A q-deformation of the Bogoliubov transformations

NASA Astrophysics Data System (ADS)

Arraut, Ivan; Segovia, Carlos

2018-02-01

An approach for q-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an *-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov transformation. Finally, we introduce a Hopf structure when q is a root of unity.

Deformation of biological cells in the acoustic field of an oscillating bubble.

PubMed

Zinin, Pavel V; Allen, John S

2009-02-01

In this work we develop a theoretical framework of the interaction of microbubbles with bacteria in the ultrasound field using a shell model of the bacteria, following an approach developed previously [P. V. Zinin, Phys. Rev. E 72, 61907 (2005)]. Within the shell model, the motion of the cell in an ultrasonic field is determined by the motion of three components: the internal viscous fluid, a thin elastic shell, and the surrounding viscous fluid. Several conclusions can be drawn from the modeling of sound interaction with a biological cell: (a) the characteristics of a cell's oscillations in an ultrasonic field are determined both by the elastic properties of the shell the viscosities of all components of the system, (b) for dipole quadrupole oscillations the cell's shell deforms due to a change in the shell area this oscillation depends on the surface area modulus K{A} , (c) the relative change in the area has a maximum at frequency f{K} approximately 1/2pi square root[K{A}(rhoa;{3})] , where a is the cell's radius and rho is its density. It was predicted that deformation of the cell wall at the frequency f{K} is high enough to rupture small bacteria such as E . coli in which the quality factor of natural vibrations is less than 1 (Q<1). For bacteria with high value quality factors (Q>1) , the area deformation has a strong peak near a resonance frequency f{K} however, the value of the deformation near the resonance frequency is not high enough to produce sufficient mechanical effect. The theoretical framework developed in this work can be extended for describing the deformation of a biological cell under any arbitrary, external periodic force including radiation forces unduced by acoustical (acoustical levitation) or optical waves (optical tweezers).

Deformation of biological cells in the acoustic field of an oscillating bubble

PubMed Central

Zinin, Pavel V.; Allen, John S.

2009-01-01

In this work we develop a theoretical framework of the interaction of microbubbles with bacteria in the ultrasound field using a shell model of the bacteria, following an approach developed previously [P. V. Zinin et al., Phys. Rev. E 72, 61907 (2005)]. Within the shell model, the motion of the cell in an ultrasonic field is determined by the motion of three components: the internal viscous fluid, a thin elastic shell, and the surrounding viscous fluid. Several conclusions can be drawn from the modeling of sound interaction with a biological cell: (a) the characteristics of a cell’s oscillations in an ultrasonic field are determined both by the elastic properties of the shell the viscosities of all components of the system, (b) for dipole quadrupole oscillations the cell’s shell deforms due to a change in the shell area this oscillation depends on the surface area modulus KA, (c) the relative change in the area has a maximum at frequency fK∼12πKA/(ρa3), where a is the cell’s radius and ρ is its density. It was predicted that deformation of the cell wall at the frequency fK is high enough to rupture small bacteria such as E. coli in which the quality factor of natural vibrations is less than 1 (Q < 1). For bacteria with high value quality factors (Q > 1), the area deformation has a strong peak near a resonance frequency fK; however, the value of the deformation near the resonance frequency is not high enough to produce sufficient mechanical effect. The theoretical framework developed in this work can be extended for describing the deformation of a biological cell under any arbitrary, external periodic force including radiation forces unduced by acoustical (acoustical levitation) or optical waves (optical tweezers). PMID:19391781

Deformation of biological cells in the acoustic field of an oscillating bubble

NASA Astrophysics Data System (ADS)

Zinin, Pavel V.; Allen, John S., III

2009-02-01

In this work we develop a theoretical framework of the interaction of microbubbles with bacteria in the ultrasound field using a shell model of the bacteria, following an approach developed previously [P. V. Zinin , Phys. Rev. E 72, 61907 (2005)]. Within the shell model, the motion of the cell in an ultrasonic field is determined by the motion of three components: the internal viscous fluid, a thin elastic shell, and the surrounding viscous fluid. Several conclusions can be drawn from the modeling of sound interaction with a biological cell: (a) the characteristics of a cell’s oscillations in an ultrasonic field are determined both by the elastic properties of the shell the viscosities of all components of the system, (b) for dipole quadrupole oscillations the cell’s shell deforms due to a change in the shell area this oscillation depends on the surface area modulus KA , (c) the relative change in the area has a maximum at frequency fK˜(1)/(2π)KA/(ρa3) , where a is the cell’s radius and ρ is its density. It was predicted that deformation of the cell wall at the frequency fK is high enough to rupture small bacteria such as E . coli in which the quality factor of natural vibrations is less than 1 (Q<1) . For bacteria with high value quality factors (Q>1) , the area deformation has a strong peak near a resonance frequency fK ; however, the value of the deformation near the resonance frequency is not high enough to produce sufficient mechanical effect. The theoretical framework developed in this work can be extended for describing the deformation of a biological cell under any arbitrary, external periodic force including radiation forces unduced by acoustical (acoustical levitation) or optical waves (optical tweezers).

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.

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.

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.

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.

(q,{mu}) and (p,q,{zeta})-exponential functions: Rogers-Szego'' polynomials and Fourier-Gauss transform

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

Hounkonnou, Mahouton Norbert; Nkouankam, Elvis Benzo Ngompe

2010-10-15

From the realization of q-oscillator algebra in terms of generalized derivative, we compute the matrix elements from deformed exponential functions and deduce generating functions associated with Rogers-Szego polynomials as well as their relevant properties. We also compute the matrix elements associated with the (p,q)-oscillator algebra (a generalization of the q-one) and perform the Fourier-Gauss transform of a generalization of the deformed exponential functions.

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.

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.

Self-sustained oscillations of a sinusoidally-deformed plate

NASA Astrophysics Data System (ADS)

Muriel, Diego F.; Cowen, Edwin A.

2015-11-01

Motivated by energy harvesting, the oscillatory motion of a deformed elastic material with aspect ratio Length/Width=2, immerse in an incompressible flow is studied experimentally. To induce the wave-like deformation a polycarbonate sheet is placed under longitudinal compression with external forcing provided by equispaced tension lines anchored in a frame. No additional constrains are placed in the material. Based on quantitative image-based edge detection, ADV, and PIV measurements, we document the existence of three natural states of motion. Bellow a critical velocity, a stable state presents a sinusoidal-like deformation with weak small perturbations. Above a critical velocity, instability appears in the form of a traveling wave with predictable dominant frequency accompanied by higher-order harmonics. As the flow velocity increases the instability converges faster to its limit cycle in the phase plane (e.g., vertical velocity and position), until the stable oscillatory mode transitions to chaos showing a broad energy spectrum and unstable limit cycle. The underlying objective is to induce the onset of the instability at lower critical velocities for higher bending rigidities, promoting possible energy extraction and increasing the range at which stable oscillations appear.

Complex metabolic oscillations in plants forced by harmonic irradiance.

PubMed Central

Nedbal, Ladislav; Brezina, Vítezslav

2002-01-01

Plants exposed to harmonically modulated irradiance, approximately 1 + cos(omegat), exhibit a complex periodic pattern of chlorophyll fluorescence emission that can be deconvoluted into a steady-state component, a component that is modulated with the frequency of the irradiance (omega), and into at least two upper harmonic components (2omega and 3omega). A model is proposed that accounts for the upper harmonics in fluorescence emission by nonlinear negative feedback regulation of photosynthesis. In contrast to simpler linear models, the model predicts that the steady-state fluorescence component will depend on the frequency of light modulation, and that amplitudes of all fluorescence components will exhibit resonance peak(s) when the irradiance frequency is tuned to an internal frequency of a regulatory component. The experiments confirmed that the upper harmonic components appear and exhibit distinct resonant peaks. The frequency of autonomous oscillations observed earlier upon an abrupt increase in CO(2) concentration corresponds to the sharpest of the resonant peaks of the forced oscillations. We propose that the underlying principles are general for a wide spectrum of negative-feedback regulatory mechanisms. The analysis by forced harmonic oscillations will enable us to examine internal dynamics of regulatory processes that have not been accessible to noninvasive fluorescence monitoring to date. PMID:12324435

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.

Ergodicity of a singly-thermostated harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, William Graham; Sprott, Julien Clinton; Hoover, Carol Griswold

2016-03-01

Although Nosé's thermostated mechanics is formally consistent with Gibbs' canonical ensemble, the thermostated Nosé-Hoover (harmonic) oscillator, with its mean kinetic temperature controlled, is far from ergodic. Much of its phase space is occupied by regular conservative tori. Oscillator ergodicity has previously been achieved by controlling two oscillator moments with two thermostat variables. Here we use computerized searches in conjunction with visualization to find singly-thermostated motion equations for the oscillator which are consistent with Gibbs' canonical distribution. Such models are the simplest able to bridge the gap between Gibbs' statistical ensembles and Newtonian single-particle dynamics.

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.

The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach

ERIC Educational Resources Information Center

Lee, Keeyung

2009-01-01

The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…

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…

Equity prices as a simple harmonic oscillator with noise

NASA Astrophysics Data System (ADS)

Ataullah, Ali; Tippett, Mark

2007-08-01

The centred return on the London Stock Exchange's FTSE All Share Index is modelled as a simple harmonic oscillator with noise over the period from 1 January, 1994 until 30 June 2006. Our empirical results are compatible with the hypothesis that there is a period in the FTSE All Share Index of between two and two and one half years. This means the centred return will on average continue to increase for about a year after reaching the minimum in its oscillatory cycle; alternatively, it will continue on average to decline for about a year after reaching a maximum. Our analysis also shows that there is potential to exploit the harmonic nature of the returns process to earn abnormal profits. Extending our analysis to the low energy states of a quantum harmonic oscillator is also suggested.

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.

Nonclassical Properties of Q-Deformed Superposition Light Field State

NASA Technical Reports Server (NTRS)

Ren, Min; Shenggui, Wang; Ma, Aiqun; Jiang, Zhuohong

1996-01-01

In this paper, the squeezing effect, the bunching effect and the anti-bunching effect of the superposition light field state which involving q-deformation vacuum state and q-Glauber coherent state are studied, the controllable q-parameter of the squeezing effect, the bunching effect and the anti-bunching effect of q-deformed superposition light field state are obtained.

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.

An algebraic cluster model based on the harmonic oscillator basis

NASA Technical Reports Server (NTRS)

Levai, Geza; Cseh, J.

1995-01-01

We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.

Predicting charmonium and bottomonium spectra with a quark harmonic oscillator

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

Quantization of the damped harmonic oscillator revisited

NASA Astrophysics Data System (ADS)

Baldiotti, M. C.; Fresneda, R.; Gitman, D. M.

2011-04-01

We return to the description of the damped harmonic oscillator with an assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model proposed by one of the authors. We argue the latter has better high energy behavior and is connected to existing open-systems approaches.

All-optical and broadband microwave fundamental/sub-harmonic I/Q down-converters.

PubMed

Gao, Yongsheng; Wen, Aijun; Jiang, Wei; Fan, Yangyu; He, You

2018-03-19

Microwave I/Q down-converters are frequently used in image-reject super heterodyne receivers, zero intermediate frequency (zero-IF) receivers, and phase/frequency discriminators. However, due to the electronic bottleneck, conventional microwave I/Q mixers face a serious bandwidth limitation, I/Q imbalance, and even-order distortion. In this paper, photonic microwave fundamental and sub-harmonic I/Q down-converters are presented using a polarization division multiplexing dual-parallel Mach-Zehnder modulator (PDM-DPMZM). Thanks to all-optical manipulation, the proposed system features an ultra-wide operating band (7-40 GHz in the fundamental I/Q down-converter, and 10-40 GHz in the sub-harmonic I/Q down-converter) and an excellent I/Q balance (maximum 0.7 dB power imbalance and 1 degree phase imbalance). The conversion gain, noise figure (NF), even-order distortion, and spurious free dynamic range (SFDR) are also improved by LO power optimization and balanced detection. Using the proposed system, a high image rejection ratio is demonstrated for a super heterodyne receiver, and good EVMs over a wide RF power range is demonstrated for a zero-IF receiver. The proposed broadband photonic microwave fundamental and sub-harmonic I/Q down-converters may find potential applications in multi-band satellite, ultra-wideband radar and frequency-agile electronic warfare systems.

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…

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.

Description Of Scoliotic Deformity Pattern By Harmonic Functions

NASA Astrophysics Data System (ADS)

Drerup, Burkhard; Hierholzer, Eberhard

1989-04-01

Frontal radiographs of scoliotic deformity of the spine reveal a characteristic pattern of lateral deviation, lateral tilt and axial rotation of vertebrae. In order to study interrelations between deformation parameters 478 radiographs of idiopathic scolioses, 23 of scolioses after Wilms-tumor treatment and 18 of scolioses following poliomyelitis were digitized. From these the curves of lateral deviation, tilt and rotation are calculated and fitted by Fourier series. By restriction to the first harmonic, analysis reduces to the analysis of a single phase and amplitude for each curve. Justification of this simplification will be discussed. Results provide a general geometric description of scoliotic deformity.

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.

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.

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.

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…

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.

Investigation of spin-zero bosons in q-deformed relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Sobhani, H.; Chung, W. S.; Hassanabadi, H.

2018-04-01

In this article, Scattering states of Klein-Gordon equation for three scatter potentials of single and double Dirac delta and a potential well in the q-deformed formalism of relativistic quantum mechanics have been derived. At first, we discussed how q-deformed formalism can be constructed and used. Postulates of this q-deformed quantum mechanics are noted. Then scattering problems for spin-zero bosons are studied.

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.

Disappearing Q operator

NASA Astrophysics Data System (ADS)

Jones, H. F.; Rivers, R. J.

2007-01-01

In the Schrödinger formulation of non-Hermitian quantum theories a positive-definite metric operator η≡e-Q must be introduced in order to ensure their probabilistic interpretation. This operator also gives an equivalent Hermitian theory, by means of a similarity transformation. If, however, quantum mechanics is formulated in terms of functional integrals, we show that the Q operator makes only a subliminal appearance and is not needed for the calculation of expectation values. Instead, the relation to the Hermitian theory is encoded via the external source j(t). These points are illustrated and amplified for two non-Hermitian quantum theories: the Swanson model, a non-Hermitian transform of the simple harmonic oscillator, and the wrong-sign quartic oscillator, which has been shown to be equivalent to a conventional asymmetric quartic oscillator.

Effective field theory in the harmonic oscillator basis

DOE PAGES

Binder, S.; Ekström, Jan A.; Hagen, Gaute; ...

2016-04-25

In this paper, we develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leadingmore » order. Finally, many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.« less

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.

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.

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)

Compact, passively Q-switched, all-solid-state master oscillator-power amplifier-optical parametric oscillator (MOPA-OPO) system pumped by a fiber-coupled diode laser generating high-brightness, tunable, ultraviolet radiation.

PubMed

Peuser, Peter; Platz, Willi; Fix, Andreas; Ehret, Gerhard; Meister, Alexander; Haag, Matthias; Zolichowski, Paul

2009-07-01

We report on a compact, tunable ultraviolet laser system that consists of an optical parametric oscillator (OPO) and a longitudinally diode-pumped Nd:YAG master oscillator-power amplifier (MOPA). The pump energy for the whole laser system is supplied via a single delivery fiber. Nanosecond pulses are produced by an oscillator that is passively Q-switched by a Cr(4+):YAG crystal. The OPO is pumped by the second harmonic of the Nd:YAG MOPA. Continuously tunable radiation is generated by an intracavity sum-frequency mixing process within the OPO in the range of 245-260 nm with high beam quality. Maximum pulse energies of 1.2 mJ were achieved, which correspond to an optical efficiency of 3.75%, relating to the pulse energy of the MOPA at 1064 nm.

A Simple Mechanical Model for the Isotropic Harmonic Oscillator

ERIC Educational Resources Information Center

Nita, Gelu M.

2010-01-01

A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)

Time-varying q-deformed dark energy interacts with dark matter

NASA Astrophysics Data System (ADS)

Dil, Emre; Kolay, Erdinç

We propose a new model for studying the dark constituents of the universe by regarding the dark energy as a q-deformed scalar field interacting with the dark matter, in the framework of standard general relativity. Here we assume that the number of particles in each mode of the q-deformed scalar field varies in time by the particle creation and annihilation. We first describe the q-deformed scalar field dark energy quantum-field theoretically, then construct the action and the dynamical structure of these interacting dark sectors, in order to study the dynamics of the model. We perform the phase space analysis of the model to confirm and interpret our proposal by searching the stable attractor solutions implying the late-time accelerating phase of the universe. We then obtain the result that when interaction and equation-of-state parameter of the dark matter evolve from the present day values into a particular value, the dark energy turns out to be a q-deformed scalar field.

Disappearing Q operator

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

Jones, H. F.; Rivers, R. J.

In the Schroedinger formulation of non-Hermitian quantum theories a positive-definite metric operator {eta}{identical_to}e{sup -Q} must be introduced in order to ensure their probabilistic interpretation. This operator also gives an equivalent Hermitian theory, by means of a similarity transformation. If, however, quantum mechanics is formulated in terms of functional integrals, we show that the Q operator makes only a subliminal appearance and is not needed for the calculation of expectation values. Instead, the relation to the Hermitian theory is encoded via the external source j(t). These points are illustrated and amplified for two non-Hermitian quantum theories: the Swanson model, a non-Hermitianmore » transform of the simple harmonic oscillator, and the wrong-sign quartic oscillator, which has been shown to be equivalent to a conventional asymmetric quartic oscillator.« less

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

BFV-BRST analysis of the classical and quantum q-deformations of the sl(2) algebra

NASA Astrophysics Data System (ADS)

Dayi, O. F.

1994-01-01

BFV--BRST charge for q-deformed algebras is not unique. Different constructions of it in the classical as well as in the quantum phase space for the $q$-deformed algebra sl_q(2) are discussed. Moreover, deformation of the phase space without deforming the generators of sl(2) is considered. $\\hbar$-q-deformation of the phase space is shown to yield the Witten's second deformation. To study the BFV--BRST cohomology problem when both the quantum phase space and the group are deformed, a two parameter deformation of sl(2) is proposed, and its BFV-BRST charge is given.

κ-deformed Dirac oscillator in an external magnetic field

NASA Astrophysics Data System (ADS)

Chargui, Y.; Dhahbi, A.; Cherif, B.

2018-04-01

We study the solutions of the (2 + 1)-dimensional κ-deformed Dirac oscillator in the presence of a constant transverse magnetic field. We demonstrate how the deformation parameter affects the energy eigenvalues of the system and the corresponding eigenfunctions. Our findings suggest that this system could be used to detect experimentally the effect of the deformation. We also show that the hidden supersymmetry of the non-deformed system reduces to a hidden pseudo-supersymmetry having the same algebraic structure as a result of the κ-deformation.

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

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.

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.

The Quantum Arnold Transformation for the damped harmonic oscillator: from the Caldirola-Kanai model toward the Bateman model

NASA Astrophysics Data System (ADS)

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

2012-08-01

Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.

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

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.

Modeling Stretching Modes of Common Organic Molecules with the Quantum Mechanical Harmonic Oscillator: An Undergraduate Vibrational Spectroscopy Laboratory Exercise

ERIC Educational Resources Information Center

Parnis, J. Mark; Thompson, Matthew G. K.

2004-01-01

An introductory undergraduate physical organic chemistry exercise that introduces the harmonic oscillator's use in vibrational spectroscopy is developed. The analysis and modeling exercise begins with the students calculating the stretching modes of common organic molecules with the help of the quantum mechanical harmonic oscillator (QMHO) model.

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

The gauge transformations of the constrained q-deformed KP hierarchy

NASA Astrophysics Data System (ADS)

Geng, Lumin; Chen, Huizhan; Li, Na; Cheng, Jipeng

2018-06-01

In this paper, we mainly study the gauge transformations of the constrained q-deformed Kadomtsev-Petviashvili (q-KP) hierarchy. Different from the usual case, we have to consider the additional constraints on the Lax operator of the constrained q-deformed KP hierarchy, since the form of the Lax operator must be kept when constructing the gauge transformations. For this reason, the selections of generating functions in elementary gauge transformation operators TD and TI must be very special, which are from the constraints in the Lax operator. At last, we consider the successive applications of n-step of TD and k-step of TI gauge transformations.

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…

Which Q-analogue of the squeezed oscillator?

NASA Technical Reports Server (NTRS)

Solomon, Allan I.

1993-01-01

The noise (variance squared) of a component of the electromagnetic field - considered as a quantum oscillator - in the vacuum is equal to one half, in appropriate units (taking Planck's constant and the mass and frequency of the oscillator all equal to 1). A practical definition of a squeezed state is one for which the noise is less than the vacuum value - and the amount of squeezing is determined by the appropriate ratio. Thus the usual coherent (Glauber) states are not squeezed, as they produce the same variance as the vacuum. However, it is not difficult to define states analogous to coherent states which do have this noise-reducing effect. In fact, they are coherent states in the more general group sense but with respect to groups other than the Heisenberg-Weyl Group which defines the Glauber states. The original, conventional squeezed state in quantum optics is that associated with the group SU(1,1). Just as the annihilation operator a of a single photon mode (and its hermitian conjugate a, the creation operator) generates the Heisenberg Weyl algebra, so the pair-photon operator a(sup 2) and its conjugate generates the algebra of the group SU(1,1). Another viewpoint, more productive from the calculational stance, is to note that the automorphism group of the Heisenberg-Weyl algebra is SU(1,1). Needless to say, each of these viewpoints generalizes differently to the quantum group context. Both are discussed. The following topics are addressed: conventional coherent and squeezed states; eigenstate definitions; exponential definitions; algebra (group) definitions; automorphism group definition; example: signal-to-noise ratio; q-coherent and q-squeezed states; M and P q-bosons; eigenstate definitions; exponential definitions; algebra (q-group) definitions; and automorphism q-group definition.

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

Towards classical spectrum generating algebras for f-deformations

NASA Astrophysics Data System (ADS)

Kullock, Ricardo; Latini, Danilo

2016-01-01

In this paper we revise the classical analog of f-oscillators, a generalization of q-oscillators given in Man'ko et al. (1997) [8], in the framework of classical spectrum generating algebras (SGA) introduced in Kuru and Negro (2008) [9]. We write down the deformed Poisson algebra characterizing the entire family of non-linear oscillators and construct its general solution algebraically. The latter, covering the full range of f-deformations, shows an energy dependence both in the amplitude and the frequency of the motion.

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.

Oscillations of a deformed liquid drop in an acoustic field

NASA Astrophysics Data System (ADS)

Shi, Tao; Apfel, Robert E.

1995-07-01

The oscillations of an axially symmetric liquid drop in an acoustic standing wave field in air have been studied using the boundary integral method. The interaction between the drop oscillation and sound field has been included in this analysis. Our computations focus on the frequency shift of small-amplitude oscillations of an acoustically deformed drop typical of a drop levitated in air. In the presence or absence of gravity, the trend and the magnitude of the frequency shift have been given in terms of drop size, drop deformation, and the strength of the sound field. Our calculations are compared with experiments performed on the United States Microgravity Laboratory (USML-1) and with ground-based measurements, and are found to be in good agreement within the accuracy of the experimental data.

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

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

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.

All-optical Photonic Oscillator with High-Q Whispering Gallery Mode Resonators

NASA Technical Reports Server (NTRS)

Savchenkov, Anatoliy A.; Matsko, Andrey B.; Strekalov, Dmitry; Mohageg, Makan; Iltchenko, Vladimir S.; Maleki, Lute

2004-01-01

We demonstrated low threshold optical photonic hyper-parametric oscillator in a high-Q 10(exp 10) CaF2 whispering gallery mode resonator which generates stable 8.5 GHz signal. The oscillations result from the resonantly enhanced four wave mixing occurring due to Kerr nonlinearity of the material.

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.

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.

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…

Smoothly deformed light

NASA Technical Reports Server (NTRS)

Stenholm, Stig

1993-01-01

A single mode cavity is deformed smoothly to change its electromagnetic eigenfrequency. The system is modeled as a simple harmonic oscillator with a varying period. The Wigner function of the problem is obtained exactly by starting with a squeezed initial state. The result is evaluated for a linear change of the cavity length. The approach to the adiabatic limit is investigated. The maximum squeezing is found to occur for smooth change lasting only a fraction of the oscillational period. However, only a factor of two improvement over the adiabatic result proves to be possible. The sudden limit cannot be investigated meaningfully within the model.

Quadratic resonance in the three-dimensional oscillations of inviscid drops with surface tension

NASA Technical Reports Server (NTRS)

Natarajan, R.; Brown, R. A.

1986-01-01

The moderate-amplitude, three-dimensional oscillations of an inviscid drop are described in terms of spherical harmonics. Specific oscillation modes are resonantly coupled by quadratic nonlinearities caused by inertia, capillarity, and drop deformation. The equations describing the interactions of these modes are derived from the variational principle for the appropriate Lagrangian by expressing the modal amplitudes to be functions of a slow time scale and by preaveraging the Lagrangian over the time scale of the primary oscillations. Stochastic motions are predicted for nonaxisymmetric deformations starting from most initial conditions, even those arbitrarily close to the axisymmetric shapes. The stochasticity is characterized by a redistribution of the energy contained in the initial deformation over all the degrees of freedom of the interacting modes.

Investigation of Bose-Einstein Condensates in q-Deformed Potentials with First Order Perturbation Theory

NASA Astrophysics Data System (ADS)

Nutku, Ferhat; Aydıner, Ekrem

2018-02-01

The Gross-Pitaevskii equation, which is the governor equation of Bose-Einstein condensates, is solved by first order perturbation expansion under various q-deformed potentials. Stationary probability distributions reveal one and two soliton behavior depending on the type of the q-deformed potential. Additionally a spatial shift of the probability distribution is found for the dark soliton solution, when the q parameter is changed.

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.

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.

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.

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

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.

Dynamical Energy Gap Engineering in Graphene via Oscillating Out-of-Plane Deformations

NASA Astrophysics Data System (ADS)

Sandler, Nancy; Zhai, Dawei

The close relation between electronic properties and mechanical deformations in graphene has been the topic of active research in recent years. Interestingly, the effect of deformations on electronic properties can be understood in terms of pseudo-magnetic fields, whose spatial distribution and intensity are controllable via the deformation geometry. Previous results showed that electromagnetic fields (light) have the potential to induce dynamical gaps in graphene's energy bands, transforming graphene from a semimetal to a semiconductor. However, laser frequencies required to achieve these regimes are in the THz regime, which imposes challenges for practical purposes. In this talk we report a novel method to create dynamical gaps using oscillating mechanical deformations, i.e., via time-dependent pseudo-magnetic fields. Using the Floquet formalism we show the existence of a dynamical gap in the band structure at energies set by the frequency of the oscillation, and with a magnitude tuned by the geometry of the deformation. This dynamical-mechanical manipulation strategy appears as a promising venue to engineer electronic properties of suspended graphene devices. Work supported by NSF-DMR 1508325.

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.

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.

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.

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.

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.

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.

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.

Axially deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: A new version of the program

NASA Astrophysics Data System (ADS)

Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.

2013-06-01

We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions

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

DOE PAGES

Schunck, N.; Dobaczewski, J.; Satuła, W.; ...

2017-03-27

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

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

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

Schunck, N.; Dobaczewski, J.; Satuła, W.

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

Nonlinear optical oscillation dynamics in high-Q lithium niobate microresonators.

PubMed

Sun, Xuan; Liang, Hanxiao; Luo, Rui; Jiang, Wei C; Zhang, Xi-Cheng; Lin, Qiang

2017-06-12

Recent advance of lithium niobate microphotonic devices enables the exploration of intriguing nonlinear optical effects. We show complex nonlinear oscillation dynamics in high-Q lithium niobate microresonators that results from unique competition between the thermo-optic nonlinearity and the photorefractive effect, distinctive to other device systems and mechanisms ever reported. The observed phenomena are well described by our theory. This exploration helps understand the nonlinear optical behavior of high-Q lithium niobate microphotonic devices which would be crucial for future application of on-chip nonlinear lithium niobate photonics.

q-Deformed Minkowski Algebra and Its Space-Time Lattice

NASA Astrophysics Data System (ADS)

Wess, J.

2Max-Planck-Institut für Physik (Werner-Heisenberg-Institut) Föhringer Ring 6, D-80805 MünchenAbstract. We have asked how the Heisenberg relations of space and time change if we replace the Lorentz group by a q-deformed Lorentz group (Lorek et al. 1997).

Effect of bimodal harmonic structure design on the deformation behaviour and mechanical properties of Co-Cr-Mo alloy.

PubMed

Vajpai, Sanjay Kumar; Sawangrat, Choncharoen; Yamaguchi, Osamu; Ciuca, Octav Paul; Ameyama, Kei

2016-01-01

In the present work, Co-Cr-Mo alloy compacts with a unique bimodal microstructural design, harmonic structure design, were successfully prepared via a powder metallurgy route consisting of controlled mechanical milling of pre-alloyed powders followed by spark plasma sintering. The harmonic structured Co-Cr-Mo alloy with bimodal grain size distribution exhibited relatively higher strength together with higher ductility as compared to the coarse-grained specimens. The harmonic Co-Cr-Mo alloy exhibited a very complex deformation behavior wherein it was found that the higher strength and the high retained ductility are derived from fine-grained shell and coarse-grained core regions, respectively. Finally, it was observed that the peculiar spatial/topological arrangement of stronger fine-grained and ductile coarse-grained regions in the harmonic structure promotes uniformity of strain distribution, leading to improved mechanical properties by suppressing the localized plastic deformation during straining. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

Quantifying cortical surface harmonic deformation with stereovision during open cranial neurosurgery

NASA Astrophysics Data System (ADS)

Ji, Songbai; Fan, Xiaoyao; Roberts, David W.; Paulsen, Keith D.

2012-02-01

Cortical surface harmonic motion during open cranial neurosurgery is well observed in image-guided neurosurgery. Recently, we quantified cortical surface deformation noninvasively with synchronized blood pressure pulsation (BPP) from a sequence of stereo image pairs using optical flow motion tracking. With three subjects, we found the average cortical surface displacement can reach more than 1 mm and in-plane principal strains of up to 7% relative to the first image pair. In addition, the temporal changes in deformation and strain were in concert with BPP and patient respiration [1]. However, because deformation was essentially computed relative to an arbitrary reference, comparing cortical surface deformation at different times was not possible. In this study, we extend the technique developed earlier by establishing a more reliable reference profile of the cortical surface for each sequence of stereo image acquisitions. Specifically, fast Fourier transform (FFT) was applied to the dynamic cortical surface deformation, and the fundamental frequencies corresponding to patient respiration and BPP were identified, which were used to determine the number of image acquisitions for use in averaging cortical surface images. This technique is important because it potentially allows in vivo characterization of soft tissue biomechanical properties using intraoperative stereovision and motion tracking.

Tsallis p, q-deformed Touchard polynomials and Stirling numbers

NASA Astrophysics Data System (ADS)

Herscovici, O.; Mansour, T.

2017-01-01

In this paper, we develop and investigate a new two-parametrized deformation of the Touchard polynomials, based on the definition of the NEXT q-exponential function of Tsallis. We obtain new generalizations of the Stirling numbers of the second kind and of the binomial coefficients and represent two new statistics for the set partitions.

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.

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

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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.

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.

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.

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.

High-Q Microsphere Cavity for Laser Stabilization and Optoelectronic Microwave Oscillator

NASA Technical Reports Server (NTRS)

Ilchenko, Vladimir S.; Yao, X. Steve; Maleki, Lute

2000-01-01

With submillimeter size and optical Q up to approximately 10 (exp 10), microspheres with whispering-gallery (WG) modes are attractive new component for fiber-optics/photonics applications and a potential core in ultra-compact high-spectral-purity optical and microwave oscillators. In addition to earlier demonstrated optical locking of diode laser to WG mode in a microsphere, we report on microsphere application in the microwave optoelectronic oscillator, OEO. In OEO, a steady-state microwave modulation of optical carrier is obtained in a closed loop including electro-optical modulator, fiber-optic delay, detector and microwave amplifier. OEO demonstrates exceptionally low phase noise (-140 dBc/Hz at l0kHz from approximately 10GHz carrier) with a fiber length approximately 2km. Current technology allows to put all parts of the OEO, except the fiber, on the same chip. Microspheres, with their demonstrated Q equivalent to a kilometer fiber storage, can replace fiber delays in a truly integrated device. We have obtained microwave oscillation in microsphere-based OEO at 5 to 18 GHz, with 1310nm and 1550nm optical carrier, in two configurations: 1) with external DFB pump laser, and 2) with a ring laser including microsphere and a fiber optic amplifier. Also reported is a simple and efficient fiber coupler for microspheres facilitating their integration with existing fiber optics devices.

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

Modeling stock return distributions with a quantum harmonic oscillator

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Affine q-deformed symmetry and the classical Yang-Baxter σ-model

NASA Astrophysics Data System (ADS)

Delduc, F.; Kameyama, T.; Magro, M.; Vicedo, B.

2017-03-01

The Yang-Baxter σ-model is an integrable deformation of the principal chiral model on a Lie group G. The deformation breaks the G × G symmetry to U(1)rank( G) × G. It is known that there exist non-local conserved charges which, together with the unbroken U(1)rank( G) local charges, form a Poisson algebra [InlineMediaObject not available: see fulltext.], which is the semiclassical limit of the quantum group {U}_q(g) , with g the Lie algebra of G. For a general Lie group G with rank( G) > 1, we extend the previous result by constructing local and non-local conserved charges satisfying all the defining relations of the infinite-dimensional Poisson algebra [InlineMediaObject not available: see fulltext.], the classical analogue of the quantum loop algebra {U}_q(Lg) , where Lg is the loop algebra of g. Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable σ-model.

An inverse hyper-spherical harmonics-based formulation for reconstructing 3D volumetric lung deformations

NASA Astrophysics Data System (ADS)

Santhanam, Anand P.; Min, Yugang; Mudur, Sudhir P.; Rastogi, Abhinav; Ruddy, Bari H.; Shah, Amish; Divo, Eduardo; Kassab, Alain; Rolland, Jannick P.; Kupelian, Patrick

2010-07-01

A method to estimate the deformation operator for the 3D volumetric lung dynamics of human subjects is described in this paper. For known values of air flow and volumetric displacement, the deformation operator and subsequently the elastic properties of the lung are estimated in terms of a Green's function. A Hyper-Spherical Harmonic (HSH) transformation is employed to compute the deformation operator. The hyper-spherical coordinate transformation method discussed in this paper facilitates accounting for the heterogeneity of the deformation operator using a finite number of frequency coefficients. Spirometry measurements are used to provide values for the airflow inside the lung. Using a 3D optical flow-based method, the 3D volumetric displacement of the left and right lungs, which represents the local anatomy and deformation of a human subject, was estimated from 4D-CT dataset. Results from an implementation of the method show the estimation of the deformation operator for the left and right lungs of a human subject with non-small cell lung cancer. Validation of the proposed method shows that we can estimate the Young's modulus of each voxel within a 2% error level.

Simulations of fully deformed oscillating flux tubes

NASA Astrophysics Data System (ADS)

Karampelas, K.; Van Doorsselaere, T.

2018-02-01

Context. In recent years, a number of numerical studies have been focusing on the significance of the Kelvin-Helmholtz instability in the dynamics of oscillating coronal loops. This process enhances the transfer of energy into smaller scales, and has been connected with heating of coronal loops, when dissipation mechanisms, such as resistivity, are considered. However, the turbulent layer is expected near the outer regions of the loops. Therefore, the effects of wave heating are expected to be confined to the loop's external layers, leaving their denser inner parts without a heating mechanism. Aim. In the current work we aim to study the spatial evolution of wave heating effects from a footpoint driven standing kink wave in a coronal loop. Methods: Using the MPI-AMRVAC code, we performed ideal, three dimensional magnetohydrodynamic simulations of footpoint driven transverse oscillations of a cold, straight coronal flux tube, embedded in a hotter environment. We have also constructed forward models for our simulation using the FoMo code. Results: The developed transverse wave induced Kelvin-Helmholtz (TWIKH) rolls expand throughout the tube cross-section, and cover it entirely. This turbulence significantly alters the initial density profile, leading to a fully deformed cross section. As a consequence, the resistive and viscous heating rate both increase over the entire loop cross section. The resistive heating rate takes its maximum values near the footpoints, while the viscous heating rate at the apex. Conclusions: We conclude that even a monoperiodic driver can spread wave heating over the whole loop cross section, potentially providing a heating source in the inner loop region. Despite the loop's fully deformed structure, forward modelling still shows the structure appearing as a loop. A movie attached to Fig. 1 is available at http://https://www.aanda.org

Multiparameter bifurcations and mixed-mode oscillations in Q-switched CO2 lasers.

PubMed

Doedel, Eusebius J; Pando L, Carlos L

2014-05-01

We study the origin of mixed-mode oscillations and related bifurcations in a fully molecular laser model that describes CO2 monomode lasers with a slow saturable absorber. Our study indicates that the presence of isolas of periodic mixed-mode oscillations, as the pump parameter and the cavity-frequency detuning change, is inherent to Q-switched CO2 monomode lasers. We compare this model, known as the dual four-level model, to the more conventional 3:2 model and to a CO2 laser model for fast saturable absorbers. In these models, we find similarities as well as qualitative differences, such as the different nature of the homoclinic tangency to a relevant unstable periodic orbit, where the Gavrilov-Shilnikov theory and its extensions may hold. We also show that there are isolas of periodic mixed-mode oscillations in a model for CO2 lasers with modulated losses, as the pump parameter varies. The coarse-grained bifurcation diagrams of the periodic mixed-mode oscillations in these models suggest that these oscillations belong to similar classes.

Evaluating signal and noise spectral density of a qPlus sensor with an active feedback control

NASA Astrophysics Data System (ADS)

Lee, Manhee; An, Sangmin; Jhe, Wonho

2018-05-01

Q-control technique enables to actively change the quality factor of the probe oscillation in dynamic atomic force microscopy. The Q-control is realized by adding a self-feedback loop into the original actuation-detection system, in which a damping force with controllable damping coefficient in magnitude and sign is applied to the oscillating probe. While the applied force alters the total damping interaction and thus the overall `signal' of the probe motion, the added feedback system changes the `noise' of the motion as well. Here, we systematically investigate the signal, the noise, and the signal-to-noise ratio of the qPlus sensor under the active Q-control. We quantify the noise of the qPlus motion by measuring the noise spectral density, which is reproduced by a harmonic oscillator model including the thermal and the measurement noises. We show that the noise signal increases with the quality factor controlled, scaling as the square root of the quality factor. Because the overall signal is linearly proportional to the quality factor, the signal-to-noise ratio scales as the square root of the quality factor. The Q-controlled qPlus with a highly enhanced Q, up to 10,000 in air, leads to the minimum detectable force gradient of 0.001 N/m, which would enhance the capability of the qPlus sensor for atomic force microscopy and spectroscopy.

A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⨁ so(n) ⨁ so(N-n)

NASA Astrophysics Data System (ADS)

Fazlul Hoque, Md; Marquette, Ian; Zhang, Yao-Zhong

2015-11-01

We introduce a new family of N dimensional quantum superintegrable models consisting of double singular oscillators of type (n, N-n). The special cases (2,2) and (4,4) have previously been identified as the duals of 3- and 5-dimensional deformed Kepler-Coulomb systems with u(1) and su(2) monopoles, respectively. The models are multiseparable and their wave functions are obtained in (n, N-n) double-hyperspherical coordinates. We obtain the integrals of motion and construct the finitely generated polynomial algebra that is the direct sum of a quadratic algebra Q(3) involving three generators, so(n), so(N-n) (i.e. Q(3) ⨁ so(n) ⨁ so(N-n)). The structure constants of the quadratic algebra itself involve the Casimir operators of the two Lie algebras so(n) and so(N-n). Moreover, we obtain the finite dimensional unitary representations (unirreps) of the quadratic algebra and present an algebraic derivation of the degenerate energy spectrum of the superintegrable model.

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.

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

NASA Astrophysics Data System (ADS)

Dobaczewski, J.; Olbratowski, P.

2005-05-01

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

Tooth-meshing-harmonic static-transmission-error amplitudes of helical gears

NASA Astrophysics Data System (ADS)

Mark, William D.

2018-01-01

The static transmission errors of meshing gear pairs arise from deviations of loaded tooth working surfaces from equispaced perfect involute surfaces. Such deviations consist of tooth-pair elastic deformations and geometric deviations (modifications) of tooth working surfaces. To a very good approximation, the static-transmission-error tooth-meshing-harmonic amplitudes of helical gears are herein expressed by superposition of Fourier transforms of the quantities: (1) the combination of tooth-pair elastic deformations and geometric tooth-pair modifications and (2) fractional mesh-stiffness fluctuations, each quantity (1) and (2) expressed as a function of involute "roll distance." Normalization of the total roll-distance single-tooth contact span to unity allows tooth-meshing-harmonic amplitudes to be computed for different shapes of the above-described quantities (1) and (2). Tooth-meshing harmonics p = 1, 2, … are shown to occur at Fourier-transform harmonic values of Qp, p = 1, 2, …, where Q is the actual (total) contact ratio, thereby verifying its importance in minimizing transmission-error tooth-meshing-harmonic amplitudes. Two individual shapes and two series of shapes of the quantities (1) and (2) are chosen to illustrate a wide variety of shapes. In most cases representative of helical gears, tooth-meshing-harmonic values p = 1, 2, … are shown to occur in Fourier-transform harmonic regions governed by discontinuities arising from tooth-pair-contact initiation and termination, thereby showing the importance of minimizing such discontinuities. Plots and analytical expressions for all such Fourier transforms are presented, thereby illustrating the effects of various types of tooth-working-surface modifications and tooth-pair stiffnesses on transmission-error generation.

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.

Study of phase transition of even and odd nuclei based on q-deforme SU(1,1) algebraic model

NASA Astrophysics Data System (ADS)

Jafarizadeh, M. A.; Amiri, N.; Fouladi, N.; Ghapanvari, M.; Ranjbar, Z.

2018-04-01

The q-deformed Hamiltonian for the SO (6) ↔ U (5) transitional case in s, d interaction boson model (IBM) can be constructed by using affine SUq (1 , 1) Lie algebra in the both IBM-1 and 2 versions and IBFM. In this research paper, we have studied the energy spectra of 120-128Xe isotopes and 123-131Xe isotopes and B(E2) transition probabilities of 120-128Xe isotopes in the shape phase transition region between the spherical and gamma unstable deformed shapes of the theory of quantum deformation. The theoretical results agree with the experimental data fairly well. It is shown that the q-deformed SO (6) ↔ U (5) transitional dynamical symmetry remains after deformation.

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.

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.

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 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.

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.

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 noise and squeezing in optical parametric oscillator with arbitrary output coupling

NASA Technical Reports Server (NTRS)

Prasad, Sudhakar

1993-01-01

The redistribution of intrinsic quantum noise in the quadratures of the field generated in a sub-threshold degenerate optical parametric oscillator exhibits interesting dependences on the individual output mirror transmittances, when they are included exactly. We present a physical picture of this problem, based on mirror boundary conditions, which is valid for arbitrary transmittances. Hence, our picture applies uniformly to all values of the cavity Q factor representing, in the opposite extremes, both perfect oscillator and amplifier configurations. Beginning with a classical second-harmonic pump, we shall generalize our analysis to the finite amplitude and phase fluctuations of the pump.

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

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.

Third harmonic generation of a short pulse laser in a plasma density ripple created by a machining beam

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

Liu, C. S.; Tripathi, V. K.

An intense machining laser beam, impinged on a gas jet target, causes space periodic ionization of the gas and heats the electrons. The nonuniform plasma pressure leads to atomic density redistribution. When, after a suitable time delay, a second more intense laser pulse is launched along the periodicity wave vector q-vector, a plasma density ripple n{sub q} is instantly created, leading to resonant third harmonic generation when q=4{omega}{sub p}{sup 2}/(3{omega}c{gamma}{sub 0}), where {omega}{sub p} is the plasma frequency, {omega} is the laser frequency, and {gamma}{sub 0} is the electron Lorentz factor. The third harmonic is produced through the beating ofmore » ponderomotive force induced second harmonic density oscillations and the quiver velocity of electrons at the fundamental. The relativistic mass nonlinearity plays no role in resonant coupling. The energy conversion efficiency scales as the square of plasma density and square of depth of density ripple, and is {approx}0.2% for normalized laser amplitude a{sub o}{approx}1 in a plasma of 1% critical density with 20% density ripple. The theory explains several features of a recent experiment.« less

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.

1645-nm single-frequency, injection-seeded Q-switched Er:YAG master oscillator and power amplifier

NASA Astrophysics Data System (ADS)

Wang, Shuo; Gao, Chunqing; Shi, Yang; Song, Rui; Na, Quanxin; Gao, Mingwei; Wang, Qing

2018-02-01

A 1645-nm injection-seeded Q-switched Er:YAG master oscillator and power amplifier system is reported. The master oscillator generates single-frequency pulse energy of 11.10 mJ with a pulse width of 188.8 ns at 200 Hz. An Er:YAG monolithic nonplanar ring oscillator is employed as a seed laser. The output pulse from the master oscillator is amplified to 14.33-mJ pulse energy through an Er:YAG amplifier, with a pulse width of 183.3 ns. The M2-factors behind the amplifier are 1.14 and 1.23 in x- and y-directions, respectively. The full width at half maximum of the fast Fourier transformation spectrum of the heterodyne beating signal is 2.84 MHz.

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…

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.

q-deformed Einstein's model to describe specific heat of solid

NASA Astrophysics Data System (ADS)

Guha, Atanu; Das, Prasanta Kumar

2018-04-01

Realistic phenomena can be described more appropriately using generalized canonical ensemble, with proper parameter sets involved. We have generalized the Einstein's theory for specific heat of solid in Tsallis statistics, where the temperature fluctuation is introduced into the theory via the fluctuation parameter q. At low temperature the Einstein's curve of the specific heat in the nonextensive Tsallis scenario exactly lies on the experimental data points. Consequently this q-modified Einstein's curve is found to be overlapping with the one predicted by Debye. Considering only the temperature fluctuation effect(even without considering more than one mode of vibration is being triggered) we found that the CV vs T curve is as good as obtained by considering the different modes of vibration as suggested by Debye. Generalizing the Einstein's theory in Tsallis statistics we found that a unique value of the Einstein temperature θE along with a temperature dependent deformation parameter q(T) , can well describe the phenomena of specific heat of solid i.e. the theory is equivalent to Debye's theory with a temperature dependent θD.

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.

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).

q-Derivatives, quantization methods and q-algebras

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

Twarock, Reidun

1998-12-15

Using the example of Borel quantization on S{sup 1}, we discuss the relation between quantization methods and q-algebras. In particular, it is shown that a q-deformation of the Witt algebra with generators labeled by Z is realized by q-difference operators. This leads to a discrete quantum mechanics. Because of Z, the discretization is equidistant. As an approach to a non-equidistant discretization of quantum mechanics one can change the Witt algebra using not the number field Z as labels but a quadratic extension of Z characterized by an irrational number {tau}. This extension is denoted as quasi-crystal Lie algebra, because thismore » is a relation to one-dimensional quasicrystals. The q-deformation of this quasicrystal Lie algebra is discussed. It is pointed out that quasicrystal Lie algebras can be considered also as a 'deformed' Witt algebra with a 'deformation' of the labeling number field. Their application to the theory is discussed.« less

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.

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

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.

q-deformed superstatistics of the Schrödinger equation in commutative and noncommutative spaces with magnetic field

NASA Astrophysics Data System (ADS)

Sargolzaeipor, S.; Hassanabadi, H.; Chung, W. S.

2018-01-01

We discuss the q-deformed algebra and study the Schrödinger equation in commutative and noncommutative spaces, under an external magnetic field. In this work, we obtain the energy spectrum by an analytical method and the thermodynamic properties of the system by using the q-deformed superstatistics are calculated. Actually, we derive a generalized version of the ordinary superstatistic for the non-equilibrium systems. Also, different effective Boltzmann factor descriptions are derived. In addition, we discuss about the results for various values of θ in commutative and noncommutative spaces and, to illustrate the results, some figures are plotted.

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.

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.

Second harmonic generation of q-Gaussian laser beam in preformed collisional plasma channel with nonlinear absorption

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

Gupta, Naveen, E-mail: naveens222@rediffmail.com; Singh, Arvinder, E-mail: arvinder6@lycos.com; Singh, Navpreet, E-mail: navpreet.nit@gmail.com

2015-11-15

This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on amore » numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.« 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.

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.

Novel characteristics of energy spectrum for 3D Dirac oscillator analyzed via Lorentz covariant deformed algebra

PubMed Central

Betrouche, Malika; Maamache, Mustapha; Choi, Jeong Ryeol

2013-01-01

We investigate the Lorentz-covariant deformed algebra for Dirac oscillator problem, which is a generalization of Kempf deformed algebra in 3 + 1 dimension of space-time, where Lorentz symmetry are preserved. The energy spectrum of the system is analyzed by taking advantage of the corresponding wave functions with explicit spin state. We obtained entirely new results from our development based on Kempf algebra in comparison to the studies carried out with the non-Lorentz-covariant deformed one. A novel result of this research is that the quantized relativistic energy of the system in the presence of minimal length cannot grow indefinitely as quantum number n increases, but converges to a finite value, where c is the speed of light and β is a parameter that determines the scale of noncommutativity in space. If we consider the fact that the energy levels of ordinary oscillator is equally spaced, which leads to monotonic growth of quantized energy with the increment of n, this result is very interesting. The physical meaning of this consequence is discussed in detail. PMID:24225900

Novel characteristics of energy spectrum for 3D Dirac oscillator analyzed via Lorentz covariant deformed algebra.

PubMed

Betrouche, Malika; Maamache, Mustapha; Choi, Jeong Ryeol

2013-11-14

We investigate the Lorentz-covariant deformed algebra for Dirac oscillator problem, which is a generalization of Kempf deformed algebra in 3 + 1 dimension of space-time, where Lorentz symmetry are preserved. The energy spectrum of the system is analyzed by taking advantage of the corresponding wave functions with explicit spin state. We obtained entirely new results from our development based on Kempf algebra in comparison to the studies carried out with the non-Lorentz-covariant deformed one. A novel result of this research is that the quantized relativistic energy of the system in the presence of minimal length cannot grow indefinitely as quantum number n increases, but converges to a finite value, where c is the speed of light and β is a parameter that determines the scale of noncommutativity in space. If we consider the fact that the energy levels of ordinary oscillator is equally spaced, which leads to monotonic growth of quantized energy with the increment of n, this result is very interesting. The physical meaning of this consequence is discussed in detail.

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.

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.

Tidal deformability and I-Love-Q relations for gravastars with polytropic thin shells

NASA Astrophysics Data System (ADS)

Uchikata, Nami; Yoshida, Shijun; Pani, Paolo

2016-09-01

The moment of inertia, the spin-induced quadrupole moment, and the tidal Love number of neutron-star and quark-star models are related through some relations which depend only mildly on the stellar equation of state. These "I-Love-Q" relations have important implications for astrophysics and gravitational-wave astronomy. An interesting problem is whether similar relations hold for other compact objects and how they approach the black hole limit. To answer these questions, here we investigate the deformation properties of a large class of thin-shell gravastars, which are exotic compact objects that do not possess an event horizon nor a spacetime singularity. Working in a small-spin and small-tidal field expansion, we calculate the moment of inertia, the quadrupole moment, and the (quadrupolar electric) tidal Love number of gravastars with a polytropic thin shell. The I-Love-Q relations of a thin-shell gravastar are drastically different from those of an ordinary neutron star. The Love number and quadrupole moment for less compact models have the opposite sign relative to those of ordinary neutron stars, and the I-Love-Q relations continuously approach the black hole limit. We consider a variety of polytropic equations of state for the matter shell and find no universality in the I-Love-Q relations. However, we cannot deny the possibility that, similarly to the neutron-star case, an approximate universality might emerge for a limited class of equations of state. Finally, we discuss how a measurement of the tidal deformability from the gravitational-wave detection of a compact-binary inspiral can be used to constrain exotic compact objects like gravastars.

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.

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.

A calculus based on a q-deformed Heisenberg algebra

DOE PAGES

Cerchiai, B. L.; Hinterding, R.; Madore, J.; ...

1999-04-27

We show how one can construct a differential calculus over an algebra where position variables $x$ and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra has a subalgebra generated by cursive Greek chi and its inverse which we call the coordinate algebra. A physical field is considered to be an element of the completion of this algebra. We can construct a derivative which leaves invariant the coordinate algebra and so takes physical fields into physical fields. A generalized Leibniz rule for this algebra can be found. Based on thismore » derivative differential forms and an exterior differential calculus can be constructed.« less

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.

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.

Expansion into lattice harmonics in cubic symmetries

NASA Astrophysics Data System (ADS)

Kontrym-Sznajd, G.

2018-05-01

On the example of a few sets of sampling directions in the Brillouin zone, this work shows how important the choice of the cubic harmonics is on the quality of approximation of some quantities by a series of such harmonics. These studies led to the following questions: (1) In the case that for a given l there are several independent harmonics, can one use in the expansion only one harmonic with a given l?; (2) How should harmonics be ordered: according to l or, after writing them in terms of (x4 + y4 + z4)n (x2y2z2)m, according to their degree q = n + m? To enable practical applications of such harmonics, they are constructed in terms of the associated Legendre polynomials up to l = 26. It is shown that electron momentum densities, reconstructed from experimental data for ErGa3 and InGa3, are described much better by harmonics ordered with q.

Approximation solution of Schrodinger equation for Q-deformed Rosen-Morse using supersymmetry quantum mechanics (SUSY QM)

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

Alemgadmi, Khaled I. K., E-mail: azozkied@yahoo.com; Suparmi; Cari

2015-09-30

The approximate analytical solution of Schrodinger equation for Q-Deformed Rosen-Morse potential was investigated using Supersymmetry Quantum Mechanics (SUSY QM) method. The approximate bound state energy is given in the closed form and the corresponding approximate wave function for arbitrary l-state given for ground state wave function. The first excited state obtained using upper operator and ground state wave function. The special case is given for the ground state in various number of q. The existence of Rosen-Morse potential reduce energy spectra of system. The larger value of q, the smaller energy spectra of system.

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.

Large deformation of self-oscillating polymer gel

NASA Astrophysics Data System (ADS)

Maeda, Shingo; Kato, Terukazu; Otsuka, Yuji; Hosoya, Naoki; Cianchetti, Matteo; Laschi, Cecilia

2016-01-01

A self-oscillating gel is a system that generates an autonomous volume oscillation. This oscillation is powered by the chemical energy of the Belousov-Zhabotinsky (BZ) reaction, which demonstrates metal ion redox oscillation. A self-oscillating gel is composed of Poly-N -isopropylacrylamide (PNIPAAm) with a metal ion. In this study, we found that the displacement of the volume oscillation in a self-oscillating gel could be controlled by its being subjected to a prestraining process. We also revealed the driving mechanism of the self-oscillating gel from the point of view of thermodynamics. We observed that the polymer-solvent interaction parameter χ is altered by the redox changes to the metal ion incorporated in the self-oscillating gel. The prestraining process leads to changes in χ and changes in enthalpy and entropy when the self-oscillating gel is in a reduced and oxidized state. We found that nonprestrained gel samples oscillate in a poor solution (χ >0.5 ) and prestrained gel samples oscillate in a good solution (χ <0.5 ).

Impact of excitation waveform on the frequency stability of electrostatically-actuated micro-electromechanical oscillators

NASA Astrophysics Data System (ADS)

Juillard, J.; Brenes, A.

2018-05-01

In this paper, the frequency stability of high-Q electrostatically-actuated MEMS oscillators with cubic restoring forces, and its relation with the amplitude, the phase and the shape of the excitation waveform, is studied. The influence on close-to-the carrier frequency noise of additive processes (such as thermomechanical noise) or parametric processes (bias voltage fluctuations, feedback phase fluctuations, feedback level fluctuations) is taken into account. It is shown that the optimal operating conditions of electrostatically-actuated MEMS oscillators are highly waveform-dependent, a factor that is largely overlooked in the existing literature. This simulation-based study covers the cases of harmonic and pulsed excitation of a parallel-plate capacitive MEMS resonator.

Energetic particle modes of q = 1 high-order harmonics in tokamak plasmas with monotonic weak magnetic shear

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

Ren, Zhen-Zhen; Wang, Feng; Fu, G. Y.

Linear and nonlinear simulations of high-order harmonics q=1 energetic particle modes excited by trapped energetic particles in tokamaks are carried out using kinetic/magnetohydrodynamic hybrid code M3D-K. It is found that with a flat safety factor profile in the core region, the linear growth rate of high-order harmonics (m=n>1) driven by energetic trapped particles can be higher than the m/n=1/1 component. The high m=n>1 modes become more unstable when the pressure of energetic particles becomes higher. Moreover, it is shown that there exist multiple resonant locations satisfying different resonant conditions in the phase space of energetic particles for the high-order harmonicsmore » modes, whereas there is only one precessional resonance for the m/n=1/1 harmonics. The fluid nonlinearity reduces the saturation level of the n=1 component, while it hardly affects those of the high n components, especially the modes with m=n=3,4. The frequency of these modes does not chirp significantly, which is different with the typical fishbone driven by trapped particles. Lastly, in addition, the flattening region of energetic particle distribution due to high-order harmonics excitation is wider than that due to m/n=1/1 component, although the m/n=1/1 component has a higher saturation amplitude.« less

Energetic particle modes of q = 1 high-order harmonics in tokamak plasmas with monotonic weak magnetic shear

DOE PAGES

Ren, Zhen-Zhen; Wang, Feng; Fu, G. Y.; ...

2017-04-24

Linear and nonlinear simulations of high-order harmonics q=1 energetic particle modes excited by trapped energetic particles in tokamaks are carried out using kinetic/magnetohydrodynamic hybrid code M3D-K. It is found that with a flat safety factor profile in the core region, the linear growth rate of high-order harmonics (m=n>1) driven by energetic trapped particles can be higher than the m/n=1/1 component. The high m=n>1 modes become more unstable when the pressure of energetic particles becomes higher. Moreover, it is shown that there exist multiple resonant locations satisfying different resonant conditions in the phase space of energetic particles for the high-order harmonicsmore » modes, whereas there is only one precessional resonance for the m/n=1/1 harmonics. The fluid nonlinearity reduces the saturation level of the n=1 component, while it hardly affects those of the high n components, especially the modes with m=n=3,4. The frequency of these modes does not chirp significantly, which is different with the typical fishbone driven by trapped particles. Lastly, in addition, the flattening region of energetic particle distribution due to high-order harmonics excitation is wider than that due to m/n=1/1 component, although the m/n=1/1 component has a higher saturation amplitude.« less

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VI) HFODD (v2.40h): A new version of the program

NASA Astrophysics Data System (ADS)

Dobaczewski, J.; Satuła, W.; Carlsson, B. G.; Engel, J.; Olbratowski, P.; Powałowski, P.; Sadziak, M.; Sarich, J.; Schunck, N.; Staszczak, A.; Stoitsov, M.; Zalewski, M.; Zduńczuk, H.

2009-11-01

We describe the new version (v2.40h) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree-Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for state-dependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the DT2h transformations and rotations of wave functions, (ix) quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei, (x) the Broyden method to accelerate the convergence, (xi) the Lipkin-Nogami method to treat pairing correlations, (xii) the exact Coulomb exchange term, (xiii) several utility options, and we have corrected three insignificant errors. New version program summaryProgram title: HFODD (v2.40h) Catalogue identifier: ADFL_v2_2 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v2_2.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 79 618 No. of bytes in distributed program, including test data, etc.: 372 548 Distribution format: tar.gz Programming language: FORTRAN-77 and Fortran-90 Computer: Pentium-III, AMD-Athlon, AMD-Opteron Operating system: UNIX, LINUX, Windows XP Has the code been

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.

Parity Deformed Jaynes-Cummings Model: “Robust Maximally Entangled States”

PubMed Central

Dehghani, A.; Mojaveri, B.; Shirin, S.; Faseghandis, S. Amiri

2016-01-01

The parity-deformations of the quantum harmonic oscillator are used to describe the generalized Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The behavior is interestingly that of a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. The dynamical characters of the system is explored under the influence of the external field. In particular, we analytically study the generation of robust and maximally entangled states formed by a two-level atom trapped in a lossy cavity interacting with an external centrifugal field. We investigate the influence of deformation and detuning parameters on the degree of the quantum entanglement and the atomic population inversion. Under the condition of a linear interaction controlled by an external field, the maximally entangled states may emerge periodically along with time evolution. In the dissipation regime, the entanglement of the parity deformed JCM are preserved more with the increase of the deformation parameter, i.e. the stronger external field induces better degree of entanglement. PMID:27917882

On the robustness of the q-Gaussian family

NASA Astrophysics Data System (ADS)

Sicuro, Gabriele; Tempesta, Piergiulio; Rodríguez, Antonio; Tsallis, Constantino

2015-12-01

We introduce three deformations, called α-, β- and γ-deformation respectively, of a N-body probabilistic model, first proposed by Rodríguez et al. (2008), having q-Gaussians as N → ∞ limiting probability distributions. The proposed α- and β-deformations are asymptotically scale-invariant, whereas the γ-deformation is not. We prove that, for both α- and β-deformations, the resulting deformed triangles still have q-Gaussians as limiting distributions, with a value of q independent (dependent) on the deformation parameter in the α-case (β-case). In contrast, the γ-case, where we have used the celebrated Q-numbers and the Gauss binomial coefficients, yields other limiting probability distribution functions, outside the q-Gaussian family. These results suggest that scale-invariance might play an important role regarding the robustness of the q-Gaussian family.

Jordanian deformation of SL(2) as a contraction of its Drinfeld-Jimbo deformation

NASA Astrophysics Data System (ADS)

Aghamohammadi, A.; Khorrami, M.; Shariati, A.

1995-04-01

We show that $h$-deformation can be obtained, by a singular limit of a similarity transformation, from $q$-deformation; to be specefic, we obtain $\\GL_h(2)$, its differential structure, its inhomogenous extension, and $\\Uh{\\sl(2)}$ from their $q$-deformed counterparts.

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.

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

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 Comparative Study of Hot Deformation Behaviors for Sand Casting and Centrifugal Casting Q235B Flange Blanks

NASA Astrophysics Data System (ADS)

Qin, Fangcheng; Li, Yongtang; Ju, Li

2017-03-01

Hot compression tests of sand casting and centrifugal casting Q235B flange blanks were performed at strain rate range of 0.01-5 s-1 and temperature range of 850-1,150 °C. The evolutions of microstructure and texture were revealed. The constitutive models based on Arrhenius constitutive modeling were proposed by considering the effects of strain on material constants. The results show that recrystallization in centrifugal casting Q235B is more apparent than that in sand casting, resulting in the finer grains and lower flow stress for centrifugal casting Q235B. The intensities of textures slightly weaken with the increase of temperature. At 1,050 °C and 5 s-1, the textures of sand casting are characterized by strong {001}<100> and {001}<110>, which are related with severe deformation, while the textures of centrifugal casting are composed of {110}<110> and {111}<112>, which are related with dynamic recovery and shear deformation. A good agreement between the predicted and experimental flow stress is achieved and demonstrates that the proposed constitutive models are reliable.

Excitation on the Coherent States of Pseudoharmonic Oscillator

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

Popov, Dusan; Pop, Nicolina; Sajfert, Vjekoslav

In the last decades, much attention has been paid to the excitation on coherent states, especially for coherent states of the harmonic oscillator ([1] and references therein). But an interesting anharmonic oscillator with many potential applications is also the pseudoharmonic oscillator (PHO). So, in the present paper we have defined the excitation on the Klauder-Perelomov coherent states (E-KP-CSs) for the PHO. These states are obtained by repeatedly operating the raising operator K{sub +} on a usual Klauder-Perelomov coherent state (KP-CS) of the PHO [2]. We have verified that really, the E-KP-CSs fulfill all the properties of the coherent states, asmore » stated by Klauder [3]. We have examined the nonclassical properties of the E-KP-CSs, by using the density matrix formalism and examining the dependence of the Mandel parameter Q{sub z,k;m}(|z|{sup 2}) on the |z|{sup 2} and on the m. It seems that these states can be used in optical communication field and in the physics of quantum information, as signal beams, due to the fact that in these fields the nonclassicality plays an important role.« less

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.

The design of a multi-harmonic step-tunable gyrotron

NASA Astrophysics Data System (ADS)

Qi, Xiang-Bo; Du, Chao-Hai; Zhu, Juan-Feng; Pan, Shi; Liu, Pu-Kun

2017-03-01

The theoretical study of a step-tunable gyrotron controlled by successive excitation of multi-harmonic modes is presented in this paper. An axis-encircling electron beam is employed to eliminate the harmonic mode competition. Physics images are depicted to elaborate the multi-harmonic interaction mechanism in determining the operating parameters at which arbitrary harmonic tuning can be realized by magnetic field sweeping to achieve controlled multiband frequencies' radiation. An important principle is revealed that a weak coupling coefficient under a high-harmonic interaction can be compensated by a high Q-factor. To some extent, the complementation between the high Q-factor and weak coupling coefficient makes the high-harmonic mode potential to achieve high efficiency. Based on a previous optimized magnetic cusp gun, the multi-harmonic step-tunable gyrotron is feasible by using harmonic tuning of first-to-fourth harmonic modes. Multimode simulation shows that the multi-harmonic gyrotron can operate on the 34 GHz first-harmonic TE11 mode, 54 GHz second-harmonic TE21 mode, 74 GHz third-harmonic TE31 mode, and 94 GHz fourth-harmonic TE41 mode, corresponding to peak efficiencies of 28.6%, 35.7%, 17.1%, and 11.4%, respectively. The multi-harmonic step-tunable gyrotron provides new possibilities in millimeter-terahertz source development especially for advanced terahertz applications.

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.

An integrated low phase noise radiation-pressure-driven optomechanical oscillator chipset

PubMed Central

Luan, Xingsheng; Huang, Yongjun; Li, Ying; McMillan, James F.; Zheng, Jiangjun; Huang, Shu-Wei; Hsieh, Pin-Chun; Gu, Tingyi; Wang, Di; Hati, Archita; Howe, David A.; Wen, Guangjun; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Wong, Chee Wei

2014-01-01

High-quality frequency references are the cornerstones in position, navigation and timing applications of both scientific and commercial domains. Optomechanical oscillators, with direct coupling to continuous-wave light and non-material-limited f × Q product, are long regarded as a potential platform for frequency reference in radio-frequency-photonic architectures. However, one major challenge is the compatibility with standard CMOS fabrication processes while maintaining optomechanical high quality performance. Here we demonstrate the monolithic integration of photonic crystal optomechanical oscillators and on-chip high speed Ge detectors based on the silicon CMOS platform. With the generation of both high harmonics (up to 59th order) and subharmonics (down to 1/4), our chipset provides multiple frequency tones for applications in both frequency multipliers and dividers. The phase noise is measured down to −125 dBc/Hz at 10 kHz offset at ~400 μW dropped-in powers, one of the lowest noise optomechanical oscillators to date and in room-temperature and atmospheric non-vacuum operating conditions. These characteristics enable optomechanical oscillators as a frequency reference platform for radio-frequency-photonic information processing. PMID:25354711

Euler flow predictions for an oscillating cascade using a high resolution wave-split scheme

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Swafford, Timothy W.; Reddy, T. S. R.

1991-01-01

A compressible flow code that can predict the nonlinear unsteady aerodynamics associated with transonic flows over oscillating cascades is developed and validated. The code solves the two dimensional, unsteady Euler equations using a time-marching, flux-difference splitting scheme. The unsteady pressures and forces can be determined for arbitrary input motions, although only harmonic pitching and plunging motions are addressed. The code solves the flow equations on a H-grid which is allowed to deform with the airfoil motion. Predictions are presented for both flat plate cascades and loaded airfoil cascades. Results are compared to flat plate theory and experimental data. Predictions are also presented for several oscillating cascades with strong normal shocks where the pitching amplitudes, cascade geometry and interblade phase angles are varied to investigate nonlinear behavior.

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (IV) HFODD (v2.08i): a new version of the program

NASA Astrophysics Data System (ADS)

Dobaczewski, J.; Olbratowski, P.

2004-04-01

We describe the new version (v2.08i) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. The new version contains an interface to the LAPACK subroutine ZHPEVX. Program summaryTitle of the program:HFODD (v2.08i) Catalogue number: ADTO Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTO Reference in CPC for earlier version of program: J. Dobaczewski and J. Dudek, Comput. Phys. Commun. 131 (2000) 164 (v1.75r) Catalogue number of previous version: ADML Licensing provisions: none Does the new version supersede the previous one: yes Computers on which the program has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems: UNIX, LINUX, Windows-2000 Programming language used: FORTRAN-77 and FORTRAN-90 Memory required to execute with typical data: 10 Mwords No. of bits in a word: The code is written in single-precision for the use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine. Has the code been vectorised?: Yes No. of bytes in distributed program, including test data, etc.: 265352 No. of lines in distributed program: 52656 Distribution format: tar gzip file Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for

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.

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.

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 » $$\

Fine Structure of Beta Decay Strength Function and Anisotropy of Isovector Nuclear Dencity Component Oscillations in Deformed Nuclei

NASA Astrophysics Data System (ADS)

Izosimov, I. N.; Solnyshkin, A. A.; Khushvaktov, J. H.; Vaganov, Yu. A.

2018-05-01

The experimental measurement data on the fine structure of beta-decay strength function S β( E) in spherical, transitional, and deformed nuclei are analyzed. Modern high-resolution nuclear spectroscopy methods made it possible to identify the splitting of peaks in S β( E) for deformed nuclei. By analogy with splitting of the peak of E1 giant dipole resonance (GDR) in deformed nuclei, the peaks in S β( E) are split into two components from the axial nuclear deformation. In this report, the fine structure of S β( E) is discussed. Splitting of the peaks connected with the oscillations of neutrons against protons (E1GDR), of proton holes against neutrons (peaks in S β( E) of β+/ EC-decay), and of protons against neutron holes (peaks in S β( E) of β--decay) is discussed.

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.

Phase diagram of q-deformed Yang-Mills theory on S 2 at non-zero θ-angle

NASA Astrophysics Data System (ADS)

Okuyama, Kazumi

2018-04-01

We study the phase diagram of q-deformed Yang-Mills theory on S 2 at non-zero θ-angle using the exact partition function at finite N . By evaluating the exact partition function numerically, we find evidence for the existence of a series of phase transitions at non-zero θ-angle as conjectured in [hep-th/0509004

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.

Study of the AC machines winding having fractional q

NASA Astrophysics Data System (ADS)

Bespalov, V. Y.; Sidorov, A. O.

2018-02-01

The winding schemes with a fractional numbers of slots per pole and phase q have been known and used for a long time. However, in the literature on the low-noise machines design there are not recommended to use. Nevertheless, fractional q windings have been realized in many applications of special AC electrical machines, allowing to improve their performance, including vibroacoustic one. This paper deals with harmonic analysis of windings having integer and fractional q in permanent magnet synchronous motors, a comparison of their characteristics is performed, frequencies of subharmonics are revealed. Optimal winding pitch design is found giving reduce the amplitudes of subharmonics. Distribution factors for subharmonics, fractional and high-order harmonics are calculated, results analysis is represented, allowing for giving recommendations how to calculate distribution factors for different harmonics when q is fractional.

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.

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

Vignat, C.; Bercher, J.-F.

The family of Tsallis entropies was introduced by Tsallis in 1988. The Shannon entropy belongs to this family as the limit case q{yields}1. The canonical distributions in R{sup n} that maximize this entropy under a covariance constraint are easily derived as Student-t (q<1) and Student-r (q>1) multivariate distributions. A nice geometrical result about these Student-r distributions is that they are marginal of uniform distributions on a sphere of larger dimension d with the relationship p = n+2+(2/q-1). As q{yields}1, we recover the famous Poincare's observation according to which a Gaussian vector can be viewed as the projection of a vectormore » uniformly distributed on the infinite dimensional sphere. A related property in the case q<1 is also available. Often associated to Renyi-Tsallis entropies is the notion of escort distributions. We provide here a geometric interpretation of these distributions. Another result concerns a universal system in physics, the harmonic oscillator: in the usual quantum context, the waveform of the n-th state of the harmonic oscillator is a Gaussian waveform multiplied by the degree n Hermite polynomial. We show, starting from recent results by Carinena et al., that the quantum harmonic oscillator on spaces with constant curvature is described by maximal Tsallis entropy waveforms multiplied by the extended Hermite polynomials derived from this measure. This gives a neat interpretation of the non-extensive parameter q in terms of the curvature of the space the oscillator evolves on; as q{yields}1, the curvature of the space goes to 0 and we recover the classical harmonic oscillator in R{sup 3}.« less

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.

Fisher information, Borges operators, and q-calculus

NASA Astrophysics Data System (ADS)

Pennini, F.; Plastino, A.; Ferri, G. L.

2008-10-01

We discuss applying the increasingly popular q-calculus, or deformed calculus, so as to suitably generalize Fisher’s information measure and the Cramer-Rao inequality. A q-deformation can be attained in multiple ways, and we show that most of them do not constitute legitimate procedures. Within such a context, the only completely acceptable q-deformation is that ensuing from using the so-called Borges derivative [E.P. Borges, Physica A 340 (2004) 95].

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.

Parameterization of deformed nuclei for Glauber modeling in relativistic heavy ion collisions

DOE PAGES

Sorensen, P.; Tang, A. H.; Videbaek, F.; ...

2015-08-04

In this study, the density distributions of large nuclei are typically modeled with a Woods–Saxon distribution characterized by a radius R 0 and skin depth a. Deformation parameters β are then introduced to describe non-spherical nuclei using an expansion in spherical harmonics R 0(1+β 2Y 2 0+β 4Y 4 0). But when a nucleus is non-spherical, the R 0 and a inferred from electron scattering experiments that integrate over all nuclear orientations cannot be used directly as the parameters in the Woods–Saxon distribution. In addition, the β 2 values typically derived from the reduced electric quadrupole transition probability B(E2)↑ aremore » not directly related to the β 2 values used in the spherical harmonic expansion. B(E2)↑ is more accurately related to the intrinsic quadrupole moment Q 0 than to β 2. One can however calculate Q 0 for a given β 2 and then derive B(E2)↑ from Q 0. In this paper we calculate and tabulate the R 0, a , and β 2 values that when used in a Woods–Saxon distribution, will give results consistent with electron scattering data. We then present calculations of the second and third harmonic participant eccentricity (ε 2 and ε 3) with the new and old parameters. We demonstrate that ε 3 is particularly sensitive to a and argue that using the incorrect value of a has important implications for the extraction of viscosity to entropy ratio (η/s) from the QGP created in Heavy Ion collisions.« less

Liquefaction, ground oscillation, and soil deformation at the Wildlife Array, California

USGS Publications Warehouse

Holzer, T.L.; Youd, T.L.

2007-01-01

Excess pore-water pressure and liquefaction at the Wildlife Liquefaction Array in 1987 were caused by deformation associated with both high-frequency strong ground motion and 5.5-second-period Love waves. The Love waves produced large (???1.5%) cyclic shear strains well after the stronger high-frequency ground motion abated. These cyclic strains generated approximately from 13 to 35% of the excess pore-water pressure in the liquefied layer and caused excess pore-water pressures ultimately to reach effective overburden stress. The deformation associated with the Love waves explains the "postearthquake" increase of pore-water pressure that was recorded at the array. This explanation suggests that conventional methods for predicting liquefaction based on peak ground acceleration are incomplete and may need to consider cyclic strains associated with long-period surface waves. A post-earthquake survey of an inclinometer casing indicated permanent shear strain associated with lateral spreading primarily occurred in the upper part of the liquefied layer. Comparison of cone penetration test soundings conducted after the earthquake with pre-earthquake soundings suggests sleeve friction increased. Natural lateral variability of the liquefied layer obscured changes in tip resistance despite a ???1% reduction in volume. The large oscillatory motion associated with surface waves explains ground oscillation that has been reported at some liquefaction sites during earthquakes.

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.)

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.

Quons, an interpolation between Bose and Fermi oscillators

NASA Technical Reports Server (NTRS)

Greenberg, O. W.

1993-01-01

After a brief mention of Bose and Fermi oscillators and of particles which obey other types of statistics, including intermediate statistics, parastatistics, paronic statistics, anyon statistics, and infinite statistics, I discuss the statistics of 'quons' (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the q-deformed commutation relation (the quon algebra or q-mutator) which interpolates between fermions and bosons. I emphasize that the operator for interaction with an external source must be an effective Bose operator in all cases. To accomplish this for parabose, parafermi and quon operators, I introduce parabose, parafermi, and quon Grassmann numbers, respectively. I also discuss interactions of non-relativistic quons, quantization of quon fields with antiparticles, calculation of vacuum matrix elements of relativistic quon fields, demonstration of the TCP theorem, cluster decomposition, and Wick's theorem for relativistic quon fields, and the failure of local commutativity of observables for relativistic quon fields. I conclude with the bound on the parameter q for electrons due to the Ramberg-Snow experiment.

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.

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.

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

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.

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

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…

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.

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…

A nonlocal strain gradient model for dynamic deformation of orthotropic viscoelastic graphene sheets under time harmonic thermal load

NASA Astrophysics Data System (ADS)

Radwan, Ahmed F.; Sobhy, Mohammed

2018-06-01

This work presents a nonlocal strain gradient theory for the dynamic deformation response of a single-layered graphene sheet (SLGS) on a viscoelastic foundation and subjected to a time harmonic thermal load for various boundary conditions. Material of graphene sheets is presumed to be orthotropic and viscoelastic. The viscoelastic foundation is modeled as Kelvin-Voigt's pattern. Based on the two-unknown plate theory, the motion equations are obtained from the dynamic version of the virtual work principle. The nonlocal strain gradient theory is established from Eringen nonlocal and strain gradient theories, therefore, it contains two material scale parameters, which are nonlocal parameter and gradient coefficient. These scale parameters have two different effects on the graphene sheets. The obtained deflection is compared with that predicted in the literature. Additional numerical examples are introduced to illustrate the influences of the two length scale coefficients and other parameters on the dynamic deformation of the viscoelastic graphene sheets.

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.

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.

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…

Subthreshold membrane potential oscillations in inferior olive neurons are dynamically regulated by P/Q- and T-type calcium channels: a study in mutant mice.

PubMed

Choi, Soonwook; Yu, Eunah; Kim, Daesoo; Urbano, Francisco J; Makarenko, Vladimir; Shin, Hee-Sup; Llinás, Rodolfo R

2010-08-15

The role of P/Q- and T-type calcium channels in the rhythmic oscillatory behaviour of inferior olive (IO) neurons was investigated in mutant mice. Mice lacking either the CaV2.1 gene of the pore-forming alpha1A subunit for P/Q-type calcium channel, or the CaV3.1 gene of the pore-forming alpha1G subunit for T-type calcium channel were used. In vitro intracellular recording from IO neurons reveals that the amplitude and frequency of sinusoidal subthreshold oscillations (SSTOs) were reduced in the CaV2.1-/- mice. In the CaV3.1-/- mice, IO neurons also showed altered patterns of SSTOs and the probability of SSTO generation was significantly lower (15%, 5 of 34 neurons) than that of wild-type (78%, 31 of 40 neurons) or CaV2.1-/- mice (73%, 22 of 30 neurons). In addition, the low-threshold calcium spike and the sustained endogenous oscillation following rebound potentials were absent in IO neurons from CaV3.1-/- mice. Moreover, the phase-reset dynamics of oscillatory properties of single neurons and neuronal clusters in IO were remarkably altered in both CaV2.1-/- and CaV3.1-/- mice. These results suggest that both alpha1A P/Q- and alpha1G T-type calcium channels are required for the dynamic control of neuronal oscillations in the IO. These findings were supported by results from a mathematical IO neuronal model that incorporated T and P/Q channel kinetics.

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

On representations of U{sub q}osp(1{vert_bar}2) when q is a root of unity

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

Chung, W.; Suzuki, T.

1997-06-01

The infinite dimensional highest weight representations of U{sub q}osp(1{vert_bar}2) for the deformation parameter q being a root of unity are investigated. As in the cases of q-deformed nongraded Lie algebras, we find that every irreducible representation is isomorphic to the tensor product of a highest weight representation of sl{sub 2}(R) and a finite dimensional one of U{sub q}osp(1{vert_bar}2). The structure is investigated in detail. {copyright} {ital 1997 American Institute of Physics.}

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

Simple Optoelectronic Feedback in Microwave Oscillators

NASA Technical Reports Server (NTRS)

Maleki, Lute; Iltchenko, Vladimir

2009-01-01

A proposed method of stabilizing microwave and millimeter-wave oscillators calls for the use of feedback in optoelectronic delay lines characterized by high values of the resonance quality factor (Q). The method would extend the applicability of optoelectronic feedback beyond the previously reported class of optoelectronic oscillators that comprise two-port electronic amplifiers in closed loops with high-Q feedback circuits.

q -deformed statistics and the role of light fermionic dark matter in SN1987A cooling

NASA Astrophysics Data System (ADS)

Guha, Atanu; J, Selvaganapathy; Das, Prasanta Kumar

2017-01-01

The light dark matter (≃1 - 30 MeV ) particles pair produced in electron-positron annihilation e-e+→ γ χ χ ¯ inside the supernova core can take away the energy released in the supernova SN1987A explosion. Working within the formalism of q -deformed statistics [with the average value of the supernovae core temperature (fluctuating) being TS N=30 MeV ] and using the Raffelt's criterion on the emissivity for any new channel ɛ ˙ (e+e-→χ χ ¯ )≤1 019 erg g-1 s-1 , we find that as the deformation parameter q changes from 1.0 (undeformed scenario) to 1.1 (deformed scenario), the lower bound on the scale Λ of the dark matter effective theory varies from 3.3 ×1 06 TeV to 3.2 ×1 07 TeV for a dark matter fermion of mass mχ=30 MeV . Using the optical depth criteria on the free streaming of the dark matter fermion, we find the lower bound on Λ ˜1 08 TeV for mχ=30 MeV . In a scenario, where the dark matter fermions are pair produced in the outermost sector of the supernova core [with radius 0.9 Rc≤r ≤Rc , Rc(=10 km ) being the supernova core radius or the radius of protoneutron star], we find that the bound on Λ (˜3 ×1 07 TeV ) obtained from SN cooling criteria (Raffelt's criteria) is comparable with the bound obtained from free streaming (optical depth criterion) for light fermion dark matter of mass mχ=10 - 30 MeV .

Deformation of Fluid Column by Action of Axial Vibration and Some Aspects of High-Rate Thermocapillary Convection

NASA Technical Reports Server (NTRS)

Feonychev, Alexander I.; Kalachinskaya, Irina S.; Pokhilko, Victor I.

1996-01-01

The deformation of the fluid column by an action of a low-frequency vibration is considered. It is shown that behavior of the free fluid surface depends on the frequency of applied vibration and its amplitude. In the area of very low frequencies when fluid has time to comment on travel of bounding solid walls limiting column, the harmonical oscillations of free surface with given frequency are observed. With increase of vibration frequency the steady-state relief on free fluid surface is formed. If the amplitude of vibration is very small and the frequency corresponding to the first peak in the vibration spectrum on the Mir orbital station, the deformation of free surface tends to zero. Fluid flow induced thermocapillary effect on deformed free surface is more unstable as in the case of smooth cylindrical surface. It was shown that width of heating zone affects very essentially the flow pattern and transition to oscillatory regime of thermocapillary convection.

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

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.

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

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

Murakami, M.; Mauritsson, J.; Schafer, K.J.

2005-01-01

We calculate the linear chirp rates of high-order harmonics in argon, generated by intense, 810 nm laser pulses, and explore the dependence of the chirp rate on harmonic order, driving laser intensity, and pulse duration. By using a time-frequency representation of the harmonic fields we can identify several different linear chirp contributions to the plateau harmonics. Our results, which are based on numerical integration of the time-dependent Schroedinger equation, are in good agreement with the adiabatic predictions of the strong field approximation for the chirp rates. Extending the theoretical analysis in the recent paper by Mauritsson et al. [Phys. Rev.more » A 70, 021801(R) (2004)], we also manipulate the chirp rates of the harmonics by adding a chirp to the driving pulse. We show that the chirp rate for harmonic q is given by the sum of the intrinsic chirp rate, which is determined by the new duration and peak intensity of the chirped driving pulse, and q times the external chirp rate.« less

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.

Electrical resistance oscillations during plastic deformation in A Ti-Al-Nb-Zr alloy at 4·2 K

NASA Astrophysics Data System (ADS)

Nikiforenko, V. N.; Lavrentev, F. F.

1986-10-01

The serrated plastic flow in titanium alloy containing 5% Al, 2·5% Zr and 2% Nb has been investigated by measuring its electrical resistance and applying selective chemical etching. The electrical resistance was found to oscillate under active deformation at 4·2 K. Analysis of the possible causes seems to indicate a dominant role of break by dislocation pile-ups through obstacles, viz second phase precipitates and grain boundaries.

Subthreshold membrane potential oscillations in inferior olive neurons are dynamically regulated by P/Q- and T-type calcium channels: a study in mutant mice

PubMed Central

Choi, Soonwook; Yu, Eunah; Kim, Daesoo; Urbano, Francisco J; Makarenko, Vladimir; Shin, Hee-Sup; Llinás, Rodolfo R

2010-01-01

The role of P/Q- and T-type calcium channels in the rhythmic oscillatory behaviour of inferior olive (IO) neurons was investigated in mutant mice. Mice lacking either the CaV2.1 gene of the pore-forming α1A subunit for P/Q-type calcium channel, or the CaV3.1 gene of the pore-forming α1G subunit for T-type calcium channel were used. In vitro intracellular recording from IO neurons reveals that the amplitude and frequency of sinusoidal subthreshold oscillations (SSTOs) were reduced in the CaV2.1−/− mice. In the CaV3.1−/− mice, IO neurons also showed altered patterns of SSTOs and the probability of SSTO generation was significantly lower (15%, 5 of 34 neurons) than that of wild-type (78%, 31 of 40 neurons) or CaV2.1−/− mice (73%, 22 of 30 neurons). In addition, the low-threshold calcium spike and the sustained endogenous oscillation following rebound potentials were absent in IO neurons from CaV3.1−/− mice. Moreover, the phase-reset dynamics of oscillatory properties of single neurons and neuronal clusters in IO were remarkably altered in both CaV2.1−/− and CaV3.1−/− mice. These results suggest that both α1A P/Q- and α1G T-type calcium channels are required for the dynamic control of neuronal oscillations in the IO. These findings were supported by results from a mathematical IO neuronal model that incorporated T and P/Q channel kinetics. PMID:20547676

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.

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.

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…

Recent progress in opto-electronic oscillator

NASA Technical Reports Server (NTRS)

Maleki, Lute

2005-01-01

The optoelectronic oscillator (OEO) is a unique device based on photonics techniques to generate highly spectrally pure microwave signals [1]. The development of the OEO was motivated by the need for high performance oscillators in the frequency range larger than 10 GHz, where conventional electronic oscillators have a number of limitations. These limitations typically stem from the product of fQ, where f is the oscillator frequency and Q is the quality factor of the resonator in the oscillator. In conventional resonators, whether electromagnetic or piezoelectric, this product is usually a constant. Thus, as the oscillator frequency is pushed higher, the quality factor degrades, resulting in degradation of the phase noise of the oscillator. An approach to mitigate the problem is to start with a very high quality signal in the 5 to 100 MHz range generated by a quartz oscillator and multiply the frequency to achieve the desired microwave signal. Here again, frequency multiplication also results in an increase of the phase noise by a factor of 2010gN, where N is the multiplication factor.

High-Temperature Creep Behaviour and Positive Effect on Straightening Deformation of Q345c Continuous Casting Slab

NASA Astrophysics Data System (ADS)

Guo, Long; Zhang, Xingzhong

2018-03-01

Mechanical and creep properties of Q345c continuous casting slab subjected to uniaxial tensile tests at high temperature were considered in this paper. The minimum creep strain rate and creep rupture life equations whose parameters are calculated by inverse-estimation using the regression analysis were derived based on experimental data. The minimum creep strain rate under constant stress increases with the increase of the temperature from 1000 °C to 1200 °C. A new casting machine curve with the aim of fully using high-temperature creep behaviour is proposed in this paper. The basic arc segment is cancelled in the new curve so that length of the straightening area can be extended and time of creep behaviour can be increased significantly. For the new casting machine curve, the maximum straightening strain rate at the slab surface is less than the minimum creep strain rate. So slab straightening deformation based on the steel creep behaviour at high temperature can be carried out in the process of Q345c steel continuous casting. The effect of creep property at high temperature on slab straightening deformation is positive. It is helpful for the design of new casting machine and improvement of old casting machine.

Quantification of focal adhesion dynamics of cell movement based on cell-induced collagen matrix deformation using second-harmonic generation microscopy.

PubMed

Kang, Yong Guk; Jang, Hwanseok; Yang, Taeseok Daniel; Notbohm, Jacob; Choi, Youngwoon; Park, Yongdoo; Kim, Beop-Min

2018-06-01

Mechanical interactions of living cells with the surrounding environment via focal adhesion (FA) in three dimensions (3-D) play a key role in dynamic biological events, such as tissue regeneration, wound healing, and cancer invasion. Recently, several methods for observing 3-D cell-extracellular matrix (ECM) interactions have been reported, lacking solid and quantitative analysis on the dynamics of the physical interaction between the cell and the ECM. We measured the submicron displacements of ECM deformation in 3-D due to protrusion-retraction dynamics during cell migration, using second-harmonic generation without labeling the matrix structures. We then quantitatively analyzed the mechanical deformation between the ECM and the cells based on spatiotemporal volumetric correlations. The greatest deformations within the collagen matrix were found to occur at sites of colocalization of the FA site-related proteins vinculin and actin, which confirms that FA sites play a critical role in living cells within the ECM as a point for adhesion, traction, and migration. We believe that this modality can be used in studies of cell-ECM interaction during angiogenesis, wound healing, and metastasis. (2018) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

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.

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

NASA Astrophysics Data System (ADS)

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

2012-01-01

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

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.

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.

Linear transformation and oscillation criteria for Hamiltonian systems

NASA Astrophysics Data System (ADS)

Zheng, Zhaowen

2007-08-01

Using a linear transformation similar to the Kummer transformation, some new oscillation criteria for linear Hamiltonian systems are established. These results generalize and improve the oscillation criteria due to I.S. Kumari and S. Umanaheswaram [I. Sowjaya Kumari, S. Umanaheswaram, Oscillation criteria for linear matrix Hamiltonian systems, J. Differential Equations 165 (2000) 174-198], Q. Yang et al. [Q. Yang, R. Mathsen, S. Zhu, Oscillation theorems for self-adjoint matrix Hamiltonian systems, J. Differential Equations 190 (2003) 306-329], and S. Chen and Z. Zheng [Shaozhu Chen, Zhaowen Zheng, Oscillation criteria of Yan type for linear Hamiltonian systems, Comput. Math. Appl. 46 (2003) 855-862]. These criteria also unify many of known criteria in literature and simplify the proofs.

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

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.

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.

Internal friction Q factor measurements in lunar rocks

NASA Technical Reports Server (NTRS)

Tittmann, B. R.

1978-01-01

In order to better interpret recently reported values for the variation of seismic Q as a function of depth below the lunar surface, we have developed apparatus and made laboratory measurements of Q as a function of hydrostatic pressure, temperature and frequency. Our measurements of the Q associated with shear deformations have demonstrated that the large difference in Q between well outgassed and volatile rich rocks persists to pressures corresponding to a depth of at least 50 km. Here we report new measurements of Q as a function of temperature, on the development of techniques to measure the Q associated with extensional deformations under hydrostatic pressure, on the derivation of theoretical relations between our laboratory Q values and the attenuation coefficient of seismic waves, and on the development of a model for mechanism of adsorption.

High-Q optical resonators: characterization and application to stabilization of lasers and high spectral purity microwave oscillators

NASA Astrophysics Data System (ADS)

Llopis, O.; Merrer, P. H.; Bouchier, A.; Saleh, K.; Cibiel, G.

2010-02-01

Microwave optical systems for frequency generation are described in this paper. The goal is to reach high spectral purity in the microwave frequency range using ultra high Q optical resonators. The resonators investigated are of two types : resonant (passive) fiber rings and WGM tridimensional resonators. They all feature ultra high optical Q factors, in excess of 108 or 109 near 1550 nm. These resonators also sustain a large number of optical resonances, and the microwave signal is stabilized on two (or more) resonances of this optical comb. Different problems have to be overcome in order to reach a functional system, such as : resonator design and coupling, laser stabilization on a resonance, overall system design, noise optimization... This paper gives an overlook on these problems, and on some solutions we found to work towards a compact and efficient microwave opto-electronic oscillator (OEO). A first result is presented on a 10 GHz OEO based on a resonant fiber ring.

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

WGM-Based Photonic Local Oscillators and Modulators

NASA Technical Reports Server (NTRS)

Matsko, Andrey; Maleki, Lute; Iltchenko, Vladimir; Savchenkov, Anatoliy

2007-01-01

Photonic local oscillators and modulators that include whispering-gallery mode (WGM) optical resonators have been proposed as power-efficient devices for generating and detecting radiation at frequencies of the order of a terahertz. These devices are intended especially to satisfy anticipated needs for receivers capable of detecting lowpower, narrow-band terahertz signals to be used for sensing substances of interest in scientific and military applications. At present, available terahertz-signal detectors are power-inefficient and do not afford the spectral and amplitude resolution needed for detecting such signals. The proposed devices would not be designed according to the conventional approach of direct detection of terahertz radiation. Instead, terahertz radiation would first be up-converted into the optical domain, wherein signals could be processed efficiently by photonic means and detected by optical photodetectors, which are more efficient than are photodetectors used in conventional direct detection of terahertz radiation. The photonic devices used to effect the up-conversion would include a tunable optical local oscillator and a novel electro-optical modulator. A local oscillator according to the proposal would be a WGM-based modelocked laser operating at a desired pulserepetition rate of the order of a terahertz. The oscillator would include a terahertz optical filter based on a WGM microresonator, a fiber-optic delay line, an optical amplifier (which could be either a semiconductor optical amplifier or an erbium-doped optical fiberamplifier), and a WGM Ka-band modulator. The terahertz repetition rate would be obtained through harmonic mode locking: for example, by modulating the light at a frequency of 33 GHz and locking each 33d optical mode, one would create a 1.089-THz pulse train. The high resonance quality factors (Q values) of WGM optical resonators should make it possible to decrease signal-generation threshold power levels significantly below

One joule per Q-switched pulse diode-pumped laser

NASA Technical Reports Server (NTRS)

Holder, Lonnie E.; Kennedy, Chandler; Long, Larry; Dube, George

1992-01-01

Q-switched 1-J output has been achieved from diode-pumped zig-zag Nd:YAG slabs in an oscillator-amplifier configuration. The oscillator was single transverse and longitudinal model. This laser set records for Q-switched energy per pulse, and for average power from a diode-pumped laser. The laser was constructed in a rugged configuration suitable for routine laboratory use.

Seismic Attenuation Structure and Intraplate Deformation

NASA Astrophysics Data System (ADS)

Bezada, M.; Kowalke, S.; Smale, J.

2017-12-01

It has been suggested that intraplate deformation and seismicity is localized at weak zones in the lithosphere and at rheological boundaries. Comparisons of intraplate deformation regions with mantle seismic velocity structure suggest a correlation, but are not universally accepted as compelling evidence. We present P-wave attenuation models built from records of teleseismic deep-focus earthquakes in three different regions that show significant correlation between attenuation structure and intraplate seismicity and deformation. In the eastern United States, the New Madrid, Wabash Valley, Eastern Tennessee, Central Virginia, and Carolina seismic zones all occur at or near the edges of high-Q (low attenuation) regions. In Spain, intraplate seismicity is absent from high-Q regions but relatively abundant in surrounding low-Q regions where intraplate orogeny is also observed. In Australia, where our model resolution is relatively poor owing to sparse and uneven station coverage, the Petermann and Alice Springs intraplate orogens occur near the edge of a high-Q feature roughly coinciding with the undeformed Amadeus basin. Our results suggest that lithospheric structure exerts important controls on the localization of intraplate deformation and seismicity and that seismic attenuation is a useful proxy for lithospheric strength.

The free oscillations of the earth excited by three strongest earthquakes of the past decade according to deformation observations

NASA Astrophysics Data System (ADS)

Milyukov, V. K.; Vinogradov, M. P.; Mironov, A. P.; Myasnikov, A. V.; Perelygin, N. A.

2015-03-01

Based on the deformation data provided by the Baksan laser interferometer-strainmeter measurements, the free oscillations of the Earth (FOE) excited by the three strongest earthquakes of the past decade are analyzed. These seismic events include the Great Sumatra-Andaman earthquake that occurred in 2004 in the Indian Ocean, the Mauli earthquake of 2010 in Chile, and the Great Tohoku earthquake of March 2011 in Japan. The frequency-time structure of the free oscillations is studied, and the pattern of interaction between the modes with close frequencies (cross-coupling effect) is explored. For each earthquake, the correspondence of the observed FOE modes to the model predictions by the PREM model is investigated. A reliable consistent shift towards the high frequency of the toroidal modes with angular degree l = 12-19 is revealed. The maximal energy density of the toroidal oscillations is concentrated in the upper mantle of the Earth. Therefore, the established effect corresponds to the higher velocity of the shear waves in the upper mantle than it is predicted by the PREM model.

Biological Effects of Laser Radiation. Volume IV. Optical Second Harmonic Generation in Biological Tissues.

DTIC Science & Technology

1978-10-17

characteristics for optical second- harmonic generation. The collage component of conective tissue may be the principal site for the observed harmonic...Generation in Tissue ; Second Harmonic Generation in Collage; Glutathione, 5MB; Mechanisms; Conversion Efficiency; Significance of order UL AIM UY#m~wmev...sclera, and skin on 694 im. Q-switched ruby laser irradiation. A possible source of this second-harmonic generation was tissue collagen; because of

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

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

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.

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.

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.

Multipolar universal relations between f -mode frequency and tidal deformability of compact stars

NASA Astrophysics Data System (ADS)

Chan, T. K.; Sham, Y.-H.; Leung, P. T.; Lin, L.-M.

2014-12-01

Though individual stellar parameters of compact stars usually demonstrate obvious dependence on the equation of state (EOS), EOS-insensitive universal formulas relating these parameters remarkably exist. In the present paper, we explore the interrelationship between two such formulas, namely the f -I relation connecting the f -mode quadrupole oscillation frequency ω2 and the moment of inertia I , and the I -Love-Q relations relating I , the quadrupole tidal deformability λ2, and the quadrupole moment Q , which have been proposed by Lau, Leung, and Lin [Astrophys. J. 714, 1234 (2010)] and Yagi and Yunes [Science 341, 365 (2013)], respectively. A relativistic universal relation between ωl and λl with the same angular momentum l =2 ,3 ,… , the so-called "diagonal f -Love relation" that holds for realistic compact stars and stiff polytropic stars, is unveiled here. An in-depth investigation in the Newtonian limit is further carried out to pinpoint its underlying physical mechanism and hence leads to a unified f -I -Love relation. We reach the conclusion that these EOS-insensitive formulas stem from a common physical origin—compact stars can be considered as quasiincompressible when they react to slow time variations introduced by f -mode oscillations, tidal forces and rotations.

Long-ranged Fermi-Pasta-Ulam systems in thermal contact: Crossover from q-statistics to Boltzmann-Gibbs statistics

NASA Astrophysics Data System (ADS)

Bagchi, Debarshee; Tsallis, Constantino

2017-04-01

The relaxation to equilibrium of two long-range-interacting Fermi-Pasta-Ulam-like models (β type) in thermal contact is numerically studied. These systems, with different sizes and energy densities, are coupled to each other by a few thermal contacts which are short-range harmonic springs. By using the kinetic definition of temperature, we compute the time evolution of temperature and energy density of the two systems. Eventually, for some time t >teq, the temperature and energy density of the coupled system equilibrate to values consistent with standard Boltzmann-Gibbs thermostatistics. The equilibration time teq depends on the system size N as teq ∼Nγ where γ ≃ 1.8. We compute the velocity distribution P (v) of the oscillators of the two systems during the relaxation process. We find that P (v) is non-Gaussian and is remarkably close to a q-Gaussian distribution for all times before thermal equilibrium is reached. During the relaxation process we observe q > 1 while close to t =teq the value of q converges to unity and P (v) approaches a Gaussian. Thus the relaxation phenomenon in long-ranged systems connected by a thermal contact can be generically described as a crossover from q-statistics to Boltzmann-Gibbs statistics.

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

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.

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%.

Fluid-Structure Interaction Study on a Pre-Buckled Deformable Flat Ribbon

NASA Astrophysics Data System (ADS)

Fovargue, Lauren; Shams, Ehsan; Watterson, Amy; Corson, Dave; Filardo, Benjamin; Zimmerman, Daniel; Shan, Bob; Oberai, Assad

2015-11-01

A Fluid-Structure Interaction study is conducted for the flow over a deformable flat ribbon. This mechanism, which is called ribbon frond, maybe used as a device for pumping water and/or harvesting energy in rivers. We use a lower dimensional mathematical model, which represents the ribbon as a pre-buckled structure. The surface forces from the fluid flow, dictate the deformation of the ribbon, and the ribbon in turn imposes boundary conditions for the incompressible Navier-Stokes equations. The mesh motion is handled using an Arbitrary Lagrangian-Eulerian (ALE) scheme and the fluid-structure coupling is handled by iterating over the staggered governing equations for the structure, the fluid and the mesh. Simulations are conducted at three different free stream velocities. The results, including the frequency of oscillations, show agreement with experimental data. The vortical structures near the surface of the ribbon and its deformation are highly correlated. It is observed that the ribbon motion exhibits deviation from a harmonic motion, especially at lower free stream velocities. The behavior of the ribbon is compared to swimming animals, such as eels, in order to better understand its performance. The authors acknowledge support from ONR SBIR Phase II, contract No. N0001412C0604 and USDA, NIFA SBIR Phase I, contract No. 2013-33610-20836 and NYSERDA PON 2569, contract No. 30364.

Ultrastable Cryogenic Microwave Oscillators

NASA Astrophysics Data System (ADS)

Mann, Anthony G.

Ultrastable cryogenic microwave oscillators are secondary frequency standards in the microwave domain. The best of these oscillators have demonstrated a short term frequency stability in the range 10-14 to a few times 10-16. The main application for these oscillators is as flywheel oscillators for the next generation of passive atomic frequency standards, and as local oscillators in space telemetry ground stations to clean up the transmitter close in phase noise. Fractional frequency stabilities of passive atomic frequency standards are now approaching 3 x10^-14 /τ where τ is the measurement time, limited only by the number of atoms that are being interrogated. This requires an interrogation oscillator whose short-term stability is of the order of 10-14 or better, which cannot be provided by present-day quartz technology. Ultrastable cryogenic microwave oscillators are based on resonators which have very high electrical Q-factors. The resolution of the resonator's linewidth is typically limited by electronics noise to about 1ppm and hence Q-factors in excess of 108 are required. As these are only attained in superconducting cavities or sapphire resonators at low temperatures, use of liquid helium cooling is mandatory, which has so far restricted these oscillators to the research or metrology laboratory. Recently, there has been an effort to dispense with the need for liquid helium and make compact flywheel oscillators for the new generation of primary frequency standards. Work is under way to achieve this goal in space-borne and mobile liquid-nitrogen-cooled systems. The best cryogenic oscillators developed to date are the ``whispering gallery'' (WG) mode sapphire resonator-oscillators of NASA's Jet Propulsion Laboratory (JPL) and the University of Western Australia (UWA), as well as Stanford University's superconducting cavity stabilized oscillator (SCSO). All of these oscillators have demonstrated frequency

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

Simultaneous two component squeezing in generalized q-coherent states

NASA Technical Reports Server (NTRS)

Mcdermott, Roger J.; Solomon, Allan I.

1994-01-01

Using a generalization of the q-commutation relations, we develop a formalism in which it is possible to define generalized q-bosonic operators. This formalism includes both types of the usual q-deformed bosons as special cases. The coherent states of these operators show interesting and novel noise reduction properties including simultaneous squeezing in both field components, unlike the conventional case in which squeezing is permitted in only one component. This also contrasts with the usual quantum group deformation which also only permits one component squeezing.

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.

Exact solutions in oscillating airfoil theory

NASA Technical Reports Server (NTRS)

Williams, M. H.

1977-01-01

A result obtained by Williams (1977) for two-dimensional airfoils oscillating in an arbitrary subsonic parallel flowfield is reformulated to show that the pressure distribution induced by any deformation can be construed from the particular solutions for heaving and pitching motions. Specific formulas are presented for an oscillating control surface with a sealed gap.

Optoelectronic oscillator with improved phase noise and frequency stability

NASA Astrophysics Data System (ADS)

Eliyahu, Danny; Sariri, Kouros; Taylor, Joseph; Maleki, Lute

2003-07-01

In this paper we report on recent improvements in phase noise and frequency stability of a 10 GHz opto-electronic oscillator. In our OEO loop, the high Q elements (the optical fiber and the narrow bandpass microwave filter) are thermally stabilized using resistive heaters and temperature controllers, keeping their temperature above ambient. The thermally stabilized free running OEO demonstrates a short-term frequency stability of 0.02 ppm (over several hours) and frequency vs. temperature slope of -0.1 ppm/°C (compared to -8.3 ppm/°C for non thermally stabilized OEO). We obtained an exceptional spectral purity with phase noise level of -143 dBc/Hz at 10 kHz of offset frequency. We also describe the multi-loop configuration that reduces dramatically the spurious level at offset frequencies related to the loop round trip harmonic frequency. The multi-loop configuration has stronger mode selectivity due to interference between signals having different cavity lengths. A drop of the spurious level below -90 dBc was demonstrated. The effect of the oscillator aging on the frequency stability was studied as well by recording the oscillator frequency (in a chamber) over several weeks. We observed reversal in aging direction with logarithmic behavior of A ln(B t+1)-C ln(D t+1), where t is the time and A, B, C, D are constants. Initially, in the first several days, the positive aging dominates. However, later the negative aging mechanism dominates. We have concluded that the long-term aging behavioral model is consistent with the experimental results.

Structure of resonances and formation of stationary points in symmetrical chains of bilinear oscillators

NASA Astrophysics Data System (ADS)

Dyskin, Arcady V.; Pasternak, Elena; Shufrin, Igor

2014-12-01

Dynamics of strongly nonlinear systems can in many cases be modelled by bilinear oscillators, which are the oscillators whose springs have different stiffnesses in compression and tension. This underpins the analysis of a wide range of phenomena, from oscillations of fragmented structures, connections and mooring lines to deformation of geological media. Single bilinear oscillators were studied previously and the presence of multiple resonances both super- and sub-harmonic was found. Less attention was paid to systems of multiple bilinear oscillators that describe many natural and engineering processes such as for example the behaviour of fragmented solids. Here we fill this gap concentrating on the simplest case - 1D symmetrical chains of bilinear oscillators. We show that the presence and structure of resonances in a symmetric chain of bilinear oscillators with fixed ends depends upon the number of oscillating masses. Two elementary chains act as the basic ones: a single mass bilinear chain (a mass connected to the fixed points by two bilinear springs) that behaves as a linear oscillator with a single resonance and a two mass chain that is a coupled bilinear oscillator (two masses connected by three bilinear springs). The latter has multiple resonances. We demonstrate that longer chains either do not have resonances or get decomposed, in the resonance, into either the single mass or two mass elementary chains with stationary masses in between. The resonance frequencies are inherited from the basic chains of decomposition. We show that if the number of masses is odd the chain can be decomposed into the single mass bilinear chains separated by stationary masses. It then inherits the resonances of the single mass bilinear chain. The chains with the number of masses minus 2 divisible by 3 can be decomposed into the two mass bilinear chains separated by stationary masses and inherit the resonances of the two mass chains. The chains whose lengths satisfy both criteria

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.

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.

Large-scale deformed quasiparticle random-phase approximation calculations of the γ -ray strength function using the Gogny force

NASA Astrophysics Data System (ADS)

Martini, M.; Péru, S.; Hilaire, S.; Goriely, S.; Lechaftois, F.

2016-07-01

Valuable theoretical predictions of nuclear dipole excitations in the whole chart are of great interest for different nuclear applications, including in particular nuclear astrophysics. Here we present large-scale calculations of the E 1 γ -ray strength function obtained in the framework of the axially symmetric deformed quasiparticle random-phase approximation based on the finite-range Gogny force. This approach is applied to even-even nuclei, the strength function for odd nuclei being derived by interpolation. The convergence with respect to the adopted number of harmonic oscillator shells and the cutoff energy introduced in the 2-quasiparticle (2 -q p ) excitation space is analyzed. The calculations performed with two different Gogny interactions, namely D1S and D1M, are compared. A systematic energy shift of the E 1 strength is found for D1M relative to D1S, leading to a lower energy centroid and a smaller energy-weighted sum rule for D1M. When comparing with experimental photoabsorption data, the Gogny-QRPA predictions are found to overestimate the giant dipole energy by typically ˜2 MeV. Despite the microscopic nature of our self-consistent Hartree-Fock-Bogoliubov plus QRPA calculation, some phenomenological corrections need to be included to take into account the effects beyond the standard 2 -q p QRPA excitations and the coupling between the single-particle and low-lying collective phonon degrees of freedom. For this purpose, three prescriptions of folding procedure are considered and adjusted to reproduce experimental photoabsorption data at best. All of them are shown to lead to somewhat similar predictions of the E 1 strength, both at low energies and for exotic neutron-rich nuclei. Predictions of γ -ray strength functions and Maxwellian-averaged neutron capture rates for the whole Sn isotopic chain are also discussed and compared with previous theoretical calculations.

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.

Surface Oscillations of a Free-Falling Droplet of an Ideal Fluid

NASA Astrophysics Data System (ADS)

Kistovich, A. V.; Chashechkin, Yu. D.

2018-03-01

According to observations, drops freely falling in the air under the action of gravity are deformed and oscillate in a wide range of frequencies and scales. A technique for calculating surface axisymmetric oscillations of a deformed droplet in the linear approximation under the assumption that the amplitude and wavelength are small when compared to the droplet diameter is proposed. The basic form of an axisymmetric droplet is chosen from observations. The calculation results for surface oscillations agree with recorded data on the varying shape of water droplets falling in the air.

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.

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.

Elastomer degradation sensor using a piezoelectric material

DOEpatents

Olness, Dolores U.; Hirschfeld, deceased, Tomas B.

1990-01-01

A method and apparatus for monitoring the degradation of elastomeric materials is provided. Piezoelectric oscillators are placed in contact with the elastomeric material so that a forced harmonic oscillator with damping is formed. The piezoelectric material is connected to an oscillator circuit,. A parameter such as the resonant frequency, amplitude or Q value of the oscillating system is related to the elasticity of the elastomeric material. Degradation of the elastomeric material causes changes in its elasticity which, in turn, causes the resonant frequency, amplitude or Q of the oscillator to change. These changes are monitored with a peak height monitor, frequency counter, Q-meter, spectrum analyzer, or other measurement circuit. Elasticity of elastomers can be monitored in situ, using miniaturized sensors.

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.

3D full-field quantification of cell-induced large deformations in fibrillar biomaterials by combining non-rigid image registration with label-free second harmonic generation.

PubMed

Jorge-Peñas, Alvaro; Bové, Hannelore; Sanen, Kathleen; Vaeyens, Marie-Mo; Steuwe, Christian; Roeffaers, Maarten; Ameloot, Marcel; Van Oosterwyck, Hans

2017-08-01

To advance our current understanding of cell-matrix mechanics and its importance for biomaterials development, advanced three-dimensional (3D) measurement techniques are necessary. Cell-induced deformations of the surrounding matrix are commonly derived from the displacement of embedded fiducial markers, as part of traction force microscopy (TFM) procedures. However, these fluorescent markers may alter the mechanical properties of the matrix or can be taken up by the embedded cells, and therefore influence cellular behavior and fate. In addition, the currently developed methods for calculating cell-induced deformations are generally limited to relatively small deformations, with displacement magnitudes and strains typically of the order of a few microns and less than 10% respectively. Yet, large, complex deformation fields can be expected from cells exerting tractions in fibrillar biomaterials, like collagen. To circumvent these hurdles, we present a technique for the 3D full-field quantification of large cell-generated deformations in collagen, without the need of fiducial markers. We applied non-rigid, Free Form Deformation (FFD)-based image registration to compute full-field displacements induced by MRC-5 human lung fibroblasts in a collagen type I hydrogel by solely relying on second harmonic generation (SHG) from the collagen fibrils. By executing comparative experiments, we show that comparable displacement fields can be derived from both fibrils and fluorescent beads. SHG-based fibril imaging can circumvent all described disadvantages of using fiducial markers. This approach allows measuring 3D full-field deformations under large displacement (of the order of 10 μm) and strain regimes (up to 40%). As such, it holds great promise for the study of large cell-induced deformations as an inherent component of cell-biomaterial interactions and cell-mediated biomaterial remodeling. Copyright © 2017 Elsevier Ltd. All rights reserved.

Deformed oscillator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational extensions

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

Marquette, Ian, E-mail: i.marquette@uq.edu.au; Quesne, Christiane, E-mail: cquesne@ulb.ac.be

2015-06-15

We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformedmore » oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.« less

Suppression of parasitic oscillations in a core-doped ceramic Nd:YAG laser by Sm:YAG cladding.

PubMed

Huss, Rafael; Wilhelm, Ralf; Kolleck, Christian; Neumann, Jörg; Kracht, Dietmar

2010-06-07

The onset of parasitic oscillations limits the extraction efficiency and therefore energy scaling of Q-switched lasers. A solid-state laser was end pumped with a fiber-coupled diode laser and operated in q-cw as well as in passively Q-switched operation. For Q-switched operation, we demonstrate the suppression of parasitic oscillations in a core-doped ceramic Nd:YAG laser by Sm:YAG cladding.

Analysis of parasitic oscillations in 42 GHz gyrotron beam tunnel

NASA Astrophysics Data System (ADS)

Kumar, N.; Singh, U.; Singh, T. P.; Sinha, A. K.

2011-02-01

Parasitic oscillation excitation analysis has been carried out for the 42 GHz gyrotron beam tunnel. This article presents a systematic approach for the analysis of parasitic oscillation excitation. The electron trajectory code EGUN has been used for the estimation of the electron beam parameters in the beam tunnel. The electromagnetic simulation code CST-MS has been used for the eigenmode and Q value analysis. The analysis of the parasitic oscillations has been performed for the symmetric TE modes and the first three cavity side copper rings. Four different approaches- the Q value study, the mode maxima-electron beam radius mismatching, the electron cyclotron frequency-mode excitation frequency mismatching and the backward wave interaction analysis- have been used for the parasitic oscillation analysis.

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.

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

High-temperature behavior of a deformed Fermi gas obeying interpolating statistics.

PubMed

Algin, Abdullah; Senay, Mustafa

2012-04-01

An outstanding idea originally introduced by Greenberg is to investigate whether there is equivalence between intermediate statistics, which may be different from anyonic statistics, and q-deformed particle algebra. Also, a model to be studied for addressing such an idea could possibly provide us some new consequences about the interactions of particles as well as their internal structures. Motivated mainly by this idea, in this work, we consider a q-deformed Fermi gas model whose statistical properties enable us to effectively study interpolating statistics. Starting with a generalized Fermi-Dirac distribution function, we derive several thermostatistical functions of a gas of these deformed fermions in the thermodynamical limit. We study the high-temperature behavior of the system by analyzing the effects of q deformation on the most important thermostatistical characteristics of the system such as the entropy, specific heat, and equation of state. It is shown that such a deformed fermion model in two and three spatial dimensions exhibits the interpolating statistics in a specific interval of the model deformation parameter 0 < q < 1. In particular, for two and three spatial dimensions, it is found from the behavior of the third virial coefficient of the model that the deformation parameter q interpolates completely between attractive and repulsive systems, including the free boson and fermion cases. From the results obtained in this work, we conclude that such a model could provide much physical insight into some interacting theories of fermions, and could be useful to further study the particle systems with intermediate statistics.

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.

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.

Deforming baryons into confining strings

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

Hartnoll, Sean A.; Portugues, Ruben

2004-09-15

We find explicit probe D3-brane solutions in the infrared of the Maldacena-Nunez background. The solutions describe deformed baryon vertices: q external quarks are separated in spacetime from the remaining N-q. As the separation is taken to infinity we recover known solutions describing infinite confining strings in N=1 gauge theory. We present results for the mass of finite confining strings as a function of length. We also find probe D2-brane solutions in a confining type IIA geometry, the reduction of a G{sub 2} holonomy M theory background. The relation between these deformed baryons and confining strings is not as straightforward.

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

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.

Electronically tunable phase locked loop oscillator

NASA Astrophysics Data System (ADS)

Balasis, M.; Davis, M. R.; Jackson, C. R.

1982-02-01

This report describes the design and development of a low noise, high power, variable oscillator incorporating a high 'Q' electronically tunable resonator as the frequency determining element. The VCO provides improved EMC performance in phase locked synthesizers which are a part of communications equipments. The oscillator combines a low noise VMOS transistor with the selectivity and out-of-band attenuation of a coaxial resonator to provide superior EMC performance. Several oscillator designs were examined and the basis for the final configuration is presented. Oscillator noise is discussed and models for analysis are explained. A brass board model was constructed and tested and the technical results are presented.

Enhanced Second-Harmonic Generation Using Broken Symmetry III–V Semiconductor Fano Metasurfaces

DOE PAGES

Vabishchevich, Polina P.; Liu, Sheng; Sinclair, Michael B.; ...

2018-01-27

All-dielectric metasurfaces, two-dimensional arrays of subwavelength low loss dielectric inclusions, can be used not only to control the amplitude and phase of optical beams, but also to generate new wavelengths through enhanced nonlinear optical processes that are free from some of the constraints dictated by the use of bulk materials. Recently, high quality factor (Q) resonances in these metasurfaces have been revealed and utilized for applications such as sensing and lasing. The origin of these resonances stems from the interference of two nanoresonator modes with vastly different Q. Here we show that nonlinear optical processes can be further enhanced bymore » utilizing these high-Q resonances in broken symmetry all-dielectric metasurfaces. As a result, we study second harmonic generation from broken symmetry metasurfaces made from III–V semiconductors and observe nontrivial spectral shaping of second-harmonic and multifold efficiency enhancement induced by high field localization and enhancement inside the nanoresonators.« less

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.

Quantization of set theory and generalization of the fermion algebra

NASA Astrophysics Data System (ADS)

Arik, M.; Tekin, S. C.

2002-05-01

The quantum states of a d-dimensional fermion algebra are in one to one correspondence with the subsets of a d-element universal set. In this paper we use this set theoretical motivation to construct a one-parameter deformation of the fermion algebra and extend it to a d-dimensional generalization which is invariant under the group U(d). This discrete fermionic oscillator system is extended to the continuous case. We also show that the q-deformation of these systems is related to supercovariant q-oscillators.

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.

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.

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.

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.

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

Clausius inequality beyond the weak-coupling limit: the quantum Brownian oscillator.

PubMed

Kim, Ilki; Mahler, Günter

2010-01-01

We consider a quantum linear oscillator coupled at an arbitrary strength to a bath at an arbitrary temperature. We find an exact closed expression for the oscillator density operator. This state is noncanonical but can be shown to be equivalent to that of an uncoupled linear oscillator at an effective temperature T*(eff) with an effective mass and an effective spring constant. We derive an effective Clausius inequality deltaQ*(eff)< or =T*(eff)dS , where deltaQ*(eff) is the heat exchanged between the effective (weakly coupled) oscillator and the bath, and S represents a thermal entropy of the effective oscillator, being identical to the von-Neumann entropy of the coupled oscillator. Using this inequality (for a cyclic process in terms of a variation of the coupling strength) we confirm the validity of the second law. For a fixed coupling strength this inequality can also be tested for a process in terms of a variation of either the oscillator mass or its spring constant. Then it is never violated. The properly defined Clausius inequality is thus more robust than assumed previously.

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.

Physical Accuracy of Q Models of Seismic Attenuation

NASA Astrophysics Data System (ADS)

Morozov, I. B.

2016-12-01

Accuracy of theoretical models is a required prerequisite for any type of seismic imaging and interpretation. Among all geophysical disciplines, the theory of seismic and tidal attenuation is the least developed, and most practical studies use viscoelastic models based on empirical Q factors. To simplify imaging and inversions, the Qs are often approximated as frequency-independent or following a power law with frequency. However, simplicity of inversion should not outweigh the problematic physical accuracy of such models. Typical images of spatially-variable crustal and mantle Qs are "apparent," analogously to pseudo-depth, apparent-resistivity images in electrical imaging. Problems with Q models can be seen from controversial general observations present in many studies; for example: 1) In global Q models, bulk attenuation is much lower than the shear one throughout the whole Earth. This is considered a fundamental relation for the Earth; nevertheless, it is also very peculiar physically and suggests a negative Q for the Lamé modulus. This relation is also not supported by most first-principle models of materials and laboratory studies. 2) The Q parameterization requires that the entire outer core of the Earth is assigned zero attenuation, despite its large volume, presence of viscosity and shear deformation in free oscillations. 3) In laboratory and surface-wave studies, the bulk and shear Qs can be different for different wave modes, different sample sizes boundary conditions on the surface. Similarly, the Qs measured from body-S, Love, Lg, or ScS waves may not equal each other. 4) In seismic coda studies, the Q is often found to be linearly (or even faster) increasing with frequency. Such character of energy dissipation is controversial physically, but can be readily explained as an artifact of inaccurately-known geometrical spreading. To overcome the physical inaccuracies and apparent character of seismic attenuation models, mechanical theories of materials

Surface waves on a soft viscoelastic layer produced by an oscillating microbubble.

PubMed

Tinguely, Marc; Hennessy, Matthew G; Pommella, Angelo; Matar, Omar K; Garbin, Valeria

2016-05-14

Ultrasound-driven bubbles can cause significant deformation of soft viscoelastic layers, for instance in surface cleaning and biomedical applications. The effect of the viscoelastic properties of a boundary on the bubble-boundary interaction has been explored only qualitatively, and remains poorly understood. We investigate the dynamic deformation of a viscoelastic layer induced by the volumetric oscillations of an ultrasound-driven microbubble. High-speed video microscopy is used to observe the deformation produced by a bubble oscillating at 17-20 kHz in contact with the surface of a hydrogel. The localised oscillating pressure applied by the bubble generates surface elastic (Rayleigh) waves on the gel, characterised by elliptical particle trajectories. The tilt angle of the elliptical trajectories varies with increasing distance from the bubble. Unexpectedly, the direction of rotation of the surface elements on the elliptical trajectories shifts from prograde to retrograde at a distance from the bubble that depends on the viscoelastic properties of the gel. To explain these behaviours, we develop a simple three-dimensional model for the deformation of a viscoelastic solid by a localised oscillating force. By using as input for the model the values of the shear modulus obtained from the propagation velocity of the Rayleigh waves, we find good qualitative agreement with the experimental observations.

Web flexibility and I-beam torsional oscillation

NASA Astrophysics Data System (ADS)

Stephen, N. G.; Wang, P. J.

1986-08-01

Two recent theories on torsional oscillation of general doubly-symmetric non-circular cross-section beams incorporate a second order effect, that of in-plane shear deformation involving a change in cross-sectional shape, and are found to give excellent agreement with exact results for an elliptical section rod. For "technical" torsional oscillation theories of I-section beams this in-plane shear has previously been considered within the flanges only; in the present work the greater effect of shear distortion of the web is included, having previously been considered only in static analysis. The theory predicts three modes of wave propagation, one of which is essentially torsional in character; a second mode may be identified with predominatly flange bending according to the second branch of Timoshenko beam theory whilst a new mode involves individual flange torsion with asymmetric web deformation, and has the lowest phase velocity except at the longest wavelength. An alternative symmetric web deformation is also considered.

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

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.

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.

Analysis of precision in chemical oscillators: implications for circadian clocks

NASA Astrophysics Data System (ADS)

d'Eysmond, Thomas; De Simone, Alessandro; Naef, Felix

2013-10-01

Biochemical reaction networks often exhibit spontaneous self-sustained oscillations. An example is the circadian oscillator that lies at the heart of daily rhythms in behavior and physiology in most organisms including humans. While the period of these oscillators evolved so that it resonates with the 24 h daily environmental cycles, the precision of the oscillator (quantified via the Q factor) is another relevant property of these cell-autonomous oscillators. Since this quantity can be measured in individual cells, it is of interest to better understand how this property behaves across mathematical models of these oscillators. Current theoretical schemes for computing the Q factors show limitations for both high-dimensional models and in the vicinity of Hopf bifurcations. Here, we derive low-noise approximations that lead to numerically stable schemes also in high-dimensional models. In addition, we generalize normal form reductions that are appropriate near Hopf bifurcations. Applying our approximations to two models of circadian clocks, we show that while the low-noise regime is faithfully recapitulated, increasing the level of noise leads to species-dependent precision. We emphasize that subcomponents of the oscillator gradually decouple from the core oscillator as noise increases, which allows us to identify the subnetworks responsible for robust rhythms.

Accidental degeneracies in nonlinear quantum deformed systems

NASA Astrophysics Data System (ADS)

Aleixo, A. N. F.; Balantekin, A. B.

2011-09-01

We construct a multi-parameter nonlinear deformed algebra for quantum confined systems that includes many other deformed models as particular cases. We demonstrate that such systems exhibit the property of accidental pairwise energy level degeneracies. We also study, as a special case of our multi-parameter deformation formalism, the extension of the Tamm-Dancoff cutoff deformed oscillator and the occurrence of accidental pairwise degeneracy in the energy levels of the deformed system. As an application, we discuss the case of a trigonometric Rosen-Morse potential, which is successfully used in models for quantum confined systems, ranging from electrons in quantum dots to quarks in hadrons.

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.

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

Drops in Space: Super Oscillations and Surfactant Studies

NASA Technical Reports Server (NTRS)

Apfel, Robert E.; Tian, Yuren; Jankovsky, Joseph; Shi, Tao; Chen, X.; Holt, R. Glynn; Trinh, Eugene; Croonquist, Arvid; Thornton, Kathyrn C.; Sacco, Albert, Jr.;

High-Q BBO whispering gallery mode resonators

NASA Astrophysics Data System (ADS)

Lin, Guoping; Fürst, Josef U.; Strekalov, Dmitry V.; Grudinin, Ivan S.; Yu, Nan

2013-02-01

We report an investigation on optical whispering gallery mode (WGM) resonators made from non z-cut beta barium borate (BBO) crystals. We first fabricated high quality (Q) factor WGM resonators made of an angle-cut BBO crystal. Q factors of 1×108 level have been demonstrated at various wavelengths including UV. They led to new upper bounds for the absorption coefficients of BBO at 1560 nm, 980 nm and 370 nm. We observed only one set of ordinarily polarized WGMs with polarization rotating along the resonator circumference. We also fabricated xy-cut BBO WGM resonators, in which the optic axis is parallel to the resonator plane. In that case, two WGM families with different polarization exist, one with constant the other with oscillatory phase velocity. This enables a novel way of broadband phase matching in WGM resonators with cyclic gain. We experimentally demonstrated efficient second harmonic generation (SHG) to a wide harmonic wavelength range from 780 nm at near infrared to 317 nm in UV. It is also the first reported direct UV SHG in a high-Q WGM resonator. This work lays a foundation for further investigations of WGM properties of non-z cut birefringent resonators and their applications in nonlinear optics.

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.

Wave Phenomena in an Acoustic Resonant Chamber

ERIC Educational Resources Information Center

Smith, Mary E.; And Others

1974-01-01

Discusses the design and operation of a high Q acoustical resonant chamber which can be used to demonstrate wave phenomena such as three-dimensional normal modes, Q values, densities of states, changes in the speed of sound, Fourier decomposition, damped harmonic oscillations, sound-absorbing properties, and perturbation and scattering problems.…

High energy, widely tunable Si-prism-array coupled terahertz-wave parametric oscillator with a deformed pump and optimal crystal location for angle tuning.

PubMed

Zhang, Ruiliang; Qu, Yanchen; Zhao, Weijiang; Chen, Zhenlei

2017-03-20

A high energy, widely tunable Si-prism-array coupled terahertz-wave parametric oscillator (TPO) has been demonstrated by using a deformed pump. The deformed pump is cut from a beam spot of 2 mm in diameter by a 1-mm-wide slit. In comparison with a small pump spot (1-mm diameter), the THz-wave coupling area for the deformed pump is increased without limitation to the low-frequency end of the tuning range. Besides, the crystal location is specially designed to eliminate the alteration of the output position of the pump during angle tuning, so the initially adjusted nearest pumped region to the THz-wave exit surface is maintained throughout the tuning range. The tuning range is 0.58-2.5 THz for the deformed pump, while its low frequency end is limited at approximately 1.2 THz for the undeformed pump with 2 mm diameter. The highest THz-wave output of 2 μJ, which is 2.25 times as large as that from the pump of 1 mm in diameter, is obtained at 1.15 THz under 38 mJ (300  MW/cm²) pumping. The energy conversion efficiency is 5.3×10^-5.

Measurement and control of the frequency chirp rate of high-order harmonic pulses

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

Mauritsson, J.; Johnsson, P.; Lopez-Martens, R.

2004-08-01

We measure the chirp rate of harmonics 13 to 23 in argon by cross correlation with a 12 femtosecond probe pulse. Under low ionization conditions, we directly measure the negative chirp due to the atomic dipole phase, and show that an additional chirp on the pump pulse is transferred to the qth harmonic as q times the fundamental chirp. Our results are in accord with simulations using the experimentally measured 815 nm pump and probe pulses. The ability to measure and manipulate the harmonic chirp rate is essential for the characterization and optimization of attosecond pulse trains.

Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity.

PubMed

Roppo, V; Raineri, F; Raj, R; Sagnes, I; Trull, J; Vilaseca, R; Scalora, M; Cojocaru, C

2011-05-15

In this Letter, we experimentally demonstrate the enhancement of the inhomogeneous second harmonic conversion in the opaque region of a GaAs cavity with efficiencies of the order of 0.1% at 612 nm, using 3 ps pump pulses having peak intensities of the order of 10 MW/cm(2). We show that the conversion efficiency of the inhomogeneous, phase-locked second harmonic component is a quadratic function of the cavity factor Q. © 2011 Optical Society of America

A harmonic adiabatic approximation to calculate highly excited vibrational levels of ``floppy molecules''

NASA Astrophysics Data System (ADS)

Lauvergnat, David; Nauts, André; Justum, Yves; Chapuisat, Xavier

2001-04-01

The harmonic adiabatic approximation (HADA), an efficient and accurate quantum method to calculate highly excited vibrational levels of molecular systems, is presented. It is well-suited to applications to "floppy molecules" with a rather large number of atoms (N>3). A clever choice of internal coordinates naturally suggests their separation into active, slow, or large amplitude coordinates q', and inactive, fast, or small amplitude coordinates q″, which leads to an adiabatic (or Born-Oppenheimer-type) approximation (ADA), i.e., the total wave function is expressed as a product of active and inactive total wave functions. However, within the framework of the ADA, potential energy data concerning the inactive coordinates q″ are required. To reduce this need, a minimum energy domain (MED) is defined by minimizing the potential energy surface (PES) for each value of the active variables q', and a quadratic or harmonic expansion of the PES, based on the MED, is used (MED harmonic potential). In other words, the overall picture is that of a harmonic valley about the MED. In the case of only one active variable, we have a minimum energy path (MEP) and a MEP harmonic potential. The combination of the MED harmonic potential and the adiabatic approximation (harmonic adiabatic approximation: HADA) greatly reduces the size of the numerical computations, so that rather large molecules can be studied. In the present article however, the HADA is applied to our benchmark molecule HCN/CNH, to test the validity of the method. Thus, the HADA vibrational energy levels are compared and are in excellent agreement with the ADA calculations (adiabatic approximation with the full PES) of Light and Bačić [J. Chem. Phys. 87, 4008 (1987)]. Furthermore, the exact harmonic results (exact calculations without the adiabatic approximation but with the MEP harmonic potential) are compared to the exact calculations (without any sort of approximation). In addition, we compare the densities of

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.

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.

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.

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.

Computational material design for Q&P steels with plastic instability theory

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

Cheng, G.; Choi, K. S.; Hu, X. H.

In this paper, the deformation limits of Quenching and Partitioning (Q&P) steels are examined with the plastic instability theory. For this purpose, the constituent phase properties of various Q&P steels were first experimentally obtained, and used to estimate the overall tensile stress-strain curves based on the simple rule of mixture (ROM) with the iso-strain and iso-stress assumptions. Plastic instability theory was then applied to the obtained overall stress-strain curves in order to estimate the deformation limits of the Q&P steels. A parametric study was also performed to examine the effects of various material parameters on the deformation limits of Q&Pmore » steels. Computational material design was subsequently carried out based on the information obtained from the parametric study. The results show that the plastic instability theory with iso-stress-based stress-strain curve may be used to provide the lower bound estimate of the uniform elongation (UE) for the various Q&P steels considered. The results also indicate that higher austenite stability/volume fractions, less strength difference between the primary phases, higher hardening exponents of the constituent phases are generally beneficial for the performance improvement of Q&P steels, and that various material parameters may be concurrently adjusted in a cohesive way in order to improve the performance of Q&P steel. The information from this study may be used to devise new heat treatment parameters and alloying elements to produce Q&P steels with the improved performance.« less

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.

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.

Suppression of Spontaneous Gas Oscillations by Acoustic Self-Feedback

NASA Astrophysics Data System (ADS)

Biwa, Tetsushi; Sawada, Yoshiki; Hyodo, Hiroaki; Kato, Soichiro

2016-10-01

This paper demonstrates a method of acoustical self-feedback to suppress spontaneous gas oscillations such as those observed in combustors of gas-turbine engines. Whereas a conventional feedback system consists of electromechanical devices, the present method achieves acoustical self-feedback with a hollow tube that connects two positions of the oscillation system. A model oscillator of combustion-driven gas oscillations is designed and built to demonstrate the applicability of the self-feedback concept. Stability analysis through measurements of Q values (quality factor) of oscillations shows that the desired delay time and gain are obtained when the tube length is equal to the odd integer times half the wavelength of the anticipated acoustic oscillations.

Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading

NASA Astrophysics Data System (ADS)

Gholami, Raheb; Ansari, Reza

2018-02-01

This article presents an attempt to study the nonlinear resonance of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates excited by a uniformly distributed harmonic transverse load. To this purpose, first, the extended rule of mixture including the efficiency parameters is employed to approximately obtain the effective material properties of FG-CNTRC annular sector plates. Then, the focus is on presenting the weak form of discretized mathematical formulation of governing equations based on the variational differential quadrature (VDQ) method and Hamilton's principle. The geometric nonlinearity and shear deformation effects are considered based on the von Kármán assumptions and Reddy's third-order shear deformation plate theory, respectively. The discretization process is performed via the generalized differential quadrature (GDQ) method together with numerical differential and integral operators. Then, an efficient multi-step numerical scheme is used to obtain the nonlinear dynamic behavior of the FG-CNTRC annular sector plates near their primary resonance as the frequency-response curve. The accuracy of the present results is first verified and then a parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of annular sector plate and sector angle on the nonlinear frequency-response curve of FG-CNTRC annular sector plates with different edge supports.

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.

Differential Calculus on h-Deformed Spaces

NASA Astrophysics Data System (ADS)

Herlemont, Basile; Ogievetsky, Oleg

2017-10-01

We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of h-deformed differential operators {Diff}_{h},σ(n) is labeled by a rational function σ in n variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system and describe some properties of the rings {Diff}_{h},σ(n).

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.

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.

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…

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.

Optical Quantification of Harmonic Acoustic Radiation Force Excitation in a Tissue-Mimicking Phantom.

PubMed

Suomi, Visa; Edwards, David; Cleveland, Robin

2015-12-01

Optical tracking was used to characterize acoustic radiation force-induced displacements in a tissue-mimicking phantom. Amplitude-modulated 3.3-MHz ultrasound was used to induce acoustic radiation force in the phantom, which was embedded with 10-μm microspheres that were tracked using a microscope objective and high-speed camera. For sine and square amplitude modulation, the harmonic components of the fundamental and second and third harmonic frequencies were measured. The displacement amplitudes were found to increase linearly with acoustic radiation force up to 10 μm, with sine modulation having 19.5% lower peak-to-peak amplitude values than square modulation. Square modulation produced almost no second harmonic, but energy was present in the third harmonic. For the sine modulation, energy was present in the second harmonic and low energy in the third harmonic. A finite-element model was used to simulate the deformation and was both qualitatively and quantitatively in agreement with the measurements. Copyright © 2015 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Triple inverter pierce oscillator circuit suitable for CMOS

DOEpatents

Wessendorf,; Kurt, O [Albuquerque, NM

2007-02-27

An oscillator circuit is disclosed which can be formed using discrete field-effect transistors (FETs), or as a complementary metal-oxide-semiconductor (CMOS) integrated circuit. The oscillator circuit utilizes a Pierce oscillator design with three inverter stages connected in series. A feedback resistor provided in a feedback loop about a second inverter stage provides an almost ideal inverting transconductance thereby allowing high-Q operation at the resonator-controlled frequency while suppressing a parasitic oscillation frequency that is inherent in a Pierce configuration using a "standard" triple inverter for the sustaining amplifier. The oscillator circuit, which operates in a range of 10 50 MHz, has applications for use as a clock in a microprocessor and can also be used for sensor applications.

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.

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.

Magnetostriction and magnetoelastic quantum oscillations in P-type lead telluride

NASA Technical Reports Server (NTRS)

Thompson, T. E.; Aron, P. R.; Chandrasekhar, B. S.; Langenberg, D. N.

1972-01-01

A detailed experimental and theoretical study of quantum oscillations in the magnetostriction and Young's modulus of p-PbTe is presented. The valance band of PbTe is approximated by a spheroidal, nonparabolic model in which the effects of strain on the valance band parameters are described by a deformation potential model. Using appropriate thermodynamic derivatives of the modified Lifshitz-Kosevich expression for the oscillatory parts of the electronic free energy, it is shown that both types of oscillations arise mainly from relative shifts of the valance band maxima due to shear strains, accompanied by intervalley charge transfer. Band parameters derived from the periods, phases, and spin splitting of the oscillations are in generally good agreement with values reported by other workers. A detailed comparison is made of the experimentally observed oscillation amplitudes with those predicted by theory, and satisfactory agreement is found. The ratio of the amplitudes of the two effects yields a value of the valance band deformation potential in good agreement with a value found from piezoresistance experiments by Burke.

Oscillations and uniaxial mechanochemical waves in a model of an active poroelastic medium: Application to deformation patterns in protoplasmic droplets of Physarum polycephalum

NASA Astrophysics Data System (ADS)

Alonso, Sergio; Strachauer, Ulrike; Radszuweit, Markus; Bär, Markus; Hauser, Marcus J. B.

2016-04-01

Self-organization in cells often manifests itself in oscillations and waves. Here, we address deformation waves in protoplasmic droplets of the plasmodial slime mould Physarum polycephalum by modelling and experiments. In particular, we extend a one-dimensional model that considered the cell as a poroelastic medium, where active tension caused mechanochemical waves that were regulated by an inhibitor (Radszuweit et al., 2013). Our extension consists of a simple, qualitative chemical reaction-diffusion model (Brusselator) that describes the regulation of the inhibitor by another biochemical species. The biochemical reaction enhances the formation of mechanochemical waves if the reaction rates and input concentrations are near or inside an oscillatory regime. The period of the waves is found to be controlled by the characteristic oscillation period, whereas their wavelength is set by mechanical parameters. The model also allows for a systematic study of the chemical activity at the onset of mechanochemical waves. We also present examples for pattern formation in protoplasmic droplets of Physarum polycephalum including global oscillations where the central region of the droplets is in antiphase to the boundary zone, as well as travelling and standing wave-like uniaxial patterns. Finally, we apply our model to reproduce these experimental results by identifying the active tension inhibitor with the intracellular calcium concentration in the Physarum droplets and by using parameter values from mechanical experiments, respectively knowledge about the properties of calcium oscillations in Physarum. The simulation results are then found to be in good agreement with the experimental observations.

Diffusion mechanism of non-interacting Brownian particles through a deformed substrate

NASA Astrophysics Data System (ADS)

Arfa, Lahcen; Ouahmane, Mehdi; El Arroum, Lahcen

2018-02-01

We study the diffusion mechanism of non-interacting Brownian particles through a deformed substrate. The study is done at low temperature for different values of the friction. The deformed substrate is represented by a periodic Remoissenet-Peyrard potential with deformability parameter s. In this potential, the particles (impurity, adatoms…) can diffuse. We ignore the interactions between these mobile particles consider them merely as non-interacting Brownian particles and this system is described by a Fokker-Planck equation. We solve this equation numerically using the matrix continued fraction method to calculate the dynamic structure factor S(q , ω) . From S(q , ω) some relevant correlation functions are also calculated. In particular, we determine the half-width line λ(q) of the peak of the quasi-elastic dynamic structure factor S(q , ω) and the diffusion coefficient D. Our numerical results show that the diffusion mechanism is described, depending on the structure of the potential, either by a simple jump diffusion process with jump length close to the lattice constant a or by a combination of a jump diffusion model with jump length close to lattice constant a and a liquid-like motion inside the unit cell. It shows also that, for different friction regimes and various potential shapes, the friction attenuates the diffusion mechanism. It is found that, in the high friction regime, the diffusion process is more important through a deformed substrate than through a non-deformed one.

Unveiling the Universality of I-Love-Q Relations

NASA Astrophysics Data System (ADS)

Sham, Y.-H.; Chan, T. K.; Lin, L.-M.; Leung, P. T.

2015-01-01

The recent discovery of the universal I-Love-Q relations connecting the moment of inertia, tidal deformability, and the spin-induced quadrupole moment of compact stars is intriguing and totally unexpected. In this paper, we provide numerical evidence showing that the universality can be attributed to the incompressible limit of the I-Love-Q relations. The fact that modern equations of state are stiff, with an effective adiabatic index larger than about two, above the nuclear density range is the key to establishing the universality for neutron stars and quark stars with typical compactness from about 0.1 to 0.3. On the other hand, the I-Love-Q relations of low-mass neutron stars near the minimum mass limit depend more sensitively on the underlying equation of state because these stars are composed mainly of softer matter at low densities. However, the I-Love-Q relations for low-mass quark stars can still be represented accurately by the incompressible limit. We also study the I-Love relation connecting the moment of inertia and tidal deformability analytically in Newtonian gravity and show why the I-Love-Q relation is weakly dependent on the underlying equation of state and can be attributed to its incompressible limit.

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.

A 4D Hyperspherical Interpretation of q-Space

PubMed Central

Hosseinbor, A. Pasha; Chung, Moo K.; Wu, Yu-Chien; Bendlin, Barbara B.; Alexander, Andrew L.

2015-01-01

3D q-space can be viewed as the surface of a 4D hypersphere. In this paper, we seek to develop a 4D hyperspherical interpretation of q-space by projecting it onto a hypersphere and subsequently modeling the q-space signal via 4D hyperspherical harmonics (HSH). Using this orthonormal basis, we derive several well-established q-space indices and numerically estimate the diffusion orientation distribution function (dODF). We also derive the integral transform describing the relationship between the diffusion signal and propagator on a hypersphere. Most importantly, we will demonstrate that for hybrid diffusion imaging (HYDI) acquisitions low order linear expansion of the HSH basis is sufficient to characterize diffusion in neural tissue. In fact, the HSH basis achieves comparable signal and better dODF reconstructions than other well-established methods, such as Bessel Fourier orientation reconstruction (BFOR), using fewer fitting parameters. All in all, this work provides a new way of looking at q-space. PMID:25624043

Temperature and frequency dependence of anelasticity in a nickel oscillator

NASA Astrophysics Data System (ADS)

Berg, Robert F.

1995-09-01

The frequency dependence of the real and imaginary parts of a nickel oscillator's transfer function is described over 3 decades in frequency by the use of simple expressions. These expressions incorporate only the resonance frequency ω0, the quality factor Q, and a characteristic exponent β determined by a single measurement of creep. They are based on the ansatz φ(ω)=Q-1(ω/ω0)-β, where φ is the imaginary part of the spring constant. Over a 100 K range of temperature T, the exponent β≂0.18 was constant even though Q(T) changed by a factor of 8. These expressions are potentially useful for accurately describing a mechanical oscillator whose transfer function must be modeled at frequencies far below ω0. Examples include accelerometers based on a flexure element and suspensions for interferometric gravitational wave detectors.

A Passively Q-Switched, CW-Pumped Fe:ZnSe Laser

DTIC Science & Technology

2014-03-01

passively Q-switched microchip lasers using semiconductor saturable absorbers,” J. Opt. Soc. Amer. B, Opt. Phys., vol. 16, no. 3, pp. 376–388, Mar. 1999...204 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 50, NO. 3, MARCH 2014 A Passively Q-Switched, CW-Pumped Fe:ZnSe Laser Jonathan W. Evans, Patrick A...Berry, and Kenneth L. Schepler Abstract— We report the demonstration of high-average-power passively Q-switched laser oscillation from Fe2+ ions in zinc

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.

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.

Nonlinear MHD simulations of QH-mode DIII-D plasmas and implications for ITER high Q scenarios

NASA Astrophysics Data System (ADS)

Liu, F.; Huijsmans, G. T. A.; Loarte, A.; Garofalo, A. M.; Solomon, W. M.; Hoelzl, M.; Nkonga, B.; Pamela, S.; Becoulet, M.; Orain, F.; Van Vugt, D.

2018-01-01

In nonlinear MHD simulations of DIII-D QH-mode plasmas it has been found that low n kink/peeling modes (KPMs) are unstable and grow to a saturated kink-peeling mode. The features of the dominant saturated KPMs, which are localised toroidally by nonlinear coupling of harmonics, such as mode frequencies, density fluctuations and their effect on pedestal particle and energy transport, are in good agreement with the observations of the edge harmonic oscillation typically present in DIII-D QH-mode experiments. The nonlinear evolution of MHD modes including both kink-peeling modes and ballooning modes, is investigated through MHD simulations by varying the pedestal current and pressure relative to the initial conditions of DIII-D QH-mode plasma. The edge current and pressure at the pedestal are key parameters for the plasma either saturating to a QH-mode regime or a ballooning mode dominant regime. The influence of E × B flow and its shear on the QH-mode plasma has been investigated. E × B flow shear has a strong stabilisation effect on the medium to high-n modes but is destabilising for the n = 2 mode. The QH-mode extrapolation results of an ITER Q = 10 plasma show that the pedestal currents are large enough to destabilise n = 1-5 KPMs, leading to a stationary saturated kink-peeling mode.

Digital Detection and Processing of Multiple Quadrature Harmonics for EPR Spectroscopy

PubMed Central

Ahmad, R.; Som, S.; Kesselring, E.; Kuppusamy, P.; Zweier, J.L.; Potter, L.C.

2010-01-01

A quadrature digital receiver and associated signal estimation procedure are reported for L-band electron paramagnetic resonance (EPR) spectroscopy. The approach provides simultaneous acquisition and joint processing of multiple harmonics in both in-phase and out-of-phase channels. The digital receiver, based on a high-speed dual-channel analog-to-digital converter, allows direct digital down-conversion with heterodyne processing using digital capture of the microwave reference signal. Thus, the receiver avoids noise and nonlinearity associated with analog mixers. Also, the architecture allows for low-Q anti-alias filtering and does not require the sampling frequency to be time-locked to the microwave reference. A noise model applicable for arbitrary contributions of oscillator phase noise is presented, and a corresponding maximum-likelihood estimator of unknown parameters is also reported. The signal processing is applicable for Lorentzian lineshape under nonsaturating conditions. The estimation is carried out using a convergent iterative algorithm capable of jointly processing the in-phase and out-of-phase data in the presence of phase noise and unknown microwave phase. Cramér-Rao bound analysis and simulation results demonstrate a significant reduction in linewidth estimation error using quadrature detection, for both low and high values of phase noise. EPR spectroscopic data are also reported for illustration. PMID:20971667

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.

Phase-matched second- and third-harmonic generation in plasmas with density ripple

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

Dahiya, Deepak; Sajal, Vivek; Sharma, A. K.

The generation of second and third harmonics by the interaction of an ultrashort laser pulse with underdense plasma having a density ripple is studied at intensities I{lambda}{sup 2}=10{sup 16}-10{sup 19} W cm{sup -2} {mu}m{sup 2} using fully relativistic two-dimensional particle-in-cell simulations with high spectral resolution. A theoretical model is developed for second- and third-harmonic conversion efficiencies. When the laser is plane polarized in the simulation plane even and odd harmonics are excited in the same polarization as the laser polarization. The highest efficiency of generation of a specific harmonic occurs when the ripple wave vector value k{sub q} satisfies phase-matchingmore » conditions. The efficiency of phase-matched harmonic generation is an order of magnitude higher than the one without phase matching. The efficiency increases rapidly in weak and moderate relativistic regime and tends to saturate in strong relativistic regime. At moderately relativistic intensities and low plasma densities, the simulation and recent experimental results are fairly reproduced by an analytical theory.« less

Forced Oscillations of Supported Drops

NASA Technical Reports Server (NTRS)

Wilkes, Edward D.; Basaran, Osman A.

1996-01-01

Oscillations of supported liquid drops are the subject of wide scientific interest, with applications in areas as diverse as liquid-liquid extraction, synthesis of ceramic powders, growing of pure crystals in low gravity, and measurement of dynamic surface tension. In this research, axisymmetric forced oscillations of arbitrary amplitude of viscous liquid drops of fixed volume which are pendant from or sessile on a rod with a fixed or moving contact line and surrounded by an inviscid ambient gas are induced by moving the rod in the vertical direction sinusiodally in time. In this paper, a preliminary report is made on the computational analysis of the oscillations of supported drops that have 'clean' interfaces and whose contact lines remain fixed throughout their motions. The relative importance of forcing to damping can be increased by either increasing the amplitude of rod motion A or Reynolds number Re. It is shown that as the ratio of forcing to damping rises, for drops starting from an initial rest state a sharp increase in deformation can occur when they are forced to oscillate in the vicinity of their resonance frequencies, indicating the incipience of hysteresis. However, it is also shown that the existence of a second stable limit cycle and the occurrence of hysteresis can be observed if the drop is subjected to a so-called frequency sweep, where the forcing frequency is first increased and then decreased over a suitable range. Because the change in drop deformation response is abrupt in the vicinity of the forcing frequencies where hysteresis occurs, it should be possible to exploit the phenomenon to accurately measure the viscosity and surface tension of the drop liquid.

Predicting the onset of high-frequency self-excited oscillations in a channel with an elastic wall

NASA Astrophysics Data System (ADS)

Ward, Thomas; Whittaker, Robert

2016-11-01

Flow-induced oscillations of fluid-conveying elastic-walled channels arise in many industrial and biological systems including the oscillation of the vocal cords during phonation. We derive a system of equations that describes the wall displacement in response to the steady and oscillatory components of the fluid pressure derived by Whittaker et al. (2010). We show that the steady pressure component results in a base state deformation assumed to be small in magnitude relative to the length of the channel. The oscillation frequency of the elastic wall is determined by an eigenvalue problem paramterised by the shape of the base state deformation, the strength of axial tension relative to azimuthal bending, F , and the size of non-linear stretching effects from the wall's initial deformation, K . We determine the slow growth or decay of the normal modes in each by considering the energy budget of the system. The amplitude of the oscillations grow or decay exponentially with a growth rate Λ, which may be expressed in terms of a critical Reynolds number Rec . We use numerical simulations to identify three distinct regions in parameter regimes space and determine the stability of oscillations in each.

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.

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

75 FR 53973 - International Conference on Harmonisation; Guidance on Q4B Evaluation and Recommendation of...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-09-02

...] International Conference on Harmonisation; Guidance on Q4B Evaluation and Recommendation of Pharmacopoeial Texts... and Recommendation of Pharmacopoeial Texts for Use in the ICH Regions; Annex 12: Analytical Sieving... provides the results of the ICH Q4B evaluation of the Analytical Sieving General Chapter harmonized text...

78 FR 31944 - International Conference on Harmonisation; Guidance on Q4B Evaluation and Recommendation of...

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2013-05-28

...] International Conference on Harmonisation; Guidance on Q4B Evaluation and Recommendation of Pharmacopoeial Texts... ``Q4B Evaluation and Recommendation of Pharmacopoeial Texts for Use in the International Conference on... evaluation of the Bulk Density and Tapped Density of Powders General Chapter harmonized text from each of the...

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.

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.

Impacts assessment of dynamic speed harmonization with queue warning : task 3, impacts assessment report.

DOT National Transportation Integrated Search

2015-06-01

This report assesses the impacts of a prototype of Dynamic Speed Harmonization (SPD-HARM) with Queue Warning (Q-WARN), which are two component applications of the Intelligent Network Flow Optimization (INFLO) bundle. The assessment is based on an ext...

The influence of a local wall deformation on the development of natural instabilities in a laminar boundary layer

NASA Technical Reports Server (NTRS)

Burnel, S.; Gougat, P.; Martin, F.

1981-01-01

The natural instabilities which propagate in the laminar boundary layer of a flat plate composed of intermittent wave trains are described. A spectral analysis determines the frequency range and gives a frequency and the harmonic 2 only if there is a wall deformation. This analysis provides the amplitude modulation spectrum of the instabilities. Plots of the evolution of power spectral density are compared with the numerical results obtained from the resolve of the Orr-Sommerfeld equation, while the harmonic is related to a micro-recirculating flow near the wall deformation.

Design considerations of Miller oscillators for high-sensitivity QCM sensors in damping media.

PubMed

Rodriguez-Pardo, Loreto; Fariña, Jose; Gabrielli, Claude; Perrot, Hubert; Brendel, Remi

2007-10-01

In this paper, a new contribution to the design of quartz crystal oscillators for high-sensitivity microbalance sensors used in liquid media is presented. The oscillation condition for a Miller configuration was studied to work in a wide dynamic range of the resonator losses. The equations relating the values of the active and passive components with the maximum supported damping and mass were obtained. Also, the conditions to obtain a stable frequency according to the resonator damping (R(Q)), the static capacity (Cp) and the filter frequency (f(F)) were found. Under these conditions, the circuit oscillation frequency will be proportional to the resonant series frequency and does not depend on the previous parameters (R(Q), f(F), and Cp). If these conditions cannot be satisfied, the expression of the oscillation frequency is given and the discrimination of these effects is obtained through resonator frequency measurements.

75 FR 17148 - International Conference on Harmonisation; Guidance on Q4B Evaluation and Recommendation of...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-04-05

...] International Conference on Harmonisation; Guidance on Q4B Evaluation and Recommendation of Pharmacopoeial Texts... Recommendation of Pharmacopoeial Texts for Use in the ICH Regions; Annex 7: Dissolution Test General Chapter... results of the ICH Q4B evaluation of the Dissolution Test General Chapter harmonized text from each of the...

75 FR 17147 - International Conference on Harmonisation; Guidance on Q4B Evaluation and Recommendation of...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-04-05

...] International Conference on Harmonisation; Guidance on Q4B Evaluation and Recommendation of Pharmacopoeial Texts... Recommendation of Pharmacopoeial Texts for Use in the ICH Regions; Annex 9: Tablet Friability General Chapter... results of the ICH Q4B evaluation of the Tablet Friability General Chapter harmonized text from each of...

Genomewide Linkage Scan for Split–Hand/Foot Malformation with Long-Bone Deficiency in a Large Arab Family Identifies Two Novel Susceptibility Loci on Chromosomes 1q42.2-q43 and 6q14.1

PubMed Central

Naveed, Mohammed; Nath, Swapan K.; Gaines, Mathew; Al-Ali, Mahmoud T.; Al-Khaja, Najib; Hutchings, David; Golla, Jeffrey; Deutsch, Samuel; Bottani, Armand; Antonarakis, Stylianos E.; Ratnamala, Uppala; Radhakrishna, Uppala

2007-01-01

Split–hand/foot malformation with long-bone deficiency (SHFLD) is a rare, severe limb deformity characterized by tibia aplasia with or without split-hand/split-foot deformity. Identification of genetic susceptibility loci for SHFLD has been unsuccessful because of its rare incidence, variable phenotypic expression and associated anomalies, and uncertain inheritance pattern. SHFLD is usually inherited as an autosomal dominant trait with reduced penetrance, although recessive inheritance has also been postulated. We conducted a genomewide linkage analysis, using a 10K SNP array in a large consanguineous family (UR078) from the United Arab Emirates (UAE) who had disease transmission consistent with an autosomal dominant inheritance pattern. The study identified two novel SHFLD susceptibility loci at 1q42.2-q43 (nonparametric linkage [NPL] 9.8, P=.000065) and 6q14.1 (NPL 7.12, P=.000897). These results were also supported by multipoint parametric linkage analysis. Maximum multipoint LOD scores of 3.20 and 3.78 were detected for genomic locations 1q42.2-43 and 6q14.1, respectively, with the use of an autosomal dominant mode of inheritance with reduced penetrance. Haplotype analysis with informative crossovers enabled mapping of the SHFLD loci to a region of ∼18.38 cM (8.4 Mb) between single-nucleotide polymorphisms rs1124110 and rs535043 on 1q42.2-q43 and to a region of ∼1.96 cM (4.1 Mb) between rs623155 and rs1547251 on 6q14.1. The study identified two novel loci for the SHFLD phenotype in this UAE family. PMID:17160898

Ultra-stable, low phase noise dielectric resonator stabilized oscillators for military and commercial systems

NASA Technical Reports Server (NTRS)

Mizan, Muhammad; Higgins, Thomas; Sturzebecher, Dana

1993-01-01

EPSD has designed, fabricated and tested, ultra-stable, low phase noise microwave dielectric resonator oscillators (DRO's) at S, X, Ku, and K-bands, for potential application to high dynamic range and low radar cross section target detection radar systems. The phase noise and the temperature stability surpass commercially available DROs. Low phase noise signals are critical for CW Doppler radars, at both very close-in and large offset frequencies from the carrier. The oscillators were built without any temperature compensation techniques and exhibited a temperature stability of 25 parts per million (ppm) over an extended temperature range. The oscillators are lightweight, small and low cost compared to BAW & SAW oscillators, and can impact commercial systems such as telecommunications, built-in-test equipment, cellular phone and satellite communications systems. The key to obtaining this performance was a high Q factor resonant structure (RS) and careful circuit design techniques. The high Q RS consists of a dielectric resonator (DR) supported by a low loss spacer inside a metal cavity. The S and the X-band resonant structures demonstrated loaded Q values of 20,300 and 12,700, respectively.

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…

Analysis of higher order harmonics with holographic reflection gratings

NASA Astrophysics Data System (ADS)

Mas-Abellan, P.; Madrigal, R.; Fimia, A.

2017-05-01

Silver halide emulsions have been considered one of the most energetic sensitive materials for holographic applications. Nonlinear recording effects on holographic reflection gratings recorded on silver halide emulsions have been studied by different authors obtaining excellent experimental results. In this communication specifically we focused our investigation on the effects of refractive index modulation, trying to get high levels of overmodulation that will produce high order harmonics. We studied the influence of the overmodulation and its effects on the transmission spectra for a wide exposure range by use of 9 μm thickness films of ultrafine grain emulsion BB640, exposed to single collimated beams using a red He-Ne laser (wavelength 632.8 nm) with Denisyuk configuration obtaining a spatial frequency of 4990 l/mm recorded on the emulsion. The experimental results show that high overmodulation levels of refractive index produce second order harmonics with high diffraction efficiency (higher than 75%) and a narrow grating bandwidth (12.5 nm). Results also show that overmodulation produce diffraction spectra deformation of the second order harmonic, transforming the spectrum from sinusoidal to approximation of square shape due to very high overmodulation. Increasing the levels of overmodulation of refractive index, we have obtained higher order harmonics, obtaining third order harmonic with diffraction efficiency (up to 23%) and narrowing grating bandwidth (5 nm). This study is the first step to develop a new easy technique to obtain narrow spectral filters based on the use of high index modulation reflection gratings.

Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20

DOE PAGES

Michael, J. Robert; Volkov, Anatoliy

2015-03-01

The widely used pseudoatom formalism in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens. It was shown that the analytical form for normalization coefficients is available primarily forl ≤ 4. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7.more » In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle–Coppens method in the Wolfram Mathematicasoftware to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.« less

Compact high-pulse-energy passively Q-switched Nd:YLF laser with an ultra-low-magnification unstable resonator: application for efficient optical parametric oscillator.

PubMed

Cho, C Y; Huang, Y P; Huang, Y J; Chen, Y C; Su, K W; Chen, Y F

2013-01-28

We exploit an ultra-low-magnification unstable resonator to develop a high-pulse-energy side-pumped passively Q-switched Nd:YLF/Cr⁴⁺:YAG laser with improving beam quality. A wedged laser crystal is employed in the cavity to control the emissions at 1047 nm and 1053 nm independently through the cavity alignment. The pulse energies at 1047 nm and 1053 nm are found to be 19 mJ and 23 mJ, respectively. The peak powers for both wavelengths are higher than 2 MW. Furthermore, the developed Nd:YLF lasers are employed to pump a monolithic optical parametric oscillator for confirming the applicability in nonlinear wavelength conversions.

Harmonic ratcheting for fast acceleration

NASA Astrophysics Data System (ADS)

Cook, N.; Brennan, J. M.; Peggs, S.

2014-04-01

A major challenge in the design of rf cavities for the acceleration of medium-energy charged ions is the need to rapidly sweep the radio frequency over a large range. From low-power medical synchrotrons to high-power accelerator driven subcritical reactor systems, and from fixed focus alternating gradient accelerators to rapid cycling synchrotrons, there is a strong need for more efficient, and faster, acceleration of protons and light ions in the semirelativistic range of hundreds of MeV/u. A conventional way to achieve a large, rapid frequency sweep (perhaps over a range of a factor of 6) is to use custom-designed ferrite-loaded cavities. Ferrite rings enable the precise tuning of the resonant frequency of a cavity, through the control of the incremental permeability that is possible by introducing a pseudoconstant azimuthal magnetic field. However, rapid changes over large permeability ranges incur anomalous behavior such as the "Q-loss" and "f-dot" loss phenomena that limit performance while requiring high bias currents. Notwithstanding the incomplete understanding of these phenomena, they can be ameliorated by introducing a "harmonic ratcheting" acceleration scheme in which two or more rf cavities take turns accelerating the beam—one turns on when the other turns off, at different harmonics—so that the radio frequency can be constrained to remain in a smaller range. Harmonic ratcheting also has straightforward performance advantages, depending on the particular parameter set at hand. In some typical cases it is possible to halve the length of the cavities, or to double the effective gap voltage, or to double the repetition rate. This paper discusses and quantifies the advantages of harmonic ratcheting in general. Simulation results for the particular case of a rapid cycling medical synchrotron ratcheting from harmonic number 9 to 2 show that stability and performance criteria are met even when realistic engineering details are taken into consideration.

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.

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

Khamzin, A. A., E-mail: airat.khamzin@rambler.ru; Sitdikov, A. S.; Nikitin, A. S.

An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.

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…

A 4D hyperspherical interpretation of q-space.

PubMed

Pasha Hosseinbor, A; Chung, Moo K; Wu, Yu-Chien; Bendlin, Barbara B; Alexander, Andrew L

2015-04-01

3D q-space can be viewed as the surface of a 4D hypersphere. In this paper, we seek to develop a 4D hyperspherical interpretation of q-space by projecting it onto a hypersphere and subsequently modeling the q-space signal via 4D hyperspherical harmonics (HSH). Using this orthonormal basis, we derive several well-established q-space indices and numerically estimate the diffusion orientation distribution function (dODF). We also derive the integral transform describing the relationship between the diffusion signal and propagator on a hypersphere. Most importantly, we will demonstrate that for hybrid diffusion imaging (HYDI) acquisitions low order linear expansion of the HSH basis is sufficient to characterize diffusion in neural tissue. In fact, the HSH basis achieves comparable signal and better dODF reconstructions than other well-established methods, such as Bessel Fourier orientation reconstruction (BFOR), using fewer fitting parameters. All in all, this work provides a new way of looking at q-space. Copyright © 2014 Elsevier B.V. All rights reserved.

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.

UNVEILING THE UNIVERSALITY OF I-LOVE-Q RELATIONS

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

Sham, Y.-H.; Lin, L.-M.; Leung, P. T.

The recent discovery of the universal I-Love-Q relations connecting the moment of inertia, tidal deformability, and the spin-induced quadrupole moment of compact stars is intriguing and totally unexpected. In this paper, we provide numerical evidence showing that the universality can be attributed to the incompressible limit of the I-Love-Q relations. The fact that modern equations of state are stiff, with an effective adiabatic index larger than about two, above the nuclear density range is the key to establishing the universality for neutron stars and quark stars with typical compactness from about 0.1 to 0.3. On the other hand, the I-Love-Qmore » relations of low-mass neutron stars near the minimum mass limit depend more sensitively on the underlying equation of state because these stars are composed mainly of softer matter at low densities. However, the I-Love-Q relations for low-mass quark stars can still be represented accurately by the incompressible limit. We also study the I-Love relation connecting the moment of inertia and tidal deformability analytically in Newtonian gravity and show why the I-Love-Q relation is weakly dependent on the underlying equation of state and can be attributed to its incompressible limit.« less

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.

Flapping response characteristics of hingeless rotor blades by a gereralized harmonic balance method

NASA Technical Reports Server (NTRS)

Peters, D. A.; Ormiston, R. A.

1975-01-01

Linearized equations of motion for the flapping response of flexible rotor blades in forward flight are derived in terms of generalized coordinates. The equations are solved using a matrix form of the method of linear harmonic balance, yielding response derivatives for each harmonic of the blade deformations and of the hub forces and moments. Numerical results and approximate closed-form expressions for rotor derivatives are used to illustrate the relationships between rotor parameters, modeling assumptions, and rotor response characteristics. Finally, basic hingeless rotor response derivatives are presented in tabular and graphical form for a wide range of configuration parameters and operating conditions.

An injection seeded single frequency Nd:YAG Q-switched laser with precisely controllable laser pulse firing time

NASA Astrophysics Data System (ADS)

Wu, Frank F.; Khizhnyak, Anatoliy; Markov, Vladimir

2010-02-01

We have realized a single frequency Q-switched Nd:YAG laser with precisely controllable lasing time and thus enabled synchronization of multi-laser systems. The use of injection seeding to the slave ring oscillator results in unidirectional Q-switched laser oscillation with suppression of bidirectional Q-switched oscillation that otherwise would be initiated from spontaneous emission if the seeding laser is not present. Under normal condition, the cavity is high in loss during the pumping period; then a Pockels cell opens the cavity to form the pulse build up, with a second Pockels cell to perform cavity dumping, generating the Q-switched pulse output with optimized characteristics. The two Pockels cells can be replaced by a single unit if an adjustable gated electrical pulse is applied to the Pockels cell in which the pulse front is used to open the cavity and the falling edge to dump the laser pulse. Proper selection of the pump parameters and Pockels-cell gating enables operation of the system in a mode in which the Q-switched pulse can be formed only under the seeding condition. The advantage of the realized regime is in stable laser operation with no need in adjustment of the seeded light wavelength and the mode of the cavity. It is found that the frequency of the Q-switched laser radiation matches well to the injected seeded laser mode. By using two-stage amplifiers, an output energy better than 300 mJ has been achieved in MOPA configuration without active control of the cavity length and with pulse width adjustability from several nanoseconds to 20 ns. The Q-switched oscillator operates not only at precisely controlled firing time but also can be tuned over wide range. This will enable multi-laser systems synchronization and frequency locking down each other if necessary.

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.

Parity-time–symmetric optoelectronic oscillator

PubMed Central

2018-01-01

An optoelectronic oscillator (OEO) is a hybrid microwave and photonic system incorporating an amplified positive feedback loop to enable microwave oscillation to generate a high-frequency and low–phase noise microwave signal. The low phase noise is ensured by the high Q factor of the feedback loop enabled by the use of a long and low-loss optical fiber. However, an OEO with a long fiber loop would have a small free spectral range, leading to a large number of closely spaced oscillation modes. To ensure single-mode oscillation, an ultranarrowband optical filter must be used, but such an optical filter is hard to implement and the stability is poor. Here, we use a novel concept to achieve single-mode oscillation without using an ultranarrowband optical filter. The single-mode operation is achieved based on parity-time (PT) symmetry by using two identical feedback loops, with one having a gain and the other having a loss of the same magnitude. The operation is analyzed theoretically and verified by an experiment. Stable single-mode oscillation at an ultralow phase noise is achieved without the use of an ultranarrowband optical filter. The use of PT symmetry in an OEO overcomes the long-existing mode-selection challenge that would greatly simplify the implementation of OEOs for ultralow–phase noise microwave generation. PMID:29888325

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.

A low power cryocooled autonomous ultra-stable oscillator

NASA Astrophysics Data System (ADS)

Fluhr, C.; Dubois, B.; Grop, S.; Paris, J.; Le Tetû, G.; Giordano, V.

2016-12-01

We present the design and the preliminary evaluation of a cryostat equipped with a low power pulse-tube cryocooler intended to maintain near 5 K a high-Q factor sapphire microwave resonator. This cooled resonator constitutes the frequency reference of an ultra-stable oscillator presenting a short term fractional frequency stability of better than 1 ×10-15 . The proposed design enables to reach a state-of-the-art frequency stability with a cryogenic oscillator consuming only 3 kW of electrical power.

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

Chung, Won Sang, E-mail: mimip4444@hanmail.net; Hounkonnou, Mahouton Norbert, E-mail: norbert.hounkonnou@cipma.uac.bj; Arjika, Sama, E-mail: rjksama2008@gmail.com

In this paper, we propose a full characterization of a generalized q-deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the condition satisfied by the deformed q-number to define the algebra structure function. Particular Fock spaces involving finite and infinite dimensions are examined. A deformed calculus is performed as well as a coordinate realization for this algebra. A relevant example is exhibited. Associated coherent states are constructed. Finally, some thermodynamics aspects are computed and discussed.

T -folds from Yang-Baxter deformations

NASA Astrophysics Data System (ADS)

Fernández-Melgarejo, José J.; Sakamoto, Jun-ichi; Sakatani, Yuho; Yoshida, Kentaroh

2017-12-01

Yang-Baxter (YB) deformations of type IIB string theory have been well studied from the viewpoint of classical integrability. Most of the works, however, are focused upon the local structure of the deformed geometries and the global structure still remains unclear. In this work, we reveal a non-geometric aspect of YB-deformed backgrounds as T -fold by explicitly showing the associated O( D, D; ℤ) T -duality monodromy. In particular, the appearance of an extra vector field in the generalized supergravity equations (GSE) leads to the non-geometric Q-flux. In addition, we study a particular solution of GSE that is obtained by a non-Abelian T-duality but cannot be expressed as a homogeneous YB deformation, and show that it can also be regarded as a T -fold. This result indicates that solutions of GSE should be non-geometric quite in general beyond the YB deformation.

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

Ultrasound-induced oscillations of gas bubbles in contact with gelatin gel surfaces

NASA Astrophysics Data System (ADS)

Fukui, Sosuke; Ando, Keita

2017-11-01

Ultrasound-induced dynamics of gas bubbles in the vicinity of deformable boundaries are studied experimentally, as a simplified model of sonoporation in medicine. In our experiment, 28-kHz underwater ultrasound was irradiated to a gas bubble nuclei (of radius from 60 μm to 200 μm) sitting at gel surfaces (of gelatin concentration from 6 wt% to 16 wt%) and the bubble dynamics were recorded by a high-speed camera. The repeated deformation of the gel surface was found to be in phase with volumetric oscillation of the bubble. A liquid jet, which can appear toward the collapse phase in the bubble oscillation in volume, produced localized surface deformation, which is an important observation in the context of sonoporation. We characterize the maximum displacement of the gel surface with varying the bubble nuclei radius (in comparison to the resonant radius fixed approximately at 117 μm). We also examine the phase difference between the ultrasound and the bubble dynamics under the influence of the deformable boundary. The Research Grant of Keio Leading-edge Laboratory of Science & Technology.

Sound Emission of Rotor Induced Deformations of Generator Casings

NASA Technical Reports Server (NTRS)

Polifke, W.; Mueller, B.; Yee, H. C.; Mansour, Nagi (Technical Monitor)

2001-01-01

The casing of large electrical generators can be deformed slightly by the rotor's magnetic field. The sound emission produced by these periodic deformations, which could possibly exceed guaranteed noise emission limits, is analysed analytically and numerically. From the deformation of the casing, the normal velocity of the generator's surface is computed. Taking into account the corresponding symmetry, an analytical solution for the acoustic pressure outside the generator is round in terms of the Hankel function of second order. The normal velocity or the generator surface provides the required boundary condition for the acoustic pressure and determines the magnitude of pressure oscillations. For the numerical simulation, the nonlinear 2D Euler equations are formulated In a perturbation form for low Mach number Computational Aeroacoustics (CAA). The spatial derivatives are discretized by the classical sixth-order central interior scheme and a third-order boundary scheme. Spurious high frequency oscillations are damped by a characteristic-based artificial compression method (ACM) filter. The time derivatives are approximated by the classical 4th-order Runge-Kutta method. The numerical results are In excellent agreement with the analytical solution.

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.

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.

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

The Selection of Q-Switch for a 350mJ Air-borne 2-micron Wind Lidar

NASA Technical Reports Server (NTRS)

Petros, Mulugeta; Yu, Jirong; Trieu, Bo; Bai, Yingxin; Petzar, Paul; Singh, Upendra N.

2008-01-01

In the process of designing a coherent, high energy 2micron, Doppler wind Lidar, various types of Q-Switch materials and configurations have been investigated for the oscillator. Designing an oscillator with a relatively low gain laser material, presents challenges related to the management high internal circulating fluence due to high reflective output coupler. This problem is compounded by the loss of hold-off. In addition, the selection has to take into account the round trip optical loss in the resonator and the loss of hold-off. For this application, a Brewster cut 5mm aperture, fused silica AO Q-switch is selected. Once the Q-switch is selected various rf frequencies were evaluated. Since the Lidar has to perform in single longitudinal and transverse mode with transform limited line width, in this paper, various seeding configurations are presented in the context of Q-Switch diffraction efficiency. The master oscillator power amplifier has demonstrated over 350mJ output when the amplifier is operated in double pass mode and higher than 250mJ when operated in single pass configuration. The repetition rate of the system is 10Hz and the pulse length 200ns.

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.

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.

Digital detection and processing of multiple quadrature harmonics for EPR spectroscopy.

PubMed

Ahmad, R; Som, S; Kesselring, E; Kuppusamy, P; Zweier, J L; Potter, L C

2010-12-01

A quadrature digital receiver and associated signal estimation procedure are reported for L-band electron paramagnetic resonance (EPR) spectroscopy. The approach provides simultaneous acquisition and joint processing of multiple harmonics in both in-phase and out-of-phase channels. The digital receiver, based on a high-speed dual-channel analog-to-digital converter, allows direct digital down-conversion with heterodyne processing using digital capture of the microwave reference signal. Thus, the receiver avoids noise and nonlinearity associated with analog mixers. Also, the architecture allows for low-Q anti-alias filtering and does not require the sampling frequency to be time-locked to the microwave reference. A noise model applicable for arbitrary contributions of oscillator phase noise is presented, and a corresponding maximum-likelihood estimator of unknown parameters is also reported. The signal processing is applicable for Lorentzian lineshape under nonsaturating conditions. The estimation is carried out using a convergent iterative algorithm capable of jointly processing the in-phase and out-of-phase data in the presence of phase noise and unknown microwave phase. Cramér-Rao bound analysis and simulation results demonstrate a significant reduction in linewidth estimation error using quadrature detection, for both low and high values of phase noise. EPR spectroscopic data are also reported for illustration. Copyright © 2010 Elsevier Inc. All rights reserved.

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.

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.