1975-01-01

The equipment and techniques are described which are to be used in a project aimed at measuring oscillating air forces and dynamic aeroelastic response of a swept wing airplane at high subsonic speeds. Electro-hydraulic inertia type shakers installed in the wing tips will excite various elastic airplane modes while the related oscillating chordwise pressures at two spanwise wing stations and the wing mode shapes are recorded on magnetic tape. The data reduction technique, following the principle of a wattmeter harmonic analyzer employed by Bratt, Wight, and Tilly, utilizes magnetic tape and high speed electronic multipliers to record directly the real and imaginary components of oscillatory data signals relative to a simple harmonic reference signal. Through an extension of this technique an automatic flight-flutter-test data analyzer is suggested in which vector plots of mechanical admittance or impedance would be plotted during the flight test.

Chimera states in nonlocally coupled phase oscillators with biharmonic interaction

NASA Astrophysics Data System (ADS)

Cheng, Hongyan; Dai, Qionglin; Wu, Nianping; Feng, Yuee; Li, Haihong; Yang, Junzhong

2018-03-01

Chimera states, which consist of coexisting domains of coherent and incoherent parts, have been observed in a variety of systems. Most of previous works on chimera states have taken into account specific form of interaction between oscillators, for example, sinusoidal coupling or diffusive coupling. Here, we investigate chimera dynamics in nonlocally coupled phase oscillators with biharmonic interaction. We find novel chimera states with features such as that oscillators in the same coherent cluster may split into two groups with a phase difference around π/2 and that oscillators in adjacent coherent clusters may have a phase difference close to π/2. The different impacts of the coupling ranges in the first and the second harmonic interactions on chimera dynamics are investigated based on the synchronous dynamics in globally coupled phase oscillators. Our study suggests a new direction in the field of chimera dynamics.

Zonal harmonic model of Saturn's magnetic field from Voyager 1 and 2 observations

NASA Technical Reports Server (NTRS)

Connerney, J. E. P.; Ness, N. F.; Acuna, M. H.

1982-01-01

An analysis of the magnetic field of Saturn is presented which takes into account both the Voyager 1 and 2 vector magnetic field observations. The analysis is based on the traditional spherical harmonic expansion of a scale potential to derive the magnetic field within 8 Saturn radii. A third-order zonal harmonic model fitted to Voyager 1 and 2 observations is found to be capable of predicting the magnetic field characteristics at one encounter based on those observed at another, unlike models including dipole and quadrupole terms only. The third-order model is noted to lead to significantly enhanced polar surface field intensities with respect to dipole models, and probably represents the axisymmetric part of a complex dynamo field.

Bright high-order harmonic generation with controllable polarization from a relativistic plasma mirror

PubMed Central

Chen, Zi-Yu; Pukhov, Alexander

2016-01-01

Ultrafast extreme ultraviolet (XUV) sources with a controllable polarization state are powerful tools for investigating the structural and electronic as well as the magnetic properties of materials. However, such light sources are still limited to only a few free-electron laser facilities and, very recently, to high-order harmonic generation from noble gases. Here we propose and numerically demonstrate a laser–plasma scheme to generate bright XUV pulses with fully controlled polarization. In this scheme, an elliptically polarized laser pulse is obliquely incident on a plasma surface, and the reflected radiation contains pulse trains and isolated circularly or highly elliptically polarized attosecond XUV pulses. The harmonic polarization state is fully controlled by the laser–plasma parameters. The mechanism can be explained within the relativistically oscillating mirror model. This scheme opens a practical and promising route to generate bright attosecond XUV pulses with desirable ellipticities in a straightforward and efficient way for a number of applications. PMID:27531047

Phase computations and phase models for discrete molecular oscillators

PubMed Central

2012-01-01

Background Biochemical oscillators perform crucial functions in cells, e.g., they set up circadian clocks. The dynamical behavior of oscillators is best described and analyzed in terms of the scalar quantity, phase. A rigorous and useful definition for phase is based on the so-called isochrons of oscillators. Phase computation techniques for continuous oscillators that are based on isochrons have been used for characterizing the behavior of various types of oscillators under the influence of perturbations such as noise. Results In this article, we extend the applicability of these phase computation methods to biochemical oscillators as discrete molecular systems, upon the information obtained from a continuous-state approximation of such oscillators. In particular, we describe techniques for computing the instantaneous phase of discrete, molecular oscillators for stochastic simulation algorithm generated sample paths. We comment on the accuracies and derive certain measures for assessing the feasibilities of the proposed phase computation methods. Phase computation experiments on the sample paths of well-known biological oscillators validate our analyses. Conclusions The impact of noise that arises from the discrete and random nature of the mechanisms that make up molecular oscillators can be characterized based on the phase computation techniques proposed in this article. The concept of isochrons is the natural choice upon which the phase notion of oscillators can be founded. The isochron-theoretic phase computation methods that we propose can be applied to discrete molecular oscillators of any dimension, provided that the oscillatory behavior observed in discrete-state does not vanish in a continuous-state approximation. Analysis of the full versatility of phase noise phenomena in molecular oscillators will be possible if a proper phase model theory is developed, without resorting to such approximations. PMID:22687330

Spectral Analysis of Vibrational Harmonic Motion by use of a Continuous-Wave CO2 Doppler Lidar

NASA Technical Reports Server (NTRS)

Jarzembski, Maurice A.; Srivastava, Vandana

1999-01-01

Vibrational motion of a harmonic oscillator was investigated using a focused continuous wave CO2 Doppler lidar at 9.1 microns wavelength. A continuum of frequencies along with many discrete, equally spaced, resonant frequency modes was observed. The frequency modes are similar in structure to the oscillatory longitudinal modes of a laser cavity and arise because of interference of the natural resonant frequency of the oscillator with specific frequencies within the continuum. The spectra revealed departures from linear motion for vigorous vibrations of the oscillator. Each consecutive resonant frequency mode occurred for a movement of the oscillator much less than the wavelength of incident lidar radiation.

Noise induced oscillations and coherence resonance in a generic model of the nonisothermal chemical oscillator

PubMed Central

Simakov, David S. A.; Pérez-Mercader, Juan

2013-01-01

Oscillating chemical reactions are common in biological systems and they also occur in artificial non-biological systems. Generally, these reactions are subject to random fluctuations in environmental conditions which translate into fluctuations in the values of physical variables, for example, temperature. We formulate a mathematical model for a nonisothermal minimal chemical oscillator containing a single negative feedback loop and study numerically the effects of stochastic fluctuations in temperature in the absence of any deterministic limit cycle or periodic forcing. We show that noise in temperature can induce sustained limit cycle oscillations with a relatively narrow frequency distribution and some characteristic frequency. These properties differ significantly depending on the noise correlation. Here, we have explored white and colored (correlated) noise. A plot of the characteristic frequency of the noise induced oscillations as a function of the correlation exponent shows a maximum, therefore indicating the existence of autonomous stochastic resonance, i.e. coherence resonance. PMID:23929212

Nonlinear oscillations in a muscle pacemaker cell model

NASA Astrophysics Data System (ADS)

González-Miranda, J. M.

2017-02-01

This article presents a numerical simulation study of the nonlinear oscillations displayed by the Morris-Lecar model [Biophys. J. 35 (1981) 193] for the oscillations experimentally observed in the transmembrane potential of a muscle fiber subject to an external electrical stimulus. We consider the model in the case when there is no external stimulation, aiming to establish the ability of the model to display biophysically reasonable pacemaker dynamics. We obtain 2D bifurcation diagrams showing that indeed the model presents oscillatory dynamics, displaying the two main types of action potentials that are observed in muscle fibers. The results obtained are shown to be structurally stable; that is, robust against changes in the values of system parameters. Moreover, it is demonstrated how the model is appropriate to analyze the action potentials observed in terms of the transmembrane currents creating them.

Wind tunnel wall effects in a linear oscillating cascade

NASA Technical Reports Server (NTRS)

Buffum, Daniel H.; Fleeter, Sanford

1991-01-01

Experiments in a linear oscillating cascade reveal that the wind tunnel walls enclosing the airfoils have, in some cases, a detrimental effect on the oscillating cascade aerodynamics. In a subsonic flow field, biconvex airfoils are driven simultaneously in harmonic, torsion-mode oscillations for a range of interblade phase angle values. It is found that the cascade dynamic periodicity - the airfoil to airfoil variation in unsteady surface pressure - is good for some values of interblade phase angle but poor for others. Correlation of the unsteady pressure data with oscillating flat plate cascade predictions is generally good for conditions where the periodicity is good and poor where the periodicity is poor. Calculations based upon linearized unsteady aerodynamic theory indicate that pressure waves reflected from the wind tunnel walls are responsible for the cases where there is poor periodicity and poor correlation with the predictions.

Energetics of oscillating lifting surfaces using integral conservation laws

NASA Technical Reports Server (NTRS)

Ahmadi, Ali R.; Widnall, Sheila E.

1987-01-01

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

The Generalized Uncertainty Principle and Harmonic Interaction in Three Spatial Dimensions

NASA Astrophysics Data System (ADS)

Hassanabadi, H.; Hooshmand, P.; Zarrinkamar, S.

2015-01-01

In three spatial dimensions, the generalized uncertainty principle is considered under an isotropic harmonic oscillator interaction in both non-relativistic and relativistic regions. By using novel transformations and separations of variables, the exact analytical solution of energy eigenvalues as well as the wave functions is obtained. Time evolution of the non-relativistic region is also reported.

The effect of delays on filament oscillations and stability

NASA Astrophysics Data System (ADS)

van den Oord, G. H. J.; Schutgens, N. A. J.; Kuperus, M.

1998-11-01

We discuss the linear response of a filament to perturbations, taking the finite communication time between the filament and the photosphere into account. The finite communication time introduces delays in the system. Recently Schutgens (1997ab) investigated the solutions of the delay equation for vertical perturbations. In this paper we expand his analysis by considering also horizontal and coupled oscillations. The latter occur in asymmetric coronal fields. We also discuss the effect of Alfven wave emission on filament oscillations and show that wave emission is important for stabilizing filaments. We introduce a fairly straightforward method to study the solutions of delay equations as a function of the filament-photosphere communication time. A solution can be described by a linear combination of damped harmonic oscillations each characterized by a frequency, a damping/growth time and, accordingly, a quality factor. As a secondary result of our analysis we show that, within the context of line current models, Kippenhahn/Schlüter-type filament equilibria can never be stable in the horizontal and the vertical direction at the same time but we also demonstrate that Kuperus/Raadu-type equilibria can account for both an inverse or a normal polarity signature. The diagnostic value of our analysis for determining, e.g., the filament current from observations of oscillating filaments is discussed.

Rapid automated superposition of shapes and macromolecular models using spherical harmonics.

PubMed

Konarev, Petr V; Petoukhov, Maxim V; Svergun, Dmitri I

2016-06-01

A rapid algorithm to superimpose macromolecular models in Fourier space is proposed and implemented ( SUPALM ). The method uses a normalized integrated cross-term of the scattering amplitudes as a proximity measure between two three-dimensional objects. The reciprocal-space algorithm allows for direct matching of heterogeneous objects including high- and low-resolution models represented by atomic coordinates, beads or dummy residue chains as well as electron microscopy density maps and inhomogeneous multi-phase models ( e.g. of protein-nucleic acid complexes). Using spherical harmonics for the computation of the amplitudes, the method is up to an order of magnitude faster than the real-space algorithm implemented in SUPCOMB by Kozin & Svergun [ J. Appl. Cryst. (2001 ▸), 34 , 33-41]. The utility of the new method is demonstrated in a number of test cases and compared with the results of SUPCOMB . The spherical harmonics algorithm is best suited for low-resolution shape models, e.g . those provided by solution scattering experiments, but also facilitates a rapid cross-validation against structural models obtained by other methods.

Oscillations of a Meterstick on Two Rotating Shafts

ERIC Educational Resources Information Center

Balta, Nuri

2016-01-01

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

A statistical model of the human core-temperature circadian rhythm

NASA Technical Reports Server (NTRS)

Brown, E. N.; Choe, Y.; Luithardt, H.; Czeisler, C. A.

2000-01-01

We formulate a statistical model of the human core-temperature circadian rhythm in which the circadian signal is modeled as a van der Pol oscillator, the thermoregulatory response is represented as a first-order autoregressive process, and the evoked effect of activity is modeled with a function specific for each circadian protocol. The new model directly links differential equation-based simulation models and harmonic regression analysis methods and permits statistical analysis of both static and dynamical properties of the circadian pacemaker from experimental data. We estimate the model parameters by using numerically efficient maximum likelihood algorithms and analyze human core-temperature data from forced desynchrony, free-run, and constant-routine protocols. By representing explicitly the dynamical effects of ambient light input to the human circadian pacemaker, the new model can estimate with high precision the correct intrinsic period of this oscillator ( approximately 24 h) from both free-run and forced desynchrony studies. Although the van der Pol model approximates well the dynamical features of the circadian pacemaker, the optimal dynamical model of the human biological clock may have a harmonic structure different from that of the van der Pol oscillator.

Angular dependence of novel magnetic quantum oscillations in a quasi-two-dimensional multiband Fermi liquid with impurities

NASA Astrophysics Data System (ADS)

Bratkovsky, A. M.; Alexandrov, A. S.

2002-03-01

The semiclassical Lifshitz-Kosevich-type description is given for the angular dependence of quantum oscillations with combination frequencies in a multiband quasi-two-dimensional Fermi liquid with a constant number of electrons. The analytical expressions are found for the Dingle, thermal, spin, and amplitude (Yamaji) reduction factors of the novel combination harmonics, where the latter two strongly oscillate with the direction of the field [1]. At the magic angles those factors reduce to the purely two-dimensional expressions given earlier. The combination harmonics are suppressed in the presence of the nonquantized background states, and they decay exponentially faster with temperature and/or disorder compared to the standard harmonics, providing an additional tool for electronic structure determination. The theory is applied to Sr2RuO4. [1] A.M. Bratkovsky and A.S. Alexandrov, Phys. Rev. B 65, xxxx (2002); cond-mat/0104520.

The effects of ion channel blockers validate the conductance-based model of saccadic oscillations

PubMed Central

Shaikh, Aasef G.; Zee, David S.; Optican, Lance M.; Miura, Kenichiro; Ramat, Stefano; Leigh, R. John

2012-01-01

Conductance-based models of reciprocally inhibiting burst neurons suggest that intrinsic membrane properties and postinhibitory rebound (PIR) determine the amplitude and frequency of saccadic oscillations. Reduction of the low-threshold calcium currents (IT) in the model decreased the amplitude but increased the frequency of the simulated oscillations. Combined reduction of hyperpolarization-activated cation current (Ih) and IT in the model abolished the simulated oscillations. We measured the effects of a selective blocker of IT (ethosuximide) in healthy subjects on the amplitude and frequency of saccadic oscillations evoked by eye closure and of a nonselective blocker of Ih and IT (propronolol) in a patient with microsaccadic oscillation and limb tremor syndrome (mSOLT). Ethosuximide significantly reduced the amplitude but increased the frequency of the saccadic oscillations during eye closure in healthy subjects. Propranolol abolished saccadic oscillations in the mSOLT patient. These results support the hypothetical role of postinhibitory rebound, Ih, and IT, in generation of saccadic oscillations and determining their kinematic properties. PMID:21950976

Testing the Model of Oscillating Magnetic Traps

NASA Astrophysics Data System (ADS)

Szaforz, Ż.; Tomczak, M.

2015-01-01

The aim of this paper is to test the model of oscillating magnetic traps (the OMT model), proposed by Jakimiec and Tomczak ( Solar Phys. 261, 233, 2010). This model describes the process of excitation of quasi-periodic pulsations (QPPs) observed during solar flares. In the OMT model energetic electrons are accelerated within a triangular, cusp-like structure situated between the reconnection point and the top of a flare loop as seen in soft X-rays. We analyzed QPPs in hard X-ray light curves for 23 flares as observed by Yohkoh. Three independent methods were used. We also used hard X-ray images to localize magnetic traps and soft X-ray images to diagnose thermal plasmas inside the traps. We found that the majority of the observed pulsation periods correlates with the diameters of oscillating magnetic traps, as was predicted by the OMT model. We also found that the electron number density of plasma inside the magnetic traps in the time of pulsation disappearance is strongly connected with the pulsation period. We conclude that the observations are consistent with the predictions of the OMT model for the analyzed set of flares.

Solvable model for chimera states of coupled oscillators.

PubMed

Abrams, Daniel M; Mirollo, Rennie; Strogatz, Steven H; Wiley, Daniel A

2008-08-22

Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.

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

DOE PAGES

Perez, R. Navarro; Schunck, N.; Lasseri, R. -D.; ...

2017-07-05

Here, 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-scalemore » mass table calculations.« less

QED effects induced harmonics generation in extreme intense laser foil interaction

NASA Astrophysics Data System (ADS)

Yu, J. Y.; Yuan, T.; Liu, W. Y.; Chen, M.; Luo, W.; Weng, S. M.; Sheng, Z. M.

2018-04-01

A new mechanism of harmonics generation (HG) induced by quantum electrodynamics (QED) effects in extreme intense laser foil interaction is found and investigated by particle-in-cell (PIC) simulations. When two laser pulses with identical intensities of 1.6× {10}24 {{W}} {{{cm}}}-2 are counter-incident on a thin foil target, harmonics emission is observed in their reflected electromagnetic waves. Such harmonics radiation is excited due to transversely oscillating electric currents coming from the vibration of QED effect generated {e}-{e}+ pairs. The effects of laser intensity and polarization were studied. By distinguishing the cascade depth of generated photons and pairs, the influence of QED cascades on HG was analyzed. Although the current HG is not an efficient way for radiation source applications, it may provide a unique way to detect the QED processes in the near future ultra-relativistic laser solid interactions.

Time Delay in the Kuramoto Model of Coupled Oscillators

NASA Astrophysics Data System (ADS)

Yeung, M. K. Stephen; Strogatz, Steven H.

1999-01-01

We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions. New phenomena include bistability between synchronized and incoherent states, and unsteady solutions with time-dependent order parameters. We derive exact formulas for the stability boundaries of the incoherent and synchronized states, as a function of the delay, in the special case where the oscillators are identical. The experimental implications of the model are discussed for populations of chirping crickets, where the finite speed of sound causes communication delays, and for physical systems such as coupled phase-locked loops or lasers.

Novel Harmonic Regularization Approach for Variable Selection in Cox's Proportional Hazards Model

PubMed Central

Chu, Ge-Jin; Liang, Yong; Wang, Jia-Xuan

2014-01-01

Variable selection is an important issue in regression and a number of variable selection methods have been proposed involving nonconvex penalty functions. In this paper, we investigate a novel harmonic regularization method, which can approximate nonconvex Lq  (1/2 < q < 1) regularizations, to select key risk factors in the Cox's proportional hazards model using microarray gene expression data. The harmonic regularization method can be efficiently solved using our proposed direct path seeking approach, which can produce solutions that closely approximate those for the convex loss function and the nonconvex regularization. Simulation results based on the artificial datasets and four real microarray gene expression datasets, such as real diffuse large B-cell lymphoma (DCBCL), the lung cancer, and the AML datasets, show that the harmonic regularization method can be more accurate for variable selection than existing Lasso series methods. PMID:25506389

Novel harmonic regularization approach for variable selection in Cox's proportional hazards model.

PubMed

Chu, Ge-Jin; Liang, Yong; Wang, Jia-Xuan

2014-01-01

Variable selection is an important issue in regression and a number of variable selection methods have been proposed involving nonconvex penalty functions. In this paper, we investigate a novel harmonic regularization method, which can approximate nonconvex Lq  (1/2 < q < 1) regularizations, to select key risk factors in the Cox's proportional hazards model using microarray gene expression data. The harmonic regularization method can be efficiently solved using our proposed direct path seeking approach, which can produce solutions that closely approximate those for the convex loss function and the nonconvex regularization. Simulation results based on the artificial datasets and four real microarray gene expression datasets, such as real diffuse large B-cell lymphoma (DCBCL), the lung cancer, and the AML datasets, show that the harmonic regularization method can be more accurate for variable selection than existing Lasso series methods.

Forced Longitudinal Oscillations of a Gas in an Open Pipe Near the Resonance Excitation Frequency

NASA Astrophysics Data System (ADS)

Zaripov, R. G.; Tkachenko, L. A.; Shaidullin, L. R.

2017-11-01

Results of theoretical and experimental investigations of forced longitudinal oscillations of a homogeneous gas in an open pipe near the first natural frequency are presented. It has been established that at the resonance frequency the shape of the gas pressure wave changes with time by a law different from the harmonic one. The amplitude-frequency characteristics of the indicated oscillations have been derived. Satisfactory agreement of the theoretical calculation of the gas pressure oscillation range with experimental data has been obtained.

Mathematical models of bipolar disorder

NASA Astrophysics Data System (ADS)

Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.

2009-07-01

We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.

Note on the coupled oscillator model solutions in crystalline optical activity

NASA Astrophysics Data System (ADS)

Vyšín, I.; Ríha, J.; Svácková, K.

2006-06-01

Many methods have been used in the crystalline optical activity solution, among them the traditional method of coupled oscillators. The two coupled oscillator model was first solved by Chandrasekhar, and the most general dispersion relations for the crystalline optical activity can be obtained from its next extensions. However, the Chandrasekhar solution method seems to be based on a mistake in the computations. For this reason, the solution of a more complicated model of coupled oscillators which better corresponds to the structure of real crystals using the Condon relations is presented. This solution leads to the conclusion that, although it is possible to object to the Chandrasekhar solution method, the form of his final dispersion relations is correct. On the other hand, the dispersion relations following from the solution of more complicated coupled oscillator models are more convenient for the interpretation of the crystalline optical activity experimental data, which is demonstrated in examples of crystals of tellurium and benzil.

Vertical vibration and shape oscillation of acoustically levitated water drops

DOE Office of Scientific and Technical Information (OSTI.GOV)

Geng, D. L.; Xie, W. J.; Yan, N.

2014-09-08

We present the vertical harmonic vibration of levitated water drops within ultrasound field. The restoring force to maintain such a vibration mode is provided by the resultant force of acoustic radiation force and drop gravity. Experiments reveal that the vibration frequency increases with the aspect ratio for drops with the same volume, which agrees with the theoretical prediction for those cases of nearly equiaxed drops. During the vertical vibration, the floating drops undergo the second order shape oscillation. The shape oscillation frequency is determined to be twice the vibration frequency.

Absorption and Reflection Experiments on High-Mobility 2DEGs in the Regime of Microwave-Induced Resistance Oscillations

NASA Astrophysics Data System (ADS)

Studenikin, S. A.; Potemski, M.; Sachrajda, A. S.; Hilke, M.; Pfeiffer, L. N.; West, K. W.

2005-04-01

We have performed microwave absorption and near-field reflection experiments on a high mobility GaAs/AlGaAs heterostructure for the same conditions for which Microwave-Induced Resistance Oscillations (MIROs) are observed. It is shown that the electrodynamic aspect of the problem is important in these experiments. In the absorption experiments a broad CR line was observed due to a large reflection from the highly conductive electron gas. There were no additional features observed related to absorption at harmonics of the cyclotron resonance. In near-field reflection experiments a very different oscillation pattern was revealed when compared to MIROs. The oscillation pattern observed in the reflection experiments is probably due to plasma effects occurring in a finite-size sample. The whole microscopic picture of MIROs is more complicated than simply a resonant absorption at harmonics of the cyclotron resonance. Nevertheless, the experimental observations are in good agreement with the model by Durst et al. involving the photo-assisted scattering in the presence of a crossed magnetic field and dc bias. The observed damping factor of MIROs may be attributed to a change in the electron mobility as a function of temperature. MIROs may be considered as a light-induced drift effect, a broad class of phenomena associated with a light-induced asymmetry in the velocity distribution function.

Absorption and Reflection Experiments on High-Mobility 2DEGs in the Regime of Microwave-Induced Resistance Oscillations

NASA Astrophysics Data System (ADS)

Studenikin, S. A.; Potemski, M.; Sachrajda, A. S.; Hilke, M.; Pfeiffer, L. N.; West, K. W.

We have performed microwave absorption and near-field reflection experiments on a high mobility GaAs/AlGaAs heterostructure for the same conditions for which Microwave-Induced Resistance Oscillations (MIROs) are observed. It is shown that the electrodynamic aspect of the problem is important in these experiments. In the absorption experiments a broad CR line was observed due to a large reflection from the highly conductive electron gas. There were no additional features observed related to absorption at harmonics of the cyclotron resonance. In near-field reflection experiments a very different oscillation pattern was revealed when compared to MIROs. The oscillation pattern observed in the reflection experiments is probably due to plasma effects occurring in a finite-size sample. The whole microscopic picture of MIROs is more complicated than simply a resonant absorption at harmonics of the cyclotron resonance. Nevertheless, the experimental observations are in good agreement with the model by Durst et al. involving the photo-assisted scattering in the presence of a crossed magnetic field and dc bias. The observed damping factor of MIROs may be attributed to a change in the electron mobility as a function of temperature. MIROs may be considered as a light-induced drift effect, a broad class of phenomena associated with a light-induced asymmetry in the velocity distribution function.

Collective signaling behavior in a networked-oscillator model

NASA Astrophysics Data System (ADS)

Liu, Z.-H.; Hui, P. M.

2007-09-01

We propose and study the collective behavior of a model of networked signaling objects that incorporates several ingredients of real-life systems. These ingredients include spatial inhomogeneity with grouping of signaling objects, signal attenuation with distance, and delayed and impulsive coupling between non-identical signaling objects. Depending on the coupling strength and/or time-delay effect, the model exhibits completely, partially, and locally collective signaling behavior. In particular, a correlated signaling (CS) behavior is observed in which there exist time durations when nearly a constant fraction of oscillators in the system are in the signaling state. These time durations are much longer than the duration of a spike when a single oscillator signals, and they are separated by regular intervals in which nearly all oscillators are silent. Such CS behavior is similar to that observed in biological systems such as fireflies, cicadas, crickets, and frogs. The robustness of the CS behavior against noise is also studied. It is found that properly adjusting the coupling strength and noise level could enhance the correlated behavior.

Phasing operator for two oscillators in classical field

NASA Technical Reports Server (NTRS)

Kim, Jong-Jean; Koo, Je-Hwan; Bae, Dong-Jae

1993-01-01

The origin of Dicke cooperative states was studied by considering two harmonic oscillators driven by a common field of radiation. The origin is assumed for superradiance in a system of molecules where no mutual interactions exist, but all of the molecules encounter the same field of radiation. A phasing operator as Phi(sub Nu) equals D(alpha) + P(sub Nu)D(alpha), where D(alpha) is the displacing operator and P(sub Nu) the projection operator for constant energy Nu for two oscillators, was derived. The eigenstates of the phasing operator Phi are found to show a finite correlation as in the Dicke cooperative states.

Temperature profile and equipartition law in a Langevin harmonic chain

NASA Astrophysics Data System (ADS)

Kim, Sangrak

2017-09-01

Temperature profile in a Langevin harmonic chain is explicitly derived and the validity of the equipartition law is checked. First, we point out that the temperature profile in previous studies does not agree with the equipartition law: In thermal equilibrium, the temperature profile deviates from the same temperature distribution against the equipartition law, particularly at the ends of the chain. The matrix connecting temperatures of the heat reservoirs and the temperatures of the harmonic oscillators turns out to be a probability matrix. By explicitly calculating the power spectrum of the probability matrix, we will show that the discrepancy comes from the neglect of the power spectrum in higher frequency ω, which is in decay mode, and related with the imaginary number of wave number q.

Nonlinear oscillations of gas in an open tube near the resonance frequency in the shock-free mode

NASA Astrophysics Data System (ADS)

Tkachenko, L. A.; Sergienko, M. V.

2014-11-01

The forced oscillations of gas in an open tube, excited by harmonical oscillations of piston in the shock-free mode were investigated near the first first eigenfrequencies. An expression for the pressure oscillations of gas was obtained for the tube with unrounded end without flange. The amplitude impact of piston displacement on the oscillations of pressure and velocity of the secondary flow of gas was investigated. The comparison of theoretical calculations with experimental data was executed. The effect of secondary flow on the particle drift along the tube axis with acoustic oscillations of gas was shown.

The effects of ion channel blockers validate the conductance-based model of saccadic oscillations.

PubMed

Shaikh, Aasef G; Zee, David S; Optican, Lance M; Miura, Kenichiro; Ramat, Stefano; Leigh, R John

2011-09-01

Conductance-based models of reciprocally inhibiting burst neurons suggest that intrinsic membrane properties and postinhibitory rebound (PIR) determine the amplitude and frequency of saccadic oscillations. Reduction of the low-threshold calcium currents (I(T)) in the model decreased the amplitude but increased the frequency of the simulated oscillations. Combined reduction of hyperpolarization-activated cation current (I(h)) and I(T) in the model abolished the simulated oscillations. We measured the effects of a selective blocker of I(T) (ethosuximide) in healthy subjects on the amplitude and frequency of saccadic oscillations evoked by eye closure and of a nonselective blocker of I(h) and I(T) (propronolol) in a patient with microsaccadic oscillation and limb tremor syndrome (mSOLT). Ethosuximide significantly reduced the amplitude but increased the frequency of the saccadic oscillations during eye closure in healthy subjects. Propranolol abolished saccadic oscillations in the mSOLT patient. These results support the hypothetical role of postinhibitory rebound, I(h), and I(T) , in generation of saccadic oscillations and determining their kinematic properties. © 2011 New York Academy of Sciences.

First-harmonic nonlinearities can predict unseen third-harmonics in medium-amplitude oscillatory shear (MAOS)

NASA Astrophysics Data System (ADS)

Carey-De La Torre, Olivia; Ewoldt, Randy H.

2018-02-01

We use first-harmonic MAOS nonlinearities from G 1' and G 1″ to test a predictive structure-rheology model for a transient polymer network. Using experiments with PVA-Borax (polyvinyl alcohol cross-linked by sodium tetraborate (borax)) at 11 different compositions, the model is calibrated to first-harmonic MAOS data on a torque-controlled rheometer at a fixed frequency, and used to predict third-harmonic MAOS on a displacement controlled rheometer at a different frequency three times larger. The prediction matches experiments for decomposed MAOS measures [ e 3] and [ v 3] with median disagreement of 13% and 25%, respectively, across all 11 compositions tested. This supports the validity of this model, and demonstrates the value of using all four MAOS signatures to understand and test structure-rheology relations for complex fluids.

Nonequilibrium simulations of model ionomers in an oscillating electric field

DOE PAGES

Ting, Christina L.; Sorensen-Unruh, Karen E.; Stevens, Mark J.; ...

2016-07-25

Here, we perform molecular dynamics simulations of a coarse-grained model of ionomer melts in an applied oscillating electric field. The frequency-dependent conductivity and susceptibility are calculated directly from the current density and polarization density, respectively. At high frequencies, we find a peak in the real part of the conductivity due to plasma oscillations of the ions. At lower frequencies, the dynamic response of the ionomers depends on the ionic aggregate morphology in the system, which consists of either percolated or isolated aggregates. We show that the dynamic response of the model ionomers to the applied oscillating field can be understoodmore » by comparison with relevant time scales in the systems, obtained from independent calculations.« less

Nonequilibrium simulations of model ionomers in an oscillating electric field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ting, Christina L.; Sorensen-Unruh, Karen E.; Stevens, Mark J.

Here, we perform molecular dynamics simulations of a coarse-grained model of ionomer melts in an applied oscillating electric field. The frequency-dependent conductivity and susceptibility are calculated directly from the current density and polarization density, respectively. At high frequencies, we find a peak in the real part of the conductivity due to plasma oscillations of the ions. At lower frequencies, the dynamic response of the ionomers depends on the ionic aggregate morphology in the system, which consists of either percolated or isolated aggregates. We show that the dynamic response of the model ionomers to the applied oscillating field can be understoodmore » by comparison with relevant time scales in the systems, obtained from independent calculations.« less

Modeling the Interaction of the Madden-Julian Oscillation and Quasi-biennial Oscillation

NASA Astrophysics Data System (ADS)

Martin, Z.; Wang, S.; Nie, J.; Sobel, A. H.

2017-12-01

The stratospheric quasi-biennial oscillation (QBO) and the intra-seasonal Madden-Julian oscillation (MJO) are two hallmark features of the tropical atmosphere. Recent observational results have demonstrated a strong correlation between the MJO and the QBO, particularly in boreal winter, with enhanced MJO activity and increased predictability during the easterly phase of the QBO. Despite the robustness of the observational result, the physical processes through which the MJO and QBO interact are unknown and largely unstudied. We demonstrate that the MJO can be simulated in the WRF cloud-resolving model with large-scale forcing taken from the DYNAMO field campaign, during a period when two MJO events were observed and the QBO was in a neutral phase. We look at the effect of forcing the model MJO with idealized temperature anomalies around the tropopause, representative of the easterly and westerly QBO phases. While the model demonstrates some robust relationships between the MJO and QBO - including an increase in the vertical velocity and cloud fraction, and a decrease in OLR during the easterly QBO phase - other variables, such as precipitation, depend on the QBO phase and the particular MJO event in a more complicated manner. We conclude with some preliminary results towards understanding the mechanisms driving the MJO-QBO relationship through examining the effects of cloud-radiative feedback and horizontal moisture advection on the model results.

Transient regime in second harmonic generation

NASA Astrophysics Data System (ADS)

Szeftel, Jacob; Sandeau, Laure; Sandeau, Nicolas; Delezoide, Camille; Khater, Antoine

2013-09-01

The time growth of the electromagnetic field at the fundamental and double frequencies is studied from the very onset of the second harmonic generation (SHG) process for a set of dipoles lacking a symmetry centre and exhibiting a nonresonant coupling with a classical electromagnetic field. This approach consists first of solving the Schrödinger equation by applying a generalised Rabi rotation to the Hamiltonian describing the light-dipole interaction. This rotation has been devised for the resulting Hamiltonian to show up time-independent for both components of the electromagnetic field at the fundamental frequency and the second harmonic one. Then an energy conservation argument, derived from the Poynting theorem, is introduced to work out an additional relationship between the electromagnetic field and its associated electric polarisation. Finally this analysis yields the full time behaviour of all physical quantities of interest. The calculated results reproduce accurately both the observed spatial oscillations of the SHG intensity (Maker's fringes) and its power law dependence on the intensity of the incoming light at the fundamental frequency.

Estimation of plasma ion saturation current and reduced tip arcing using Langmuir probe harmonics.

PubMed

Boedo, J A; Rudakov, D L

2017-03-01

We present a method to calculate the ion saturation current, I sat , for Langmuir probes at high frequency (>100 kHz) using the harmonics technique and we compare that to a direct measurement of I sat . It is noted that the I sat estimation can be made directly by the ratio of harmonic amplitudes, without explicitly calculating T e . We also demonstrate that since the probe tips using the harmonic method are oscillating near the floating potential, drawing little power, this method reduces tip heating and arcing and allows plasma density measurements at a plasma power flux that would cause continuously biased tips to arc. A multi-probe array is used, with two spatially separated tips employing the harmonics technique and measuring the amplitude of at least two harmonics per tip. A third tip, located between the other two, measures the ion saturation current directly. We compare the measured and calculated ion saturation currents for a variety of plasma conditions and demonstrate the validity of the technique and its use in reducing arcs.

Estimation of plasma ion saturation current and reduced tip arcing using Langmuir probe harmonics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boedo, J. A.; Rudakov, D. L.

Here we present a method to calculate the ion saturation current, I sat, for Langmuir probes at high frequency (>100 kHz) using the harmonics technique and we compare that to a direct measurement of I sat. It is noted that the Isat estimation can be made directly by the ratio of harmonic amplitudes, without explicitly calculating T e. We also demonstrate that since the probe tips using the harmonic method are oscillating near the floating potential, drawing little power, this method reduces tip heating and arcing and allows plasma density measurements at a plasma power flux that would cause continuouslymore » biased tips to arc. A multi-probe array is used, with two spatially separated tips employing the harmonics technique and measuring the amplitude of at least two harmonics per tip. A third tip, located between the other two, measures the ion saturation current directly. We compare the measured and calculated ion saturation currents for a variety of plasma conditions and demonstrate the validity of the technique and it’s use in reducing arcs.« less

Estimation of plasma ion saturation current and reduced tip arcing using Langmuir probe harmonics

DOE PAGES

Boedo, J. A.; Rudakov, D. L.

2017-03-20

Here we present a method to calculate the ion saturation current, I sat, for Langmuir probes at high frequency (>100 kHz) using the harmonics technique and we compare that to a direct measurement of I sat. It is noted that the Isat estimation can be made directly by the ratio of harmonic amplitudes, without explicitly calculating T e. We also demonstrate that since the probe tips using the harmonic method are oscillating near the floating potential, drawing little power, this method reduces tip heating and arcing and allows plasma density measurements at a plasma power flux that would cause continuouslymore » biased tips to arc. A multi-probe array is used, with two spatially separated tips employing the harmonics technique and measuring the amplitude of at least two harmonics per tip. A third tip, located between the other two, measures the ion saturation current directly. We compare the measured and calculated ion saturation currents for a variety of plasma conditions and demonstrate the validity of the technique and it’s use in reducing arcs.« less

Oscillations in epidemic models with spread of awareness.

PubMed

Just, Winfried; Saldaña, Joan; Xin, Ying

2018-03-01

We study ODE models of epidemic spreading with a preventive behavioral response that is triggered by awareness of the infection. Previous studies of such models have mostly focused on the impact of the response on the initial growth of an outbreak and the existence and location of endemic equilibria. Here we study the question whether this type of response is sufficient to prevent future flare-ups from low endemic levels if awareness is assumed to decay over time. In the ODE context, such flare-ups would translate into sustained oscillations with significant amplitudes. Our results show that such oscillations are ruled out in Susceptible-Aware-Infectious-Susceptible models with a single compartment of aware hosts, but can occur if we consider two distinct compartments of aware hosts who differ in their willingness to alert other susceptible hosts.

Rigorous quantum limits on monitoring free masses and harmonic oscillators

NASA Astrophysics Data System (ADS)

Roy, S. M.

2018-03-01

There are heuristic arguments proposing that the accuracy of monitoring position of a free mass m is limited by the standard quantum limit (SQL): σ2( X (t ) ) ≥σ2( X (0 ) ) +(t2/m2) σ2( P (0 ) ) ≥ℏ t /m , where σ2( X (t ) ) and σ2( P (t ) ) denote variances of the Heisenberg representation position and momentum operators. Yuen [Phys. Rev. Lett. 51, 719 (1983), 10.1103/PhysRevLett.51.719] discovered that there are contractive states for which this result is incorrect. Here I prove universally valid rigorous quantum limits (RQL), viz. rigorous upper and lower bounds on σ2( X (t ) ) in terms of σ2( X (0 ) ) and σ2( P (0 ) ) , given by Eq. (12) for a free mass and by Eq. (36) for an oscillator. I also obtain the maximally contractive and maximally expanding states which saturate the RQL, and use the contractive states to set up an Ozawa-type measurement theory with accuracies respecting the RQL but beating the standard quantum limit. The contractive states for oscillators improve on the Schrödinger coherent states of constant variance and may be useful for gravitational wave detection and optical communication.

2D and 3D Models of Convective Turbulence and Oscillations in Intermediate-Mass Main-Sequence Stars

NASA Astrophysics Data System (ADS)

Guzik, Joyce Ann; Morgan, Taylor H.; Nelson, Nicholas J.; Lovekin, Catherine; Kitiashvili, Irina N.; Mansour, Nagi N.; Kosovichev, Alexander

2015-08-01

We present multidimensional modeling of convection and oscillations in main-sequence stars somewhat more massive than the sun, using three separate approaches: 1) Applying the spherical 3D MHD ASH (Anelastic Spherical Harmonics) code to simulate the core convection and radiative zone. Our goal is to determine whether core convection can excite low-frequency gravity modes, and thereby explain the presence of low frequencies for some hybrid gamma Dor/delta Sct variables for which the envelope convection zone is too shallow for the convective blocking mechanism to drive g modes; 2) Using the 3D planar ‘StellarBox’ radiation hydrodynamics code to model the envelope convection zone and part of the radiative zone. Our goals are to examine the interaction of stellar pulsations with turbulent convection in the envelope, excitation of acoustic modes, and the role of convective overshooting; 3) Applying the ROTORC 2D stellar evolution and dynamics code to calculate evolution with a variety of initial rotation rates and extents of core convective overshooting. The nonradial adiabatic pulsation frequencies of these nonspherical models will be calculated using the 2D pulsation code NRO of Clement. We will present new insights into gamma Dor and delta Sct pulsations gained by multidimensional modeling compared to 1D model expectations.

Spherical Cap Harmonic Modelling of 400 Years of Secular Variation in the South-west Pacific

NASA Astrophysics Data System (ADS)

Ingham, M.; Alfheid, M.; Ingham, E. M.; Turner, G. M.

2014-12-01

Historical magnetic data recorded in ship's logs on voyages of exploration and trade in the south-west Pacific have been used as a basis for constructing a model of secular variation in the region using spherical cap harmonic (SCH) analysis. The spherical cap used is centred on colatitude 115° and longitude 160° and has a radius of 50°, thus covering New Zealand, Australia and parts of Antarctica. Gaps in the observational data have been filled by an iterative procedure started by using IGRF field values to obtain SCH models for 2000, 1950 and 1900 and assuming that the spherical cap coefficients have a linear variation in time over the 400 year time period of the model, as is observed to a first approximation for Gauss coefficients calculated from a global spherical harmonic analysis. The resulting field models have generally smooth spatial and temporal variations in declination, inclination and intensity which show some differences from the variations calculated using the global spherical harmonic model gufm1. The technique clearly shows promise for producing more refined models of secular variation in the south-west Pacific when the historical data are supplemented by archeomagnetic and paleomagnetic data.

A masking level difference due to harmonicity.

PubMed

Treurniet, W C; Boucher, D R

2001-01-01

The role of harmonicity in masking was studied by comparing the effect of harmonic and inharmonic maskers on the masked thresholds of noise probes using a three-alternative, forced-choice method. Harmonic maskers were created by selecting sets of partials from a harmonic series with an 88-Hz fundamental and 45 consecutive partials. Inharmonic maskers differed in that the partial frequencies were perturbed to nearby values that were not integer multiples of the fundamental frequency. Average simultaneous-masked thresholds were as much as 10 dB lower with the harmonic masker than with the inharmonic masker, and this difference was unaffected by masker level. It was reduced or eliminated when the harmonic partials were separated by more than 176 Hz, suggesting that the effect is related to the extent to which the harmonics are resolved by auditory filters. The threshold difference was not observed in a forward-masking experiment. Finally, an across-channel mechanism was implicated when the threshold difference was found between a harmonic masker flanked by harmonic bands and a harmonic masker flanked by inharmonic bands. A model developed to explain the observed difference recognizes that an auditory filter output envelope is modulated when the filter passes two or more sinusoids, and that the modulation rate depends on the differences among the input frequencies. For a harmonic masker, the frequency differences of adjacent partials are identical, and all auditory filters have the same dominant modulation rate. For an inharmonic masker, however, the frequency differences are not constant and the envelope modulation rate varies across filters. The model proposes that a lower variability facilitates detection of a probe-induced change in the variability, thus accounting for the masked threshold difference. The model was supported by significantly improved predictions of observed thresholds when the predictor variables included envelope modulation rate variance measured

Intraseasonal Oscillations over South America: A Study with a Regional Climate Model

NASA Technical Reports Server (NTRS)

Chen, Baode; Chao, Winston

2003-01-01

The National Center for Atmospheric Research (NCAR) regional climate model version 2 (RegCM2) is used to investigate the observed characteristics of intraseasonal oscillations over South America. Our study is mainly concentrated on an intraseaonal mode, which is observed to account for a large portion of the intraseasonal variation, to have a standing feature and to be independent of the MJO. The NCEPDOE AMIP-II reanalysis is utilized to provide initial and lateral boundary conditions for the RegCM2 based upon the OOZ, 062, 122 and 182 data.Our results indicate that the intraseasonal oscillation still exists with time- averaged lateral boundary condition, which prevents the MJO and other outside disturbances from entering the model's domain, suggesting a locally forced oscillation responsible for ths intraseasonal mode independent of the MJO. Further experiments show that the annual and daily variabilities and a radiative-convective interaction are not essential to the locally forced intraseasonal oscillation. The intraseasonal oscillations over Amazon in our model essentially result from interactions among atmospheric continental- scale circulation, surface radiation, surface sensible and latent heat fluxes, and cumulus convection. The wavelet analyses of various surface energy fluxes and surface energy budget also verify that the primary cause of intraseasonal oscillation is the interaction of land surface processes with the atmosphere.

Numerical simulation of the nonlinear dynamics of harmonically driven Riesz-fractional extensions of the Fermi-Pasta-Ulam chains

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2018-02-01

In this work, we introduce a spatially discrete model that is a modification of the well-known α-Fermi-Pasta-Ulam chain with damping. The system is perturbed at one end by a harmonic disturbance irradiating at a frequency in the forbidden band-gap of the classical regime, and a nonlocal coupling between the oscillators is considered using discrete Riesz fractional derivatives. We propose fully discrete expressions to approximate an energy functional of the system, and we use them to calculate the total energy of fractional chains over a relatively long period of time [Fract. Diff. Appl. 4 (2004) 153-162]. The approach is thoroughly tested in the case of local couplings against known qualitative results, including simulations of the process of nonlinear recurrence in the traditional chains of anharmonic oscillators. As an application, we provide evidence that the process of supratransmission is present in spatially discrete Fermi-Pasta-Ulam lattices with Riesz fractional derivatives in space. Moreover, we perform numerical experiments for small and large amplitudes of the harmonic disturbance. In either case, we establish the dependency of the critical amplitude at which supratransmission begins as a function of the driving frequency. Our results are in good agreement with the analytic predictions for the classical Fermi-Pasta-Ulam chain.

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

NASA Astrophysics Data System (ADS)

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.

Model of Wave Driven Flow Oscillation for Solar Cycle

NASA Technical Reports Server (NTRS)

Mayr, Hans G.; Wolff, Charles L.; Einaudi, Franco (Technical Monitor)

2001-01-01

At low latitudes in the Earth's atmosphere, the observed zonal flow velocities are dominated by the semi-annual and quasi-biennial oscillations with periods of 6 months and 20 to 32 months respectively. These terrestrial oscillations, the SAO and QBO respectively, are driven by wave-mean flow interactions due to upward propagating planetary-scale waves (periods of days) and small-scale gravity waves (periods of hours). We are proposing (see also Mayr et al., GRL, 2001) that such a mechanism may drive long period oscillations (reversing flows) in stellar and planetary interiors, and we apply it to the Sun. The reversing flows would occur below the convective envelope where waves can propagate. We apply a simplified, one dimensional, analytical flow model that incorporates a gravity wave parameterization due to Hines (1997). Based on this analysis, our estimates show that relatively small wave amplitudes less than 10 m/s can produce zonal flow amplitudes of 20 m/s, which should be sufficient to generate the observed variations in the magnetic field. To produce the 22-year period of oscillation, a low buoyancy frequency must be chosen, and this places the proposed flow in a region that is close to (and below) the base of the convective envelope. Enhanced turbulence associated with this low stability should help to generate the dynamo currents. With larger stability at deeper levels in the solar interior, the model can readily produce also oscillations with much longer periods. To provide an understanding of the fluid dynamics involved, we present numerical results from a 2D model for the terrestrial atmosphere that exemplify the non-linear nature of the wave interaction for which a mechanical analog is the escapement mechanism of the clock.

Stochastic mixed-mode oscillations in a three-species predator-prey model

NASA Astrophysics Data System (ADS)

Sadhu, Susmita; Kuehn, Christian

2018-03-01

The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For suitable parameter values, the deterministic drift part of the model admits a folded node singularity and exhibits a singular Hopf bifurcation. We focus on the parameter regime near the Hopf bifurcation, where small amplitude oscillations exist as stable dynamics in the absence of noise. In this regime, the stochastic model admits noise-driven mixed-mode oscillations (MMOs), which capture the intermediate dynamics between two cycles of population outbreaks. We perform numerical simulations to calculate the distribution of the random number of small oscillations between successive spikes for varying noise intensities and distance to the Hopf bifurcation. We also study the effect of noise on a suitable Poincaré map. Finally, we prove that the stochastic model can be transformed into a normal form near the folded node, which can be linked to recent results on the interplay between deterministic and stochastic small amplitude oscillations. The normal form can also be used to study the parameter influence on the noise level near folded singularities.

Coupling mechanism in the gate and oscillator model of the SCN

NASA Astrophysics Data System (ADS)

Li, Ying; Liu, Zengrong

2016-09-01

In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus is considered as the master circadian pacemaker. The SCN is divided into two subgroups of gate and oscillator cells: the ventrolateral (VL) neurons, which receive the periodic light-dark (LD) signal, and the dorsomedial (DM) neurons, which are coupled to the VL cells. The fundamental question is how the individual cellular oscillators, expressing a wide range of periods, interact and assemble to create an integrated pacemaker that can govern behavioral and physiological rhythmicity and be reset by environmental light. The key is that the heterogeneous network formed by the cellular clocks within the SCN must synchronize to maintain timekeeping activity. Based on the structural and functional heterogeneity of the SCN, the authors bring forward a mathematical model including gate cells and oscillator cells with a wide range of periods. The gate neurons offer daily injection to oscillator neurons and the activation of gate is determined by the output of the oscillator neurons. In this model, the authors consider two kinds of coupling: interior coupling among the oscillator cells and exterior coupling from the gate cells to the oscillator cells. The authors mainly analyze the combined effects of these two kinds of coupling on the entrainment of the oscillator cells in the DM part. It is found that the interior coupling is conducive to entrainment, but a stronger coupling is not beneficial to entrainment. The gate mechanism in exterior coupling is more propitious to entrainment than continuous coupling. This study helps to understand collective circadian rhythm in the mammals.

MICRO-SCALE CFD MODELING OF OSCILLATING FLOW IN A REGENERATOR

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheadle, M. J.; Nellis, G. F.; Klein, S. A.

2010-04-09

Regenerator models used by designers are macro-scale models that do not explicitly consider interactions between the fluid and the solid matrix. Rather, the heat transfer coefficient and pressure drop are calculated using correlations for Nusselt number and friction factor. These correlations are typically based on steady flow data. The error associated with using steady flow correlations to characterize the oscillatory flow that is actually present in the regenerator is not well understood. Oscillating flow correlations based on experimental data do exist in the literature; however, these results are often conflicting. This paper uses a micro-scale computational fluid dynamic (CFD) modelmore » of a unit-cell of a regenerator matrix to determine the conditions for which oscillating flow affects friction factor. These conditions are compared to those found in typical pulse tube regenerators to determine whether oscillatory flow is of practical importance. CFD results clearly show a transition Valensi number beyond which oscillating flow significantly increases the friction factor. This transition Valensi number increases with Reynolds number. Most practical pulse tube regenerators will operate below this Valensi transition number and therefore this study suggests that the effect of flow oscillation on pressure drop can be neglected in macro-scale regenerator models.« less

A Resonantly Excited Disk-Oscillation Model of High-Frequency QPOs of Microquasars

NASA Astrophysics Data System (ADS)

Kato, Shoji

2012-12-01

A possible model of twin high-frequency QPOs (HF QPOs) of microquasars is examined. The disk is assumed to have global magnetic fields and to be deformed with a two-armed pattern. In this deformed disk, a set of a two-armed (m = 2) vertical p-mode oscillation and an axisymmetric (m = 0) g-mode oscillation is considered. They resonantly interact through the disk deformation when their frequencies are the same. This resonant interaction amplifies the set of the above oscillations in the case where these two oscillations have wave energies of opposite signs. These oscillations are assumed to be excited most efficiently in the case where the radial group velocities of these two waves vanish at the same place. The above set of oscillations is not unique, depending on the node number n, of oscillations in the vertical direction. We consider that the basic two sets of oscillations correspond to the twin QPOs. The frequencies of these oscillations depend on the disk parameters, such as the strength of the magnetic fields. For observational mass ranges of GRS 1915+ 105, GRO J1655-40, XTE J1550-564, and HEAO H1743-322, the spins of these sources are estimated. High spins of these sources can be described if the disks have weak poloidal magnetic fields as well as toroidal magnetic fields of moderate strength. In this model the 3:2 frequency ratio of high-frequency QPOs is not related to their excitation, but occurs by chance.

Higher order supersymmetric truncated oscillators

NASA Astrophysics Data System (ADS)

Fernández C., David J.; Morales-Salgado, Vicente Said

2018-01-01

We study the supersymmetric partners of the harmonic oscillator with an infinite potential barrier at the origin and obtain the conditions under which it is possible to add levels to the energy spectrum of these systems. It is found that instead of the usual rule for non-singular potentials, where the order of the transformation corresponds to the maximum number of levels which can be added, now it is the integer part of half the order of the transformation which gives the maximum number of levels to be created.

Singular Behaviour of the Electrodynamic Fields of an Oscillating Dipole

ERIC Educational Resources Information Center

Leung, P. T.

2008-01-01

The singularity of the exact electromagnetic fields is derived to include the "source terms" for harmonically oscillating electric (and magnetic) dipoles, so that the fields will be consistent with the full Maxwell equations with a source. It is shown explicitly, as somewhat expected, that the same [delta]-function terms for the case of static…

A cardioid oscillator with asymmetric time ratio for establishing CPG models.

PubMed

Fu, Q; Wang, D H; Xu, L; Yuan, G

2018-01-13

Nonlinear oscillators are usually utilized by bionic scientists for establishing central pattern generator models for imitating rhythmic motions by bionic scientists. In the natural word, many rhythmic motions possess asymmetric time ratios, which means that the forward and the backward motions of an oscillating process sustain different times within one period. In order to model rhythmic motions with asymmetric time ratios, nonlinear oscillators with asymmetric forward and backward trajectories within one period should be studied. In this paper, based on the property of the invariant set, a method to design the closed curve in the phase plane of a dynamic system as its limit cycle is proposed. Utilizing the proposed method and considering that a cardioid curve is a kind of asymmetrical closed curves, a cardioid oscillator with asymmetric time ratios is proposed and realized. Through making the derivation of the closed curve in the phase plane of a dynamic system equal to zero, the closed curve is designed as its limit cycle. Utilizing the proposed limit cycle design method and according to the global invariant set theory, a cardioid oscillator applying a cardioid curve as its limit cycle is achieved. On these bases, the numerical simulations are conducted for analyzing the behaviors of the cardioid oscillator. The example utilizing the established cardioid oscillator to simulate rhythmic motions of the hip joint of a human body in the sagittal plane is presented. The results of the numerical simulations indicate that, whatever the initial condition is and without any outside input, the proposed cardioid oscillator possesses the following properties: (1) The proposed cardioid oscillator is able to generate a series of periodic and anti-interference self-exciting trajectories, (2) the generated trajectories possess an asymmetric time ratio, and (3) the time ratio can be regulated by adjusting the oscillator's parameters. Furthermore, the comparison between the

Modeling of termokinetic oscillations at partial oxidation of methane

NASA Astrophysics Data System (ADS)

Arutyunov, A. V.; Belyaev, A. A.; Inovenkov, I. N.; Nefedov, V. V.

2017-12-01

Partial oxidation of natural gas at moderate temperatures below 1500 K has significant interest for a number of industrial applications. But such processes can proceed at different unstable regimes including oscillating modes. Nonlinear phenomena at partial oxidation of methane were observed at different conditions. The investigation of the complex nonlinear system of equations that describes this process is a real method to insure its stability at industrial conditions and, at the same time, is an effective tool for its further enhancement. Numerical analysis of methane oxidation kinetics in the continuous stirred-tank reactor, with the use of detailed kinetic model has shown the possibility of the appearance of oscillating modes in the appropriate range of reaction parameters that characterize the composition, pressure, reagents flow, thermophysical features of the system, and geometry of the reactor. The appearance of oscillating modes is connected both with the reaction kinetics, heat release and sink and reagents introduction and removing. At that, oscillations appear only at a limited range of parameters, but can be accompanied by significant change in the yield of products. We have determined the range of initial temperature and pressure at which oscillations can be observed, if all other parameters remained fixed. The boundaries of existence of oscillations on the phase plane were calculated. It was shown that depending on the position inside the oscillation region the oscillations have different frequency and amplitude. It was reviled the role of heat exchange with the environment: at the absence of heat exchange the oscillating modes are impossible. In the vicinity of the boundary of phase range, where oscillations exist, significant change of concentration of some products were observed, for example, that of CO2, which in this case one of the principal products is. At that, insignificant increase in pressure not only change the character of CO2 behaving

Bit storage and bit flip operations in an electromechanical oscillator.

PubMed

Mahboob, I; Yamaguchi, H

2008-05-01

The Parametron was first proposed as a logic-processing system almost 50 years ago. In this approach the two stable phases of an excited harmonic oscillator provide the basis for logic operations. Computer architectures based on LC oscillators were developed for this approach, but high power consumption and difficulties with integration meant that the Parametron was rendered obsolete by the transistor. Here we propose an approach to mechanical logic based on nanoelectromechanical systems that is a variation on the Parametron architecture and, as a first step towards a possible nanomechanical computer, we demonstrate both bit storage and bit flip operations.

Spin-oscillator model for the unzipping of biomolecules by mechanical force.

PubMed

Prados, A; Carpio, A; Bonilla, L L

2012-08-01

A spin-oscillator system models unzipping of biomolecules (such as DNA, RNA, or proteins) subject to an external force. The system comprises a macroscopic degree of freedom, represented by a one-dimensional oscillator, and internal degrees of freedom, represented by Glauber spins with nearest-neighbor interaction and a coupling constant proportional to the oscillator position. At a critical value F(c) of an applied external force F, the oscillator rest position (order parameter) changes abruptly and the system undergoes a first-order phase transition. When the external force is cycled at different rates, the extension given by the oscillator position exhibits a hysteresis cycle at high loading rates, whereas it moves reversibly over the equilibrium force-extension curve at very low loading rates. Under constant force, the logarithm of the residence time at the stable and metastable oscillator rest position is proportional to F-F(c) as in an Arrhenius law.

Melnikov method approach to control of homoclinic/heteroclinic chaos by weak harmonic excitations.

PubMed

Chacón, Ricardo

2006-09-15

A review on the application of Melnikov's method to control homoclinic and heteroclinic chaos in low-dimensional, non-autonomous and dissipative oscillator systems by weak harmonic excitations is presented, including diverse applications, such as chaotic escape from a potential well, chaotic solitons in Frenkel-Kontorova chains and chaotic-charged particles in the field of an electrostatic wave packet.

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

ERIC Educational Resources Information Center

Triana, C. A.; Fajardo, F.

2012-01-01

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

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

ERIC Educational Resources Information Center

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

2013-01-01

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

Observation of dynamic interactions between fundamental and second-harmonic modes in a high-power sub-terahertz gyrotron operating in regimes of soft and hard self-excitation.

PubMed

Saito, Teruo; Tatematsu, Yoshinori; Yamaguchi, Yuusuke; Ikeuchi, Shinji; Ogasawara, Shinya; Yamada, Naoki; Ikeda, Ryosuke; Ogawa, Isamu; Idehara, Toshitaka

2012-10-12

Dynamic mode interaction between fundamental and second-harmonic modes has been observed in high-power sub-terahertz gyrotrons [T. Notake et al., Phys. Rev. Lett. 103, 225002 (2009); T. Saito et al. Phys. Plasmas 19, 063106 (2012)]. Interaction takes place between a parasitic fundamental or first-harmonic (FH) mode and an operating second-harmonic (SH) mode, as well as among SH modes. In particular, nonlinear excitation of the parasitic FH mode in the hard self-excitation regime with assistance of a SH mode in the soft self-excitation regime was clearly observed. Moreover, both cases of stable two-mode oscillation and oscillation of the FH mode only were observed. These observations and theoretical analyses of the dynamic behavior of the mode interaction verify the nonlinear hard self-excitation of the FH mode.

Simulation Study on the Self-Sustained Oscillations in DC Driven Glow Discharges at Atmospheric Pressure Under Different Gas Gaps

NASA Astrophysics Data System (ADS)

Wang, Xiaofei; He, Yafeng; Liu, Fucheng

2015-06-01

In this paper, a one-dimensional plasma fluid model is employed to study the self-sustained oscillations in DC-driven helium glow discharges at atmospheric pressure under different gas gaps. Our simulation results indicate that a harmonic current oscillation with tiny amplitude always occur at the onset of instability and transits into a relaxation one as the conductivity of the semiconductor is decreased. It is found that the dynamics of the oscillations are dependent on the gas gaps. The discharge can only exhibit a simple oscillation with unique amplitude and frequency at smaller gas gaps (<2 mm) while it can exhibit a more complex oscillation with several different amplitudes and frequencies at larger gas gaps (>2 mm). The discharge modes in these current oscillations have also been analyzed. supported by National Natural Science Foundation of China (Nos. 11205044 and 11405042), Hebei Natural Science Fund of China (Nos. A2012201015 and A2011201006), the Research Foundation of Education Bureau of Hebei Province of China (No. Y2012009), the Postdoctoral Science Foundation of Hebei Province of China (No. B2014003004) and the Postdoctoral Foundation of Hebei University

Further investigation of a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Weatherill, W. H.; Ehlers, F. E.; Yip, E.; Sebastian, J. D.

1980-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.

Stuttering Min oscillations within E. coli bacteria: a stochastic polymerization model

NASA Astrophysics Data System (ADS)

Sengupta, Supratim; Derr, Julien; Sain, Anirban; Rutenberg, Andrew D.

2012-10-01

We have developed a 3D off-lattice stochastic polymerization model to study the subcellular oscillation of Min proteins in the bacteria Escherichia coli, and used it to investigate the experimental phenomenon of Min oscillation stuttering. Stuttering was affected by the rate of immediate rebinding of MinE released from depolymerizing filament tips (processivity), protection of depolymerizing filament tips from MinD binding and fragmentation of MinD filaments due to MinE. Processivity, protection and fragmentation each reduce stuttering, speed oscillations and MinD filament lengths. Neither processivity nor tip protection were, on their own, sufficient to produce fast stutter-free oscillations. While filament fragmentation could, on its own, lead to fast oscillations with infrequent stuttering; high levels of fragmentation degraded oscillations. The infrequent stuttering observed in standard Min oscillations is consistent with short filaments of MinD, while we expect that mutants that exhibit higher stuttering frequencies will exhibit longer MinD filaments. Increased stuttering rate may be a useful diagnostic to find observable MinD polymerization under experimental conditions.

Phase diagram for the Winfree model of coupled nonlinear oscillators.

PubMed

Ariaratnam, J T; Strogatz, S H

2001-05-07

In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.

Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators

NASA Astrophysics Data System (ADS)

Ariaratnam, Joel T.; Strogatz, Steven H.

2001-05-01

In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.

The Ohio State 1991 geopotential and sea surface topography harmonic coefficient models

NASA Technical Reports Server (NTRS)

Rapp, Richard H.; Wang, Yan Ming; Pavlis, Nikolaos K.

1991-01-01

The computation is described of a geopotential model to deg 360, a sea surface topography model to deg 10/15, and adjusted Geosat orbits for the first year of the exact repeat mission (ERM). This study started from the GEM-T2 potential coefficient model and it's error covariance matrix and Geosat orbits (for 22 ERMs) computed by Haines et al. using the GEM-T2 model. The first step followed the general procedures which use a radial orbit error theory originally developed by English. The Geosat data was processed to find corrections to the a priori geopotential model, corrections to a radial orbit error model for 76 Geosat arcs, and coefficients of a harmonic representation of the sea surface topography. The second stage of the analysis took place by doing a combination of the GEM-T2 coefficients with 30 deg gravity data derived from surface gravity data and anomalies obtained from altimeter data. The analysis has shown how a high degree spherical harmonic model can be determined combining the best aspects of two different analysis techniques. The error analysis was described that has led to the accuracy estimates for all the coefficients to deg 360. Significant work is needed to improve the modeling effort.

Corrosion process monitoring by AFM higher harmonic imaging

NASA Astrophysics Data System (ADS)

Babicz, S.; Zieliński, A.; Smulko, J.; Darowicki, K.

2017-11-01

The atomic force microscope (AFM) was invented in 1986 as an alternative to the scanning tunnelling microscope, which cannot be used in studies of non-conductive materials. Today the AFM is a powerful, versatile and fundamental tool for visualizing and studying the morphology of material surfaces. Moreover, additional information for some materials can be recovered by analysing the AFM’s higher cantilever modes when the cantilever motion is inharmonic and generates frequency components above the excitation frequency, usually close to the resonance frequency of the lowest oscillation mode. This method has been applied and developed to monitor corrosion processes. The higher-harmonic imaging is especially helpful for sharpening boundaries between objects in heterogeneous samples, which can be used to identify variations in steel structures (e.g. corrosion products, steel heterogeneity). The corrosion products have different chemical structures because they are composed of chemicals other than the original metal base (mainly iron oxides). Thus, their physicochemical properties are different from the primary basis. These structures have edges at which higher harmonics should be more intense because of stronger interference between the tip and the specimen structure there. This means that the AFM’s higher-harmonic imaging is an excellent tool for monitoring surficial effects of the corrosion process.

Reference Model 6 (RM6): Oscillating Wave Energy Converter.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bull, Diana L; Smith, Chris; Jenne, Dale Scott

This report is an addendum to SAND2013-9040: Methodology for Design and Economic Analysis of Marine Energy Conversion (MEC) Technologies. This report describes an Oscillating Water Column Wave Energy Converter reference model design in a complementary manner to Reference Models 1-4 contained in the above report. In this report, a conceptual design for an Oscillating Water Column Wave Energy Converter (WEC) device appropriate for the modeled reference resource site was identified, and a detailed backward bent duct buoy (BBDB) device design was developed using a combination of numerical modeling tools and scaled physical models. Our team used the methodology in SAND2013-9040more » for the economic analysis that included costs for designing, manufacturing, deploying, and operating commercial-scale MEC arrays, up to 100 devices. The methodology was applied to identify key cost drivers and to estimate levelized cost of energy (LCOE) for this RM6 Oscillating Water Column device in dollars per kilowatt-hour ($/kWh). Although many costs were difficult to estimate at this time due to the lack of operational experience, the main contribution of this work was to disseminate a detailed set of methodologies and models that allow for an initial cost analysis of this emerging technology. This project is sponsored by the U.S. Department of Energy's (DOE) Wind and Water Power Technologies Program Office (WWPTO), within the Office of Energy Efficiency & Renewable Energy (EERE). Sandia National Laboratories, the lead in this effort, collaborated with partners from National Laboratories, industry, and universities to design and test this reference model.« less

Coronal loop seismology using damping of standing kink oscillations by mode coupling. II. additional physical effects and Bayesian analysis

NASA Astrophysics Data System (ADS)

Pascoe, D. J.; Anfinogentov, S.; Nisticò, G.; Goddard, C. R.; Nakariakov, V. M.

2017-04-01

Context. The strong damping of kink oscillations of coronal loops can be explained by mode coupling. The damping envelope depends on the transverse density profile of the loop. Observational measurements of the damping envelope have been used to determine the transverse loop structure which is important for understanding other physical processes such as heating. Aims: The general damping envelope describing the mode coupling of kink waves consists of a Gaussian damping regime followed by an exponential damping regime. Recent observational detection of these damping regimes has been employed as a seismological tool. We extend the description of the damping behaviour to account for additional physical effects, namely a time-dependent period of oscillation, the presence of additional longitudinal harmonics, and the decayless regime of standing kink oscillations. Methods: We examine four examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). We use forward modelling of the loop position and investigate the dependence on the model parameters using Bayesian inference and Markov chain Monte Carlo (MCMC) sampling. Results: Our improvements to the physical model combined with the use of Bayesian inference and MCMC produce improved estimates of model parameters and their uncertainties. Calculation of the Bayes factor also allows us to compare the suitability of different physical models. We also use a new method based on spline interpolation of the zeroes of the oscillation to accurately describe the background trend of the oscillating loop. Conclusions: This powerful and robust method allows for accurate seismology of coronal loops, in particular the transverse density profile, and potentially reveals additional physical effects.

MAVRIC Flutter Model Transonic Limit Cycle Oscillation Test

NASA Technical Reports Server (NTRS)

Edwards, John W.; Schuster, David M.; Spain, Charles V.; Keller, Donald F.; Moses, Robert W.

2001-01-01

The Models for Aeroelastic Validation Research Involving Computation semi-span wind-tunnel model (MAVRIC-I), a business jet wing-fuselage flutter model, was tested in NASA Langley's Transonic Dynamics Tunnel with the goal of obtaining experimental data suitable for Computational Aeroelasticity code validation at transonic separation onset conditions. This research model is notable for its inexpensive construction and instrumentation installation procedures. Unsteady pressures and wing responses were obtained for three wingtip configurations clean, tipstore, and winglet. Traditional flutter boundaries were measured over the range of M = 0.6 to 0.9 and maps of Limit Cycle Oscillation (LCO) behavior were made in the range of M = 0.85 to 0.95. Effects of dynamic pressure and angle-of-attack were measured. Testing in both R134a heavy gas and air provided unique data on Reynolds number, transition effects, and the effect of speed of sound on LCO behavior. The data set provides excellent code validation test cases for the important class of flow conditions involving shock-induced transonic flow separation onset at low wing angles, including Limit Cycle Oscillation behavior.

Neurodynamic oscillators

NASA Technical Reports Server (NTRS)

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.

Transonic streamline of symmetric wing under the influence unilateral oscillations characterized by the spectrum of two frequencies

NASA Astrophysics Data System (ADS)

Zamuraev, V. P.; Kalinina, A. P.

2017-10-01

Forced high-frequency vibrations of the airfoil surface part with the amplitude almost equal to the sound velocity can change significantly the lift force of the symmetric profile streamlined at zero angle of attack. The oscillation consists of two harmonics. The ratio of harmonics frequencies values is equal to 2. The present work shows that the aerodynamic properties depend significantly on the specific energy contribution of each frequency.

Unified thalamic model generates multiple distinct oscillations with state-dependent entrainment by stimulation

PubMed Central

2017-01-01

The thalamus plays a critical role in the genesis of thalamocortical oscillations, yet the underlying mechanisms remain elusive. To understand whether the isolated thalamus can generate multiple distinct oscillations, we developed a biophysical thalamic model to test the hypothesis that generation of and transition between distinct thalamic oscillations can be explained as a function of neuromodulation by acetylcholine (ACh) and norepinephrine (NE) and afferent synaptic excitation. Indeed, the model exhibited four distinct thalamic rhythms (delta, sleep spindle, alpha and gamma oscillations) that span the physiological states corresponding to different arousal levels from deep sleep to focused attention. Our simulation results indicate that generation of these distinct thalamic oscillations is a result of both intrinsic oscillatory cellular properties and specific network connectivity patterns. We then systematically varied the ACh/NE and input levels to generate a complete map of the different oscillatory states and their transitions. Lastly, we applied periodic stimulation to the thalamic network and found that entrainment of thalamic oscillations is highly state-dependent. Our results support the hypothesis that ACh/NE modulation and afferent excitation define thalamic oscillatory states and their response to brain stimulation. Our model proposes a broader and more central role of the thalamus in the genesis of multiple distinct thalamo-cortical rhythms than previously assumed. PMID:29073146

Self-tuning bistable parametric feedback oscillator: Near-optimal amplitude maximization without model information

NASA Astrophysics Data System (ADS)

Braun, David J.; Sutas, Andrius; Vijayakumar, Sethu

2017-01-01

Theory predicts that parametrically excited oscillators, tuned to operate under resonant condition, are capable of large-amplitude oscillation useful in diverse applications, such as signal amplification, communication, and analog computation. However, due to amplitude saturation caused by nonlinearity, lack of robustness to model uncertainty, and limited sensitivity to parameter modulation, these oscillators require fine-tuning and strong modulation to generate robust large-amplitude oscillation. Here we present a principle of self-tuning parametric feedback excitation that alleviates the above-mentioned limitations. This is achieved using a minimalistic control implementation that performs (i) self-tuning (slow parameter adaptation) and (ii) feedback pumping (fast parameter modulation), without sophisticated signal processing past observations. The proposed approach provides near-optimal amplitude maximization without requiring model-based control computation, previously perceived inevitable to implement optimal control principles in practical application. Experimental implementation of the theory shows that the oscillator self-tunes itself near to the onset of dynamic bifurcation to achieve extreme sensitivity to small resonant parametric perturbations. As a result, it achieves large-amplitude oscillations by capitalizing on the effect of nonlinearity, despite substantial model uncertainties and strong unforeseen external perturbations. We envision the present finding to provide an effective and robust approach to parametric excitation when it comes to real-world application.

Diagonal ordering operation technique applied to Morse oscillator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Popov, Dušan, E-mail: dusan_popov@yahoo.co.uk; Dong, Shi-Hai; Popov, Miodrag

2015-11-15

We generalize the technique called as the integration within a normally ordered product (IWOP) of operators referring to the creation and annihilation operators of the harmonic oscillator coherent states to a new operatorial approach, i.e. the diagonal ordering operation technique (DOOT) about the calculations connected with the normally ordered product of generalized creation and annihilation operators that generate the generalized hypergeometric coherent states. We apply this technique to the coherent states of the Morse oscillator including the mixed (thermal) state case and get the well-known results achieved by other methods in the corresponding coherent state representation. Also, in the lastmore » section we construct the coherent states for the continuous dynamics of the Morse oscillator by using two new methods: the discrete–continuous limit, respectively by solving a finite difference equation. Finally, we construct the coherent states corresponding to the whole Morse spectrum (discrete plus continuous) and demonstrate their properties according the Klauder’s prescriptions.« less

Perturbation of a radially oscillating single-bubble by a micron-sized object.

PubMed

Montes-Quiroz, W; Baillon, F; Louisnard, O; Boyer, B; Espitalier, F

2017-03-01

A single bubble oscillating in a levitation cell is acoustically monitored by a piezo-ceramics microphone glued on the cell external wall. The correlation of the filtered signal recorded over distant cycles on one hand, and its harmonic content on the other hand, are shown to carry rich information on the bubble stability and existence. For example, the harmonic content of the signal is shown to increase drastically once air is fully dissociated in the bubble, and the resulting pure argon bubble enters into the upper branch of the sonoluminescence regime. As a consequence, the bubble disappearance can be unambiguously detected by a net drop in the harmonic content. On the other hand, we perturb a stable sonoluminescing bubble by approaching a micron-sized fiber. The bubble remains unperturbed until the fiber tip is approached within a critical distance, below which the bubble becomes unstable and disappears. This distance can be easily measured by image treatment, and is shown to scale roughly with 3-4 times the bubble maximal radius. The bubble disappearance is well detected by the drop of the microphone harmonic content, but several thousands of periods after the bubble actually disappeared. The delay is attributed to the slow extinction of higher modes of the levitation cell, excited by the bubble oscillation. The acoustic detection method should however allow the early detection and imaging of non-predictable perturbations of the bubble by foreign micron-sized objects, such as crystals or droplets. Copyright © 2016 Elsevier B.V. All rights reserved.

Reply to Steele & Ferrer: Modeling Oscillation, Approximately or Exactly?

ERIC Educational Resources Information Center

Oud, Johan H. L.; Folmer, Henk

2011-01-01

This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure…

Synthetic dimensions for cold atoms from shaking a harmonic trap

NASA Astrophysics Data System (ADS)

Price, Hannah M.; Ozawa, Tomoki; Goldman, Nathan

2017-02-01

We introduce a simple scheme to implement synthetic dimensions in ultracold atomic gases, which only requires two basic and ubiquitous ingredients: the harmonic trap, which confines the atoms, combined with a periodic shaking. In our approach, standard harmonic oscillator eigenstates are reinterpreted as lattice sites along a synthetic dimension, while the coupling between these lattice sites is controlled by the applied time modulation. The phase of this modulation enters as a complex hopping phase, leading straightforwardly to an artificial magnetic field upon adding a second dimension. We show that this artificial gauge field has important consequences, such as the counterintuitive reduction of average energy under resonant driving, or the realization of quantum Hall physics. Our approach offers significant advantages over previous implementations of synthetic dimensions, providing an intriguing route towards higher-dimensional topological physics and strongly-correlated states.

Amplitude-Stabilized Oscillator for a Capacitance-Probe Electrometer

NASA Technical Reports Server (NTRS)

Blaes, Brent R.; Schaefer, Rembrandt T.

2012-01-01

A multichannel electrometer voltmeter that employs a mechanical resonator maintained in sustained amplitude-stabilized oscillation has been developed for the space-based measurement of an Internal Electrostatic Discharge Monitor (IESDM) sensor. The IESDM is new sensor technology targeted for integration into a Space Environmental Monitor (SEM) subsystem used for the characterization and monitoring of deep dielectric charging on spacecraft. Creating a stable oscillator from the mechanical resonator was achieved by employing magnetic induction for sensing the resonator s velocity, and forcing a current through a coil embedded in the resonator to produce a Lorentz actuation force that overcomes the resonator s dissipative losses. Control electronics employing an AGC loop provide conditions for stabilized, constant amplitude harmonic oscillation. The prototype resonator was composed of insulating FR4 printed-wireboard (PWB) material containing a flat, embedded, rectangular coil connected through flexure springs to a base PWB, and immersed in a magnetic field having two regions of opposite field direction generated by four neodymium block magnets. In addition to maintaining the mechanical movement needed for the electrometer s capacitor-probe transducer, this oscillator provides a reference signal for synchronous detection of the capacitor probe s output signal current so drift of oscillation frequency due to environmental effects is inconsequential.

Improvement of the low frequency oscillation model for Hall thrusters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Chunsheng, E-mail: wangcs@hit.edu.cn; Wang, Huashan

2016-08-15

The low frequency oscillation of the discharge current in Hall thrusters is a major aspect of these devices that requires further study. While the existing model captures the ionization mechanism of the low frequency oscillation, it unfortunately fails to express the dynamic characteristics of the ion acceleration. The analysis in this paper shows this is because of the simplification of the electron equation, which affects both the electric field distribution and the ion acceleration process. Additionally, the electron density equation is revised and a new model that is based on the physical properties of ion movement is proposed.

The extratropical 40-day oscillation in the UCLA general circulation model. Part 1: Atmospheric angular momentum

NASA Technical Reports Server (NTRS)

Marcus, S. L.; Ghil, M.; Dickey, J. O.

1994-01-01

Variations in atmospheric angular momentum (AAM) are examined in a three-year simulation of the large-scale atmosphere with perpetual January forcing. The simulation is performed with a version of the University of California at Los Angeles (UCLA) general circulation model that contains no tropical Madden-Julian Oscillation (MJO). In addition, the results of three shorter experiments with no topography are analyzed. The three-year standard topography run contains no significant intraseasonal AAM periodicity in the tropics, consistent with the lack of the MJO, but produces a robust, 42-day AAM oscillation in the Northern Hemisphere (NH) extratropics. The model tropics undergoes a barotropic, zonally symmetric oscillation, driven by an exchange of mass with the NH extratropics. No intraseasonal periodicity is found in the average tropical latent heating field, indicating that the model oscillation is dynamically rather than thermodynamically driven. The no-mountain runs fail to produce an intraseasonal AAM oscillation, consistent with a topographic origin for the NH extratropical oscillation in the standard model. The spatial patterns of the oscillation in the 500-mb height field, and the relationship of the extratropical oscillation to intraseasonal variations in the tropics, will be discussed in Part 2 of this study.

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

NASA Astrophysics Data System (ADS)

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.

Quantum damped oscillator II: Bateman’s Hamiltonian vs. 2D parabolic potential barrier

NASA Astrophysics Data System (ADS)

Chruściński, Dariusz

2006-04-01

We show that quantum Bateman’s system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba.

Mass and Radius Constraints Using Magnetar Giant Flare Oscillations

NASA Astrophysics Data System (ADS)

Deibel, Alex T.; Steiner, A. W.; Brown, E. F.

2013-04-01

We extend the study of oscillating neutron stars to include observed magnetic field strengths. The strong magnetic field will alter the equilibrium composition of the outer neutron star crust. We construct a new neutron star crust model which predicts nuclear masses with an accuracy very close to that of the Finite Range Droplet Model. The mass model for equilibrium nuclei also includes recent developments in the nuclear physics, in particular, shell corrections and an updated neutron-drip line. We perturb our crust model to predict axial crust modes and assign them to observed giant flare quasi-periodic oscillation (QPO) frequencies from SGR 1806-20. The QPOs associated with the fundamental and harmonic crust modes can be used to constrain magnetar masses and radii. We use these modes and the phenomenological equations of state from Steiner et al. to find a magnetar crust which reproduces observations of SGR 1806-20. We find magnetar crusts which match observations for various magnetic field strengths and values of entrainment of the free neutron gas in the inner crust. For a crust without a magnetic field we obtain the approximate values of M = 1.35 Msun and R = 11.85 km. For a magnetized crust with the surface dipole field of SGR 1806-20 we obtain the approximate values of M = 1.25 Msun and R = 12.41 km. If there is less entrainment of the free neutron gas the magnetar requires a larger mass and radius to reproduce observations.

Thickness dependent quantum oscillations of transport properties in topological insulator Bi2Te3 thin films

NASA Astrophysics Data System (ADS)

Rogacheva, E. I.; Budnik, A. V.; Sipatov, A. Yu.; Nashchekina, O. N.; Dresselhaus, M. S.

2015-02-01

The dependences of the electrical conductivity, the Hall coefficient, and the Seebeck coefficient on the layer thickness d (d = 18-600 nm) of p-type topological insulator Bi2Te3 thin films grown by thermal evaporation in vacuum on glass substrates were obtained at room temperature. In the thickness range of d = 18-100 nm, sustained oscillations with a substantial amplitude were revealed. The observed oscillations are well approximated by a harmonic function with a period Δd = (9.5 ± 0.5) nm. At d > 100 nm, the transport coefficients practically do not change as d is increased. The oscillations of the kinetic properties are attributed to the quantum size effects due to the hole confinement in the Bi2Te3 quantum wells. The results of the theoretical calculations of Δd within the framework of a model of an infinitely deep potential well are in good agreement with the experimental results. It is suggested that the substantial amplitude of the oscillations and their sustained character as a function of d are connected with the topologically protected gapless surface states of Bi2Te3 and are inherent to topological insulators.

Statistics of work performed on a forced quantum oscillator.

PubMed

Talkner, Peter; Burada, P Sekhar; Hänggi, Peter

2008-07-01

Various aspects of the statistics of work performed by an external classical force on a quantum mechanical system are elucidated for a driven harmonic oscillator. In this special case two parameters are introduced that are sufficient to completely characterize the force protocol. Explicit results for the characteristic function of work and the corresponding probability distribution are provided and discussed for three different types of initial states of the oscillator: microcanonical, canonical, and coherent states. Depending on the choice of the initial state the probability distributions of the performed work may greatly differ. This result in particular also holds true for identical force protocols. General fluctuation and work theorems holding for microcanonical and canonical initial states are confirmed.

Resource-Competing Oscillator Network as a Model of Amoeba-Based Neurocomputer

NASA Astrophysics Data System (ADS)

Aono, Masashi; Hirata, Yoshito; Hara, Masahiko; Aihara, Kazuyuki

An amoeboid organism, Physarum, exhibits rich spatiotemporal oscillatory behavior and various computational capabilities. Previously, the authors created a recurrent neurocomputer incorporating the amoeba as a computing substrate to solve optimization problems. In this paper, considering the amoeba to be a network of oscillators coupled such that they compete for constant amounts of resources, we present a model of the amoeba-based neurocomputer. The model generates a number of oscillation modes and produces not only simple behavior to stabilize a single mode but also complex behavior to spontaneously switch among different modes, which reproduces well the experimentally observed behavior of the amoeba. To explore the significance of the complex behavior, we set a test problem used to compare computational performances of the oscillation modes. The problem is a kind of optimization problem of how to allocate a limited amount of resource to oscillators such that conflicts among them can be minimized. We show that the complex behavior enables to attain a wider variety of solutions to the problem and produces better performances compared with the simple behavior.

Finite-element time evolution operator for the anharmonic oscillator

NASA Technical Reports Server (NTRS)

Milton, Kimball A.

1995-01-01

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

Functional dependence of resonant harmonics on nanomechanical parameters in dynamic mode atomic force microscopy.

PubMed

Gramazio, Federico; Lorenzoni, Matteo; Pérez-Murano, Francesc; Rull Trinidad, Enrique; Staufer, Urs; Fraxedas, Jordi

2017-01-01

We present a combined theoretical and experimental study of the dependence of resonant higher harmonics of rectangular cantilevers of an atomic force microscope (AFM) as a function of relevant parameters such as the cantilever force constant, tip radius and free oscillation amplitude as well as the stiffness of the sample's surface. The simulations reveal a universal functional dependence of the amplitude of the 6th harmonic (in resonance with the 2nd flexural mode) on these parameters, which can be expressed in terms of a gun-shaped function. This analytical expression can be regarded as a practical tool for extracting qualitative information from AFM measurements and it can be extended to any resonant harmonics. The experiments confirm the predicted dependence in the explored 3-45 N/m force constant range and 2-345 GPa sample's stiffness range. For force constants around 25 N/m, the amplitude of the 6th harmonic exhibits the largest sensitivity for ultrasharp tips (tip radius below 10 nm) and polymers (Young's modulus below 20 GPa).

Fourier functional analysis for unsteady aerodynamic modeling

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Chin, Suei

1991-01-01

A method based on Fourier analysis is developed to analyze the force and moment data obtained in large amplitude forced oscillation tests at high angles of attack. The aerodynamic models for normal force, lift, drag, and pitching moment coefficients are built up from a set of aerodynamic responses to harmonic motions at different frequencies. Based on the aerodynamic models of harmonic data, the indicial responses are formed. The final expressions for the models involve time integrals of the indicial type advocated by Tobak and Schiff. Results from linear two- and three-dimensional unsteady aerodynamic theories as well as test data for a 70-degree delta wing are used to verify the models. It is shown that the present modeling method is accurate in producing the aerodynamic responses to harmonic motions and the ramp type motions. The model also produces correct trend for a 70-degree delta wing in harmonic motion with different mean angles-of-attack. However, the current model cannot be used to extrapolate data to higher angles-of-attack than that of the harmonic motions which form the aerodynamic model. For linear ramp motions, a special method is used to calculate the corresponding frequency and phase angle at a given time. The calculated results from modeling show a higher lift peak for linear ramp motion than for harmonic ramp motion. The current model also shows reasonably good results for the lift responses at different angles of attack.

Identification of aerodynamic models for maneuvering aircraft

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Hu, C. C.

1992-01-01

A Fourier analysis method was developed to analyze harmonic forced-oscillation data at high angles of attack as functions of the angle of attack and its time rate of change. The resulting aerodynamic responses at different frequencies are used to build up the aerodynamic models involving time integrals of the indicial type. An efficient numerical method was also developed to evaluate these time integrals for arbitrary motions based on a concept of equivalent harmonic motion. The method was verified by first using results from two-dimensional and three-dimensional linear theories. The developed models for C sub L, C sub D, and C sub M based on high-alpha data for a 70 deg delta wing in harmonic motions showed accurate results in reproducing hysteresis. The aerodynamic models are further verified by comparing with test data using ramp-type motions.

Large enhancement of interface second-harmonic generation near the zero-n(-) gap of a negative-index Bragg grating.

PubMed

D'Aguanno, Giuseppe; Mattiucci, Nadia; Bloemer, Mark J; Scalora, Michael

2006-03-01

We predict a large enhancement of interface second-harmonic generation near the zero-n(-) gap of a Bragg grating made of alternating layers of negative- and positive-index materials. Field localization and coherent oscillations of the nonlinear dipoles located at the structure's interfaces conspire to yield conversion efficiencies at least an order of magnitude greater than those achievable in the same length of nonlinear, phase-matched bulk material. These findings thus point to a new class of second-harmonic-generation devices made of standard centrosymmetric materials.

Modeling Bloch oscillations in ultra-small Josephson junctions

NASA Astrophysics Data System (ADS)

Vora, Heli; Kautz, Richard; Nam, Sae Woo; Aumentado, Jose

In a seminal paper, Likharev et al. developed a theory for ultra-small Josephson junctions with Josephson coupling energy (Ej) less than the charging energy (Ec) and showed that such junctions demonstrate Bloch oscillations which could be used to make a fundamental current standard that is a dual of the Josephson volt standard. Here, based on the model of Geigenmüller and Schön, we numerically calculate the current-voltage relationship of such an ultra-small junction which includes various error processes present in a nanoscale Josephson junction such as random quasiparticle tunneling events and Zener tunneling between bands. This model allows us to explore the parameter space to see the effect of each process on the width and height of the Bloch step and serves as a guide to determine whether it is possible to build a quantum current standard of a metrological precision using Bloch oscillations.

A frequency doubled pressure-tunable oscillator-amplifier dye laser system

NASA Technical Reports Server (NTRS)

Moriarty, A.; Heaps, W.; Davis, D. D.

1976-01-01

A tunable high-repetition-rate oscillator-amplifier dye-laser system is reported. The dye laser described was longitudinally pumped with the second harmonic of a Nd-YAG laser operating at 10 Hz. Using three Faraday-Perot etalons and pressure tuning, a maximum fundamental output power of the order of 6 MW with a corresponding spectral width of less than 0.003 nm at 564 nm was obtained. The fundamental at 564 nm was frequency doubled to give a maximum power level of 0.6 MW of second-harmonic output power with a spectral width less than 0.0015 nm at 282 nm. Frequency stability could be maintained to within approximately 15% of the line-width.

Mixed-mode oscillations in a three-store calcium dynamics model

NASA Astrophysics Data System (ADS)

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.

Oscillating water column structural model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Copeland, Guild; Bull, Diana L; Jepsen, Richard Alan

2014-09-01

An oscillating water column (OWC) wave energy converter is a structure with an opening to the ocean below the free surface, i.e. a structure with a moonpool. Two structural models for a non-axisymmetric terminator design OWC, the Backward Bent Duct Buoy (BBDB) are discussed in this report. The results of this structural model design study are intended to inform experiments and modeling underway in support of the U.S. Department of Energy (DOE) initiated Reference Model Project (RMP). A detailed design developed by Re Vision Consulting used stiffeners and girders to stabilize the structure against the hydrostatic loads experienced by amore » BBDB device. Additional support plates were added to this structure to account for loads arising from the mooring line attachment points. A simplified structure was designed in a modular fashion. This simplified design allows easy alterations to the buoyancy chambers and uncomplicated analysis of resulting changes in buoyancy.« less

Behavioral Model of Spin-Transfer Torque Driven Oscillation in a Nanomagnet

NASA Astrophysics Data System (ADS)

Buford, Benjamin; Jander, Albrecht; Dhagat, Pallavi

2011-10-01

We present a model written in Verilog-A, a behavioral description language, for spin-torque driven oscillations in a nanomagnet. Recent experiments have shown that spin-polarized current passing through a nanomagnet can cause magnetic dynamics from transfer of spin angular momentum. This can result in steady state oscillation of the magnetization at microwave frequencies [1]. Such spin torque oscillators are of interest due to the ability to rapidly tune their operating frequency by adjusting the applied magnetic field and their compatibility with existing CMOS fabrication methods. Our model is based upon the Landau-Lifshitz-Gilbert dynamics of a single- domain nanomagnet [2] and includes thermal agitation. We demonstrate the ability to model small angle, large angle, and out-of-plane precession. Additionally, we characterize the field and current boundaries between these regimes. Our Verilog-A model can be used in industry standard simulation tools alongside CMOS device models to simulate circuits that combine spintronic devices with CMOS control and processing circuitry. [4pt] [1] S. I. Kiselev et al., Nature, Vol. 425, pp. 380(3), (2003). [0pt] [2] L. Engelbrecht, Ph.D. Dissertation, Dept. Elect. Eng., Oregon State Univ., Corvallis, OR, (2011).

Chemical oscillator as a generalized Rayleigh oscillator.