Damping of coupled harmonic oscillators
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.
Rabi oscillation between states of a coupled harmonic oscillator
International Nuclear Information System (INIS)
Park, Tae Jun
2003-01-01
Rabi oscillation between bound states of a single potential is well known. However the corresponding formula between the states of two different potentials has not been obtained yet. In this work, we derive Rabi formula between the states of a coupled harmonic oscillator which may be used as a simple model for the electron transfer. The expression is similar to typical Rabi formula for a single potential. This result may be used to describe transitions between coupled diabatic potential curves
Coupled harmonic oscillators and their quantum entanglement
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.
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearity...... in the coupling transconductances, in conjunction with a finite amplitude relaxation time and de-tuning of the individual oscillators, cause close-to-carrier AM-to-PM noise conversion. A discussion is presented of how the theoretic results translate into design rules for quadrature oscillator ICs. SPECTRE RF...
Controllability in tunable chains of coupled harmonic oscillators
DEFF Research Database (Denmark)
Buchmann, Lukas Filip; Mølmer, Klaus; Petrosyan, David
2018-01-01
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......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...... 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....
Spontaneous decoherence of coupled harmonic oscillators confined in a ring
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.
Nonlinear Analysis of a Cross-Coupled Quadrature Harmonic Oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2004-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator leading to an expression for the trade-off between signal quadrature and close-in phase noise. The theory shows that nonlinearity in the coupling transconductance results in AM-PM noise close to the carrier, which...... increases with the coupling strength. The results are compared with SPECTRE RF simulations....
Investigation of Coupled Harmonic Oscillations with a V-Scope.
Trumper, Ricardo; Wiener, Achiam
1994-01-01
In this paper, experiments with equal-length and different-length coupled pendulums were carried out measuring the frequency of energy exchange between them using microcomputer-based technology. The experiment described in this paper would be most appropriate for an introductory mechanics laboratory course. (15 references) (LZ)
Quantum entanglement in coupled harmonic oscillator systems: from micro to macro
Kao, Jhih-Yuan; Chou, Chung-Hsien
2016-07-01
We investigate the entanglement dynamics of several models of coupled harmonic oscillators, whereby a number of properties concerning entanglement have been scrutinized, such as how the environment affects entanglement of a system, and death and revival of entanglement. Among them, there are two models for which we are able to vary their particle numbers easily by assuming identicalness, thereby examining how the particle number affects entanglement. We have found that the upper bound of entanglement between identical oscillators is approximately inversely proportional to the particle number.
Harmonic oscillator Green's function
International Nuclear Information System (INIS)
Macek, J.H.; Ovchinnikov, S.Yu.; Khrebtukov, D.B.
2000-01-01
The Green's function for the harmonic oscillator in three dimensions plays an important role in the theory of atomic collisions. One representation of low-energy ion-atom collisions involves harmonic oscillator potentials. A closed-form expression for the harmonic oscillator Green's function, needed to exploit this representation, is derived. This expression is similar to the expression for the Coulomb Green's function obtained by Hostler and Pratt. Calculations of electron distributions for a model system of ion-atom collisions are reported to illustrate the theory.
Effective harmonic oscillator description of anharmonic molecular ...
Indian Academy of Sciences (India)
... a harmonic oscillator eigenfunction with the centroid and width parameter as variational paraeters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar to the vibrational self consistent field results. Coriolis coupling is also included in these studies.
Effective harmonic oscillator description of anharmonic molecular ...
Indian Academy of Sciences (India)
Administrator
function as a harmonic oscillator eigenfunction with the centroid and width parameter as variational para- eters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar to the vibrational self consistent field results. Coriolis coupling is also included in ...
AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2006-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...... with the coupling strength. A simple linear time-domain model is employed to illustrate the results...
On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress
International Nuclear Information System (INIS)
Bocko, M.F.; Onofrio, R.
1996-01-01
Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them, have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves et al., 1980, Rev. Mod. Phys. 52, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review. copyright 1996 The American Physical Society
Quantum wormholes and harmonic oscillators
Garay, Luis J.
1993-01-01
The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface which divides the space time manifold into two disconnected parts. Minisuperspace models which consist of a homogeneous massless scalar field coupled to a Friedmann-Robertson-Walker space time are considered. Once the path integral over the lapse function is performed, the requirement that the space time be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is argued that there does not exist any wave function which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. Then, the wormhole wave functions can be written as linear combinations of harmonic oscillator wave functions.
Non-singular spiked harmonic oscillator
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Guardiola, R.
1990-01-01
A perturbative study of a class of non-singular spiked harmonic oscillators defined by the hamiltonian H = d sup(2)/dr sup(2) + r sup(2) + λ/r sup(α) in the domain [0,∞] is carried out, in the two extremes of a weak coupling and a strong coupling regimes. A path has been found to connect both expansions for α near 2. (author)
Effective harmonic oscillator description of anharmonic molecular ...
Indian Academy of Sciences (India)
Administrator
The effective harmonic oscillator is constructed variationally, by taking the trial wave function as a harmonic oscillator eigenfunction with the centroid and width parameter as variational para- eters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar ...
Introduction to Classical and Quantum Harmonic Oscillators
International Nuclear Information System (INIS)
Latal, H
1997-01-01
As the title aptly states, this book deals with harmonic oscillators of various kinds, from classical mechanical and electrical oscillations up to quantum oscillations. It is written in a lively language, and occasional interspersed anecdotes make the reading of an otherwise mathematically oriented text quite a pleasure. Although the author claims to have written an 'elementary introduction', it is certainly necessary to have a good deal of previous knowledge in physics (mechanics, electrodynamics, quantum theory), electrical engineering and, of course, mathematics in order to follow the general line of his arguments. The book begins with a thorough treatment of classical oscillators (free, damped, forced) that is followed by an elaboration on Fourier analysis. Lagrange and Hamilton formalisms are then introduced before the problem of coupled oscillations is attacked. A chapter on statistical perspectives leads over to the final discussion of quantum oscillations. With the book comes a diskette containing a number of worksheets (Microsoft Excel) that can be used by the reader for instant visualization to get a better qualitative and quantitative understanding of the material. To the reviewer it seems difficult to pinpoint exactly the range of prospective readership of the book. It can certainly not be intended as a textbook for students, but rather as a reference book for teachers of physics or researchers, who want to look up one or other aspect of harmonic oscillations, for which purpose the diskette represents a very valuable tool. (book review)
Harmonic oscillator and nuclear pseudospin
International Nuclear Information System (INIS)
Lisboa, Ronai; Malheiro, Manuel; Castro, Antonio S. de; Alberto, Pedro; Fiolhais, Manuel
2004-01-01
A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U, linear in r. Setting either Σ = S + V or Δ = V - S to zero, analytical solutions for bound states are found. The eingenenergies and their nonrelativistic limits are presented and particular cases are discussed, especially the case Σ = 0, for which pseudospin symmetry is exact
Harmonic oscillator on a lattice
International Nuclear Information System (INIS)
Ader, J.P.; Bonnier, B.; Hontebeyrie, M.; Meyers, C.
1983-01-01
The continuum limit of the ground state energy for the harmonic oscillator with discrete time is derived for all possible choices of the lattice derivative. The occurrence of unphysical values is shown to arise whenever the lattice laplacian is not strictly positive on its Brillouin zone. These undesirable limits can either be finite and arbitrary (multiple spectrum) or infinite (overlapping sublattices with multiple spectrum). (orig.)
Harmonic oscillator and nuclear pseudospin
International Nuclear Information System (INIS)
Lisboa, Ronai; Malheiro, Manuel; Castro, Antonio S. de; Alberto, Pedro; Fiolhais, M.
2004-01-01
A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonians contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U, linear in r. Setting either Σ=S+V or Δ=V - S to zero, analytical solutions for bound states are found. The eigenenergies and their nonrelativistic limits are present and particular cases are discussed, especially the case Σ=0, for which pseudospin symmetry is exact. (author)
Making space for harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Michelotti, Leo; /Fermilab
2004-11-01
If we restrict the number of harmonic oscillator energy eigenstates to some finite value, N, then the discrete spectrum of the corresponding position operator comprise the roots of the Hermite polynomial H{sub N+1}. Its range is just large enough to accommodate classical motion at high energy. A negative energy term must be added to the Hamiltonian which affects only the last eigenstate, |N>, suggesting it is concentrated at the extrema of this finite ''space''. Calculations support a conjecture that, in the limit of large N, the global distribution of points approaches the differential form for classical action.
Introduction to classical and quantum harmonic oscillators
Bloch, Sylvan C
2013-01-01
From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating con
Pseudospin symmetry and the relativistic harmonic oscillator
International Nuclear Information System (INIS)
Lisboa, R.; Malheiro, M.; Castro, A.S. de; Alberto, P.; Fiolhais, M.
2004-01-01
A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U linear in r. Setting either or both combinations Σ=S+V and Δ=V-S to zero, analytical solutions for bound states of the corresponding Dirac equations are found. The eigenenergies and wave functions are presented and particular cases are discussed, devoting a special attention to the nonrelativistic limit and the case Σ=0, for which pseudospin symmetry is exact. We also show that the case U=Δ=0 is the most natural generalization of the nonrelativistic harmonic oscillator. The radial node structure of the Dirac spinor is studied for several combinations of harmonic-oscillator potentials, and that study allows us to explain why nuclear intruder levels cannot be described in the framework of the relativistic harmonic oscillator in the pseudospin limit
Discontinuities in a damped quantum harmonic oscillator
International Nuclear Information System (INIS)
Giraldi, Filippo; Petruccione, Francesco
2012-01-01
The quantum model for a damped harmonic oscillator linearly coupled to a reservoir of continuous frequency modes has been exactly diagonalized either with or without the rotating wave approximation. The exact dynamics, formally described in terms of the coupling function, is analyzed for the Drude model. In this scenario, we focus on a class of couplings recovering the Drude form as a limiting case. The exact time evolution of the expectation values of the position, momentum and number operators are described through Fox H-functions, as well as the correlation function of the reservoir. In correspondence with the critical values of the frequency, discontinuities appear in the long time scale dynamics, arbitrarily slowing down the relaxations of the above observables. This effect allows one to enhance arbitrarily the lifetime of the excitations, giving relevant applications in the study of the quantum domain of opto-mechanical and nano-mechanical resonators. The critical frequency approach constitutes a further method of control in the scenario of environment-induced decoherence via reservoir engineering. (paper)
Second International Workshop on Harmonic Oscillators
Han, Daesoo (Editor); Wolf, Kurt Bernardo (Editor)
1995-01-01
The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as we explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory.
Laguerre polynomials by a harmonic oscillator
Baykal, Melek; Baykal, Ahmet
2014-09-01
The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators.
Laguerre polynomials by a harmonic oscillator
International Nuclear Information System (INIS)
Baykal, Melek; Baykal, Ahmet
2014-01-01
The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators. (paper)
Sobolev spaces associated to the harmonic oscillator
Indian Academy of Sciences (India)
2Departamento de Matemática, Facultad de Ciencias, Universidad Autónoma de. Madrid, Spain. E-mail: bbongio@math.unl.edu.ar; joseluis.torrea@uam.es. MS received 27 September 2005. Abstract. We define the Hermite–Sobolev spaces naturally associated to the harmonic oscillator H = − + |x|2. Structural properties ...
Information cloning of harmonic oscillator coherent states
Indian Academy of Sciences (India)
Abstract. We show that in the case of unknown harmonic oscillator coherent states it is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state.
Information cloning of harmonic oscillator coherent states
Indian Academy of Sciences (India)
article/fulltext/pram/059/02/0263-0267. Keywords. Cloning; coherent states. Abstract. We show that in the case of unknown harmonic oscillator coherent statesit is possible to achieve what we call perfect information cloning. By this we mean that ...
Information cloning of harmonic oscillator coherent states
Indian Academy of Sciences (India)
We show that in the case of unknown harmonic oscillator coherent statesit is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state. By making use ...
Variational and perturbative schemes for a spiked harmonic oscillator
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Estevez, G.A.; Guardiola, R.
1989-01-01
A variational analysis of the spiked harmonic-oscillator Hamiltonian operator -d 2 /dx 2 + x 2 + l(l+1)/x 2 + λ |x| -α , where α is a real positive parameter, is reported in this work. The formalism makes use of the functional space spanned by the solutions of the Schroedinger equation for the linear harmonic-oscillator Hamiltonian supplemented by a Dirichlet boundary condition, and a standard procedure for diagonalizing symmetric matrices. The eigenvalues obtained by increasing the dimension of the basis set provides accurate approximations for the ground-state energy of the model system, valid for positive and relatively large values of the coupling parameter λ. Additionally, a large-coupling pertubative-expansion is carried out and the contributions up to fourth order to the ground-state energy are explicitly evaluated. Numerical results are compared for the special case α=5/2. (author) [pt
Spectral inverse problem for q-deformed harmonic oscillator
Indian Academy of Sciences (India)
The supersymmetric quantization condition is used to study the wave functions of SWKB equivalent -deformed harmonic oscillator which are obtained by using only the knowledge of bound-state spectra of -deformed harmonic oscillator. We have also studied the nonuniqueness of the obtained interactions by this ...
First harmonic injection locking of 24-GHz-oscillators
Directory of Open Access Journals (Sweden)
M. R. Kühn
2003-01-01
Full Text Available An increasing number of applications is proposed for the 24 GHz ISM-band, like automotive radar systems and short-range communication links. These applications demand for oscillators providing moderate output power of a few mW and moderate frequency stability of about 0.5%. The maximum oscillation frequency of low-cost off-theshelf transistors is too low for stable operation of a fundamental 24GHz oscillator. Thus, we designed a 24 GHz first harmonic oscillator, where the power generated at the fundamental frequency (12 GHz is reflected resulting in effective generation of output power at the first harmonic. We measured a radiated power from an integrated planar antenna of more than 1mW. Though this oscillator provides superior frequency stability compared to fundamental oscillators, for some applications additional stabilization is required. As a low-cost measure, injection locking can be used to phase lock oscillators that provide sufficient stability in free running mode. Due to our harmonic oscillator concept injection locking has to be achieved at the first harmonic, since only the antenna is accessible for signal injection. We designed, fabricated and characterized a harmonic oscillator using the antenna as a port for injection locking. The locking range was measured versus various parameters. In addition, phase-noise improvement was investigated. A theoretical approach for the mechanism of first harmonic injection locking is presented.
Hyperchaos in coupled Colpitts oscillators
DEFF Research Database (Denmark)
Cenys, Antanas; Tamasevicius, Arunas; Baziliauskas, Antanas
2003-01-01
The paper suggests a simple solution of building a hyperchaotic oscillator. Two chaotic Colpitts oscillators, either identical or non-identical ones are coupled by means of two linear resistors R-k. The hyperchaotic output signal v(t) is a linear combination, specifically the mean of the individual...
Harmonic and Anharmonic Behaviour of a Simple Oscillator
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…
Driven damped harmonic oscillator resonance with an Arduino
Goncalves, A. M. B.; Cena, C. R.; Bozano, D. F.
2017-07-01
In this paper we propose a simple experimental apparatus that can be used to show quantitative and qualitative results of resonance in a driven damped harmonic oscillator. The driven oscillation is made by a servo motor, and the oscillation amplitude is measured by an ultrasonic position sensor. Both are controlled by an Arduino board. The frequency of free oscillation measured was campatible with the resonance frequency that was measured.
Harmonic oscillator in quantum rotational spectra: Molecules and nuclei
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.
A harmonic oscillator having “volleyball damping”
Mickens, R. E.; Oyedeji, K.; Rucker, S. A.
2006-05-01
Volleyball damping corresponds to linear damping up to a certain critical velocity, with zero damping above this value. The dynamics of a linear harmonic oscillator is investigated with this damping mechanism.
Chimera states in nonlocally coupled phase oscillators with biharmonic interaction
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.
A new analytical approximation to the Duffing-harmonic oscillator
International Nuclear Information System (INIS)
Fesanghary, M.; Pirbodaghi, T.; Asghari, M.; Sojoudi, H.
2009-01-01
In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations.
Two-dimensional generalized harmonic oscillators and their Darboux partners
International Nuclear Information System (INIS)
Schulze-Halberg, Axel
2011-01-01
We construct two-dimensional Darboux partners of the shifted harmonic oscillator potential and of an isotonic oscillator potential belonging to the Smorodinsky–Winternitz class of superintegrable systems. The transformed solutions, their potentials and the corresponding discrete energy spectra are computed in explicit form. (paper)
On quantum harmonic oscillator being subjected to absolute
Indian Academy of Sciences (India)
In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. In this paper, assuming a boundary condition that the product of momentum and position, or the product of energy density and position remains constant in the QHO, it is established that a particle subjected to increasing ...
Magnetically Coupled Magnet-Spring Oscillators
Donoso, G.; Ladera, C. L.; Martin, P.
2010-01-01
A system of two magnets hung from two vertical springs and oscillating in the hollows of a pair of coils connected in series is a new, interesting and useful example of coupled oscillators. The electromagnetically coupled oscillations of these oscillators are experimentally and theoretically studied. Its coupling is electromagnetic instead of…
Coupled oscillators and Feynman's three papers
International Nuclear Information System (INIS)
Kim, Y S
2007-01-01
According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the 'rest of the universe' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators
Fundamental and Harmonic Oscillations in Neighboring Coronal Loops
Li, Hongbo; Liu, Yu; Vai Tam, Kuan
2017-06-01
We present observations of multimode (fundamental and harmonic) oscillations in a loop system, which appear to be simultaneously excited by a GOES C-class flare. Analysis of the periodic oscillations reveals that (1) the primary loop with a period of P a ≈ 4 minutes and a secondary loop with two periods of P a ≈ 4 minutes and P b ≈ 2 minutes are detected simultaneously in closely spaced loop strands; (2) both oscillation components have their peak amplitudes near the loop apex, while in the second loop the low-frequency component P a dominates in a loop segment that is two times larger than the high-frequency component P b ; (3) the harmonic mode P b shows the largest deviation from a sinusoidal loop shape at the loop apex. We conclude that multiple harmonic modes with different displacement profiles can be excited simultaneously even in closely spaced strands, similar to the overtones of a violin string.
Damped driven coupled oscillators: entanglement, decoherence and the classical limit
Energy Technology Data Exchange (ETDEWEB)
Mancilla, R D Guerrero; Rey-Gonzalez, R R; Fonseca-Romero, K M [Grupo de Optica e Informacion Cuantica, Departamento de Fisica, Universidad Nacional de Colombia, Bogota (Colombia)], E-mail: rdguerrerom@unal.edu.co, E-mail: rrreyg@unal.edu.co, E-mail: kmfonsecar@unal.edu.co
2009-03-13
We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, comprising a first subsystem (a harmonic oscillator) coupled to a driven and damped second subsystem (another harmonic oscillator). We choose initial states whose dynamics is confined to a couple of two-level systems, and show that the maximum value of entanglement between the two subsystems, as measured by concurrence, depends on the dissipation rate to the coupling-constant ratio and the initial state. While in a related model the entropy of the first subsystem (a two-level system) never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model.
Harmonic oscillator in an elastic medium with a spiral dislocation
Maia, A. V. D. M.; Bakke, K.
2018-02-01
We investigate the behaviour of a two-dimensional harmonic oscillator in an elastic medium that possesses a spiral dislocation (an edge dislocation). We show that the Schrödinger equation for harmonic oscillator in the presence of a spiral dislocation can be solved analytically. Further, we discuss the effects of this topological defect on the confinement to a hard-wall confining potential. In both cases, we analyse if the effects of the topology of the spiral dislocation gives rise to an Aharonov-Bohm-type effect for bound states.
Predicting charmonium and bottomonium spectra with a quark harmonic oscillator
Norbury, J. W.; Badavi, F. F.; Townsend, L. W.
1986-01-01
The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.
Parametric Resonance in a Time-Dependent Harmonic Oscillator
Directory of Open Access Journals (Sweden)
P. N. Nesterov
2013-01-01
Full Text Available In this paper, we study the phenomenon of appearance of new resonances in a timedependent harmonic oscillator under an oscillatory decreasing force. The studied equation belongs to the class of adiabatic oscillators and arises in connection with the spectral problem for the one-dimensional Schr¨odinger equation with Wigner–von Neumann type potential. We use a specially developed method for asymptotic integration of linear systems of differential equations with oscillatory decreasing coefficients. This method uses the ideas of the averaging method to simplify the initial system. Then we apply Levinson’s fundamental theorem to get the asymptotics for its solutions. Finally, we analyze the features of a parametric resonance phenomenon. The resonant frequencies of perturbation are found and the pointwise type of the parametric resonance phenomenon is established. In conclusion, we construct an example of a time-dependent harmonic oscillator (adiabatic oscillator in which the parametric resonances, mentioned in the paper, may occur.
Hyperchaotic circuit with damped harmonic oscillators
DEFF Research Database (Denmark)
Lindberg, Erik; Murali, K.; Tamasevicius, A.
2001-01-01
capacitors and one nonlinear active conductor. The Lyapunov exponents are presented to confirm the hyperchaotic nature of the oscillations of the circuit. The nonlinear conductor is realized with a diode. A negative impedance converter and a linear resistor. The performance of the circuit is investigated...
QUANTUM THEORY OF DAMPED HARMONIC OSCILLATOR
African Journals Online (AJOL)
DJFLEX
However, the problem of quantum oscillator with time-varying frequency had been solved (Um et al,. 1987). The Hamiltonian of this model is usually quadratic in co-ordinates and momentum operators (Ikot et al, 2008). The quantum calculation is applied because it will give the information about the particle at intermediate ...
Local Mechanical Behavior of Steel Exposed to Nonlinear Harmonic Oscillation
Cole, D. P.; Habtour, E. M.; Sano, T.; Fudger, S. J.; Grendahl, S. M.; Dasgupta, Anshuman
2017-01-01
The local mechanical behavior of fatigued steel specimens was probed using nanoindentation. High-carbon steel cantilevers were exposed to nonlinear harmonic oscillation. The indentation modulus on the beam surface and plastic work during indentation decreased as a function of cycles, which was
A simple mechanical model for the isotropic harmonic oscillator
International Nuclear Information System (INIS)
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.
Coherent states of general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
The wave function can then be found easily, by making use of these ladder operators. Glauber proposed standard coherent states for a harmonic oscillator which is the prototype for most of the coherent states [3,4]. The coherent states form a very convenient representation for problems of quantum mechanics and can be ...
Thermal state of the general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. ... The domain part of the email address of all email addresses used by the office of Indian Academy of Sciences, including those of the staff, the journals, various programmes, and ...
Coherent states of general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
Abstract. By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator. The coherent states, both in x- and p-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger than Η/2 and is equal to the minimum of the ...
The forced harmonic oscillator with damping and thermal effects
International Nuclear Information System (INIS)
Menezes Franca, H. de; Thomaz, M.T.
1984-01-01
Nonperturbative quantum mechanical solutions of the forced harmonic oscillator with radiation reaction damping are obtained from previous analysis based on Stochastic Electrodynamics. The transition to excited states is shown to be to coherent states which follow the classical trajectory. The quantum Wigner distribution in phase space is constructed. All the results are extended to finite temperatures. (Author) [pt
Statistical mechanics of quantum one-dimensional damped harmonic oscillator
International Nuclear Information System (INIS)
Borges, E.N.M.; Borges, O.N.; Ribeiro, L.A.A.
1985-01-01
We calculate the thermal correlation functions of the one-dimensional damped harmonic oscillator in contact with a reservoir, in an exact form by applying Green's function method. In this way the thermal fluctuations are incorporated in the Caldirola-Kanai Hamiltonian
The resonating group method in an harmonic oscillator basis
International Nuclear Information System (INIS)
Silvestre-Brac, B.; Gignoux, C.; Ayant, Y.
1987-05-01
The scattering states for a general many body system is formulated within the resonating group method. The resulting Lippman-Schwinger equation is solved in an harmonic oscillator basis for which a number of advantages are emphasized. The analytical formula giving the free propagator in that basis is fully derived
Harmonic oscillator in Snyder space: The classical case and the ...
Indian Academy of Sciences (India)
Departamento de Fısica, Facultad de Ciencias, Universidad de Tarapacá, Casilla 7-D,. Arica, Chile. E-mail: cleivas@uta.cl; cleivas2008@live.cl. MS received 18 August 2009; revised 20 October 2009; accepted 27 October 2009. Abstract. The harmonic oscillator in Snyder space is investigated in its classical and quantum ...
Maximal Regularity of the Discrete Harmonic Oscillator Equation
Directory of Open Access Journals (Sweden)
Airton Castro
2009-01-01
Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.
New construction of coherent states for generalized harmonic oscillators
International Nuclear Information System (INIS)
El Baz, M.; Hassouni, Y.; Madouri, F.
2001-08-01
A dynamical algebra A q , englobing many of the deformed harmonic oscillator algebras is introduced. One of its special cases is extensively developed. A general method for constructing coherent states related to any algebra of the type A q is discussed. The construction following this method is carried out for the special case. (author)
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
no difficulty to accommodate them. This observation tend to present one of the main difficulties in applying Noether's theorem on the damped harmonic oscillator. Being nonself-adjoint (1) does not satisfy the Helmholtz criterion [4] to have a. Lagrangian representation. However, multiplying (1) by eλt we can convert it to.
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the ...
Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps
Pendrill, Ann-Marie; Eager, David
2015-01-01
Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…
Harmonic oscillator in Snyder space: The classical case and the ...
Indian Academy of Sciences (India)
The harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. An effective cut-off to high frequencies is found. The quantum version is developed and an equivalent usual ...
Thermal state of the general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
Harmonic oscillator that has time-dependent mass or frequency may be a good example of time-dependent Hamiltonian systems. Although a large number of dynamical systems have been investigated using approximation and perturbation method in the literature [2,3], we confine our concern to the exact quantum solution ...
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
2017-02-22
Feb 22, 2017 ... Phase-space treatment of the driven quantum harmonic oscillator. DIÓGENES CAMPOS1,2,∗. 1Universidad La Gran .... whereas some other treatments deal with the coordi- nate representation of the Schrödinger ...... Im[ +(q,p,t)] a structure of leaves that gradually appears over time and, for the values of (q ...
On quantum harmonic oscillator being subjected to absolute ...
Indian Academy of Sciences (India)
On quantum harmonic oscillator being subjected to absolute potential state. SWAMI NITYAYOGANANDA. Ramakrishna Mission Ashrama, R.K. Beach, Visakhapatnam 530 003, India. E-mail: nityayogananda@gmail.com. MS received 1 May 2015; accepted 6 May 2016; published online 3 December 2016. Abstract.
Quantum theory of damped harmonic oscillator | Antia | Global ...
African Journals Online (AJOL)
The exact solutions of the Schrödinger equation for damped harmonic oscillator with pulsating mass and modified Caldirola-Kanai Hamiltonian are evaluated. We also investigated the case of under-damped for the two models constructed and the results obtained in both cases do not violate Heisenberg uncertainty principle ...
The harmonic and anharmonic oscillator in classical stochastic electrodynamics
International Nuclear Information System (INIS)
Moore, S.M.; Ramirez, J.A.
1981-01-01
The sensitivity of the spectral density and the correlation of the harmonic oscillator to the charge distribution is examined in the context of classical stochastic electrodynamics. While the first exhibits some degree of sensitivity, the second exhibits none in the limit of zero charge. Thus, a comparison can be made with nonrelativistic quantum mechanics independent of the charge distribution. In the same spirit, the anharmonic oscillator is examined. In the limit of zero charge, it is shown that classical stochastic electrodynamics qualitatively agrees with quantum mechanics, but ambiguities make a quantitative comparison difficult. In an appendix, the oscillator approximation to the hydrogen atom is briefly discussed. (author)
Brownian motion with adhesion: harmonic oscillator with fluctuating mass.
Gitterman, M; Klyatskin, V I
2010-05-01
In contrast to the cases usually studied of a harmonic oscillator subject to a random force (Brownian motion) or having random frequency or random damping, we consider a random mass which corresponds to an oscillator for which the particles of the surrounding medium adhere to it for some (random) time after the collision, thereby changing the oscillator mass. This model, which describes Brownian motion with adhesion, can be useful for the analysis of chemical and biological solutions as well as nanotechnological devices. We consider dichotomous noise and its limiting case, white noise.
Oscillation death in a coupled van der Pol–Mathieu system
Indian Academy of Sciences (India)
Abstract. We report an investigation of the oscillation death (OD) of a parametrically excited cou- pled van der Pol–Mathieu (vdPM) system. The system can be considered as a pair of harmonically forced van der Pol oscillators under a double-well potential. The two oscillators are coupled with a cubic nonlinearity. We have ...
Energy Technology Data Exchange (ETDEWEB)
Rosu, H.C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosi, S.L.P. (Mexico); Khmelnytskaya, K.V. [Universidad Autonoma de Queretaro, Centro Universitario, Cerro de las Campanas s/n, C.P. 76010 Santiago de Queretaro, Qro. (Mexico)
2011-09-19
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned. -- Highlights: → A particular Riccati solution of the classical harmonic oscillator is shifted by a constant. → Such a solution is used in the factorization brackets to get different equations of motion. → The properties of the parametric oscillators obtained in this way are examined.
First, Second Quantization and Q-Deformed Harmonic Oscillator
Van Ngu, Man; Gia Vinh, Ngo; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Viet, Nguyen Ai
2015-06-01
Relations between the first, the second quantized representations and deform algebra are investigated. In the case of harmonic oscillator, the axiom of first quantization (the commutation relation between coordinate and momentum operators) and the axiom of second quantization (the commutation relation between creation and annihilation operators) are equivalent. We shown that in the case of q-deformed harmonic oscillator, a violence of the axiom of second quantization leads to a violence of the axiom of first quantization, and inverse. Using the coordinate representation, we study fine structures of the vacuum state wave function depend in the deformation parameter q. A comparison with fine structures of Cooper pair of superconductivity in the coordinate representation is also performed.
Spectral inverse problem for q-deformed harmonic oscillator
Indian Academy of Sciences (India)
surable quantities for known interparticle forces and confronting them with ex- perimental data. In quantum theory [1], the .... the q-numbers take the form. [k] = sin(βk) sin(β) . (7). It is clear that in both cases [k] → k in the limit q → 1. The Hamiltonian of the q-deformed harmonic oscillator [17] is. Hq = p2 q. 2m. +. 1. 2. mω2Q2 q.
Coherent and squeezed states for the 3D harmonic oscillator
Mazouz, Amel; Bentaiba, Mustapha; Mahieddine, Ali
2017-01-01
A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.
An analogue of the Berry phase for simple harmonic oscillators
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.
Phenomenology of coupled nonlinear oscillators
Estevez-Rams, E.; Estevez-Moya, D.; Aragón-Fernández, B.
2018-02-01
A recently introduced model of coupled nonlinear oscillators in a ring is revisited in terms of its information processing capabilities. The use of Lempel-Ziv based entropic measures allows to study thoroughly the complex patterns appearing in the system for different values of the control parameters. Such behaviors, resembling cellular automata, have been characterized both spatially and temporally. Information distance is used to study the stability of the system to perturbations in the initial conditions and in the control parameters. The latter is not an issue in cellular automata theory, where the rules form a numerable set, contrary to the continuous nature of the parameter space in the system studied in this contribution. The variation in the density of the digits, as a function of time is also studied. Local transitions in the control parameter space are also discussed.
Fractal Scaling Models of Resonant Oscillations in Chain Systems of Harmonic Oscillators
Müller H.
2009-01-01
Logarithmic scaling invariance is a wide distributed natural phenomenon and was proved in the distributions of physical properties of various processes — in high en- ergy physics, chemistry, seismicity, biology, geology and technology. Based on the Gantmacher-Krein continued fraction method the present paper introduces fractal scal- ing models of resonant oscillations in chain systems of harmonic oscillators. These models generate logarithmic scaling spect...
Pisot q-coherent states quantization of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Gazeau, J.P., E-mail: gazeau@apc.univ-paris7.fr [Laboratoire APC, Univ. Paris Diderot, Sorbonne Paris Cite, 75205 Paris (France); Olmo, M.A. del, E-mail: olmo@fta.uva.es [Departamento de Fisica Teorica and IMEVA, Universidad de Valladolid, E-47005, Valladolid (Spain)
2013-03-15
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories. - Highlights: Black-Right-Pointing-Pointer Quantized version of the harmonic oscillator (HO) through a q-family of coherent states. Black-Right-Pointing-Pointer For q,0
oscillator.
Compensation of oscillation coupling induced by solenoids
International Nuclear Information System (INIS)
Zelinskij, A.Yu.; Karnaukhov, I.M.; Shcherbakov, A.A.
1988-01-01
Methods for construction of various schemes of oscillation coupling compensation, induced by solenoids in charged particle storage rings, are described. Peculiarities of magnetic structure, enabling to localize oscillation coupling in wide energy range are discussed. Results of calculation of compensation schemes for design of NR-2000 storage ring spin rotation are presented
Synchronization of weakly coupled canard oscillators
Köksal Ersöz, Elif; Desroches, Mathieu; Krupa, Martin
2017-01-01
International audience; Synchronization has been studied extensively in the context of weakly coupled oscillators using the so-called phase response curve (PRC) which measures how a change of the phase of an oscillator is affected by a small perturbation. This approach was based upon the work of Malkin, and it has been extended to relaxation oscillators. Namely, synchronization conditions were established under the weak coupling assumption, leading to a criterion for the existence of synchron...
Fractal Scaling Models of Resonant Oscillations in Chain Systems of Harmonic Oscillators
Directory of Open Access Journals (Sweden)
Müller H.
2009-04-01
Full Text Available Logarithmic scaling invariance is a wide distributed natural phenomenon and was proved in the distributions of physical properties of various processes — in high en- ergy physics, chemistry, seismicity, biology, geology and technology. Based on the Gantmacher-Krein continued fraction method the present paper introduces fractal scal- ing models of resonant oscillations in chain systems of harmonic oscillators. These models generate logarithmic scaling spectra. The introduced models are not based on any statements about the nature of the link or interaction between the elements of the oscillating system. Therefore the model statements are quite generally, what opens a wide field of possible applications.
The Harmonically Coupled 2-Beam FEL
McNeil, Brian W J
2004-01-01
A 1-D model of a 2-beam Free Electron Laser amplifier is presented. The two co-propagating electron beams have different energies, chosen so that the fundamental resonant FEL interaction of the higher energy beam is at an harmonic of the lower energy beam. In this way, a coupling between the FEL interactions of the two beams occurs via the harmonic components of the electron bunching and radiation emission of the lower energy interaction. Such resonantly coupled FEL interactions may offer potential benefits over existing single beam FEL schemes. A simple example is presented where the lower energy FEL interaction only is seeded with radiation at its fundamental resonant wavelength. It is predicted that the coherence properties of this seed field are transfered via the resonantly coupled FEL interaction to the un-seeded higher energy FEL interaction, thereby improving its coherence properties over that of a SASE interaction alone. This method may offer an alternative seeding scheme for FELs operating in the XU...
Detecting the harmonics of oscillations with time-variable frequencies
Sheppard, L. W.; Stefanovska, A.; McClintock, P. V. E.
2011-01-01
A method is introduced for the spectral analysis of complex noisy signals containing several frequency components. It enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency. The method is based on mutual information and surrogate testing combined with the wavelet transform, and it is applicable to relatively short time series containing frequencies that are time variable. Where the fundamental frequency and harmonics of a process can be identified, the characteristic shape of the corresponding oscillation can be determined, enabling adaptive filtering to remove other components and nonoscillatory noise from the signal. Thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately. The method is first demonstrated on numerical examples. It is then used to identify the higher harmonics of oscillations in human skin blood flow, both spontaneous and associated with periodic iontophoresis of a vasodilatory agent. The method should be equally relevant to all situations where signals of comparable complexity are encountered, including applications in astrophysics, engineering, and electrical circuits, as well as in other areas of physiology and biology.
Harmonic-oscillator pattern arising from an algebraic approach to chiral symmetry
Buccella, F; Savoy, C A
1972-01-01
The Weinberg equation for the (mass)/sup 2/ operator (Q/sub 5//sup +/, (Q/sub 5//sup +/, m/sup 2/))=0, between meson states, is saturated in a perturbative approach. The generator Z of the mixing operators is completely established as Z=(W*M)/sub z/, where W is the W-spin operator and M is the co-ordinate of the three-dimensional harmonic oscillator. In a perturbative expansion of the (mass)/sup 2/ operator, the lowest term consists of two parts, the harmonic-oscillator energy and a spin-orbit coupling of the form (-1)/sup L+1/(L.S+/sup 1///sub 2 /). The resulting (mass)/sup 2/ consists of families of equispaced linearly rising trajectories. (11 refs).
Reentrant transition in coupled noisy oscillators.
Kobayashi, Yasuaki; Kori, Hiroshi
2015-01-01
We report on a synchronization-breaking instability observed in a noisy oscillator unidirectionally coupled to a pacemaker. Using a phase oscillator model, we find that, as the coupling strength is increased, the noisy oscillator lags behind the pacemaker more frequently and the phase slip rate increases, which may not be observed in averaged phase models such as the Kuramoto model. Investigation of the corresponding Fokker-Planck equation enables us to obtain the reentrant transition line between the synchronized state and the phase slip state. We verify our theory using the Brusselator model, suggesting that this reentrant transition can be found in a wide range of limit cycle oscillators.
Studies on phase and squeezed states of quantum harmonic oscillators
International Nuclear Information System (INIS)
Ma, Xin.
1989-01-01
A fundamental quantum-mechanical problem on the phase of quantum harmonic oscillators, which has remained an enigma for more than sixty years since the first treatment by Dirac, is completely solved. Contrary to the common belief that no Hermitian phase operators can be found to describe the phase properties of a quantum harmonic oscillator, a well-defined Hermitian phase operator with an appropriate classical limit is constructed unambiguously. The approach is different in nature from those of many previous attempts which were more or less based on the idea of polar decomposition of the annihilation operator. The fundamental difference between the quantum phase and the classical phase in spite of their conceptual consistency is pointed out and explained. The eigenvalue spectrum and eigenstates of the phase operator are obtained. Some important properties of the phase operator and phase states are investigated. The rest of this research is devoted to the studies of multimode Gaussian squeezed states of quantum harmonic oscillators. Multimode squeeze operators and rotation operators are defined such that they have extremely similar algebraic properties as those of their single-mode counterparts. It is shown that the introduction of N-mode squeeze operators provides a convenient set of parameters to describe squeezing in multimode Gaussian squeezed states. The disentangling, normal ordering, and some other properties of N-mode squeeze operators are investigated. It is also shown that the time-evolution operator for a general N-mode quadratic Hamiltonian can be conveniently expressed as an operator product containing an N-mode squeeze operator, an N-mode rotation operator, and an N-mode displacement operator
Complex-potential description of the damped harmonic oscillator
International Nuclear Information System (INIS)
Exner, P.
1981-01-01
Multidimensional damped harmonic oscillator is treated by means of a non-selfadjoint Hamiltonian with complex potential. The latter is chosen as V(x)=xx(A-iW)x with positive matrices A, W, By a perturbation-theory argument, the corresponding Hamiltonian H=-1/2Δ+V with the natural domain is shown to be closed and such that Vsub(t)=exp(-iHt) is a continuous contractive semigroup. Explicit integral-operator form of Vsub(t) is found by use of Lie-Trotter formula [ru
Elementary derivation of the quantum propagator for the harmonic oscillator
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.
A method of solving simple harmonic oscillator Schroedinger equation
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.
Intensity noise coupling in soliton fiber oscillators.
Wan, Chenchen; Schibli, Thomas R; Li, Peng; Bevilacqua, Carlo; Ruehl, Axel; Hartl, Ingmar
2017-12-15
We present an experimental and numerical study on the spectrally resolved pump-to-output intensity noise coupling in soliton fiber oscillators. In our study, we observe a strong pump noise coupling to the Kelly sidebands, while the coupling to the soliton pulse is damped. This behavior is observed in erbium-doped as well as holmium-doped fiber oscillators and confirmed by numerical modeling. It can be seen as a general feature of laser oscillators in which soliton pulse formation is dominant. We show that spectral blocking of the Kelly sidebands outside the laser cavity can improve the intensity noise performance of the laser dramatically.
Wang, Fei; Nie, Wei; Feng, Xunli; Oh, C. H.
2016-07-01
The correlated emission lasing (CEL) is experimentally demonstrated in harmonic oscillators coupled via a single three-level artificial atom [Phys. Rev. Lett. 115, 223603 (2015), 10.1103/PhysRevLett.115.223603] in which two-mode entanglement only exists in a certain time period when the harmonic oscillators are resonant with the atomic transitions. Here we examine this system and show that it is possible to obtain the steady-state entanglement when the two harmonic oscillators are resonant with Rabi sidebands. Applying dressed atomic states and Bogoliubov-mode transformation, we obtain the analytical results of the variance sum of a pair of Einstein-Podolsky-Rosen (EPR)-like operators. The stable entanglement originates from the dissipation process of the Bogoliubov modes because the atomic system can act as a reservoir in dressed state representation. We also show that the entanglement is robust against the dephasing rates of the superconducing atom, which is expected to have important applications in quantum information processing.
The Aerodynamic Behavior of a Harmonically Oscillating Finite Sweptback Wing in Supersonic Flow
National Research Council Canada - National Science Library
Chang, Chieh-Chien
1951-01-01
By an extension of Evvard's "diaphragm" concept outside the wing tip, the present paper presents two approximate methods for calculating the aerodynamic behavior of harmonically oscillating, sweptback...
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw
2016-10-15
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Directory of Open Access Journals (Sweden)
P. A. Deymier
2016-12-01
Full Text Available We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.
International Nuclear Information System (INIS)
Yeh, Y.S.; Chang, T.H.; Wu, T.S.
2004-01-01
A comparative analysis between the fundamental and second cyclotron harmonics of gyrotron backward-wave oscillators (gyro-BWOs) is presented. The simulation results reveal that nonlinear field contraction is a common feature for both harmonic interactions. Besides, the electron transit angle, used to characterize the axial modes of the fundamental harmonic TE 11 mode at the start-oscillation conditions, is found to be applicable even for the second harmonic TE 21 mode. Each axial mode of either the fundamental harmonic TE 11 or the second harmonic TE 21 modes is maintained at a constant value of the electron transit angle while changing the operating parameters, such as magnetic field and beam voltage. Extensive numerical calculations are conducted for the start-oscillation currents and tuning properties. Moreover, single-mode operating regimes are suggested where the second harmonic TE 21 gyro-BWO could generate a considerable output power, comparing with the fundamental harmonic TE 11 gyro-BWO
Synchronization of indirectly coupled Lorenz oscillators: An ...
Indian Academy of Sciences (India)
E-mail: m.shrimali@gmail.com. Abstract. The dynamics of indirectly coupled Lorenz circuits is investigated experimentally. The in-phase and anti-phase synchronization of indirectly coupled chaotic oscillators reported in Phys. Rev. E 81, 046216 (2010) is verified by physical experiments with electronic circuits. Two chaotic.
Synchronization of indirectly coupled Lorenz oscillators: An ...
Indian Academy of Sciences (India)
Partial synchronization occurs in a population of chemical oscillators coupled through the concentration of chemical in the surrounding solutions [19]. Two nonlinear chaotic systems coupled indirectly through a common dynamic environment synchronize to in-phase or anti-phase state [20]. The early stages of Alzheimer's ...
Exact solution of a quantum forced time-dependent harmonic oscillator
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.
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
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…
High spin rotations of nuclei with the harmonic oscillator potential
International Nuclear Information System (INIS)
Cerkaski, M.; Szymanski, Z.
1978-01-01
Calculations of the nuclear properties at high angular momentum have been performed recently. They are based on the liquid drop model of a nucleus and/or on the assumption of the single particle shell structure of the nucleonic motion. The calculations are usually complicated and involve long computer codes. In this article we shall discuss general trends in fast rotating nuclei in the approximation of the harmonic oscillator potential. We shall see that using the Bohr Mottelson simplified version of the rigorous solution of Valatin one can perform a rather simple analysis of the rotational bands, structure of the yrast line, moments of inertia etc. in the rotating nucleus. While the precision fit to experimental data in actual nuclei is not the purpose of this paper, one can still hope to reach some general understanding within the model of the simple relations resulting in nuclei at high spin. (author)
Spectral theory of non-commutative harmonic oscillators an introduction
Parmeggiani, Alberto
2010-01-01
This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of “classical” invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.
Modeling stock return distributions with a quantum harmonic oscillator
Ahn, K.; Choi, M. Y.; Dai, B.; Sohn, S.; Yang, B.
2017-11-01
We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.
Adaptive elimination of synchronization in coupled oscillator
International Nuclear Information System (INIS)
Zhou, Shijie; Lin, Wei; Ji, Peng; Feng, Jianfeng; Zhou, Qing; Kurths, Jürgen
2017-01-01
We present here an adaptive control scheme with a feedback delay to achieve elimination of synchronization in a large population of coupled and synchronized oscillators. We validate the feasibility of this scheme not only in the coupled Kuramoto’s oscillators with a unimodal or bimodal distribution of natural frequency, but also in two representative models of neuronal networks, namely, the FitzHugh–Nagumo spiking oscillators and the Hindmarsh–Rose bursting oscillators. More significantly, we analytically illustrate the feasibility of the proposed scheme with a feedback delay and reveal how the exact topological form of the bimodal natural frequency distribution influences the scheme performance. We anticipate that our developed scheme will deepen the understanding and refinement of those controllers, e.g. techniques of deep brain stimulation, which have been implemented in remedying some synchronization-induced mental disorders including Parkinson disease and epilepsy. (paper)
Adaptive elimination of synchronization in coupled oscillator
Zhou, Shijie; Ji, Peng; Zhou, Qing; Feng, Jianfeng; Kurths, Jürgen; Lin, Wei
2017-08-01
We present here an adaptive control scheme with a feedback delay to achieve elimination of synchronization in a large population of coupled and synchronized oscillators. We validate the feasibility of this scheme not only in the coupled Kuramoto’s oscillators with a unimodal or bimodal distribution of natural frequency, but also in two representative models of neuronal networks, namely, the FitzHugh-Nagumo spiking oscillators and the Hindmarsh-Rose bursting oscillators. More significantly, we analytically illustrate the feasibility of the proposed scheme with a feedback delay and reveal how the exact topological form of the bimodal natural frequency distribution influences the scheme performance. We anticipate that our developed scheme will deepen the understanding and refinement of those controllers, e.g. techniques of deep brain stimulation, which have been implemented in remedying some synchronization-induced mental disorders including Parkinson disease and epilepsy.
Structural Vibration of A Flexible Complex System Under A Harmonic Oscillation Moving Force
Rusin, Jarosław
2017-10-01
This paper focuses on the free and forced transverse vibration of a double-string complex system with elastic interlayer under a harmonic oscillation moving force. The paper includes the study of a dynamic behaviour of a finite, simply supported double-string flexible complex system subject to harmonic force moving with a constant velocity on the top string. The strings are identical, parallel one upon the other. The elastic interlayer is described by the Winkler’s model consists of a Hookean resilient spring distributed in parallel. The classical solution of the response of complex systems subjected to harmonic oscillation force moving with a constant velocity has a form of an infinite series. But also, it is possible to show that in the considered case part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method to search for a solution in a closed-form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations. The double string connected in parallel by linear elastic elements can be studied as a theoretical model of composite structure in which impact of layer interaction, interlayer coupling effects and transverse wave effects is taken into account.
Excitation of high numbers harmonics by flows of oscillators in a periodic potential
International Nuclear Information System (INIS)
Buts, V.A.; Marekha, V.I.; Tolstoluzhsky, A.P.
2005-01-01
It is shown that the maximum of radiation spectrum of nonrelativistic oscillators, which move into a periodically inhomogeneous potential, can be in the region of high numbers harmonics. Spectrum of such oscillators radiation becomes similar to the radiation spectrum of relativistic oscillators. The equations, describing the non-linear self-consistent theory of excitations, of high numbers harmonics by ensemble of oscillators are formulated and its numerical analysis is conducted. The numerical analysis has confirmed the capability of radiation of high numbers of harmonics. Such peculiarity of radiation allows t expect of creation of nonrelativistic FEL
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.
Flashing coupled density wave oscillation
International Nuclear Information System (INIS)
Jiang Shengyao; Wu Xinxin; Zhang Youjie
1997-07-01
The experiment was performed on the test loop (HRTL-5), which simulates the geometry and system design of the 5 MW reactor. The phenomenon and mechanism of different kinds of two-phase flow instabilities, namely geyser instability, flashing instability and flashing coupled density wave instability are described. The especially interpreted flashing coupled density wave instability has never been studied well, it is analyzed by using a one-dimensional non-thermo equilibrium two-phase flow drift model computer code. Calculations are in good agreement with the experiment results. (5 refs.,5 figs., 1 tab.)
Synchronization of weakly coupled canard oscillators
Köksal Ersöz, Elif; Desroches, Mathieu; Krupa, Martin
2017-06-01
Synchronization has been studied extensively in the context of weakly coupled oscillators using the so-called phase response curve (PRC) which measures how a change of the phase of an oscillator is affected by a small perturbation. This approach was based upon the work of Malkin, and it has been extended to relaxation oscillators. Namely, synchronization conditions were established under the weak coupling assumption, leading to a criterion for the existence of synchronous solutions of weakly coupled relaxation oscillators. Previous analysis relies on the fact that the slow nullcline does not intersect the fast nullcline near one of its fold points, where canard solutions can arise. In the present study we use numerical continuation techniques to solve the adjoint equations and we show that synchronization properties of canard cycles are different than those of classical relaxation cycles. In particular, we highlight a new special role of the maximal canard in separating two distinct synchronization regimes: the Hopf regime and the relaxation regime. Phase plane analysis of slow-fast oscillators undergoing a canard explosion provides an explanation for this change of synchronization properties across the maximal canard.
The quantum harmonic oscillator on a circle and a deformed quantum field theory
International Nuclear Information System (INIS)
Rego-Monteiro, M.A.
2001-05-01
We construct a deformed free quantum field theory with an standard Hilbert space based on a deformed Heisenberg algebra. This deformed algebra is a Heisenberg-type algebra describing the first levels of the quantum harmonic oscillator on a circle of large length L. The successive energy levels of this quantum harmonic oscillator on a circle of large length L are interpreted, similarly to the standard quantum one-dimensional harmonic oscillator on an infinite line, as being obtained by the creation of a quantum particle of frequency w at very high energies. (author)
Interferometric output coupling of ring optical oscillators.
Chaitanya Kumar, S; Esteban-Martin, A; Ebrahim-Zadeh, M
2011-04-01
We demonstrate the successful deployment of an antiresonant ring (ARR) interferometer within a ring optical resonator and its use for absolute optimization of output power. The integration of the ARR interferometer in a folded arm of the ring oscillator provides continuously variable output coupling over broad spectral range and under any operating conditions. We demonstrate the technique using a picosecond optical parametric oscillator (OPO), where we show continuously adjustable output coupling and optimization of the output power for different pump power conditions, from 3.5 W to 13.5 W. By operating the OPO under an optimized output coupling at 14 W of pump power, we obtain >5 W of extracted signal power, more than 2.6 times that with a ~5% conventional output coupler. We also show that the inclusion of the ARR interferometer has no detrimental effect on the spatial, temporal, and spectral characteristics of OPO output.
Dynamics of microbubble oscillators with delay coupling
Heckman, C. R.; Sah, S. M.; Rand, R. H.
2010-10-01
We investigate the stability of the in-phase mode in a system of two delay-coupled bubble oscillators. The bubble oscillator model is based on a 1956 paper by Keller and Kolodner. Delay coupling is due to the time it takes for a signal to travel from one bubble to another through the liquid medium that surrounds them. Using techniques from the theory of differential-delay equations as well as perturbation theory, we show that the equilibrium of the in-phase mode can be made unstable if the delay is long enough and if the coupling strength is large enough, resulting in a Hopf bifurcation. We then employ Lindstedt's method to compute the amplitude of the limit cycle as a function of the time delay. This work is motivated by medical applications involving noninvasive localized drug delivery via microbubbles.
Primer on coupling collective electronic oscillations to nuclei
Energy Technology Data Exchange (ETDEWEB)
Solem, J.C.; Biedenharn, L.C. Jr.
1987-07-01
On the basis of simple heuristic models, we show that atomic electrons can amplify fields observed at the nucleus, generate harmonics, and drive higher multipolarities. Considered is a model with the nucleus at the focus of a uniformly charged ellipsoid. It amplifies an oscillating external electric field and produces an oscillating electric-field gradient but no higher derivatives. The electric field has only odd harmonics and the electric-field gradient has only even harmonics. There is an optimum intensity for driving each harmonic. Commented on is the relevance of these results to the U/sup 235/ experiment and to the gamma-ray laser.
Supersymmetry and the constants of motion of the two-dimensional isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Torres del Castillo, G.F. [Departamento de Fisica Matematica, Instituto de Ciencias, Universidad Autonoma de Puebla, 72570 Puebla (Mexico); Tepper G, T. [Escuela de Ciencias, Departamento de Fisica y Matematicas, Universidad de Las Americas-Puebla, Santa Catarina Martir, 72820 Cholula, Puebla (Mexico)
2002-07-01
It is shown that the constants of motion of the two-dimensional isotropic harmonic oscillator not related to the rotational invariance of the Hamiltonian can be derived using the ideas of supersymmetric quantum mechanics. (Author)
Supersymmetry and the constants of motion of the two-dimensional isotropic harmonic oscillator
International Nuclear Information System (INIS)
Torres del Castillo, G.F.; Tepper G, T.
2002-01-01
It is shown that the constants of motion of the two-dimensional isotropic harmonic oscillator not related to the rotational invariance of the Hamiltonian can be derived using the ideas of supersymmetric quantum mechanics. (Author)
Study of the phase delay in the amplitude-modulated harmonic oscillator
International Nuclear Information System (INIS)
Krupska, Aldona; Krupski, Marcin
2003-01-01
The delayed response of a damped harmonic oscillator (RLC circuit) to a slow periodic disturbance is presented. This communication is supplementary to the paper published recently (Krupska et al 2001 Eur. J. Phys. 22 133-8)
Meson spectra with a harmonic-oscillator potential in the Klein-Gordon equation
International Nuclear Information System (INIS)
Ram, B.; Halasa, R.
1979-01-01
Meson masses are calculated using a harmonic-oscillator potential in the Klein-Gordon equation, and compared with those from a linear potential. Values of the transmission coefficient are also given for both cases
Time-evolution operators for (coupled) time-dependent oscillators and Lie algebraic structure theory
Wolf, F.; Korsch, H. J.
1988-03-01
This paper deals with the application of Lie algebraic structure theory to time-dependent quantum systems making use of the Levi-Malcev decomposition of the Lie algebra generated by the Hamiltonian and the Wei-Norman representation of the time-evolution operator. In particular, (coupled) harmonic-oscillator systems are studied. Explicit formulas for expectation values and transition probabilities are derived.
Exact diagonalization of the D-dimensional spatially confined quantum harmonic oscillator
Directory of Open Access Journals (Sweden)
Kunle Adegoke
2016-01-01
Full Text Available In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.
The adiabatic invariant of the n-degree-of-freedom harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Devaud, M; Bacri, J-C; Hocquet, T [Laboratoire Matiere et Systemes Complexes, Universite Paris 7 and CNRS UMR 7057, 10 rue Alice Domon et Leonie Duquet, 75013 Paris (France); Leroy, V [Laboratoire Ondes et Acoustique, Universite Paris 7 and CNRS UMR 7587, ESPCI, 10 rue Vauquelin, 75005 Paris (France)], E-mail: Thierry.Hocquet@upmc.fr
2008-07-15
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 this simplest result: the oscillator's adiabatic invariant is just the sum of all the semiclassical quanta numbers associated with its different eigenmodes.
A coupled-oscillator model of olfactory bulb gamma oscillations.
Directory of Open Access Journals (Sweden)
Guoshi Li
2017-11-01
Full Text Available The olfactory bulb transforms not only the information content of the primary sensory representation, but also its underlying coding metric. High-variance, slow-timescale primary odor representations are transformed by bulbar circuitry into secondary representations based on principal neuron spike patterns that are tightly regulated in time. This emergent fast timescale for signaling is reflected in gamma-band local field potentials, presumably serving to efficiently integrate olfactory sensory information into the temporally regulated information networks of the central nervous system. To understand this transformation and its integration with interareal coordination mechanisms requires that we understand its fundamental dynamical principles. Using a biophysically explicit, multiscale model of olfactory bulb circuitry, we here demonstrate that an inhibition-coupled intrinsic oscillator framework, pyramidal resonance interneuron network gamma (PRING, best captures the diversity of physiological properties exhibited by the olfactory bulb. Most importantly, these properties include global zero-phase synchronization in the gamma band, the phase-restriction of informative spikes in principal neurons with respect to this common clock, and the robustness of this synchronous oscillatory regime to multiple challenging conditions observed in the biological system. These conditions include substantial heterogeneities in afferent activation levels and excitatory synaptic weights, high levels of uncorrelated background activity among principal neurons, and spike frequencies in both principal neurons and interneurons that are irregular in time and much lower than the gamma frequency. This coupled cellular oscillator architecture permits stable and replicable ensemble responses to diverse sensory stimuli under various external conditions as well as to changes in network parameters arising from learning-dependent synaptic plasticity.
Collective dynamics of delay-coupled limit cycle oscillators
Indian Academy of Sciences (India)
We present a brief overview of the effect of time-delayed coupling on the collective dynamics of such coupled systems. Simple model equations describing two oscillators with a discrete time-delayed coupling as well as those describing linear arrays of a large number of oscillators with time-delayed global or local couplings ...
Bistability in Coupled Oscillators Exhibiting Synchronized Dynamics
Olusola, O. I.; Vincent, U. E.; Njah, A. N.; Olowofela, J. A.
2010-05-01
We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators (DDOs). Some sufficient algebraic criteria for global chaos synchronization of the drive and response DDOs via linear state error feedback control are obtained by means of Lyapunov stability theory. The synchronization is achieved through a bistable state in which a periodic attractor co-exists with a chaotic attractor. Using the linear perturbation analysis, the prevalence of attractors in parameter space and the associated bifurcations are examined. Subcritical and supercritical Hopf bifurcations and abundance of Arnold tongues — a signature of mode locking phenomenon are found.
Falling coupled oscillators and trigonometric sums
Holcombe, S. R.
2018-02-01
A method for evaluating finite trigonometric summations is applied to a system of N coupled oscillators under acceleration. Initial motion of the nth particle is shown to be of the order T^{2{n}+2} for small time T, and the end particle in the continuum limit is shown to initially remain stationary for the time it takes a wavefront to reach it. The average velocities of particles at the ends of the system are shown to take discrete values in a step-like manner.
Momentum diffusion for coupled atom-cavity oscillators
International Nuclear Information System (INIS)
Murr, K.; Maunz, P.; Pinkse, P. W. H.; Puppe, T.; Schuster, I.; Rempe, G.; Vitali, D.
2006-01-01
It is shown that the momentum diffusion of free-space laser cooling has a natural correspondence in optical cavities when the internal state of the atom is treated as a harmonic oscillator. We derive a general expression for the momentum diffusion, which is valid for most configurations of interest: The atom or the cavity or both can be probed by lasers, with or without the presence of traps inducing local atomic frequency shifts. It is shown that, albeit the (possibly strong) coupling between atom and cavity, it is sufficient for deriving the momentum diffusion to consider that the atom couples to a mean cavity field, which gives a first contribution, and that the cavity mode couples to a mean atomic dipole, giving a second contribution. Both contributions have an intuitive form and present a clear symmetry. The total diffusion is the sum of these two contributions plus the diffusion originating from the fluctuations of the forces due to the coupling to the vacuum modes other than the cavity mode (the so-called spontaneous emission term). Examples are given that help to evaluate the heating rates induced by an optical cavity for experiments operating at low atomic saturation. We also point out intriguing situations where the atom is heated although it cannot scatter light
SOLUTION OF HARMONIC OSCILLATOR OF NONLINEAR MASTER SCHRÃ–DINGER
Directory of Open Access Journals (Sweden)
T B Prayitno
2012-02-01
Full Text Available We have computed the solution of a nonrelativistic particle motion in a harmonic oscillator potential of the nonlinear master SchrÃ¶dinger equation. The equation itself is based on two classical conservation laws, the Hamilton-Jacobi and the continuity equations. Those two equations give each contribution for the definition of quantum particle. We also prove that the solution canâ€™t be normalized. Â Keywords : harmonic oscillator, nonlinear SchrÃ¶dinger.
International Nuclear Information System (INIS)
Tian Youwei; Yu Wei; Lu Peixiang; Senecha, Vinod K; Han, Xu; Deng Degang; Li Ruxin; Xu Zhizhan
2006-01-01
The characteristics of backward harmonic radiation due to electron oscillations driven by a linearly polarized fs laser pulse are analysed considering a single electron model. The spectral distributions of the electron's backward harmonic radiation are investigated in detail for different parameters of the driver laser pulse. Higher order harmonic radiations are possible for a sufficiently intense driving laser pulse. We have shown that for a realistic pulsed photon beam, the spectrum of the radiation is red shifted as well as broadened because of changes in the longitudinal velocity of the electrons during the laser pulse. These effects are more pronounced at higher laser intensities giving rise to higher order harmonics that eventually leads to a continuous spectrum. Numerical simulations have further shown that by increasing the laser pulse width the broadening of the high harmonic radiations can be controlled
Generalized Lyapunov exponents of the random harmonic oscillator: Cumulant expansion approach
Vallejos, Raúl O.; Anteneodo, Celia
2012-02-01
The cumulant expansion is used to estimate generalized Lyapunov exponents of the random-frequency harmonic oscillator. Three stochastic processes are considered: Gaussian white noise, Ornstein-Uhlenbeck, and Poisson shot noise. In some cases, nontrivial numerical difficulties arise. These are mostly solved by implementing an appropriate importance-sampling Monte Carlo scheme. We analyze the relation between random-frequency oscillators and many-particle systems with pairwise interactions like the Lennard-Jones gas.
Behavior of orbits of two coupled oscillators
International Nuclear Information System (INIS)
Greene, J.M.
1984-06-01
There has been very considerable progress in the past few years on the theory of two conservative, coupled, nonlinear oscillators. This is a very general theory, and applies to many equivalent systems. A typical problem of this class has a solution that is so complicated that it is impossible to find an expression for the state of the system that is valid for all time. However, recent results are making it possible to determine the next most useful type of information. This is the asymptotic behavior of individual orbits in the limit of very long times. It is just the information that is desired in many situations. For example, it determines the stability of the motion. The key to our present understanding is renormalization. The present state of the art has been described in Robert MacKay's thesis, for which this is an advertisement
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.
Barragán-Gil, L. F.; Walser, R.
2018-01-01
A first-order partial differential equation is derived whose solution enables us to find straightforwardly the off-diagonal matrix elements in the position representation of the harmonic oscillator density operator. This approach constitutes an alternative to techniques that require advanced knowledge of mathematical and quantum mechanical results.
On the Pseudospectrum of the Harmonic Oscillator with Imaginary Cubic Potential
Czech Academy of Sciences Publication Activity Database
Novák, Radek
2015-01-01
Roč. 54, č. 11 (2015), s. 4142-4153 ISSN 0020-7748 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : pseudospectrum * harmonic oscillator * imaginary qubic potential * PT-symmetry * semiclassical method Subject RIV: BE - Theoretical Physics Impact factor: 1.041, year: 2015
Experiment on Impulsive Excitation, Resonance, and Fourier Analysis of a Harmonic Oscillator.
Macomber, Hilliard K.
1981-01-01
Describes an electric circuit permitting easy observation and measurement of the response of a damped harmonic oscillator to impulsive excitation. The impulse analysis is carried out and related to experimental observations. The phenomenon of resonance is then interpreted and demonstrated, and through it, contact is made with Fourier analysis.…
Root System of Singular Perturbations of the Harmonic Oscillator Type Operators
Czech Academy of Sciences Publication Activity Database
Mityagin, B.; Siegl, Petr
2016-01-01
Roč. 106, č. 2 (2016), s. 147-167 ISSN 0377-9017 Institutional support: RVO:61389005 Keywords : non-self-adjoint operators * harmonic oscillator * Riesz basis * quadratic forms * singular petentials Subject RIV: BE - Theoretical Physics Impact factor: 1.671, year: 2016
The study of entanglement and teleportation of the harmonic oscillator bipartite coherent states
Directory of Open Access Journals (Sweden)
A Rabeie and
2015-01-01
Full Text Available In this paper, we reproduce the harmonic oscillator bipartite coherent states with imperfect cloning of coherent states. We show that if these entangled coherent states are embedded in a vacuum environment, their entanglement is degraded but not totally lost . Also, the optimal fidelity of these states is worked out for investigating their teleportation
Attainable conditions and exact invariant for the time-dependent harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)
2006-09-22
The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.
Phase patterns of coupled oscillators with application to wireless communication
Energy Technology Data Exchange (ETDEWEB)
Arenas, A.
2008-01-02
Here we study the plausibility of a phase oscillators dynamical model for TDMA in wireless communication networks. We show that emerging patterns of phase locking states between oscillators can eventually oscillate in a round-robin schedule, in a similar way to models of pulse coupled oscillators designed to this end. The results open the door for new communication protocols in a continuous interacting networks of wireless communication devices.
Quorum Sensing and Synchronization in Populations of Coupled Chemical Oscillators
Taylor, Annette F.; Tinsley, Mark R.; Showalter, Kenneth
2013-12-01
Experiments and simulations of populations of coupled chemical oscillators, consisting of catalytic particles suspended in solution, provide insights into density-dependent dynamics displayed by many cellular organisms. Gradual synchronization transitions, the "switching on" of activity above a threshold number of oscillators (quorum sensing) and the formation of synchronized groups (clusters) of oscillators have been characterized. Collective behavior is driven by the response of the oscillators to chemicals emitted into the surrounding solution.
Microbubble generator excited by fluidic oscillator's third harmonic frequency
Czech Academy of Sciences Publication Activity Database
Tesař, Václav
2014-01-01
Roč. 92, č. 9 (2014), s. 1603-1615 ISSN 0263-8762 R&D Projects: GA ČR GA13-23046S Institutional support: RVO:61388998 Keywords : fluidic oscillator * microbubble generation * fluidic feedback loop Subject RIV: BK - Fluid Dynamics Impact factor: 2.348, year: 2014 http://dx.doi.org/10.1016/j.cherd.2013.12.004
The Slinky Wilberforce pendulum: A simple coupled oscillator
Mewes, Matthew
2014-03-01
The Wilberforce pendulum is an effective classroom demonstration of coupled oscillations and the beat-like behavior that arises in weakly coupled tuned oscillators. We describe a simple and inexpensive version constructed from a Slinky spring toy and a soup can.
Synchronization of two coupled fractional-order chaotic oscillators
International Nuclear Information System (INIS)
Gao Xin; Yu, Juebang
2005-01-01
The dynamics of fractional-order systems have attracted increasing attentions in recent years. In this paper, the synchronization of two coupled nonlinear fractional order chaotic oscillators is numerically demonstrated using the master-slave synchronization scheme. It is shown that fractional-order chaotic oscillators can be synchronized with appropriate coupling strength
Nonclassical phase-space trajectories for the damped harmonic quantum oscillator
Energy Technology Data Exchange (ETDEWEB)
Pachon, L.A. [Departamento de Fisica, Universidad Nacional de Colombia, Bogota D.C. (Colombia); Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany); CeiBA - Complejidad, Bogota D.C. (Colombia); Ingold, G.-L., E-mail: gert.ingold@physik.uni-augsburg.de [Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany); Dittrich, T. [Departamento de Fisica, Universidad Nacional de Colombia, Bogota D.C. (Colombia); CeiBA - Complejidad, Bogota D.C. (Colombia)
2010-10-05
Graphical abstract: The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation and the appearance of nonclassical trajectories is discussed. - Abstract: The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation. It is found that pairs of nonclassical trajectories contribute to the path-integral representation of the Wigner propagating function. Due to the linearity of the problem, the sum coordinate of a pair still satisfies the classical equation of motion. Furthermore, it is shown that the broadening of the Wigner propagating function of the damped oscillator arises due to the time-nonlocal interaction mediated by the heat bath.
Dynamics of nonlinear oscillators with time-varying conjugate coupling
Indian Academy of Sciences (India)
We explore the dynamical consequences of time-varying conjugate coupling in a system of nonlinear oscillators. We analyze the behavior of coupled ... Conjugate coupling; time varying coupling. PACS Nos 05.45.Xt. 1. Introduction ..... MDS acknowledges the financial support from DST,. New Delhi. References. [1] L Glass ...
Fidler, Andrew F.; Engel, Gregory S.
2013-10-01
We present a theory for a bath model in which we approximate the adiabatic nuclear potential surfaces on the ground and excited electronic states by displaced harmonic oscillators that differ in curvature. Calculations of the linear and third-order optical response functions employ an effective short-time approximation coupled with the cumulant expansion. In general, all orders of correlation contribute to the optical response, indicating that the solvation process cannot be described as Gaussian within the model. Calculations of the linear absorption and fluorescence spectra resulting from the theory reveal a stronger temperature dependence of the Stokes shift along with a general asymmetry between absorption and fluorescence line shapes, resulting purely from the difference in the phonon side band. We discuss strategies for controlling spectral tuning and energy-transfer dynamics through the manipulation of the excited-state and ground-state curvature. Calculations of the nonlinear response also provide insights into the dynamics of the system-bath interactions and reveal that multidimensional spectroscopies are sensitive to a difference in curvature between the ground- and excited-state adiabatic surfaces. This extension allows for the elucidation of short-time dynamics of dephasing that are accessible in nonlinear spectroscopic methods.
Rigorous quantum limits on monitoring free masses and harmonic oscillators
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.
Behavior of orbits of two coupled oscillators
International Nuclear Information System (INIS)
Greene, J.M.
1985-01-01
There has been very considerable progress in the past few years on the theory of two conservative, coupled, nonlinear oscillators. This work also applies to many equivalent systems, so it has applications to particle containment and heating, for example, and wherever else in plasma physics that the validity of adiabatic invariants is a matter of concern. A general problem of this class has a solution that is so complicated that it is impossible to find an expression for the state of the system that is valid for all time. However, recent results are making it possible to determine the next most useful type of information. This is the asymptotic behavior of individual orbits in the limit of very long times. This is just the information that is desired in many situations. For example, it determines the stability of the motion. The key to our present understanding is renormalization. The present state of the art has been described in Robert Mackay's thesis, for which this is an advertisement
Instabilities of the harmonic oscillator with fluctuating damping
Méndez, Vicenç; Horsthemke, Werner; Mestres, Pau; Campos, Daniel
2011-10-01
We investigate the instabilities of a linear damped oscillator due to fluctuations of the damping parameter. The fluctuations are driven either by Gaussian white noise or Poisson white noise (white shot noise). We consider three notions of stability. The first two are the well-known notions of stability in the mean and stability in the mean square. We introduce the concept of thermodynamic stability, corresponding to a nonpositive rate of energy dissipation at all times. We derive analytical results for the various instability thresholds, confirm the validity of our approach for white shot noise by numerical simulations, and obtain the unexpected result that mean-square and thermodynamic stability coincide for the two types of white noise.
Phase Multistability in Coupled Oscillator Systems
DEFF Research Database (Denmark)
Mosekilde, Erik; Postnov, D.E.; Sosnovtseva, Olga
2003-01-01
along the orbit of the individual oscillator. Focusing on the mechanisms underlying the appearance of phase multistability, the paper examines a variety of phase-locked patterns. In particular we demonstrate the nested structure of synchronization regions for oscillations with multicrest wave forms...
DEFF Research Database (Denmark)
Lodahl, P.; Saffman, M.
1999-01-01
fundamental field, and its coupling to a pair of nondegenerate parametric fields. The parametric fields are driven by the nonresonant second-harmonic field. Analysis indicates the existence of transverse instability of the pump field alone, as well as the possibility of simultaneous instability of the pump......We theoretically investigate the generation of spatial patterns in intracavity second-harmonic generation. We consider a cavity with planar mirrors that is resonant at the fundamental frequency, but not at the second-harmonic frequency. A mean-field model is derived that describes the resonant...
Laser cooling of a harmonic oscillator's bath with optomechanics
Xu, Xunnong; Taylor, Jacob
Thermal noise reduction in mechanical systems is a topic both of fundamental interest for studying quantum physics at the macroscopic level and for application of interest, such as building high sensitivity mechanics based sensors. Similar to laser cooling of neutral atoms and trapped ions, the cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce additional damping channel to mechanical motion, while keeping its thermal noise at the same level, and as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of temperature to quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an efficient scheme for reducing the thermal load on a mechanical resonator while improving its quality factor. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme. Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA.
DEFF Research Database (Denmark)
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-01-01
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...... to the extent that it is interpreted as a damped harmonic oscillator at finite temperature-such as an AFM cantilever. (iii) Three other models of fundamental interest are limiting cases of the damped harmonic oscillator at finite temperature; it consequently bridges their differences and describes the effects...
International Nuclear Information System (INIS)
Wang Qing; Hou Yu-Long; Jing Jian; Long Zheng-Wen
2014-01-01
In this paper, we study symmetrical properties of two-dimensional (2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude (SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly, the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed. (general)
International Nuclear Information System (INIS)
McCracken, Richard A; Balskus, Karolis; Zhang, Zhaowei; Reid, Derryck T
2015-01-01
Various schemes allow femtosecond optical parametric oscillators to produce pulses at harmonics of their pump laser repetition frequency, each apparently offering the possibility of generating widely-spaced, tunable frequency combs. Using a 100-MHz Ti:sapphire pump laser, we have compared two alternative optical parametric oscillator architectures, both leading to 300-MHz pulses but one configured in a cavity three times shorter than the pump laser and the other in a cavity one-third longer. Heterodyne measurements between the pump and each of these two systems show that they possess different carrier-envelope offset characteristics, with implications on the coherence and stabilization of the resulting combs
Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method
Directory of Open Access Journals (Sweden)
A. M. El-Naggar
2015-11-01
Full Text Available Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.
Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Midya, Bikashkali; Dube, P P; Roychoudhury, Rajkumar, E-mail: bikash.midya@gmail.com, E-mail: ppdube1@gmail.com, E-mail: raj@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)
2011-02-11
The generalized Swanson Hamiltonian H{sub GS}=w(a-tilde a-tilde{sup {dagger}}+1/2)+{alpha}{alpha}-tilde{sup 2}+{beta}a-tilde{sup {dagger}}{sup 2} with a-tilde = A(x) d/dx + B(x) can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as [a-ilde,a-tilde{sup {dagger}}]=constant. However, the main objective of this communication is to show that though the commutator of a-tilde and a-tilde{sup {dagger}} is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. The reason for this anomaly is discussed in the framework of position-dependent mass models by choosing A(x) as the inverse square root of the mass function. (fast track communication)
Chaotic synchronization of three coupled oscillators with ring connection
Kyprianidis, I M
2003-01-01
We study the evolution of three identical, resistively coupled with ring connection, nonlinear and nonautonomous electric circuits from nonsynchronized oscillations to synchronized ones, when they exhibit chaotic behavior. Phase-locked states are also observed, as the coupling parameter is varied. The system's dynamics depends on the way of coupling (unidirectional or bidirectional).
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
DEFF Research Database (Denmark)
Jensen, Arne; Yajima, Kenji
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials, which grow at spatial infinity slower than quadratic, but faster than linear functions, and whose Hessian matrices have a fixed sign. We prove that the fundamental...... solution at resonant times grows indefinitely at spatial infinity with the algebraic growth rate, which increases indefinitely, when the growth rate of perturbations at infinity decrease from the near quadratic to the near linear ones....
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
DEFF Research Database (Denmark)
Jensen, Arne; Yajima, Kenji
2010-01-01
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials which grow at spatial infinity slower than quadratic but faster than linear functions and whose Hessian matrices have a fixed sign. We prove that the fundamental...... solution at resonant times grows indefinitely at spatial infinity with an algebraic growth rate, which increases indefinitely when the growth rate of perturbations at infinity decreases from the near quadratic to the near linear ones....
Double Fourier Harmonic Balance Method for Nonlinear Oscillators by Means of Bessel Series
2014-10-16
contrast to say the homotopy method [12, 13], especially because of the ready availability of Fourier analysis and Bessel functions in computer algebraic...Models Methods Appl. Sci. 3, 395–416 (1993). [13] A. Bel, W. Reartes, and A. Torresi, “Global study of the simple pendulum by the homotopy analysis ...other approaches for analyzing nonlinear oscillators, including the homotopy and the variational iteration methods [2]. More widespread is the harmonic
Daoud, M.; Jellal, A.; Choubabi, E. B.; El Kinani, E. H.
2011-08-01
We introduce a special class of truncated Weyl-Heisenberg algebra and discuss the corresponding Hilbertian and analytical representations. Subsequently, we study the effect of a quantum network of beam splitting on coherent states of this nonlinear class of harmonic oscillators. We particularly focus on quantum networks involving one and two beam splitters and examine the degree of bipartite as well as tripartite entanglement using the linear entropy.
Daoud, M.; Jellal, A.; Choubabi, E. B.; Kinani, E. H. El
2012-01-01
We introduce a special class of truncated Weyl-Heisenberg algebra and discuss the corresponding Hilbertian and analytical representations. Subsequently, we study the effect of a quantum network of beam splitting on coherent states of this nonlinear class of harmonic oscillators. We particularly focus on quantum networks involving one and two beam splitters and examine the degree of bipartite as well as tripartite entanglement using the linear entropy.
A non-orthogonal harmonic-oscillator basis for three-body problems
International Nuclear Information System (INIS)
Agrello, D.A.; Aguilera-Navarro, V.C.; Chacon, E.
1979-01-01
A set of harmonic-oscillator states suitable for the representation of the wave function of the bound states of a system of three identical particles, is presented. As an illustration of the possibilities of the states defined in this paper, they are applied in a variational determination of the lowest symmetric S state of 12 C, in the model of three structureless α particles interacting through the Coulomb force plus a phenomenological two-body force. (author) [pt
Selective Coupling Enhances Harmonic Generation of Whispering-Gallery Modes
Trainor, Luke S.; Sedlmeir, Florian; Peuntinger, Christian; Schwefel, Harald G. L.
2018-02-01
We demonstrate second-harmonic generation (SHG) in an x -cut congruent lithium niobate (LN) whispering-gallery mode (WGM) resonator. First, we show theoretically that independent control of the coupling of the pump and signal modes is optimal for high conversion rates. A coupling scheme based on our earlier work [F. Sedlmeir et al., Phys. Rev. Applied 7, 024029 (2017), 10.1103/PhysRevApplied.7.024029] is then implemented experimentally to verify this improvement. Thereby, we are able to improve on the efficiency of SHG by more than an order of magnitude by selectively outcoupling using a LN prism, utilizing the birefringence of it and the resonator in kind. This method is also applicable to other nonlinear processes in WGM resonators.
A quantitative analysis of coupled oscillations using mobile accelerometer sensors
Castro-Palacio, Juan Carlos; Velázquez-Abad, Luisberis; Giménez, Fernando; Monsoriu, Juan A.
2013-05-01
In this paper, smartphone acceleration sensors were used to perform a quantitative analysis of mechanical coupled oscillations. Symmetric and asymmetric normal modes were studied separately in the first two experiments. In the third, a coupled oscillation was studied as a combination of the normal modes. Results indicate that acceleration sensors of smartphones, which are very familiar to students, represent valuable measurement instruments for introductory and first-year physics courses.
A quantitative analysis of coupled oscillations using mobile accelerometer sensors
International Nuclear Information System (INIS)
Castro-Palacio, Juan Carlos; Velázquez-Abad, Luisberis; Giménez, Fernando; Monsoriu, Juan A
2013-01-01
In this paper, smartphone acceleration sensors were used to perform a quantitative analysis of mechanical coupled oscillations. Symmetric and asymmetric normal modes were studied separately in the first two experiments. In the third, a coupled oscillation was studied as a combination of the normal modes. Results indicate that acceleration sensors of smartphones, which are very familiar to students, represent valuable measurement instruments for introductory and first-year physics courses. (paper)
On harmonic oscillators on the two-dimensional sphere S2 and the hyperbolic plane H2
International Nuclear Information System (INIS)
Ranada, Manuel F.; Santander, Mariano
2002-01-01
Two Harmonic Oscillators (isotropic and nonisotropic 2:1) are studied on the two-dimensional sphere S 2 and the hyperbolic plane H 2 . Both systems are integrable and super-integrable with constants of motion quadratic in the momenta. These properties are shown to derive from a complex factorization for the constants of motion, which holds for arbitrary values of the curvature κ, and the dynamics of the Euclidean harmonic 1:1 and 2:1 oscillators is directly recovered for κ=0. The harmonic oscillators on either the standard unit sphere (radius R=1) or the unit Lobachewski plane ('radius' R=1) appear as the particular values of the κ-dependent potentials for the values κ=1 and κ=-1. Finally a particular potential is proposed for representing the general spherical (hyperbolic) n:1 anisotropic harmonic oscillator on a two-dimensional manifold of constant curvature
The vertical oscillations of coupled magnets
Kewei, Li; Jiahuang, Lin; Yang, Kang Zi; Liang, Samuel Yee Wei; Wong Say Juan, Jeremias
2011-07-01
The International Young Physicists' Tournament (IYPT) is a worldwide, annual competition for high school students. This paper is adapted from the winning solution to Problem 14, Magnetic Spring, as presented in the final round of the 23rd IYPT in Vienna, Austria. Two magnets were arranged on top of each other on a common axis. One was fixed, while the other could move vertically. Various parameters of interest were investigated, including the effective gravitational acceleration, the strength, size, mass and geometry of the magnets, and damping of the oscillations. Despite its simplicity, this setup yielded a number of interesting and unexpected relations. The first stage of the investigation was concerned only with the undamped oscillations of small amplitudes, and the period of small amplitude oscillations was found to be dependent only on the eighth root of important magnet properties such as its strength and mass. The second stage sought to investigate more general oscillations. A numerical model which took into account magnet size, magnet geometry and damping effects was developed to model the general oscillations. Air resistance and friction were found to be significant sources of damping, while eddy currents were negligible.
Crypto-harmonic oscillator in higher dimensions: classical and quantum aspects
International Nuclear Information System (INIS)
Ghosh, Subir; Majhi, Bibhas Ranjan
2008-01-01
We study complexified harmonic oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga (2007 Preprint 0706.4064 (J. Phys. A: Math. Theor. at press)) who initiated the study of these Crypto-gauge invariant models that can be related to PT-symmetric models. We show that rotational symmetry in higher spatial dimensions naturally introduces more constraints (in contrast to Smilga (2007 Preprint 0706.4064 (J. Phys. A: Math. Theor. at press)) where one deals with a single constraint) with a much richer constraint structure. Some common as well as distinct features in the study of the same Crypto-oscillator in different dimensions are revealed. We also quantize the two dimensional Crypto-oscillator
Methods for Stability and Noise Analysis of Coupled Oscillating Systems
DEFF Research Database (Denmark)
Djurhuus, Torsten
2008-01-01
In this thesis a study of analytical and numerical models of coupled oscillating systems, perturbed by delta-correlated noise sources, is undertaken. These models are important for the attainment of a qualitative understanding of the complex dynamics seen in various physical, biological, electron......, perturbed by white noise.......In this thesis a study of analytical and numerical models of coupled oscillating systems, perturbed by delta-correlated noise sources, is undertaken. These models are important for the attainment of a qualitative understanding of the complex dynamics seen in various physical, biological, electronic...... and phase-noise filters; to name but a few of the possible applications areas. Taking outset in the established single-oscillator phase-macro model, a novel numerical algorithm for the automated phase-noise characterization of coupled oscillators, perturbed by noise, is developed. The algorithm, which...
Gain-modulated plasmonic Rabi oscillations of coupled nanocomplex
Yang, Da-Jie; Pan, Gui-Ming; Ding, Si-Jing; Hao, Zhong-Hua; Zhou, Li; Wang, Qu-Quan
2017-11-01
Strong coupling in nanostructures can bring intriguing optical phenomena such as ultrafast Rabi oscillation-periodical energy exchange phenomenon between two modes. Rabi splitting appears in the frequency-domain spectra for strong coupling system. However, in metallic nanosystems the time-domain Rabi oscillations are hard to be observed because the plasmon lifetime is limited by the heavy ohmic losses. Here we report a theoretical investigation of surface plasmon coupling behaviour of two gold nanorods with one being a core-shell rod filled with a gain material and find the periodic energy exchange phenomenon which recalls the concept of Rabi oscillation. The gain material-cored gold-shell structure dipolar mode hybridizes with the solid gold rod quadrupolar mode to form the Fano resonances. Energy exchange between the two rods happens through the near field coupling. Two approaches, to prolong plasmon lifetime by increasing the gain efficiency and to increase Rabi oscillation frequency by increasing the coupling strength, are suggested to increase the Rabi oscillation cycles. Our results offer a way to achieve unique control of light at the nanoscale and further to explore plasmonic Rabi oscillation phenomena in plasmonic nanosystems.
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing
2010-12-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
Synchronization of hyperchaotic oscillators via single unidirectional chaotic-coupling
International Nuclear Information System (INIS)
Zou Yanli; Zhu Jie; Chen Guanrong; Luo Xiaoshu
2005-01-01
In this paper, synchronization of two hyperchaotic oscillators via a single variable's unidirectional coupling is studied. First, the synchronizability of the coupled hyperchaotic oscillators is proved mathematically. Then, the convergence speed of this synchronization scheme is analyzed. In order to speed up the response with a relatively large coupling strength, two kinds of chaotic coupling synchronization schemes are proposed. In terms of numerical simulations and the numerical calculation of the largest conditional Lyapunov exponent, it is shown that in a given range of coupling strengths, chaotic-coupling synchronization is quicker than the typical continuous-coupling synchronization. Furthermore, A circuit realization based on the chaotic synchronization scheme is designed and Pspice circuit simulation validates the simulated hyperchaos synchronization mechanism
Collective behavior of chaotic oscillators with environmental coupling
International Nuclear Information System (INIS)
Quintero-Quiroz, C.; Cosenza, M.G.
2015-01-01
Highlights: •A system of chaotic oscillators coupled through a common environment is considered. •The environment has its own dynamics which in turn is affected by the oscillators. •Nontrivial collective behavior occurs for some values of coupling strength parameter. •Dynamical clustering is found for some values of the coupling parameter. -- Abstract: We investigate the collective behavior of a system of chaotic Rössler oscillators indirectly coupled through a common environment that possesses its own dynamics and which in turn is modulated by the interaction with the oscillators. By varying the parameter representing the coupling strength between the oscillators and the environment, we find two collective states previously not reported in systems with environmental coupling: (i) nontrivial collective behavior, characterized by a periodic evolution of macroscopic variables coexisting with the local chaotic dynamics; and (ii) dynamical clustering, consisting of the formation of differentiated subsets of synchronized elements within the system. These states are relevant for many physical and biological systems where interactions with a dynamical environment are frequent
Cluster synchronization modes in an ensemble of coupled chaotic oscillators
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Belykh, Igor V.; Mosekilde, Erik
2001-01-01
Considering systems of diffusively coupled identical chaotic oscillators, an effective method to determine the possible states of cluster synchronization and ensure their stability is presented. The method, which may find applications in communication engineering and other fields of science and t...... and technology, is illustrated through concrete examples of coupled biological cell models....
Synchronization and basin bifurcations in mutually coupled oscillators
Indian Academy of Sciences (India)
cillators exhibiting cross-well chaos is examined. Synchronization of the subsystems was observed for coupling strength k > 0.4. It is found that when the oscillators are operated in the regime for which two attractors coexist in phase space, basin bifurcation sequences occur leading to n + 1, n ≥ 2 basins as the coupling is ...
Thermal coupling and effect of subharmonic synchronization in a system of two VO2 based oscillators
Velichko, Andrey; Belyaev, Maksim; Putrolaynen, Vadim; Perminov, Valentin; Pergament, Alexander
2018-03-01
We explore a prototype of an oscillatory neural network (ONN) based on vanadium dioxide switching devices. The model system under study represents two oscillators based on thermally coupled VO2 switches. Numerical simulation shows that the effective action radius RTC of coupling depends both on the total energy released during switching and on the average power. It is experimentally and numerically proved that the temperature change ΔT commences almost synchronously with the released power peak and T-coupling reveals itself up to a frequency of about 10 kHz. For the studied switching structure configuration, the RTC value varies over a wide range from 4 to 45 μm, depending on the external circuit capacitance C and resistance Ri, but the variation of Ri is more promising from the practical viewpoint. In the case of a "weak" coupling, synchronization is accompanied by attraction effect and decrease of the main spectra harmonics width. In the case of a "strong" coupling, the number of effects increases, synchronization can occur on subharmonics resulting in multilevel stable synchronization of two oscillators. An advanced algorithm for synchronization efficiency and subharmonic ratio calculation is proposed. It is shown that of the two oscillators the leading one is that with a higher main frequency, and, in addition, the frequency stabilization effect is observed. Also, in the case of a strong thermal coupling, the limit of the supply current parameters, for which the oscillations exist, expands by ∼10%. The obtained results have a universal character and open up a new kind of coupling in ONNs, namely, T-coupling, which allows for easy transition from 2D to 3D integration. The effect of subharmonic synchronization hold promise for application in classification and pattern recognition.
Use of videos for students to see the effect of changing gravity on harmonic oscillators
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.
Synchronization of diffusively coupled oscillators near the homoclinic bifurcation
International Nuclear Information System (INIS)
Postnov, D.; Han, Seung Kee; Kook, Hyungtae
1998-09-01
It has been known that a diffusive coupling between two limit cycle oscillations typically leads to the inphase synchronization and also that it is the only stable state in the weak coupling limit. Recently, however, it has been shown that the coupling of the same nature can result in the distinctive dephased synchronization when the limit cycles are close to the homoclinic bifurcation, which often occurs especially for the neuronal oscillators. In this paper we propose a simple physical model using the modified van der Pol equation, which unfolds the generic synchronization behaviors of the latter kind and in which one may readily observe changes in the synchronization behaviors between the distinctive regimes as well. The dephasing mechanism is analyzed both qualitatively and quantitatively in the weak coupling limit. A general form of coupling is introduced and the synchronization behaviors over a wide range of the coupling parameters are explored to construct the phase diagram using the bifurcation analysis. (author)
International Nuclear Information System (INIS)
Santos, Marcelo Franca
2005-01-01
We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an auxiliary three-level system and a classical external driving source, and enables any unitary operations on Fock states, two by two. One circuit is equivalent to a single qubit unitary logical gate on Fock states qubits. Sequences of similar protocols allow for complete, deterministic, and state-independent manipulation of the harmonic oscillator quantum state
Harmonic Coupling Analysis of a Multi-Drive System with Slim DC-link Drive
DEFF Research Database (Denmark)
Yang, Feng; Kwon, Jun Bum; Blaabjerg, Frede
2017-01-01
One of the problems with slim dc-link adjustable speed drive is the difficulties to analyze the harmonic coupling when it is integrated into a multi-drive system. The traditional methods analyze this harmonic issue by neglecting the harmonic coupling, and base on the linear time-invariant methods....... Its disadvantages include the time consumption and large computer memory. This paper proposes to do harmonic analysis by using the harmonic state-space modeling method by using the linear time-periodic theory. By using the proposed model, the harmonic couplings, between dc-link and point of common...... coupling in different drives, are all analyzed in the multi-drive system. In the meantime, the effects of the small film dc-link capacitance and the nonlinear characteristic of the diode rectifier are considered. The detailed modeling procedure, the simulations and the lab experiment on a two-drive system...
Oscillations in magnetoresistance and interlayer coupling in magnetic sandwich structures
International Nuclear Information System (INIS)
Barnas, J.; Bulka, B.
1997-01-01
Kubo formalism is used to calculate the magnetoresistance due to magnetization rotation in a structure consisting two magnetic films separated by nonmagnetic layer. In the approximation of an uniform relaxation time of each layer, the oscillatory term in magnetoresistance corresponds to the oscillation period which depends on the potential barriers at the interfaces. This period is longer than the oscillation period observed in the coupling parameter. (author)
Instrumentation and control of harmonic oscillators via a single-board microprocessor-FPGA device
Picone, Rico A. R.; Davis, Solomon; Devine, Cameron; Garbini, Joseph L.; Sidles, John A.
2017-04-01
We report the development of an instrumentation and control system instantiated on a microprocessor-field programmable gate array (FPGA) device for a harmonic oscillator comprising a portion of a magnetic resonance force microscope. The specific advantages of the system are that it minimizes computation, increases maintainability, and reduces the technical barrier required to enter the experimental field of magnetic resonance force microscopy. Heterodyne digital control and measurement yields computational advantages. A single microprocessor-FPGA device improves system maintainability by using a single programming language. The system presented requires significantly less technical expertise to instantiate than the instrumentation of previous systems, yet integrity of performance is retained and demonstrated with experimental data.
International Nuclear Information System (INIS)
Young, T. D.; Armiento, R.
2010-01-01
A Schroedinger eigenvalue problem is solved for the 2D quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, (i) an application of the Kelly error estimator, and (ii) a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver. (general)
DEFF Research Database (Denmark)
Dahl, Jens Peder; Schleich, W. P.
2009-01-01
For a closed quantum system the state operator must be a function of the Hamiltonian. When the state is degenerate, additional constants of the motion enter the play. But although it is the Weyl transform of the state operator, the Wigner function is not necessarily a function of the Weyl...... transforms of the constants of the motion. We derive conditions for which this is actually the case. The Wigner functions of the energy eigenstates of a two-dimensional isotropic harmonic oscillator serve as an important illustration....
Harmonic oscillators and resonance series generated by a periodic unstable classical orbit
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.
Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2014-09-02
A complete equation of state (EOS) for a molecular solid is derived utilizing a Helmholtz free energy. Assuming that the solid is nonconducting, phonon excitations dominate the specific heat. Phonons are approximated as independent quasi-harmonic oscillators with vibrational frequencies depending on the specific volume. The model is suitable for calibrating an EOS based on isothermal compression data and infrared/Raman spectroscopy data from high pressure measurements utilizing a diamond anvil cell. In contrast to a Mie-Gruneisen EOS developed for an atomic solid, the specific heat and Gruneisen coefficient depend on both density and temperature.
(1 + 1) Newton-Hooke group for the simple and damped harmonic oscillator
Brzykcy, Przemysław
2018-03-01
It is demonstrated that, in the framework of the orbit method, a simple and damped harmonic oscillator is indistinguishable at the level of an abstract Lie algebra. This opens a possibility for treating the dissipative systems within the orbit method. An in-depth analysis of the coadjoint orbits of the (1 + 1) dimensional Newton-Hooke group is presented. Furthermore, it is argued that the physical interpretation is carried by a specific realisation of the Lie algebra of smooth functions on a phase space rather than by an abstract Lie algebra.
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
International Nuclear Information System (INIS)
Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung
2009-01-01
We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung [Department of Physics, HCMC University of Pedagogy, 280 An Duong Vuong, Ward 10, Dist. 5, Ho Chi Minh City (Viet Nam)
2009-05-01
We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./.
Yue, Xiaole; Xu, Wei; Jia, Wantao; Wang, Liang
2013-07-01
The transient and stationary probability density functions (PDFs) of stochastic response of the ϕ6 Duffing oscillator under combined harmonic and external and parametric Poisson white noises excitations are investigated by the generalized cell mapping method in this paper. Based on the digraph analysis method, the global qualitative properties are obtained such as attractors, basins of attraction, basin boundaries, saddles and invariant manifolds. The evolutionary process of transient and stationary PDFs are shown based on the matrix analysis method. It is observed that there is a close relationship between evolutionary direction of PDF and the unstable manifold. Monte Carlo (MC) simulation is used to verify the accuracy of the matrix analysis method.
International Nuclear Information System (INIS)
Mota, R D; Granados, V D; Queijeiro, A; Garcia, J; Guzman, L
2003-01-01
We show that the supersymmetric radial ladder operators of the three-dimensional isotropic harmonic oscillator are contained in the spherical components of the creation and annihilation operators of the system. Also, we show that the constants of motion of the problem, written in terms of these spherical components, lead us to second-order radial operators. Further, we show that these operators change the orbital angular momentum quantum number by two units and are equal to those obtained by the Infeld-Hull factorization method
Control of coupled oscillator networks with application to microgrid technologies
Skardal, Per Sebastian; Arenas, Alex
2015-01-01
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions—a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself. PMID:26601231
Control of coupled oscillator networks with application to microgrid technologies
Arenas, Alex
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions-a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable syn- chronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.
Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback
Directory of Open Access Journals (Sweden)
A.F. EL-Bassiouny
2006-01-01
Full Text Available Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. We investigate the fundamental resonance and subharmonic resonance of order one-half of a harmonically oscillation under state feedback control with a time delay. By using the multiple scale perturbation technique, the first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the external excitation-response and frequency-response curves. We analyze the effect of time delay and the other different parameters on these oscillations.
A time-discrete harmonic oscillator model of human car-following
Wagner, P.
2011-12-01
A time-discrete stochastic harmonic oscillator is presented as a model of human car-following behaviour. This describes especially the non-continuous control of a human driver - acceleration changes from time to time at so called action-points and is kept constant in between. Analytical results can be derived which allow to classify the different types of motion possible within this approach. These results show that with weaker control by the human, unstable behaviour of the oscillator becomes more likely. This is in line with common understanding about the causes of accidents. Finally, since even the stochastic behaviour of this model is in parts analytically tractable, the width of the speed-difference and distance fluctuations can be expressed as function of the model's parameter. This allows a fresh view on empirical car-following data and the identification of parameters from real data in the context of the theory presented here.
Dynamics of order parameters for globally coupled oscillators
DEFF Research Database (Denmark)
De Monte, Silvia; D'ovidio, Francesco
2002-01-01
The equation of motion for the centroid of globally coupled oscillators with natural frequency mismatch is obtained through a series expansion in order parameters, valid for any population size. In the case of strong coupling and narrow-frequency distribution the first-order expansion (correspond......The equation of motion for the centroid of globally coupled oscillators with natural frequency mismatch is obtained through a series expansion in order parameters, valid for any population size. In the case of strong coupling and narrow-frequency distribution the first-order expansion...... (corresponding to a system where the centroid is coupled to a second macroscopic variable), predicts transient and asymptotic properties of the dynamics of the centroid. Phase transitions appear as macroscopic bifurcations. Collective properties arising in the transient, and particularly critical perturbations...
Holliday, Ezekiel S. (Inventor)
2014-01-01
Vibrations at harmonic frequencies are reduced by injecting harmonic balancing signals into the armature of a linear motor/alternator coupled to a Stirling machine. The vibrations are sensed to provide a signal representing the mechanical vibrations. A harmonic balancing signal is generated for selected harmonics of the operating frequency by processing the sensed vibration signal with adaptive filter algorithms of adaptive filters for each harmonic. Reference inputs for each harmonic are applied to the adaptive filter algorithms at the frequency of the selected harmonic. The harmonic balancing signals for all of the harmonics are summed with a principal control signal. The harmonic balancing signals modify the principal electrical drive voltage and drive the motor/alternator with a drive voltage component in opposition to the vibration at each harmonic.
The dynamics of two linearly coupled Goodwin oscillators
Antonova, A. O.; Reznik, S. N.; Todorov, M. D.
2017-10-01
In this paper the Puu model of the interaction of Goodwin's business cycles for two regions is reconsidered. We investigated the effect of the accelerator coefficients and the Hicksian 'ceiling' and 'floor' parameters on the time dynamics of incomes for different values of marginal propensity to import. The cases when the periods of isolated Goodwin's cycles are close, and when they differ approximately twice are considered. By perturbation theory we obtained the formulas for slowly varying amplitudes and phase difference of weakly nonlinear coupled Goodwin oscillations. The coupled oscillations of two Goodwin's cycles with piecewise linear accelerators with only 'floor' are considered.
International Nuclear Information System (INIS)
Mshelia, E.D.
1994-07-01
The method of normal coordinates of the theory of vibrations is used in decoupling the motion of n oscillators (1 ≤ n ≤4) representing intrinsic degrees of freedom coupled to collective motion in a quantum mechanical model that allows the determination of the probability for energy transfer from collective to intrinsic excitations in a dissipative system. (author). 21 refs
ABC of ladder operators for rationally extended quantum harmonic oscillator systems
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.
PT -symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
In this case there are three solutions of the coupled dimer eqs (1) and (2) out of which we present two solutions now and the third one (a novel superposed solution) in the next subsection. Solution I: It is easy to check that u(t) = ±v(t) = Adn[β(t + t0), m]. (22) is an exact solution provided. (ǫ + δ)β2 = −2β2, (2 − m)β2 = −1 ± k.
Nori, Franco; Ashhab, Sahel
2011-03-01
We consider a system composed of a two-level system (i.e. a qubit) and a harmonic oscillator in the ultrastrong-coupling regime, where the coupling strength is comparable to the qubit and oscillator energy scales. We explore the possibility of preparing nonclassical states in this system, especially in the ground state of the combined system. The nonclassical states that we consider include squeezed states, Schrodinger-cat states and entangled states. We also analyze the nature of the change in the ground state as the coupling strength is increased, going from a separable ground state in the absence of coupling to a highly entangled ground state in the case of very strong coupling. Reference: S. Ashhab and F. Nori, Phys. Rev. A 81, 042311 (2010). We thank support from DARPA, AFOSR, NSA, LPS, ARO, NSF, MEXT, JSPS, FIRST, and JST.
Microwave Imaging Reflectometry for the study of Edge Harmonic Oscillations on DIII-D
Ren, X.; Chen, M.; Chen, X.; Domier, C. W.; Ferraro, N. M.; Kramer, G. J.; Luhmann, N. C., Jr.; Muscatello, C. M.; Nazikian, R.; Shi, L.; Tobias, B. J.; Valeo, E.
2015-10-01
Quiescent H-mode (QH-mode) 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 indicate a counter-propagation between dominant (n=1) and higher harmonic modes of coherent EHOs in the steep gradient regions of the pedestal. To preclude diagnostic artifacts, we have performed forward modeling that includes possible optical mis-alignments to show that offsets between transmitting and receiving antennas do not account for this feature. We have also simulated the non-linear structure of the EHO modes, which induces multiple harmonics that are properly charaterized in the synthetic diagnostic. By excluding mis-alignments of optics as well as patially eliminating non-linearity of EHO mode structure as possible explanation for the data, 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. The identification of a non-ideal structure motivates further exploration of nonlinear models of this instability. A shorter version of this contribution is due to be published in PoS at: 1st EPS conference on Plasma Diagnostics
String-Coupled Pendulum Oscillators: Theory and Experiment.
Moloney, Michael J.
1978-01-01
A coupled-oscillator system is given which is readily set up, using only household materials. The normal-mode analysis of this system is worked out, and an experiment or demonstration is recommended in which one verifies the theory by measuring two times and four lengths. (Author/GA)
Scaling Features of Multimode Motions in Coupled Chaotic Oscillators
DEFF Research Database (Denmark)
Pavlov, A.N.; Sosnovtseva, Olga; Mosekilde, Erik
2003-01-01
Two different methods (the WTMM- and DFA-approaches) are applied to investigate the scaling properties in the return-time sequences generated by a system of two coupled chaotic oscillators. Transitions from twomode asynchronous dynamics (torus or torus-Chaos) to different states of chaotic phase ...
Synchronization and basin bifurcations in mutually coupled oscillators
Indian Academy of Sciences (India)
... basin bifurcation sequences occur leading to + 1, ≥ 2 basins as the coupling is varied – a signature of Wada structure and ﬁnal-state sensitivity. However, in the region of complete synchronization, the basins structure is identical with that of the single oscillators and retains its essential features including fractal basin ...
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.
Three people can synchronize as coupled oscillators during sports activities.
Directory of Open Access Journals (Sweden)
Keiko Yokoyama
2011-10-01
Full Text Available We experimentally investigated the synchronized patterns of three people during sports activities and found that the activity corresponded to spatiotemporal patterns in rings of coupled biological oscillators derived from symmetric Hopf bifurcation theory, which is based on group theory. This theory can provide catalogs of possible generic spatiotemporal patterns irrespective of their internal models. Instead, they are simply based on the geometrical symmetries of the systems. We predicted the synchronization patterns of rings of three coupled oscillators as trajectories on the phase plane. The interactions among three people during a 3 vs. 1 ball possession task were plotted on the phase plane. We then demonstrated that two patterns conformed to two of the three patterns predicted by the theory. One of these patterns was a rotation pattern (R in which phase differences between adjacent oscillators were almost 2π/3. The other was a partial anti-phase pattern (PA in which the two oscillators were anti-phase and the third oscillator frequency was dead. These results suggested that symmetric Hopf bifurcation theory could be used to understand synchronization phenomena among three people who communicate via perceptual information, not just physically connected systems such as slime molds, chemical reactions, and animal gaits. In addition, the skill level in human synchronization may play the role of the bifurcation parameter.
Entanglement dynamics of two coupled mechanical oscillators in modulated optomechanics
Chakraborty, Subhadeep; Sarma, Amarendra K.
2018-02-01
We study the entanglement dynamics of two coupled mechanical oscillators, within a modulated optomechanical system. We find that, depending on the strength of the mechanical coupling, one could observe either a stationary or a dynamical behavior of the mechanical entanglement, which is extremely robust against the oscillator temperature. Moreover, we have shown that this entanglement dynamics is strongly related to the stability of the normal modes. Taking mechanical damping effects into account, an analytical expression corresponding to the critical mechanical coupling strength, where the transition from stationary to dynamical entanglement occurs, is also reported. The proposed scheme is analyzed with experimentally realistic parameters, making it a promising means to realize macroscopic quantum entanglement within current state-of-the-art experimental setups.
Energy Technology Data Exchange (ETDEWEB)
Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)
2012-10-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
International Nuclear Information System (INIS)
Belendez, A.; Fernandez, E.; Rodes, J.J.; Fuentes, R.; Pascual, I.
2009-01-01
The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed
Nonlinear coupling between cortical oscillations and muscle activity during isotonic wrist flexion
Directory of Open Access Journals (Sweden)
Yuan Yang
2016-12-01
Full Text Available Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been demonstrated to be highly nonlinear. A full assessment of corticomuscular coupling, including the nonlinear part, is essential to understand the neuronal communication within the sensorimotor system. In this study, we applied the recently developed n:m coherence method to assess nonlinear corticomuscular coupling during isotonic wrist flexion. The n:m coherence is a generalized metric for quantifying nonlinear cross-frequency coupling as well as linear iso-frequency coupling. By using independent component analysis and equivalent current dipole source localization, we identify four sensorimotor related brain areas based on the locations of the dipoles, i.e. the contralateral primary sensorimotor areas, supplementary motor area, prefrontal area and posterior parietal cortex. For all these areas, linear coupling between EEG and EMG is present with peaks in the beta band (15-35 Hz, while nonlinear coupling is detected with both integer (1:2, 1:3, 1:4 and non-integer (2:3 harmonics. Significant differences between brain areas is shown in linear coupling with stronger coherence for the primary sensorimotor areas and motor association cortices (supplementary motor area, prefrontal area compared to the sensory association area (posterior parietal cortex; but not for the nonlinear coupling. Moreover, the detected nonlinear coupling is similar to previously reported nonlinear coupling of cortical activity to somatosensory stimuli. We suggest that the descending motor pathways mainly contribute to linear corticomuscular coupling, while nonlinear coupling likely originates from sensory feedback.
Lozano-Soldevilla, Diego; ter Huurne, Niels; Oostenveld, Robert
2016-01-01
Neuronal oscillations support cognitive processing. Modern views suggest that neuronal oscillations do not only reflect coordinated activity in spatially distributed networks, but also that there is interaction between the oscillations at different frequencies. For example, invasive recordings in animals and humans have found that the amplitude of fast oscillations (>40 Hz) occur non-uniformly within the phase of slower oscillations, forming the so-called cross-frequency coupling (CFC). However, the CFC patterns might be influenced by features in the signal that do not relate to underlying physiological interactions. For example, CFC estimates may be sensitive to spectral correlations due to non-sinusoidal properties of the alpha band wave morphology. To investigate this issue, we performed CFC analysis using experimental and synthetic data. The former consisted in a double-blind magnetoencephalography pharmacological study in which participants received either placebo, 0.5 or 1.5 mg of lorazepam (LZP; GABAergic enhancer) in different experimental sessions. By recording oscillatory brain activity with during rest and working memory (WM), we were able to demonstrate that posterior alpha (8–12 Hz) phase was coupled to beta-low gamma band (20–45 Hz) amplitude envelope during all sessions. Importantly, bicoherence values around the harmonics of the alpha frequency were similar both in magnitude and topographic distribution to the cross-frequency coherence (CFCoh) values observed in the alpha-phase to beta-low gamma coupling. In addition, despite the large CFCoh we found no significant cross-frequency directionality (CFD). Critically, simulations demonstrated that a sizable part of our empirical CFCoh between alpha and beta-low gamma coupling and the lack of CFD could be explained by two-three harmonics aligned in zero phase-lag produced by the physiologically characteristic alpha asymmetry in the amplitude of the peaks relative to the troughs. Furthermore, we
Directory of Open Access Journals (Sweden)
Diego Lozano-Soldevilla
2016-08-01
Full Text Available Neuronal oscillations support cognitive processing. Modern views suggest that neuronal oscillations do not only reflect coordinated activity in spatially distributed networks, but also that there is interaction between the oscillations at different frequencies. For example, invasive recordings in animals and humans have found that the amplitude of fast oscillations (> 40 Hz occur non-uniformly within the phase of slower oscillations, forming the so-called cross-frequency coupling (CFC. However, the CFC patterns be influenced by features in the signal that do not relate to underlying physiological interactions. For example, CFC estimates may be sensitive to spectral correlations due to non-sinusoidal properties of the alpha band wave morphology. To investigate this issue, we performed CFC analysis using experimental and synthetic data. The former consisted in a double-blind magnetoencephalography pharmacological study in which participants received either placebo, 0.5 mg or 1.5 mg of lorazepam (LZP; GABAergic enhancer in different experimental sessions. By recording oscillatory brain activity with during rest and working memory (WM, we were able to demonstrate that posterior alpha (8 – 12 Hz phase was coupled to beta-low gamma band (20 – 45 Hz amplitude envelope during all sessions. Importantly, bicoherence values around the harmonics of the alpha frequency were similar both in magnitude and topographic distribution to the cross-frequency coherence (CFCoh values observed in the alpha-phase to beta-low gamma coupling. In addition, despite the large CFCoh we found no significant cross-frequency directionality (CFD. Critically, simulations demonstrated that a sizable part of our empirical CFCoh between alpha and beta-low gamma coupling and the lack of CFD could be explained by two-three harmonics aligned in zero phase-lag produced by the physiologically characteristic alpha asymmetry in the amplitude of the peaks relative to the troughs
Harmonic oscillator states with integer and non-integer orbital angular momentum
International Nuclear Information System (INIS)
Land, Martin
2011-01-01
We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as basis states for representing their respective symmetry groups — O(2), O(1,1), O(3), and O(2,1). The goal of this study is to establish a correspondence between Hilbert space descriptions found by solving the Schrodinger equation in polar coordinates, and Fock space descriptions constructed by expressing the symmetry operators in terms of creation/annihilation operators. We obtain wavefunctions characterized by a principal quantum number, the group Casimir eigenvalue, and one group generator whose eigenvalue is m + s, for integer m and real constant parameter s. For the three groups that contain O(2), the solutions split into two inequivalent representations, one associated with s = 0, from which we recover the familiar description of the oscillator as a product of one-dimensional solutions, and the other with s > 0 (in three dimensions, solutions are found for s = 0 and s = 1/2) whose solutions are non-separable in Cartesian coordinates, and are hence overlooked by the standard Fock space approach. The O(1,1) solutions are singlet states, restricted to zero eigenvalue of the symmetry operator, which represents the boost, not angular momentum. For O(2), a single set of creation and annihilation operators forms a ladder representation for the allowed oscillator states for any s, and the degeneracy of energy states is always finite. However, in three dimensions, the integer and half-integer eigenstates are qualitatively different: the former can be expressed as finite dimensional irreducible tensors under O(3) or O(2,1) while the latter exhibit infinite degeneracy. Creation operators that produce the allowed integer states by acting on the non-degenerate ground state are constructed as irreducible tensor products of the fundamental vector representation. However, the half-integer eigenstates are infinite-dimensional, as expected for the non
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…
Sang, Nguyen Anh; Thu Thuy, Do Thi; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai
2017-06-01
Using the simple deformed three-level model (D3L model) proposed in our early work, we study the entanglement problem of composite bosons. Consider three first energy levels are known, we can get two energy separations, and can define the level deformation parameter δ. Using connection between q-deformed harmonic oscillator and Morse-like anharmonic potential, the deform parameter q also can be derived explicitly. Like the Einstein’s theory of special relativity, we introduce the observer e˙ects: out side observer (looking from outside the studying system) and inside observer (looking inside the studying system). Corresponding to those observers, the outside entanglement entropy and inside entanglement entropy will be defined.. Like the case of Foucault pendulum in the problem of Earth rotation, our deformation energy level investigation might be useful in prediction the environment e˙ect outside a confined box.
The Klauder-Daubechies construction of the phase-space path integral and the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Govaerts, Jan; Mattelaer, Olivier [Center for Particle Physics and Phenomenology (CP3), Institut de Physique Nucleaire, Universite catholique de Louvain (UCL), 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve (Belgium); Bwayi, Calvin Matondo [Department of Physics, University of Kinshasa (UNIKIN), Kinshasa (Congo, The Democratic Republic of the)], E-mail: Jan.Govaerts@uclouvain.be, E-mail: matymatondo@yahoo.fr, E-mail: Olivier.Mattelaer@uclouvain.be
2009-11-06
The canonical operator quantization formulation corresponding to the Klauder-Daubechies construction of the phase-space path integral is considered. This formulation is explicitly applied and solved in the case of the harmonic oscillator, thereby illustrating in a manner complementary to Klauder and Daubechies' original work some of the promising features offered by their construction of a quantum dynamics. The Klauder-Daubechies functional integral involves a regularization parameter eventually taken to vanish, which defines a new physical time scale. When extrapolated to the field theory context, besides providing a new regularization of short distance divergences, keeping a finite value for that time scale offers some tantalizing prospects when it comes to strong gravitational quantum systems.
The optimal performance of a quantum refrigeration cycle working with harmonic oscillators
Lin Bi Hong; Hua Ben
2003-01-01
The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here ...
Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
International Nuclear Information System (INIS)
Alvarez, Pedro D.; Gomis, Joaquim; Kamimura, Kiyoshi; Plyushchay, Mikhail S.
2008-01-01
We investigate the planar anisotropic harmonic oscillator with explicit rotational symmetry as a particle model with non-commutative coordinates. It includes the exotic Newton-Hooke particle and the non-commutative Landau problem as special, isotropic and maximally anisotropic, cases. The system is described by the same (2+1)-dimensional exotic Newton-Hooke symmetry as in the isotropic case, and develops three different phases depending on the values of the two central charges. The special cases of the exotic Newton-Hooke particle and non-commutative Landau problem are shown to be characterized by additional, so(3) or so(2,1) Lie symmetry, which reflects their peculiar spectral properties
The optimal performance of a quantum refrigeration cycle working with harmonic oscillators
International Nuclear Information System (INIS)
Lin Bihong; Chen Jincan; Hua Ben
2003-01-01
The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here are compared with those of an Ericsson or Stirling refrigeration cycle using an ideal gas as the working substance. Finally, the optimal performance of a harmonic quantum Carnot refrigeration cycle at high temperatures is derived easily
Stochastic and superharmonic stochastic resonances of a confined overdamped harmonic oscillator
Zhang, Lu; Lai, Li; Peng, Hao; Tu, Zhe; Zhong, Suchuan
2018-01-01
The dynamics of many soft condensed matter and biological systems is affected by space limitations, which produce some peculiar effects on the systems' stochastic resonance (SR) behavior. In this study, we propose a model where SR can be observed: a confined overdamped harmonic oscillator that is subjected to a sinusoidal driving force and is under the influence of a multiplicative white noise. The output response of the system is a periodic signal with harmonic frequencies that are odd multiples of the driving frequency. We verify the amplitude resonances at the driving frequencies and superharmonic frequencies that are equal to three, five, and seven times the driving frequency, using a numerical method based on the stochastic Taylor expansion. The synergistic effect of the multiplicative white noise, constant boundaries, and periodic driving force that can induce a SR in the output amplitude at the driving and superharmonic frequencies is found. The SR phenomenon found in this paper is sensitive to the driving amplitude and frequency, inherent potential parameter, and boundary width, thus leading to various resonance conditions. Therefore, the mechanism found could be beneficial for the characterization of these confined systems and could constitute an important tool for controlling their basic properties.
Forced nonlinear resonance in a system of coupled oscillators.
Glebov, Sergei; Kiselev, Oleg; Tarkhanov, Nikolai
2011-06-01
We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time t∼ɛ(-2) one component of the system is described for the most part by the inhomogeneous Mathieu equation while the other component represents pulsation of large amplitude. A Hamiltonian system is obtained which describes for the most part the behavior of the envelope in a special case. The analytic results agree with numerical simulations.
Synchronization of Cross-Well Chaos in Coupled Duffing Oscillators
Vincent, U. E.; Njah, A. N.; Akinlade, O.; Solarin, A. R. T.
Numerical simulations have been used to investigate the synchronization behavior of a unidirectionally coupled pair of double-well duffing oscillators (DDOs). The DDOs were simulated in their structurally stable chaotic zone and their state variables were found to completely synchronized. The essential feature of the transition to the synchronous state is shown to correspond to a boundary crisis in which the cross-well chaotic attractor is destroyed.
Gyrotropy in achiral materials: the coupled oscillator model.
Oates, Thomas W H; Shaykhutdinov, Timur; Wagner, Tolga; Furchner, Andreas; Hinrichs, Karsten
2014-11-12
A coupled oscillator model is developed to explain the observation of gyrotropy in achiral metamaterials. By the action of distinct excitation modes, which only combine under oblique incidence, the measurement of circular birefringence in a split-ring resonator (SRR) array is explained. The symmetry of the SRR resembles the water molecule, and parallels between the systems are drawn. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Projection operator techniques in Lagrangian mechanics: symmetrically coupled oscillators
J. N. Boyd; P. N. Raychowdhury
1980-01-01
We apply projection operator techniques to the computation of the natural frequencies of oscillation for three symmetrically coupled mechanical systems. In each case, the rotation subgroup of the full symmetry group is used to determine the projection operators with the result that the Lagrangian must be expressed in terms of complex-valued coordinates. In the coordinate system obtained from the action of the projection operators upon the original coordinates, the Lagrangian yields equations ...
Improved time-dependent harmonic oscillator method for vibrationally inelastic collisions
International Nuclear Information System (INIS)
DePristo, A.E.
1985-01-01
A quantal solution to vibrationally inelastic collisions is presented based upon a linear expansion of the interaction potential around the time-dependent classical positions of all translational and vibrational degrees of freedom. The full time-dependent wave function is a product of a Gaussian translational wave packet and a multidimensional harmonic oscillator wave function, both centered around the appropriate classical position variables. The computational requirements are small since the initial vibrational coordinates are the equilibrium values in the classical trajectory (i.e., phase space sampling does not occur). Different choices of the initial width of the translational wave packet and the initial classical translational momenta are possible, and two combinations are investigated. The first involves setting the initial classical momenta equal to the quantal expectation value, and varying the width to satisfy normalization of the transition probability matrix. The second involves adjusting the initial classical momenta to ensure detailed balancing for each set of transitions, i→f and f→i, and varying the width to satisfy normalization. This choice illustrates the origin of the empirical correction of using the arithmetic average momenta as the initial classical momenta in the forced oscillator approximation. Both methods are tested for the collinear collision systems CO 2 --(He, Ne), and are found to be accurate except for near-resonant vibration--vibration exchange at low initial kinetic energies
Ponomarenko, V I; Kulminskiy, D D; Prokhorov, M D
2017-08-01
We study the collective dynamics of oscillators in a network of identical bistable time-delayed feedback systems globally coupled via the mean field. The influence of delay and inertial properties of the mean field on the collective behavior of globally coupled oscillators is investigated. A variety of oscillation regimes in the network results from the presence of bistable states with substantially different frequencies in coupled oscillators. In the physical experiment and numerical simulation we demonstrate the existence of chimeralike states, in which some of the oscillators in the network exhibit synchronous oscillations, while all other oscillators remain asynchronous.
Eigenmode analysis of coupled magnetohydrodynamic oscillations in the magnetosphere
International Nuclear Information System (INIS)
Fujita, S.; Patel, V.L.
1992-01-01
The authors have performed an eigenmode analysis of the coupled magnetohydrodynamic oscillations in the magnetosphere with a dipole magnetic field. To understand the behavior of the spatial structure of the field perturbations with a great accuracy, they use the finite element method. The azimuthal and radial electric field perturbations are assumed to vanish at the ionosphere, and the azimuthal electric field is assumed to be zero on the outer boundary. The global structures of the electromagnetic field perturbations associated with the coupled magnetohydrodynamic oscillations are presented. In addition, the three-dimensional current system associated with the coupled oscillations is numerically calculated and the following characteristics are found: (1) A strong field-aligned current flows along a resonant field line. The current is particularly strong near the ionosphere. (2) The radial current changes its direction on the opposite sides of the resonant L shell. Unlike the field-aligned current, the radial currents exist in the entire magnetosphere. (3) Although the azimuthal and radial currents are intense on the resonant field line, these currents do not form a loop in the plane perpendicular to the ambient magnetic field. Therefore the field-aligned component of the perturbed magnetic field does not have a maximum at the resonant L shell
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
International Nuclear Information System (INIS)
Belendez, A.; Mendez, D.I.; Fernandez, E.; Marini, S.; Pascual, I.
2009-01-01
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the ...
Ohsuga, M; Yamaguchi, Y; Shimizu, H
1985-01-01
A system composed of two coupled internal oscillators and an external oscillation is studied as a model of biological control systems. The type of interaction between the internal oscillators is a mutual and dissipative one. Three macroscopic states of the internal oscillators are demonstrated in the absence of the external oscillation. Strict and loose entrainment regions of the internal oscillators by the external oscillation are shown in respect to the intensity of the mutual interaction, the intrinsic frequency difference of the internal oscillations, and the magnitude and frequency of the external oscillation. On the other hand, an idea of "holonic system" is introduced and the fundamental properties of the model as a holonic system are elucidated.
Coupled Person Orientation Estimation and Appearance Modeling using Spherical Harmonics
Liem, M.C.; Gavrila, D.M.
2014-01-01
We present a novel approach for the estimation of a person's overall body orientation, 3D shape and texture, from overlapping cameras. A distinguishing aspect of our approach is the use of spherical harmonics for 3D shape- and texture-representation; it offers a compact, low-dimensional
Vasil'ev, M. G.
2017-02-01
A technique for measuring the crystal cross-sectional area with a weight sensor based on the difference between its readings at the extreme rod positions in the stepwise and continuous modes of modulation of the pulling rate is proposed for the low-thermal gradient Czochralski method. A change in the crystallization rate at harmonic oscillations of the pulling rate is estimated with the aim of conserving the quality of the growing crystal for this measurement method.
Pacemakers in large arrays of oscillators with nonlocal coupling
Jaramillo, Gabriela; Scheel, Arnd
2016-02-01
We model pacemaker effects of an algebraically localized heterogeneity in a 1 dimensional array of oscillators with nonlocal coupling. We assume the oscillators obey simple phase dynamics and that the array is large enough so that it can be approximated by a continuous nonlocal evolution equation. We concentrate on the case of heterogeneities with positive average and show that steady solutions to the nonlocal problem exist. In particular, we show that these heterogeneities act as a wave source. This effect is not possible in 3 dimensional systems, such as the complex Ginzburg-Landau equation, where the wavenumber of weak sources decays at infinity. To obtain our results we use a series of isomorphisms to relate the nonlocal problem to the viscous eikonal equation. We then use Fredholm properties of the Laplace operator in Kondratiev spaces to obtain solutions to the eikonal equation, and by extension to the nonlocal problem.
Investigation of coupled optical parametric oscillators for novel applications
Ding, Yujie J.
2016-03-01
In this proceedings article, we summarize our previous results on the novel applications using the coupled optical parametric oscillators (OPO's). In a conventional OPO, a single pump wavelength is capable of generating a pair of the signal and idler beams by placing a bulk nonlinear crystal inside an OPO cavity. When a nonlinear crystal composite consisting of periodically-inverted KTiOPO4 (KTP) plates bonded together by the adhesive-free-bonded (AFB) technique is used instead of the bulk nonlinear crystal, the optical parametric oscillation takes place at two sets of the new wavelengths for the signal and idler beams due to the phase shifts occurring at the interfaces of the adjacent domains making up the composite. These two sets of the signal and idler waves are effectively generated by the two OPO's being coupled to each other. These signals and idlers exhibit ultrastability in terms of their frequency separation. We review the progress made by us on the applications being realized by using such coupled OPO's such as THz generation and restoration of the blurred images after propagating through a distortion plate and a phase plate simulating atmospheric turbulence.
International Nuclear Information System (INIS)
Cole, D.C.
1985-01-01
The theory of stochastic electrodynamics involves the behavior of classical charged particles in the presence of classical electromagnetic zero-point radiation. Past researchers have shown that this theory has close connections with quantum phenomena. Here, this theory is further explored with regard to its predictions of the physical behavior of classical harmonic dipole oscillators relativistically uniformly accelerated through classical electromagnetic zero-point radiation. Part One treats a uniformly accelerated oscillator, unrestricted in its direction of oscillation. In Part Two, for the first time in either the classical or quantum literature, the thermal effects of acceleration are shown to hold for a particular spatially extended system. A set of relationships are derived in Part Three between the electromagnetic fields of an unaccelerated, fluctuating electric dipole oscillator and the correlation functions of homogeneous, isotopic random classical electromagnetic radiation
Coupled-oscillator based active-array antennas
Pogorzelski, Ronald J
2012-01-01
Describing an innovative approach to phased-array control in antenna design This book explores in detail phased-array antennas that use coupled-oscillator arrays, an arrangement featuring a remarkably simple beam steering control system and a major reduction in complexity compared with traditional methods of phased-array control. It brings together in one convenient, self-contained volume the many salient research results obtained over the past ten to fifteen years in laboratories around the world, including the California Institute of Technology's Jet Propulsion Laboratory.
Projection operator techniques in Lagrangian mechanics: symmetrically coupled oscillators
Directory of Open Access Journals (Sweden)
J. N. Boyd
1980-01-01
Full Text Available We apply projection operator techniques to the computation of the natural frequencies of oscillation for three symmetrically coupled mechanical systems. In each case, the rotation subgroup of the full symmetry group is used to determine the projection operators with the result that the Lagrangian must be expressed in terms of complex-valued coordinates. In the coordinate system obtained from the action of the projection operators upon the original coordinates, the Lagrangian yields equations of motion which are separated to the maximum extent made possible by symmetry considerations.
𝒩 = 2 supersymmetric harmonic oscillator: Basic brackets without canonical conjugate momenta
Srinivas, N.; Shukla, A.; Malik, R. P.
2015-09-01
We exploit the ideas of spin-statistics theorem, normal-ordering and the key concepts behind the symmetry principles to derive the canonical (anti)commutators for the case of a one (0 + 1)-dimensional (1D) 𝒩 = 2 supersymmetric (SUSY) harmonic oscillator (HO) without taking the help of the mathematical definition of canonical conjugate momenta with respect to the bosonic and fermionic variables of this toy model for the Hodge theory (where the continuous and discrete symmetries of the theory provide the physical realizations of the de Rham cohomological operators of differential geometry). In our present endeavor, it is the full set of continuous symmetries and their corresponding generators that lead to the derivation of basic (anti)commutators amongst the creation and annihilation operators that appear in the normal mode expansions of the dynamical fermionic and bosonic variables of our present 𝒩 = 2 SUSY theory of a HO. These basic brackets are in complete agreement with such kind of brackets that are derived from the standard canonical method of quantization scheme.
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.
A new look at the quantum mechanics of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Kastrup, H.A.
2006-12-15
At first sight it is probably hard to believe that something new can be said about the harmonic oscillator (HO). But that is so indeed: Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables {phi} element of R mod 2{pi} and I>0. However, the transformation q= {radical}(2I)cos {phi}, p=-{radical}(2I)sin {phi} is only locally symplectic and singular for (q,p)=(0,0). Globally the phase space {l_brace}(q,p){r_brace} has the topological structure of the plane R{sup 2}, whereas the phase space {l_brace}({phi},I){r_brace} corresponds globally to the punctured plane R{sup 2}-(0,0) or to a simple cone S{sup 1} x R{sup +} with the tip deleted. This makes a qualitative difference as to the quantum theory of the two phase spaces: The quantizing canonical group for the plane R{sup 2} consists of the (centrally extended) translations generated by the Poisson Lie algebra basis {l_brace}q,p,1{r_brace}, whereas the corresponding canonical group of the phase space {l_brace}({phi},I){r_brace} is the group SO{up_arrow}(1,2)=Sp(2,R)/Z{sub 2}, where Sp(2,R) is the sympletic group of the plane, with the generating Poisson Lie algebra basis {l_brace}h{sub 0}=I,h{sub 1}=Icos{phi},h{sub 2}=-Isin{phi}{r_brace} which provides also the basic ''observables'' on {l_brace}({phi}, I){r_brace}. In the quantum mechanics of the ({phi},I)-model of the HO the three h{sub j} correspond to self-adjoint generators K{sub j}, j=0,1,2, of irreducible unitary representations from the positive discrete series of the group SO{up_arrow}(1,2) or one of its infinitely many covering groups, the representations parametrized by the Bargmann index k>0. This index k determines the ground state energy E{sub k,n=0}={Dirac_h}{omega}k of the ({phi},I)-Hamiltonian H(anti K)={Dirac_h}{omega}K{sub 0}. For an m-fold covering the lowest possible value for k is k=1/m, which can be made arbitrarily small by choosing m accordingly. This is not in contraction to
Analytical insights on theta-gamma coupled neural oscillators.
Fontolan, Lorenzo; Krupa, Maciej; Hyafil, Alexandre; Gutkin, Boris
2013-08-14
In this paper, we study the dynamics of a quadratic integrate-and-fire neuron, spiking in the gamma (30-100 Hz) range, coupled to a delta/theta frequency (1-8 Hz) neural oscillator. Using analytical and semianalytical methods, we were able to derive characteristic spiking times for the system in two distinct regimes (depending on parameter values): one regime where the gamma neuron is intrinsically oscillating in the absence of theta input, and a second one in which gamma spiking is directly gated by theta input, i.e., windows of gamma activity alternate with silence periods depending on the underlying theta phase. In the former case, we transform the equations such that the system becomes analogous to the Mathieu differential equation. By solving this equation, we can compute numerically the time to the first gamma spike, and then use singular perturbation theory to find successive spike times. On the other hand, in the excitable condition, we make direct use of singular perturbation theory to obtain an approximation of the time to first gamma spike, and then extend the result to calculate ensuing gamma spikes in a recursive fashion. We thereby give explicit formulas for the onset and offset of gamma spike burst during a theta cycle, and provide an estimation of the total number of spikes per theta cycle both for excitable and oscillator regimes.
Coupled oscillations of flow along a perforated plate
International Nuclear Information System (INIS)
Celik, E.; Rockwell, D.
2004-01-01
Turbulent shear flow past a perforated plate bounded by a closed cavity can give rise to highly coherent oscillations, which have a wavelength of the order of the plate length. The present investigation focuses on the coupling between unsteady events on either side of the plate when the oscillations are self-sustaining. A cinema technique of high-image-density particle image velocimetry, which provides a space-time representation of the unsteadiness at a large number of locations over entire planes, is employed to characterize the distinctively different patterns of flow structure on the back (low-speed) side of the plate relative to those on the front (high-speed) side. Global cross-spectral analysis leads to patterns of spectral peaks and phase variations, along and across the plate. This approach, along with complementary types of image evaluation, delineates the physics of the oscillations, which include downstream propagating disturbances along either side of the plate and a coherent region of unsteadiness at its trailing-edge. On the backside of the plate, a sequence of upstream-oriented, pulsatile jets are formed, and the time-averaged flow pattern is a counterflow wall jet
Magnetic oscillations measure interlayer coupling in cuprate superconductors
Grigoriev, P. D.; Ziman, Timothy
2017-10-01
The magnetic oscillations in YBCO high-temperature superconductors have been widely studied over the last decade and consist of three equidistant low frequencies with a central frequency several times more intense than its two shoulders. This remains a puzzle in spite of numerous attempts to explain the corresponding small Fermi-surface pockets. Furthermore, the ARPES data indicate only four Fermi arcs with bilayer splitting, and show no sign of such small areas in the Fermi surface. Here we argue that the magnetic oscillations measured in underdoped bilayer high-temperature superconductors, in particular YBa2Cu3O6 +δ , provide a measure of the interplanar electronic coupling rather than the areas of fine-grain reconstruction of the Fermi surfaces coming from induced charge density waves. This identification is based on the relative intensities of the different peaks, as well as their angular dependence, which points to an effective Fermi surface that is larger than the oscillation frequencies, and is compatible with several indications from ARPES. The dominance of such frequencies with respect to the fundamental frequencies from the Fermi surface is natural for a strongly correlated quasi-two-dimensional electronic system where nonlinear mixings of frequencies are more resistant to sample inhomogeneity.
Wu, Hao; Fan, Hong-Yi
2008-12-01
Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator (IEO) method to solving the energy spectrum of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1,X2] = [X2,X3] = [X3,X1] = iθ, and this method seems effective and concise.
International Nuclear Information System (INIS)
Fueloep, L.
1987-10-01
The forceless mechanics of Hertz is a reformulation of the classical mechanics in a curved configuration space. The relationship between the forceless mechanics and the general relativity theory which uses curved Riemann spaces as well is investigated on the simple example of the harmonic oscillator. The mathematical similarities and differences and the different interpretations of similar formulas are discussed. Some formal constants of the Hertz mechanics have got concrete physical meanings in the general relativity. (D.Gy.)
Link between truncated fractals and coupled oscillators in biological systems.
Paar, V; Pavin, N; Rosandić, M
2001-09-07
This article aims at providing a new theoretical insight into the fundamental question of the origin of truncated fractals in biological systems. It is well known that fractal geometry is one of the characteristics of living organisms. However, contrary to mathematical fractals which are self-similar at all scales, the biological fractals are truncated, i.e. their self-similarity extends at most over a few orders of magnitude of separation. We show that nonlinear coupled oscillators, modeling one of the basic features of biological systems, may generate truncated fractals: a truncated fractal pattern for basin boundaries appears in a simple mathematical model of two coupled nonlinear oscillators with weak dissipation. This fractal pattern can be considered as a particular hidden fractal property. At the level of sufficiently fine precision technique the truncated fractality acts as a simple structure, leading to predictability, but at a lower level of precision it is effectively fractal, limiting the predictability of the long-term behavior of biological systems. We point out to the generic nature of our result. Copyright 2001 Academic Press.
Coupled nonlinear oscillation and stability evolution of viscoelastic dielectric elastomers.
Zhang, Junshi; Chen, Hualing; Li, Bo; McCoul, David; Pei, Qibing
2015-10-14
This article describes the development of an analytical model to study the coupled nonlinear oscillation and stability evolution of viscoelastic dielectric elastomers (DEs) under non-equibiaxial tensile forces by utilizing the method of virtual work. Numerically calculated results are employed to predict this nonlinear dynamic behavior. The resonant frequency (where the amplitude-frequency response curve peaks) and the amplitude-frequency response of the deformation in both in-plane directions are tuned by varying the values of tensile force. The oscillation response in the two in-plane directions exhibits strong nonlinearity and coupling with each other, and is tuned by the changing tensile forces under a specific excitation frequency. By varying the values of tensile forces, the dynamic viscoelastic creep in a certain in-plane direction can be eliminated. Phase diagrams and Poincaré maps under several values of tensile forces are utilized to study the stability evolution of the DE system under non-equibiaxial tensile forces.
Mota, R. D.; Xicoténcatl, M. A.; Granados, V. D.
2004-02-01
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.
Energy Technology Data Exchange (ETDEWEB)
Mota, R D [Unidad Profesional Interdisciplinaria de IngenierIa y TecnologIas Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, 07340 Mexico DF (Mexico); Xicotencatl, M A [Departamento de Matematicas del Centro de Investigacion y Estudios Avanzados del IPN, Mexico DF, 07000 (Mexico); Granados, V D [Escuela Superior de FIsica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)
2004-02-20
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.
International Nuclear Information System (INIS)
Lewis, Zachary; Takeuchi, Tatsu
2011-01-01
We analyze the position and momentum uncertainties of the energy eigenstates of the harmonic oscillator in the context of a deformed quantum mechanics, namely, that in which the commutator between the position and momentum operators is given by [x-circumflex,p-circumflex]=i(ℎ/2π)(1+βp-circumflex 2 ). This deformed commutation relation leads to the minimal length uncertainty relation Δx≥((ℎ/2π)/2)(1/Δp+βΔp), which implies that Δx∼1/Δp at small Δp while Δx∼Δp at large Δp. We find that the uncertainties of the energy eigenstates of the normal harmonic oscillator (m>0), derived in L. N. Chang, D. Minic, N. Okamura, and T. Takeuchi, Phys. Rev. D 65, 125027 (2002), only populate the Δx∼1/Δp branch. The other branch, Δx∼Δp, is found to be populated by the energy eigenstates of the 'inverted' harmonic oscillator (m min =(ℎ/2π)√(β)>√(2)[(ℎ/2π) 2 /k|m|] 1/4 . Correspondence with the classical limit is also discussed.
CSIR Research Space (South Africa)
Grobler, TL
2012-06-01
Full Text Available It is proposed that the time series extracted from moderate resolution imaging spectroradiometer satellite data be modeled as a simple harmonic oscillator with additive colored noise. The colored noise ismodeled with an Ornstein–Uhlenbeck process...
Laas, Katrin; Mankin, Romi; Rekker, Astrid
2009-05-01
The influences of noise flatness and friction coefficient on the long-time behavior of the first two moments and the correlation function for the output signal of a harmonic oscillator with fluctuating frequency subjected to an external periodic force are considered. The colored fluctuations of the oscillator frequency are modeled as a trichotomous noise. The study is a follow up of the previous investigation of a stochastic oscillator [Phys. Rev. E 78, 031120 (2008)], where the connection between the occurrence of energetic instability and stochastic multiresonance is established. Here we report some unexpected results not considered in the previous work. Notably, we have found a nonmonotonic dependence of several stochastic resonance characteristics such as spectral amplification, variance of the output signal, and signal-to-noise ratio on the friction coefficient and on the noise flatness. In particular, in certain parameter regions spectral amplification exhibits a resonancelike enhancement at intermediate values of the friction coefficient.
Chowdhury, M. S. H.; Hosen, Md. Alal; Ahmad, Kartini; Ali, M. Y.; Ismail, A. F.
In this paper, a new reliable analytical technique has been introduced based on the Harmonic Balance Method (HBM) to determine higher-order approximate solutions of the strongly nonlinear cubic-quintic Duffing oscillator. The application of the HBM leads to very complicated sets of nonlinear algebraic equations. In this technique, the high-order nonlinear algebraic equations are approximated in the form of a power series solution, and this solution produces desired results even for small as well as large amplitudes of oscillation. Moreover, a suitable truncation formula is found in which the solution measures better results than existing results and it saves a lot of calculation. It is highly noteworthy that using the proposed technique, the third-order approximate solutions gives an excellent agreement as compared with the numerical solutions (considered to be exact). The proposed technique is applied to the strongly nonlinear cubic-quintic Duffing oscillator to reveals its novelty, reliability and wider applicability.
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.
Theory of mode coupling in spin torque oscillators coupled to a thermal bath of magnons
Zhou, Yan; Zhang, Shulei; Li, Dong; Heinonen, Olle
Recently, numerous experimental investigations have shown that the dynamics of a single spin torque oscillator (STO) exhibits complex behavior stemming from interactions between two or more modes of the oscillator. Examples are the observed mode-hopping and mode coexistence. There has been some initial work indicating how the theory for a single-mode (macro-spin) spin torque oscillator should be generalized to include several modes and the interactions between them. In this work, we rigorously derive such a theory starting with the generalized Landau-Lifshitz-Gilbert equation in the presence of the current-driven spin transfer torques. We will first show, in general, that how a linear mode coupling would arise through the coupling of the system to a thermal bath of magnons, which implies that the manifold of orbits and fixed points may shift with temperature. We then apply our theory to two experimentally interesting systems: 1) a STO patterned into nano-pillar with circular or elliptical cross-sections and 2) a nano-contact STO. For both cases, we found that in order to get mode coupling, it would be necessary to have either a finite in-plane component of the external field or an Oersted field. We will also discuss the temperature dependence of the linear mode coupling. Y. Zhou acknowledges the support by the Seed Funding Program for Basic Research from the University of Hong Kong, and University Grants Committee of Hong Kong (Contract No. AoE/P-04/08).
Pintér, Balázs; Erdélyi, R.
2018-01-01
Solar fundamental (f) acoustic mode oscillations are investigated analytically in a magnetohydrodynamic (MHD) model. The model consists of three layers in planar geometry, representing the solar interior, the magnetic atmosphere, and a transitional layer sandwiched between them. Since we focus on the fundamental mode here, we assume the plasma is incompressible. A horizontal, canopy-like, magnetic field is introduced to the atmosphere, in which degenerated slow MHD waves can exist. The global (f-mode) oscillations can couple to local atmospheric Alfvén waves, resulting, e.g., in a frequency shift of the oscillations. The dispersion relation of the global oscillation mode is derived, and is solved analytically for the thin-transitional layer approximation and for the weak-field approximation. Analytical formulae are also provided for the frequency shifts due to the presence of a thin transitional layer and a weak atmospheric magnetic field. The analytical results generally indicate that, compared to the fundamental value (ω =√{ gk }), the mode frequency is reduced by the presence of an atmosphere by a few per cent. A thin transitional layer reduces the eigen-frequencies further by about an additional hundred microhertz. Finally, a weak atmospheric magnetic field can slightly, by a few percent, increase the frequency of the eigen-mode. Stronger magnetic fields, however, can increase the f-mode frequency by even up to ten per cent, which cannot be seen in observed data. The presence of a magnetic atmosphere in the three-layer model also introduces non-permitted propagation windows in the frequency spectrum; here, f-mode oscillations cannot exist with certain values of the harmonic degree. The eigen-frequencies can be sensitive to the background physical parameters, such as an atmospheric density scale-height or the rate of the plasma density drop at the photosphere. Such information, if ever observed with high-resolution instrumentation and inverted, could help to
Elementary modes of coupled oscillators as whispering-gallery microresonators
Banerjee, Rabin; Mukherjee, Pradip
2015-10-01
We obtain the elementary modes of a system of parity-time reversal (PT)-symmetric coupled oscillators with balanced loss and gain. These modes are used to give a physical picture of the phase transition recently reported [C. M. Bender, M. Gianfreda, B. Peng, S. K. Özdemir and L. Yang, Phys. Rev. A 88, 062111 (2013); L. Yang, S. K. Özdemir and B. Peng, 12th Int. Workshop and Conf. Pseudo-Hermitian Hamiltonians in Quantum Physics, Istanbul, Turkey, July 2013; B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender and L. Yang, Nat. Phys. 10, 394 (2014)] in experiments with whispering-gallery microresonators.
Ming, Yi; Li, Hui-Min; Ding, Ze-Jun
2016-03-01
Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [Eichler et al., Nat. Nanotech. 6, 339 (2011), 10.1038/nnano.2011.71]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed compared to the results of weak linear coupling constant.
Higher dimensional models of cross-coupled oscillators and application to design
Elwakil, Ahmed S.
2010-06-01
We present four-dimensional and five-dimensional models for classical cross-coupled LC oscillators. Using these models, sinusoidal oscillation condition, frequency and amplitude can be found. Further, undesired behaviors such as relaxation-mode oscillations and latchup can be explained and detected. A simple graphical design procedure is also described. © 2010 World Scientific Publishing Company.
Harmonically trapped attractive and repulsive spin–orbit and Rabi coupled Bose–Einstein condensates
International Nuclear Information System (INIS)
Chiquillo, Emerson
2017-01-01
Numerically we investigate the ground state of effective one-dimensional spin–orbit (SO) and Rabi coupled two pseudo-spinor Bose–Einstein condensates (BECs) under the effect of harmonic traps. For both signs of the interaction, density profiles of SO and Rabi coupled BECs in harmonic potentials, which simulate a real experimental situation are obtained. The harmonic trap causes a strong reduction of the multi-peak nature of the condensate and it increases its density. For repulsive interactions, the increase of SO coupling results in an uncompressed less dense condensate and with increased multi-peak nature of the density. The increase of Rabi coupling leads to a density increase with an almost constant number of multi-peaks. For both signs of the interaction and negative values of Rabi coupling, the condensate develops a notch in the central point and it seems to a dark-in-bright soliton. In the case of the attractive nonlinearity, an interesting result is the increase of the collapse threshold under the action of the SO and Rabi couplings. (paper)
Nonlinear coupling between cortical oscillations and muscle activity during isotonic wrist flexion
Yang, Y.; Solis Escalante, T.; van de Ruit, M.L.; van der Helm, F.C.T.; Schouten, A.C.
2016-01-01
Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been
Chimera states in two-dimensional networks of locally coupled oscillators
Kundu, Srilena; Majhi, Soumen; Bera, Bidesh K.; Ghosh, Dibakar; Lakshmanan, M.
2018-02-01
Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and existence of chimera states by considering locally coupled two-dimensional networks of identical oscillators where each node is interacting through nonlinear coupling function. This is in contrast with the existence of chimera states in two-dimensional nonlocally coupled oscillators with rectangular kernel in the coupling function. We find that the presence of nonlinearity in the coupling function plays a key role to produce chimera states in two-dimensional locally coupled oscillators. We analytically verify explicitly in the case of a network of coupled Stuart-Landau oscillators in two dimensions that the obtained results using Ott-Antonsen approach and our analytical finding very well matches with the numerical results. Next, we consider another type of important nonlinear coupling function which exists in neuronal systems, namely chemical synaptic function, through which the nearest-neighbor (locally coupled) neurons interact with each other. It is shown that such synaptic interacting function promotes the emergence of chimera states in two-dimensional lattices of locally coupled neuronal oscillators. In numerical simulations, we consider two paradigmatic neuronal oscillators, namely Hindmarsh-Rose neuron model and Rulkov map for each node which exhibit bursting dynamics. By associating various spatiotemporal behaviors and snapshots at particular times, we study the chimera
Negative Resistance Circuit for Damping an Array of Coupled FitzHugh-Nagumo Oscillators
DEFF Research Database (Denmark)
Tamaševičius, Arūnas; Adomaitienė, Elena; Bumelienė, Skaidra
2015-01-01
An analog circuit, based on a negative impedance converter and a capacitor, for damping oscillations in an array of mean-field coupled neuronal FitzHugh–Nagumo (FHN) type oscillators is described. The circuit is essentially a two-terminal feedback controller. When coupled to an array of the FHN o...... oscillators, it stabilizes their unstable steady states. Both, numerical simulations and hardware experiments with the analog electronic circuits have been performed. The results for an array, composed of three mean-field coupled FHN oscillators, are presented....
DEFF Research Database (Denmark)
Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth
2015-01-01
Understanding about harmonic propagation in wind turbine converter is fundamental to research the influence of these on a large network harmonic distortion. Therefore, the analysis of wind turbine converter harmonic spectrum as well as the influence of converter operating point into the network...... method. The modeling and analysis results are remarkable that this model can include non-linear component and also show different operating points and harmonic coupling point, where this means each wind power converter can show the different impedance characteristics. The developed model can easily...... is urgently important issues in harmonic studies on wind farm. However, the conventional modeling procedure and simplified model for controller design are not enough to analyze such complicated systems. Besides, they have many limitations in terms of including a non-linear component, different operating...
The Madden-Julian Oscillation in NCEP Coupled Model Simulation
Directory of Open Access Journals (Sweden)
Wanqiu Wang Kyong-Hwan Seo
2009-01-01
Full Text Available This study documents a detailed analysis on the Madden-Julian Oscillation (MJO simulated by the National Centers for Environmental Prediction (NCEP using the Global Forecast System (GFS model version 2003 coupled with the Climate Forecast System model (CFS consisting of the 2003 version of GFS and the Geophysical Fluid Dynamics Laboratory (GFDL Modular Ocean Model V.3 (MOM3. The analyses are based upon a 21-year simulation of AMIP-type with GFS and CMIP-type with CFS. It is found that air-sea coupling in CFS is shown to improve the coherence between convection and large-scale circulation associated with the MJO. The too fast propagation of convection from the Indian Ocean to the maritime continents and the western Pacific in GFS is improved (slowed down in CFS. Both GFS and CFS produce too strong intraseasonal convective heating and circulation anomalies in the central-eastern Pacific; further, the air-sea coupling in CFS enhances this unrealistic feature. The simulated mean slow phase speed of east ward propagating low-wavenumber components shown in the wavenumber-frequency spectra is due to the slow propagation in the central-eastern Pacific in both GFS and CFS. Errors in model climatology may have some effect upon the simulated MJO and two possible influences are: (i CFS fails to simulate the westerlies over maritime continents and western Pacific areas, resulting in an unrealistic representation of surface latent heat flux associated with the MJO; and (ii vertical easterly wind shear from the Indian Ocean to the western Pacific in CFS is much weaker than that in the observation and in GFS, which may adversely affect the eastward propagation of the simulated MJO.
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.
International Nuclear Information System (INIS)
Kovacic, Ivana; Brennan, Michael J.
2008-01-01
An analytical approach to determine the steady-state response of a damped and undamped harmonically excited oscillator with no linear term and with cubic non-linearity is presented. The governing equation is transformed into a form suitable for the application of a classical series expansion technique. The Linstedt-Poincare method and the method of multiple scales are then used to determine the amplitude-frequency response and approximate solution for the response at the excitation frequency. The results obtained are compared with numerical solutions and analytical solutions found in the literature for the case when there is strong non-linearity
Demiralp, Metin
2010-09-01
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 the dynamic of the system is related to a set of ODEs.
International Nuclear Information System (INIS)
Hernandez-Tenorio, C.; Belyaeva, T.L.; Serkin, V.N.
2007-01-01
The dynamics of nonlinear solitary waves is studied in the framework of the nonlinear Schroedinger equation model with time-dependent harmonic oscillator potential. The model allows one to analyse on general basis a variety of nonlinear phenomena appearing both in Bose-Einstein condensate, condensed matter physics, nonlinear optics, and biophysics. The soliton parametric resonance is investigated by using two complementary methods: the adiabatic perturbation theory and direct numerical experiments. Conditions for reversible and irreversible denaturation of soliton bound states are also considered
Leach, P. G. L.; Nucci, M. C.
2004-09-01
The classical MICZ-Kepler problem is shown to be reducible to an isotropic two-dimensional system of linear harmonic oscillators and a conservation law in terms of new variables related to the Ermanno-Bernoulli constants and the components of the Poincaré vector. An algorithmic route to linearization is shown based on Lie symmetry analysis and the reduction method [ Nucci, J. Math. Phys. 37, 1772 (1996) ]. First integrals are also obtained by symmetry analysis and the reduction method [ Marcelli and Nucci,J. Math. Phys. 44, 2111 (2002) ].
Harmonic cavities and the transverse mode-coupling instability driven by a resistive wall
Directory of Open Access Journals (Sweden)
M. Venturini
2018-02-01
Full Text Available The effect of rf harmonic cavities on the transverse mode-coupling instability (TMCI is still not very well understood. We offer a fresh perspective on the problem by proposing a new numerical method for mode analysis and investigating a regime of potential interest to the new generation of light sources where resistive wall is the dominant source of transverse impedance. When the harmonic cavities are tuned for maximum flattening of the bunch profile we demonstrate that at vanishing chromaticities the transverse single-bunch motion is unstable at any current, with growth rate that in the relevant range scales as the 6th power of the current. With these assumptions and radiation damping included, we find that for machine parameters typical of 4th-generation light sources the presence of harmonic cavities could reduce the instability current threshold by more than a factor two.
Harmonic cavities and the transverse mode-coupling instability driven by a resistive wall
Venturini, M.
2018-02-01
The effect of rf harmonic cavities on the transverse mode-coupling instability (TMCI) is still not very well understood. We offer a fresh perspective on the problem by proposing a new numerical method for mode analysis and investigating a regime of potential interest to the new generation of light sources where resistive wall is the dominant source of transverse impedance. When the harmonic cavities are tuned for maximum flattening of the bunch profile we demonstrate that at vanishing chromaticities the transverse single-bunch motion is unstable at any current, with growth rate that in the relevant range scales as the 6th power of the current. With these assumptions and radiation damping included, we find that for machine parameters typical of 4th-generation light sources the presence of harmonic cavities could reduce the instability current threshold by more than a factor two.
International Nuclear Information System (INIS)
Chung, N. N.; Chew, L. Y.
2007-01-01
We have generalized the two-step approach to the solution of systems of N coupled quantum anharmonic oscillators. By using the squeezed vacuum state of each individual oscillator, we construct the tensor product state, and obtain the optimal squeezed vacuum product state through energy minimization. We then employ this optimal state and its associated bosonic operators to define a basis set to construct the Heisenberg matrix. The diagonalization of the matrix enables us to obtain the energy eigenvalues of the coupled oscillators. In particular, we have applied our formalism to determine the eigenenergies of systems of two coupled quantum anharmonic oscillators perturbed by a general polynomial potential, as well as three and four coupled systems. Furthermore, by performing a first-order perturbation analysis about the optimal squeezed vacuum product state, we have also examined into the squeezing properties of two coupled oscillator systems
International Nuclear Information System (INIS)
Belendez, A.; Fernandez, E.; Rodes, J.J.; Fuentes, R.; Pascual, I.
2009-01-01
In a previous short communication [A. Belendez, E. Fernandez, J.J. Rodes, R. Fuentes, I. Pascual, Phys. Lett. A 373 (2009) 735] the nonlinear oscillations of a punctual charge in the electric field of a charged ring were analyzed. Approximate frequency-amplitude relations and periodic solutions were obtained using the harmonic balance method. Now we clarify an important aspect about of this oscillation charge. Taking into account Earnshaw's theorem, this punctual charge cannot be a free charge and so it must be confined, for example, on a finite conducting wire placed along the axis of the ring. Then, the oscillatory system may consist of a punctual charge on a conducting wire placed along the axis of the uniformly charged ring.
Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators.
Senthilkumar, D V; Muruganandam, P; Lakshmanan, M; Kurths, J
2010-06-01
Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at (mN(c)+1)-th oscillators in the ring, where m is an integer and N(c) is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by size instability. We also demonstrate that there exists an exponential relation between the number of oscillators that can support stable synchronization in the ring with the external drive and the critical coupling strength ε(c) with a scaling exponent γ. The critical coupling strength is calculated by numerically estimating the synchronization error and is also confirmed from the conditional Lyapunov exponents of the coupled systems. We find that the same scaling relation exists for m couplings between the drive and the ring. Further, we have examined the robustness of the synchronous states against Gaussian white noise and found that the synchronization error exhibits a power-law decay as a function of the noise intensity indicating the existence of both noise-enhanced and noise-induced synchronizations depending on the value of the coupling strength ε. In addition, we have found that ε(c) shows an exponential decay as a function of the number of additional couplings. These results are demonstrated using the paradigmatic models of Rössler and Lorenz oscillators.
International Nuclear Information System (INIS)
Raghavan, S.; Smerzi, A.; Fantoni, S.; Shenoy, S.R.
2001-03-01
We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The boson Josephson junction (BJJ) dynamics is described by the two-mode nonlinear Gross-Pitaevskii equation that is solved analytically in terms of elliptic functions. The BJJ, being a neutral, isolated system, allows the investigations of dynamical regimes for the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ's). These include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to π (π-phase oscillations); (ii) the average population imbalance is nonzero, in states with macroscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJJ ac and plasma oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single universal curve for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of 3 He-B and the internal Josephson effect in 3 He-A are also discussed. (author)
Photonic harmonic up-converter based on a self-oscillating optical frequency comb using a DP-DPMZM
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.
An Application of the Harmonic Oscillator Model to Verify Dunning’s Theory of the Economic Growth
Directory of Open Access Journals (Sweden)
Marcin Salamaga
2013-09-01
Full Text Available Analogies with mechanisms ruling the natural world have oft en been sought in the course of economic phenomena.Th is paper is also an attempt to combine the physical phenomenon of a harmonious oscillator withthe theory of economic growth by J. H. Dunning (1981. In his theory, Dunning distinguished stages of economicgrowth of countries that imply the dependency between the investment position of countries and theirGDP per capita, while the graph presenting this dependency reminds a trajectory of oscillating motion of adamped harmonic oscillator. Th is analogy has given inspiration to reinterpret the theory of economy on thegrounds of the mechanism of a physical model. In this paper, the harmonious oscillator motion equation wasadapted to the description of dependencies shown in the theory of economic growth by J. H. Dunning. Th emathematical solution of this equation is properly parameterised and parameters are estimated with the useof the Gauss-Newton algorithm. Th e main objective of this paper is to allocate a specifi c stage in the economicgrowth to each country on the basis of the values of parameter estimations of the proposed cyclical models ofchanges in the net investment indicator.
Collective motions of globally coupled oscillators and some probability distributions on circle
International Nuclear Information System (INIS)
Jaćimović, Vladimir; Crnkić, Aladin
2017-01-01
In 2010 Kato and Jones described a new family of probability distributions on circle, obtained as Möbius transformation of von Mises distribution. We present the model demonstrating that these distributions appear naturally in study of populations of coupled oscillators. We use this opportunity to point out certain relations between Directional Statistics and collective motion of coupled oscillators. - Highlights: • We specify probability distributions on circle that arise in Kuramoto model. • We study how the mean-field coupling affects the shape of distribution of phases. • We discuss potential applications in some experiments on cell cycle. • We apply Directional Statistics to study collective dynamics of coupled oscillators.
Collective motions of globally coupled oscillators and some probability distributions on circle
Energy Technology Data Exchange (ETDEWEB)
Jaćimović, Vladimir [Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put, bb., 81000 Podgorica (Montenegro); Crnkić, Aladin, E-mail: aladin.crnkic@hotmail.com [Faculty of Technical Engineering, University of Bihać, Ljubijankićeva, bb., 77000 Bihać, Bosnia and Herzegovina (Bosnia and Herzegovina)
2017-06-28
In 2010 Kato and Jones described a new family of probability distributions on circle, obtained as Möbius transformation of von Mises distribution. We present the model demonstrating that these distributions appear naturally in study of populations of coupled oscillators. We use this opportunity to point out certain relations between Directional Statistics and collective motion of coupled oscillators. - Highlights: • We specify probability distributions on circle that arise in Kuramoto model. • We study how the mean-field coupling affects the shape of distribution of phases. • We discuss potential applications in some experiments on cell cycle. • We apply Directional Statistics to study collective dynamics of coupled oscillators.
An efficient method for simulation of noisy coupled multi-dimensional oscillators
Stinchcombe, Adam R.; Forger, Daniel B.
2016-09-01
We present an efficient computational method for the study of populations of noisy coupled oscillators. By taking a population density approach in which the probability density of observing an oscillator at a point of state space is the primary variable instead of the states of all of the oscillators, we are able to seamlessly account for intrinsic noise within the oscillators and global coupling within the population. The population is assumed to consist of a large number of oscillators so that the noise process is well sampled over the population. Our numerical method is able to solve the governing equation even in the challenging case of limit cycle oscillators with a large number of state variables. Instead of simulating a prohibitive number of oscillators, our particle method simulates relatively few particles allowing for the efficient solution of the governing equation.
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
Abstract. Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative.
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we ...
Principal component analysis of the nonlinear coupling of harmonic modes in heavy-ion collisions
BoŻek, Piotr
2018-03-01
The principal component analysis of flow correlations in heavy-ion collisions is studied. The correlation matrix of harmonic flow is generalized to correlations involving several different flow vectors. The method can be applied to study the nonlinear coupling between different harmonic modes in a double differential way in transverse momentum or pseudorapidity. The procedure is illustrated with results from the hydrodynamic model applied to Pb + Pb collisions at √{sN N}=2760 GeV. Three examples of generalized correlations matrices in transverse momentum are constructed corresponding to the coupling of v22 and v4, of v2v3 and v5, or of v23,v33 , and v6. The principal component decomposition is applied to the correlation matrices and the dominant modes are calculated.
International Nuclear Information System (INIS)
Castro, A.S. de; Alberto, P.; Lisboa, R.; Malheiro, M.
2006-01-01
We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and γ 5 chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry-related problems have the same spectrum but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector, and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states
International Nuclear Information System (INIS)
Wang, C M; Lei, X L
2014-01-01
We study dc-current effects on the magnetoresistance oscillation in a two-dimensional electron gas with Rashba spin-orbit coupling, using the balance-equation approach to nonlinear magnetotransport. In the weak current limit the magnetoresistance exhibits periodical Shubnikov-de Haas oscillation with changing Rashba coupling strength for a fixed magnetic field. At finite dc bias, the period of the oscillation halves when the interbranch contribution to resistivity dominates. With further increasing current density, the oscillatory resistivity exhibits phase inversion, i.e., magnetoresistivity minima (maxima) invert to maxima (minima) at certain values of the dc bias, which is due to the current-induced magnetoresistance oscillation. (paper)
International Nuclear Information System (INIS)
Cari, C; Suparmi, A
2013-01-01
The energy eigenvalues and eigenfunctions of Schrodinger equation for three dimensional harmonic oscillator potential plus Rosen-Morse non-central potential are investigated using NU method and Romanovski polynomial. The bound state energy eigenvalues are given in a closed form and corresponding radial wave functions are expressed in associated Laguerre polynomials while angular eigen functions are given in terms of Romanovski polynomials. The Rosen-Morse potential is considered to be a perturbation factor to the three dimensional harmonic oscillator potential that causes the increase of radial wave function amplitude and decrease of angular momentum length. Keywords: Schrodinger Equation, Three dimensional Harmonic Oscillator potential, Rosen-morse non-central potential, NU method, Romanovski Polynomials
Aging transition in systems of oscillators with global distributed-delay coupling.
Rahman, B; Blyuss, K B; Kyrychko, Y N
2017-09-01
We consider a globally coupled network of active (oscillatory) and inactive (nonoscillatory) oscillators with distributed-delay coupling. Conditions for aging transition, associated with suppression of oscillations, are derived for uniform and gamma delay distributions in terms of coupling parameters and the proportion of inactive oscillators. The results suggest that for the uniform distribution increasing the width of distribution for the same mean delay allows aging transition to happen for a smaller coupling strength and a smaller proportion of inactive elements. For gamma distribution with sufficiently large mean time delay, it may be possible to achieve aging transition for an arbitrary proportion of inactive oscillators, as long as the coupling strength lies in a certain range.
Lai, Yi Ming
2013-07-09
We study ensembles of globally coupled, nonidentical phase oscillators subject to correlated noise, and we identify several important factors that cause noise and coupling to synchronize or desynchronize a system. By introducing noise in various ways, we find an estimate for the onset of synchrony of a system in terms of the coupling strength, noise strength, and width of the frequency distribution of its natural oscillations. We also demonstrate that noise alone can be sufficient to synchronize nonidentical oscillators. However, this synchrony depends on the first Fourier mode of a phase-sensitivity function, through which we introduce common noise into the system. We show that higher Fourier modes can cause desynchronization due to clustering effects, and that this can reinforce clustering caused by different forms of coupling. Finally, we discuss the effects of noise on an ensemble in which antiferromagnetic coupling causes oscillators to form two clusters in the absence of noise. © 2013 American Physical Society.
Application of He’s Energy Balance Method to Duffing-Harmonic Oscillators
DEFF Research Database (Denmark)
Momeni, M.; Jamshidi, j.; Barari, Amin
2011-01-01
In this article, He's energy balance method is applied for calculating angular frequencies of nonlinear Duffing oscillators. This method offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. We illustrate that the energy balance is very effective and convenient...... and does not require linearization or small perturbation. Contrary to the conventional methods, in energy balance, only one iteration leads to high accuracy of the solutions. It is predicted that the energy balance method finds wide applications in engineering problems....
On the dynamics of traveling phase-oscillators with positive and negative couplings
International Nuclear Information System (INIS)
Choi, Jungzae; Choi, Mooyoung; Yoon, Byunggook
2014-01-01
We investigate numerically the dynamics of traveling clusters in systems of phase oscillators, some of which possess positive couplings and others negative couplings. The phase distribution, speed of traveling, and average separation between clusters, as well as the order parameters for positive and negative oscillators, are computed as the ratio of the two coupling constants and the fraction of positive oscillators are varied. The dependence of the traveling speed on these parameters is obtained and is observed to fit well with the numerical data of the systems. With the help of this, we describe the conditions for the traveling state to appear in the systems with and without a periodic driving field.
Harmonic incursion at the point of common coupling due to small grid-connected power stations
Directory of Open Access Journals (Sweden)
Majid Mumtaz
2015-12-01
Full Text Available The orthodox electric power distribution systems used to be generally radial and direction of flow of power was often from grid towards consumer. Sometimes, the transmission of power generated from newly set small power stations by using transmission network is not feasible due to the transmission losses, service cost on transmission lines and other related issues. That is why, in many cases, small power stations are connected directly to the local distribution network. These small power stations inject active and reactive power to the existing network, badly disturbing the flow of power hence injecting harmonics in the system at the point of common coupling (PCC. This harmonic injection at PCC due to a direct grid-connection of small power stations to the existing large electric power systems is identified. Also, the impact of harmonic incursion by these small generation units is analysed using a straightforward and an effortless method. This simulation based method uses power system components simplified to basic inductive and capacitive elements and can be very helpful for a fast assessment of harmonic incursion at PCC if extended to the practical large inter-connected electric power systems.
Cross-frequency coupling of brain oscillations in studying motivation and emotion.
Schutter, Dennis J L G; Knyazev, Gennady G
2012-03-01
Research has shown that brain functions are realized by simultaneous oscillations in various frequency bands. In addition to examining oscillations in pre-specified bands, interactions and relations between the different frequency bandwidths is another important aspect that needs to be considered in unraveling the workings of the human brain and its functions. In this review we provide evidence that studying interdependencies between brain oscillations may be a valuable approach to study the electrophysiological processes associated with motivation and emotional states. Studies will be presented showing that amplitude-amplitude coupling between delta-alpha and delta-beta oscillations varies as a function of state anxiety and approach-avoidance-related motivation, and that changes in the association between delta-beta oscillations can be observed following successful psychotherapy. Together these studies suggest that cross-frequency coupling of brain oscillations may contribute to expanding our understanding of the neural processes underlying motivation and emotion.
Energy Technology Data Exchange (ETDEWEB)
Wang, Yang; Song, Hai-Ying; Liu, H.Y.; Liu, Shi-Bing, E-mail: sbliu@bjut.edu.cn
2017-07-12
Highlights: • Proposed a valid mechanism of high harmonic generation by laser grating target interaction: oscillation of equivalent electric dipole (OEED). • Found that there also exist harmonic emission at large emission angle but not just near-surface direction as the former researches had pointed out. • Show the process of the formation and motion of electron bunches at the grating-target surface irradiating with femtosecond laser pulse. - Abstract: We theoretically study high-order harmonic generation (HHG) from relativistically driven overdense plasma targets with rectangularly grating-structured surfaces by femtosecond laser pulses. Our particle-in-cell (PIC) simulations show that, under the conditions of low laser intensity and plasma density, the harmonics emit principally along small angles deviating from the target surface. Further investigation of the surface electron dynamics reveals that the electron bunches are formed by the interaction between the laser field and the target surface, giving rise to the oscillation of equivalent electric-dipole (OEED), which enhances specific harmonic orders. Our work helps understand the mechanism of harmonic emissions from grating targets and the distinction from the planar harmonic scheme.
The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation
Directory of Open Access Journals (Sweden)
Xi Fu
2016-01-01
Full Text Available Let B be the real unit ball in Rn and f∈CN(B. Given a multi-index m=(m1,…,mn of nonnegative integers with |m|=N, we set the quantity supx∈B,y∈E(x,r,x≠y(1-|x|2α(1-|y|2β|∂mf(x-∂mf(y|/|x-y|γ[x,y]1-γ, x≠y, where 0≤γ≤1 and α+β=N+1. In terms of it, we characterize harmonic Bloch and Besov spaces on the real unit ball. This generalizes the main results of Yoneda, 2002, into real harmonic setting.
Finite-size scaling in the system of coupled oscillators with heterogeneity in coupling strength.
Hong, Hyunsuk
2017-07-01
We consider a mean-field model of coupled phase oscillators with random heterogeneity in the coupling strength. The system that we investigate here is a minimal model that contains randomness in diverse values of the coupling strength, and it is found to return to the original Kuramoto model [Y. Kuramoto, Prog. Theor. Phys. Suppl. 79, 223 (1984)10.1143/PTPS.79.223] when the coupling heterogeneity disappears. According to one recent paper [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015)10.1103/PhysRevE.92.022122], when the natural frequency of the oscillator in the system is "deterministically" chosen, with no randomness in it, the system is found to exhibit the finite-size scaling exponent ν[over ¯]=5/4. Also, the critical exponent for the dynamic fluctuation of the order parameter is found to be given by γ=1/4, which is different from the critical exponents for the Kuramoto model with the natural frequencies randomly chosen. Originally, the unusual finite-size scaling behavior of the Kuramoto model was reported by Hong et al. [H. Hong, H. Chaté, H. Park, and L.-H. Tang, Phys. Rev. Lett. 99, 184101 (2007)10.1103/PhysRevLett.99.184101], where the scaling behavior is found to be characterized by the unusual exponent ν[over ¯]=5/2. On the other hand, if the randomness in the natural frequency is removed, it is found that the finite-size scaling behavior is characterized by a different exponent, ν[over ¯]=5/4 [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015)10.1103/PhysRevE.92.022122]. Those findings brought about our curiosity and led us to explore the effects of the randomness on the finite-size scaling behavior. In this paper, we pay particular attention to investigating the finite-size scaling and dynamic fluctuation when the randomness in the coupling strength is considered.
Stability of The Synchronization Manifold in An All-To-All Time LAG- Diffusively Coupled Oscillators
Directory of Open Access Journals (Sweden)
Adu A.M. Wasike
2009-06-01
Full Text Available we consider a lattice system of identical oscillators that are all coupled to one another with a diffusive coupling that has a time lag. We use the natural splitting of the system into synchronized manifold and transversal manifold to estimate the value of the time lag for which the stability of the system follows from that without a time lag. Each oscillator has a unique periodic solution that is attracting.
ELM-free and inter-ELM divertor heat flux broadening induced by edge harmonics oscillation in NSTX
Gan, K. F.; Ahn, J.-W.; Gray, T. K.; Zweben, S. J.; Fredrickson, E. D.; Scotti, F.; Maingi, R.; Park, J.-K.; Canal, G. P.; Soukhanovskii, V. A.; Mclean, A. G.; Wirth, B. D.
2017-12-01
A new n = 1 dominated edge harmonic oscillation (EHO) has been found in NSTX. The new EHO, rotating toroidally in the counter-current direction and the opposite direction of the neutral beam, was observed during certain inter-ELM and ELM-free periods of H-mode operation. This EHO is associated with a significant broadening of the integral heat flux width ({λ\\operatorname{int}} ) by up to 150%, and a decrease in the divertor peak heat flux by >60%. An EHO induced filament was also observed by the gas puff imaging diagnostic. The toroidal rotating filaments could change the edge magnetic topology resulting in toroidal rotating strike point splitting and heat flux broadening. Experimental result of the counter current rotation of strike points splitting is consistent with the counter-current EHO.
Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling.
Ryu, Jung-Wan; Kim, Jong-Ho; Son, Woo-Sik; Hwang, Dong-Uk
2017-08-01
We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.
Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling
Ryu, Jung-Wan; Kim, Jong-Ho; Son, Woo-Sik; Hwang, Dong-Uk
2017-08-01
We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.
He, Yong
2017-06-23
We utilize the surface plasmon field of a metal nanoparticle (MNP) to show strain-mediated coupling in a quantum dot-mechanical resonator hybrid system including a quantum dot (QD) embedded within a conical nanowire (NW) and a MNP in the presence of an external field. Based on the numerical solutions of the master equation, we find that a slow oscillation, originating from the strain-mediated coupling between the QD and the NW, appears in the time evolution of the plasmon field enhancement. The results show that the period (about [Formula: see text]) of the slow oscillation is equal to that of the mechanical resonator of NW, which suggests that the time-resolved measurement of the plasmon field enhancement can be easily achieved based on the current experimental conditions. Its amplitude increases with the increasing strain-mediated coupling strength, and under certain conditions there is a linear relationship between them. The slow oscillation of the plasmon field enhancement provides valuable tools for measurements of the mechanical frequency and the strain-mediated coupling strength.
He, Yong
2017-06-01
We utilize the surface plasmon field of a metal nanoparticle (MNP) to show strain-mediated coupling in a quantum dot-mechanical resonator hybrid system including a quantum dot (QD) embedded within a conical nanowire (NW) and a MNP in the presence of an external field. Based on the numerical solutions of the master equation, we find that a slow oscillation, originating from the strain-mediated coupling between the QD and the NW, appears in the time evolution of the plasmon field enhancement. The results show that the period (about 2 μ s) of the slow oscillation is equal to that of the mechanical resonator of NW, which suggests that the time-resolved measurement of the plasmon field enhancement can be easily achieved based on the current experimental conditions. Its amplitude increases with the increasing strain-mediated coupling strength, and under certain conditions there is a linear relationship between them. The slow oscillation of the plasmon field enhancement provides valuable tools for measurements of the mechanical frequency and the strain-mediated coupling strength.
Border Figure Detection Using a Phase Oscillator Network with Dynamical Coupling
Directory of Open Access Journals (Sweden)
L. H. A. Monteiro
2008-01-01
Full Text Available Oscillator networks have been developed in order to perform specific tasks related to image processing. Here we analytically investigate the existence of synchronism in a pair of phase oscillators that are short-range dynamically coupled. Then, we use these analytical results to design a network able of detecting border of black-and-white figures. Each unit composing this network is a pair of such phase oscillators and is assigned to a pixel in the image. The couplings among the units forming the network are also dynamical. Border detection emerges from the network activity.
On the origin of interdecadal oscillations in a coupled ocean–atmosphere model
Arzel, Olivier; De Verdière, Alain Colin; Huck, Thierry
2007-01-01
Interdecadal oscillations are analysed in a coupled ocean–atmosphere model made of a planetary geostrophic ocean model within an idealized geometry, coupled to a zonally-averaged tropospheric atmosphere model. The interdecadal variability that arises spontaneously in this coupled system is caused by intrinsic ocean dynamics, the coupled air-sea feedbacks being not essential. The spatial pattern of the variability bears some resemblance with observations and results obtained with atmosphere-oc...
Maxfield, Lynn; Palaparthi, Anil; Titze, Ingo
2017-03-01
The traditional source-filter theory of voice production describes a linear relationship between the source (glottal flow pulse) and the filter (vocal tract). Such a linear relationship does not allow for nor explain how changes in the filter may impact the stability and regularity of the source. The objective of this experiment was to examine what effect unpredictable changes to vocal tract dimensions could have on fo stability and individual harmonic intensities in situations in which low frequency harmonics cross formants in a fundamental frequency glide. To determine these effects, eight human subjects (five male, three female) were recorded producing fo glides while their vocal tracts were artificially lengthened by a section of vinyl tubing inserted into the mouth. It was hypothesized that if the source and filter operated as a purely linear system, harmonic intensities would increase and decrease at nearly the same rates as they passed through a formant bandwidth, resulting in a relatively symmetric peak on an intensity-time contour. Additionally, fo stability should not be predictably perturbed by formant/harmonic crossings in a linear system. Acoustic analysis of these recordings, however, revealed that harmonic intensity peaks were asymmetric in 76% of cases, and that 85% of fo instabilities aligned with a crossing of one of the first four harmonics with the first three formants. These results provide further evidence that nonlinear dynamics in the source-filter relationship can impact fo stability as well as harmonic intensities as harmonics cross through formant bandwidths. Copyright © 2017 The Voice Foundation. Published by Elsevier Inc. All rights reserved.
Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh-Nagumo system
Desroches, M.; Krauskopf, B.; Osinga, H.M.
2008-01-01
We investigate the organization of mixed-mode oscillations in the self-coupled FitzHugh-Nagumo system. These types of oscillations can be explained as a combination of relaxation oscillations and small-amplitude oscillations controlled by canard solutions that are associated with a folded
Trade-off between phase-noise and signal quadrature in unilaterally coupled oscillators
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2005-01-01
We present a comprehensive nonlinear analysis of coupled oscillators and examine the trade-off between phase-noise of the oscillator and the quadrature precision. We show that asymmetry gives rise to amplitude and phase imbalance which are proportional to the inverse and inverse square, respectiv...... strengths. The additional contribution of the internal noise sources in the coupling circuit together with the AM-PM noise contribution explains why the 3dB noise reduction is rarely seen in measurements of this particular circuit.......We present a comprehensive nonlinear analysis of coupled oscillators and examine the trade-off between phase-noise of the oscillator and the quadrature precision. We show that asymmetry gives rise to amplitude and phase imbalance which are proportional to the inverse and inverse square......, respectively, of the relative coupling strength. It is shown that the level of AM-PM is determined by the nonlinearity of the coupling transconductance. The 3dB noise reduction in close-to-carrier phase-noise in quadrature oscillators due to mutual coupling is lost to the extra AM-PM noise for large coupling...
International Nuclear Information System (INIS)
Castellanos-Gomez, A
2013-01-01
A simple strobe setup with the potential to study higher-order eigenmodes and multifrequency oscillations in micromechanical resonators is described. It requires standard equipment, commonly found in many laboratories, and it can thus be employed for public demonstrations of mechanical resonances. Moreover, the work presented here can be used by undergraduate students and/or teachers to prepare practical work in laboratory courses at physics or engineering universities. The dynamics of a micromachined cantilever is analysed as an example. In fact, using our stroboscopic setup, the first and second flexural eigenmodes, as well as a multifrequency oscillation composed by a superposition of both modes, have been successfully filmed with a conventional optical microscope equipped with a digital camera. (paper)
Synchronization of coupled stochastic oscillators: The effect of ...
Indian Academy of Sciences (India)
master–slave' coupling scenario, where the two subsystems share a com- mon drive and consequently the dynamics of the remaining variables becomes correlated. Both the above forms of couplings are easily realized in practice. In the case of.
Directory of Open Access Journals (Sweden)
Yongfeng Wu
2014-04-01
Full Text Available By taking two-coupled duffing oscillator system as the research object, the study found under the synergistic effect of weak periodic signal and noise, the two-coupled duffing oscillator system has typical stochastic resonance and even could achieve better output of stochastic resonance than single duffing oscillator. Based on this phenomenon, this paper proposes a new method to detect the weak periodic signal through the stochastic resonance of two-coupled duffing oscillator. The experimental study indicates that we could achieve excellent detection effect by using the method we mentioned in this paper at low SNR (signal-to-noise ratios, especially, it has excellent filter effect for filtering and shaping of weak square signals and has potential values in the application of digital communications.
The variational spiked oscillator
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Ullah, N.
1992-08-01
A variational analysis of the spiked harmonic oscillator Hamiltonian -d 2 / d x 2 + x 2 + δ/ x 5/2 , δ > 0, is reported in this work. A trial function satisfying Dirichlet boundary conditions is suggested. The results are excellent for a large range of values of the coupling parameter. (author)
Emergent organization of oscillator clusters in coupled self ...
Indian Academy of Sciences (India)
We observe that the sizes of these oscillator clusters have a power-law distribution. Moreover, we find that the transient dynamics gives rise to a 1/ power spectrum. All these characteristics indicate self-organization and emergent scaling behavior in this system. We also interpret the power-law characteristics of the ...
2012-01-01
Background Feedback loops, both positive and negative are embedded in the Mitogen Activated Protein Kinase (MAPK) cascade. In the three layer MAPK cascade, both feedback loops originate from the terminal layer and their sites of action are either of the two upstream layers. Recent studies have shown that the cascade uses coupled positive and negative feedback loops in generating oscillations. Two plausible designs of coupled positive and negative feedback loops can be elucidated from the literature; in one design the positive feedback precedes the negative feedback in the direction of signal flow and vice-versa in another. But it remains unexplored how the two designs contribute towards triggering oscillations in MAPK cascade. Thus it is also not known how amplitude, frequency, robustness or nature (analogous/digital) of the oscillations would be shaped by these two designs. Results We built two models of MAPK cascade that exhibited oscillations as function of two underlying designs of coupled positive and negative feedback loops. Frequency, amplitude and nature (digital/analogous) of oscillations were found to be differentially determined by each design. It was observed that the positive feedback emerging from an oscillating MAPK cascade and functional in an external signal processing module can trigger oscillations in the target module, provided that the target module satisfy certain parametric requirements. The augmentation of the two models was done to incorporate the nuclear-cytoplasmic shuttling of cascade components followed by induction of a nuclear phosphatase. It revealed that the fate of oscillations in the MAPK cascade is governed by the feedback designs. Oscillations were unaffected due to nuclear compartmentalization owing to one design but were completely abolished in the other case. Conclusion The MAPK cascade can utilize two distinct designs of coupled positive and negative feedback loops to trigger oscillations. The amplitude, frequency and
Decay of Rabi Oscillations by Dipolar-Coupled Dynamical Spin Environments
Dobrovitski, V.V.; Feiguin, A.E.; Hanson, R.; Awschalom, D.D.
2009-01-01
We study the Rabi oscillations decay of a spin decohered by a spin bath whose internal dynamics is caused by dipolar coupling between the bath spins. The form and rate of decay as a function of the intrabath coupling is obtained analytically, and confirmed numerically. The complex form of decay
Correlations in a chain of three oscillators with nearest neighbour coupling
Idrus, B.; Konstadopoulou, A.; Spiller, T.; Vourdas, A.
2010-04-01
A chain of three oscillators A, B, C with nearest neighbour coupling, is considered. It is shown that the correlations between A, C (which are not coupled directly) can be stronger than the correlations between A, B. Also in some cases various witnesses of entanglement show that A, C are entangled but they cannot lead to any conclusion about A, B.
Intermittency in delay-coupled FitzHugh–Nagumo oscillators and ...
Indian Academy of Sciences (India)
out intermittency occurs. We introduce a definition of phase such that loss of phase synchrony can be used as a precursor to the intermittent behavior. This sys- tem is comprised of two identical FitzHugh–Nagumo. (FHN) oscillators which are coupled to each other using multiple time-delay diffusive couplings. Such a form of.
Li, Bing-Wei; Cao, Xiao-Zhi; Fu, Chenbo
2017-12-01
Many biological and chemical systems could be modeled by a population of oscillators coupled indirectly via a dynamical environment. Essentially, the environment by which the individual element communicates with each other is heterogeneous. Nevertheless, most of previous works considered the homogeneous case only. Here we investigated the dynamical behaviors in a population of spatially distributed chaotic oscillators immersed in a heterogeneous environment. Various dynamical synchronization states (such as oscillation death, phase synchronization, and complete synchronized oscillation) as well as their transitions were explored. In particular, we uncovered a non-traditional quorum sensing transition: increasing the population density leaded to a transition from oscillation death to synchronized oscillation at first, but further increasing the density resulted in degeneration from complete synchronization to phase synchronization or even from phase synchronization to desynchronization. The underlying mechanism of this finding was attributed to the dual roles played by the population density. What's more, by treating the environment as another component of the oscillator, the full system was then effectively equivalent to a locally coupled system. This fact allowed us to utilize the master stability functions approach to predict the occurrence of complete synchronization oscillation, which agreed with that from the direct numerical integration of the system. The potential candidates for the experimental realization of our model were also discussed.
DEFF Research Database (Denmark)
Granados, Albert
2017-01-01
Energy harvesting systems based on oscillators aim to capture energy from mechanical oscillations and convert it into electrical energy. Widely extended are those based on piezoelectric materials, whose dynamics are Hamiltonian submitted to different sources of dissipation: damping and coupling...... in Hamiltonian systems and hence could be very useful in energy harvesting applications. This article is a first step towards this goal. We consider two piezoelectric beams submitted to a small forcing and coupled through an electric circuit. By considering the coupling, damping and forcing as perturbations, we...
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Energy Technology Data Exchange (ETDEWEB)
Lepri, Stefano, E-mail: stefano.lepri@isc.cnr.it [Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Pikovsky, Arkady [Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str 24/25, Potsdam (Germany); Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
Beam splitter coupled CdSe optical parametric oscillator
International Nuclear Information System (INIS)
Levinos, N.J.; Arnold, G.P.
1980-01-01
An optical parametric oscillator is disclosed in which the resonant radiation is separated from the pump and output radiation so that it can be manipulated without interfering with them. Thus, for example, very narrow band output may readily be achieved by passing the resonant radiation through a line narrowing device which does not in itself interfere with either the pump radiation or the output radiation
Emergent organization of oscillator clusters in coupled self ...
Indian Academy of Sciences (India)
Here we introduce a model of parametrically coupled logistic maps on a one- dimensional lattice. In this model, each element has its internal self-regulatory dynamics, whereby at fixed intervals of time the nonlinearity parameter at each site is adjusted by feedback from its past evolution. Additionally, the maps are coupled.
International Nuclear Information System (INIS)
Bragt, D.D.B. van.
1995-10-01
A theoretical model for out-of-phase power oscillations in BWRs is proposed. This model describes the dynamic behavior of the neutronic and thermohydraulic subsystems during out-of-phase oscillations, and the coupling of these subsystems via the fuel temperature dynamics and void- and Doppler feedback effects. The zero-power neutron kinetics of the out-of-phase flux density mode is derived by expanding the (time- and space-dependent) neutron flux density in the static solutions of the neutron transport equation. This procedure yields the modal point-kinetic equations for the (first-harmonic) out-of-phase mode. The fuel temperature dynamics is described by a lumped parameter first-order process, characterized by a typical fuel time constant. Using the quasistatic approach, the basic equations of the channel thermohydraulics are derived from the conservation laws of mass and energy and the momentum equation. The momentum equation is coupled with the appropriate boundary condition (constant core pressure drop) for out-of phase oscillations. This procedure yields a set of nonlinear equations describing the dynamic behavior of the boiling boundary, void fraction and mass flux density in the cooling channel. A frequency-domain parametric study confirms that if the out-of-phase mode has a more negative subcriticality, reactor stability increases. On the other hand, a more negative void reactivity coefficient has a destabilizing effect. Besides these two parameters, the fuel time constant was found to be an important parameter determining stability. Where possible, the linearized equations describing the channel thermohydraulics were compare with exact solutions of the governing partial-differential channel equations. This comparison shows that in the frequency range of interest, discrepancies between the proposed quasi-static model and more complicated exact solutions are to be expected. (orig.)
DEFF Research Database (Denmark)
Thoke, Henrik Seir; Tobiesen, Asger; Brewer, Jonathan R.
2015-01-01
conditions, ii) water dipolar relaxation oscillates with glycolysis and in phase with ATP concentration, iii) this phenomenon is scale-invariant from the subcellular to the ensemble of synchronized cells and, iv) the periodicity of both glycolytic oscillations and dipolar relaxation are equally affected by D......We detected very strong coupling between the oscillating concentration of ATP and the dynamics of intracellular water during glycolysis in Saccharomyces cerevisiae. Our results indicate that: i) dipolar relaxation of intracellular water is heterogeneous within the cell and different from dilute......2O in a dose-dependent manner. These results offer a new insight into the coupling of an emergent intensive physicochemical property of the cell, i.e. cell-wide water dipolar relaxation, and a central metabolite (ATP) produced by a robustly oscillating metabolic process....
Uwate, Y; Nishio, Y; Stoop, R
2009-01-01
We explore the synchronization and switching behavior of a system of two identical van der Pol oscillators coupled by a stochastically timevarying resistor. Triggered by the time-varying resistor, the system of oscillators switches between synchronized and anti-synchronized behavior. We find that the preference of the synchronized/antisynchronized state is determined by the ratio of the probabilities of the two resistor states. The length of the phases of maintained resistor states, however, ...
Chimera states in an ensemble of linearly locally coupled bistable oscillators
Shchapin, D. S.; Dmitrichev, A. S.; Nekorkin, V. I.
2017-11-01
Chimera states in a system with linear local connections have been studied. The system is a ring ensemble of analog bistable self-excited oscillators with a resistive coupling. It has been shown that the existence of chimera states is not due to the nonidentity of oscillators and noise, which is always present in real experiments, but is due to the nonlinear dynamics of the system on invariant tori with various dimensions.
Zhu, Yenan; Hsieh, Yee-Hsee; Dhingra, Rishi R.; Dick, Thomas E.; Jacono, Frank J.; Galán, Roberto F.
2013-02-01
Interactions between oscillators can be investigated with standard tools of time series analysis. However, these methods are insensitive to the directionality of the coupling, i.e., the asymmetry of the interactions. An elegant alternative was proposed by Rosenblum and collaborators [M. G. Rosenblum, L. Cimponeriu, A. Bezerianos, A. Patzak, and R. Mrowka, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.65.041909 65, 041909 (2002); M. G. Rosenblum and A. S. Pikovsky, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.64.045202 64, 045202 (2001)] which consists in fitting the empirical phases to a generic model of two weakly coupled phase oscillators. This allows one to obtain the interaction functions defining the coupling and its directionality. A limitation of this approach is that a solution always exists in the least-squares sense, even in the absence of coupling. To preclude spurious results, we propose a three-step protocol: (1) Determine if a statistical dependency exists in the data by evaluating the mutual information of the phases; (2) if so, compute the interaction functions of the oscillators; and (3) validate the empirical oscillator model by comparing the joint probability of the phases obtained from simulating the model with that of the empirical phases. We apply this protocol to a model of two coupled Stuart-Landau oscillators and show that it reliably detects genuine coupling. We also apply this protocol to investigate cardiorespiratory coupling in anesthetized rats. We observe reciprocal coupling between respiration and heartbeat and that the influence of respiration on the heartbeat is generally much stronger than vice versa. In addition, we find that the vagus nerve mediates coupling in both directions.
Understanding Synchrony and Stochasticity in Coupled Neuronal and Genetic Oscillators
2015-09-01
mechanism to form a sun compass . In a collaboration...found a mechanism that explains how day length is encoded within the neuronal network of suprachiasmatic...clock but also a seasonal clock. This neural network of ∼10,000 circadian oscillators encodes
Yashin, Victor V.; Levitan, Steven P.; Balazs, Anna C.
2015-06-01
Lightweight, deformable materials that can sense and respond to human touch and motion can be the basis of future wearable computers, where the material itself will be capable of performing computations. To facilitate the creation of “materials that compute”, we draw from two emerging modalities for computation: chemical computing, which relies on reaction-diffusion mechanisms to perform operations, and oscillatory computing, which performs pattern recognition through synchronization of coupled oscillators. Chemical computing systems, however, suffer from the fact that the reacting species are coupled only locally; the coupling is limited by diffusion as the chemical waves propagate throughout the system. Additionally, oscillatory computing systems have not utilized a potentially wearable material. To address both these limitations, we develop the first model for coupling self-oscillating polymer gels to a piezoelectric (PZ) micro-electro-mechanical system (MEMS). The resulting transduction between chemo-mechanical and electrical energy creates signals that can be propagated quickly over long distances and thus, permits remote, non-diffusively coupled oscillators to communicate and synchronize. Moreover, the oscillators can be organized into arbitrary topologies because the electrical connections lift the limitations of diffusive coupling. Using our model, we predict the synchronization behavior that can be used for computational tasks, ultimately enabling “materials that compute”.
Farner, Snorre; Vergez, Christophe; Kergomard, Jean; Lizée, Aude
2006-03-01
The harmonic balance method (HBM) was originally developed for finding periodic solutions of electronical and mechanical systems under a periodic force, but has been adapted to self-sustained musical instruments. Unlike time-domain methods, this frequency-domain method does not capture transients and so is not adapted for sound synthesis. However, its independence of time makes it very useful for studying any periodic solution, whether stable or unstable, without care of particular initial conditions in time. A computer program for solving general problems involving nonlinearly coupled exciter and resonator, HARMBAL, has been developed based on the HBM. The method as well as convergence improvements and continuation facilities are thoroughly presented and discussed in the present paper. Applications of the method are demonstrated, especially on problems with severe difficulties of convergence: the Helmholtz motion (square signals) of single-reed instruments when no losses are taken into account, the reed being modeled as a simple spring.
Lin, Lifeng; Wang, Huiqi; Huang, Xipei; Wen, Yongxian
2018-03-01
For a fractional linear oscillator subjected to both parametric excitation of trichotomous noise and external excitation of bias-signal-modulated trichotomous noise, the generalized stochastic resonance (GSR) phenomena are investigated in this paper in case the noises are cross-correlative. First, the generalized Shapiro-Loginov formula and generalized fractional Shapiro-Loginov formula are derived. Then, by using the generalized (fractional) Shapiro-Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is obtained. The numerical results show that the evolution of the output amplitude amplification is nonmonotonic with the frequency of periodic signal, the noise parameters, and the fractional order. The GSR phenomena, including single-peak GSR, double-peak GSR and triple-peak GSR, are observed in this system. In addition, the interplay of the multiplicative trichotomous noise, bias-signal-modulated trichotomous noise and memory can induce and diversify the stochastic multi-resonance (SMR) phenomena, and the two kinds of trichotomous noises play opposite roles on the GSR.
Entanglement of higher-derivative oscillators in holographic systems
Dimov, Hristo; Mladenov, Stefan; Rashkov, Radoslav C.; Vetsov, Tsvetan
2017-05-01
We study the quantum entanglement of coupled Pais-Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of N coupled Pais-Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. We also make remarks on the appearance of instabilities of higher-derivative oscillators in the context of AdS/CFT correspondence. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.
Entanglement of higher-derivative oscillators in holographic systems
Energy Technology Data Exchange (ETDEWEB)
Dimov, Hristo, E-mail: h_dimov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Mladenov, Stefan, E-mail: smladenov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Rashkov, Radoslav C., E-mail: rash@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstr. 8–10, 1040 Vienna (Austria); Vetsov, Tsvetan, E-mail: vetsov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria)
2017-05-15
We study the quantum entanglement of coupled Pais–Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of N coupled Pais–Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. We also make remarks on the appearance of instabilities of higher-derivative oscillators in the context of AdS/CFT correspondence. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.
Energy funneling in a bent chain of Morse oscillators with long-range coupling
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Christiansen, Peter Leth; Bang, Ole
2004-01-01
A bent chain of coupled Morse oscillators with long-range dispersive interaction is considered. Moving localized excitations may be trapped in the bending region. Thus chain geometry acts like an impurity. An energy funneling effect is observed in the case of random initial conditions.......A bent chain of coupled Morse oscillators with long-range dispersive interaction is considered. Moving localized excitations may be trapped in the bending region. Thus chain geometry acts like an impurity. An energy funneling effect is observed in the case of random initial conditions....
Harmonic suppressed coupled stepped-impedance resonator based dual-band tunable bandpass filter
Directory of Open Access Journals (Sweden)
Amarjit Kumar
2017-10-01
Full Text Available In this paper, a tunable dual-band bandpass filter (BPF based on a varactor-loaded coupled stepped-impedance resonator is presented. Transmission matrices techniques are employed to explain the working concept of proposed tunable BPF. For validating the proposed concept, a hardware prototype is fabricated and characterized. As per the measured results, when the center frequency of the lower band is tuning from 2.15 to 2.40 GHz, the upper band is fixed at 4.5 GHz; and when the center frequency of the upper band is tuning from 4.5 to 4.75 GHz, the lower passband almost remains constant at 2.25 GHz. Proposed tunable filter is capable of working at higher passband frequencies. Spurious harmonic suppression up to 15 GHz is demonstrated. Center frequency of dual-passband is tunable using only two dc control voltages.
Dynamics of nonlinear oscillators with time-varying conjugate coupling
Indian Academy of Sciences (India)
1Department of Physics, Central University of Rajasthan, Ajmer 305 817, India. 2The Institute of Mathematical Science, CIT Campus, .... Now, based on the choice of k1 and k2, we consider two cases, (1) C1: both k1 and k2 ... 2.5, coupled systems show multiple transitions between synchronized and unsynchronized states.
Emergent organization of oscillator clusters in coupled self ...
Indian Academy of Sciences (India)
dimensional lattice. In this model, each element has its internal self-regulatory dynamics, whereby at fixed intervals of time the nonlinearity parameter at each site is adjusted by feedback from its past evolution. Additionally, the maps are coupled ...
Synchronization and basin bifurcations in mutually coupled oscillators
Indian Academy of Sciences (India)
its motivation from its role in understanding the basic features of coupled nonlinear systems and in view of potential applications in communication systems, time ..... [21] U E Vincent, A N Njah, O Akinlade and A R T Solarin, Physica A360, 186 (2006). [22] U E Vincent, A N Njah, O Akinlade and A R T Solarin, Chaos 14, 1018 ...
Energy Technology Data Exchange (ETDEWEB)
Noguera, Norman, E-mail: norman.noguera@ucr.ac.cr [Departamento de Matemática, Universidad de Costa Rica. S.O (Costa Rica); Rózga, Krzysztof, E-mail: krzysztof.rozga@upr.edu [Department of Mathematical Sciences, University of Puerto Rico, Mayagüez, Puerto Rico 00681-5000 (United States)
2015-07-15
In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case of a slightly more general potential than the one for harmonic oscillator.
International Nuclear Information System (INIS)
Menouar, Salah; Maamache, Mustapha; Choi, Jeong Ryeol
2010-01-01
The dynamics of the time-dependent coupled oscillator model for the motion of a charged particle subjected to a time-dependent external magnetic field is investigated. We use the canonical transformation approach for the classical treatment of the system, whereas the unitary transformation approach is used in managing the system in the framework of quantum mechanics. For both approaches, the original system is transformed into a much more simple system that is the sum of two independent harmonic oscillators with time-dependent frequencies. We therefore easily identify the wavefunctions in the transformed system with the help of an invariant operator of the system. The full wavefunctions in the original system are derived from the inverse unitary transformation of the wavefunctions associated with the transformed system.
International Nuclear Information System (INIS)
Menouar, Salah; Maamache, Mustapha; Choi, Jeong Ryeol
2010-01-01
The quantum states of time-dependent coupled oscillator model for charged particles subjected to variable magnetic field are investigated using the invariant operator methods. To do this, we have taken advantage of an alternative method, so-called unitary transformation approach, available in the framework of quantum mechanics, as well as a generalized canonical transformation method in the classical regime. The transformed quantum Hamiltonian is obtained using suitable unitary operators and is represented in terms of two independent harmonic oscillators which have the same frequencies as that of the classically transformed one. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators. One can easily take a complete description of how the charged particle behaves under the given Hamiltonian by taking advantage of these analytical wave functions.
A Nanotechnology-Ready Computing Scheme based on a Weakly Coupled Oscillator Network
Vodenicarevic, Damir; Locatelli, Nicolas; Abreu Araujo, Flavio; Grollier, Julie; Querlioz, Damien
2017-03-01
With conventional transistor technologies reaching their limits, alternative computing schemes based on novel technologies are currently gaining considerable interest. Notably, promising computing approaches have proposed to leverage the complex dynamics emerging in networks of coupled oscillators based on nanotechnologies. The physical implementation of such architectures remains a true challenge, however, as most proposed ideas are not robust to nanotechnology devices’ non-idealities. In this work, we propose and investigate the implementation of an oscillator-based architecture, which can be used to carry out pattern recognition tasks, and which is tailored to the specificities of nanotechnologies. This scheme relies on a weak coupling between oscillators, and does not require a fine tuning of the coupling values. After evaluating its reliability under the severe constraints associated to nanotechnologies, we explore the scalability of such an architecture, suggesting its potential to realize pattern recognition tasks using limited resources. We show that it is robust to issues like noise, variability and oscillator non-linearity. Defining network optimization design rules, we show that nano-oscillator networks could be used for efficient cognitive processing.
Energy Technology Data Exchange (ETDEWEB)
Chae, Jongchul [Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 08826 (Korea, Republic of); Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand)
2017-08-01
The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D{sub 2} and H α lines.
Phase models and clustering in networks of oscillators with delayed coupling
Campbell, Sue Ann; Wang, Zhen
2018-01-01
We consider a general model for a network of oscillators with time delayed coupling where the coupling matrix is circulant. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay enters as a phase shift. We use the phase model to determine model independent existence and stability results for symmetric cluster solutions. Our results extend previous work to systems with time delay and a more general coupling matrix. We show that the presence of the time delay can lead to the coexistence of multiple stable clustering solutions. We apply our analytical results to a network of Morris Lecar neurons and compare these results with numerical continuation and simulation studies.
Permanent Rabi oscillations in coupled exciton-photon systems with PT-symmetry.
Chestnov, Igor Yu; Demirchyan, Sevak S; Alodjants, Alexander P; Rubo, Yuri G; Kavokin, Alexey V
2016-01-21
We propose a physical mechanism which enables permanent Rabi oscillations in driven-dissipative condensates of exciton-polaritons in semiconductor microcavities subjected to external magnetic fields. The method is based on stimulated scattering of excitons from the incoherent reservoir. We demonstrate that permanent non-decaying oscillations may appear due to the parity-time symmetry of the coupled exciton-photon system realized in a specific regime of pumping to the exciton state and depletion of the reservoir. At non-zero exciton-photon detuning, robust permanent Rabi oscillations occur with unequal amplitudes of exciton and photon components. Our predictions pave way to realization of integrated circuits based on exciton-polariton Rabi oscillators.
Analysis and observation of moving domain fronts in a ring of coupled electronic self-oscillators
English, L. Q.; Zampetaki, A.; Kevrekidis, P. G.; Skowronski, K.; Fritz, C. B.; Abdoulkary, Saidou
2017-10-01
In this work, we consider a ring of coupled electronic (Wien-bridge) oscillators from a perspective combining modeling, simulation, and experimental observation. Following up on earlier work characterizing the pairwise interaction of Wien-bridge oscillators by Kuramoto-Sakaguchi phase dynamics, we develop a lattice model for a chain thereof, featuring an exponentially decaying spatial kernel. We find that for certain values of the Sakaguchi parameter α, states of traveling phase-domain fronts involving the coexistence of two clearly separated regions of distinct dynamical behavior, can establish themselves in the ring lattice. Experiments and simulations show that stationary coexistence domains of synchronization only manifest themselves with the introduction of a local impurity; here an incoherent cluster of oscillators can arise reminiscent of the chimera states in a range of systems with homogeneous oscillators and suitable nonlocal interactions between them.
Coupled oscillators in identification of nonlinear damping of a real parametric pendulum
Olejnik, Paweł; Awrejcewicz, Jan
2018-01-01
A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.
DEFF Research Database (Denmark)
Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth
2015-01-01
change compared to the conventional operation. In this paper, a Harmonic State Space modeling method, which is based on the Linear Time varying theory, is used to analyze different operating points of the parallel connected converters. The analyzed results show that the HSS modeling approach explicitly...... be difficult in terms of complex multi-parallel connected systems, especially in the case of renewable energy, where possibilities for intermittent operation due to the weather conditions exist. Hence, it can bring many different operating points to the power converter, and the impedance characteristics can...
Strong Coupling of a Quantum Oscillator to a Flux Qubit at Its Symmetry Point
Fedorov, A.; Feofanov, A.K.; Macha, P.; Forn-Díaz, P.; Harmans, C.J.P.M.; Mooij, J.E.
2010-01-01
A flux qubit biased at its symmetry point shows a minimum in the energy splitting (the gap), providing protection against flux noise. We have fabricated a qubit of which the gap can be tuned fast and have coupled this qubit strongly to an LC oscillator. We show full spectroscopy of the
Teaching the Physics of a String-Coupled Pendulum Oscillator: Not Just for Seniors Anymore
Cho, Young-Ki
2012-01-01
Coupled oscillators are an example of resonant energy exchange that is an interesting topic for many students in various majors, such as physics, chemistry, and electrical and mechanical engineering. However, this subject matter is considered too advanced for freshmen and sophomores, usually because of the level of mathematics involved.…
Statistical properties of multiphoton time-dependent three-boson coupled oscillators
Czech Academy of Sciences Publication Activity Database
Abdalla, M. S.; Peřina, Jan; Křepelka, Jaromír
2006-01-01
Roč. 23, č. 6 (2006), s. 1146-1160 ISSN 0740-3224 R&D Projects: GA MŠk(CZ) OC P11.003 Institutional research plan: CEZ:AV0Z10100522 Keywords : quantum statistic * coupled oscillators * multiphoton Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.002, year: 2006
Intermittency in delay-coupled FitzHugh–Nagumo oscillators and ...
Indian Academy of Sciences (India)
We study the dynamical properties of in-out intermittency in a system of two identical FitzHugh–. Nagumo oscillators coupled by multiple .... In this section we briefly describe the general qualitative properties of the system described by ... case where the synchronization manifold is transver- sally unstable is quite distinct from ...
Kuwahara, Jun; Miyata, Hajime; Konno, Hidetoshi
2017-09-01
Recently, complex dynamics of globally coupled oscillators have been attracting many researcher's attentions. In spite of their numerous studies, their features of nonlinear oscillator systems with global and local couplings in two-dimension (2D) are not understood fully. The paper focuses on 2D states of coherent, clustered and chaotic oscillation especially under the effect of negative global coupling (NGC) in 2D Alief-Panfilov model. It is found that the tuning NGC can cause various new coupling-parameter dependency on the features of oscillations. Then quantitative characterization of various states of oscillations (so called spiral wave turbulence) is examined by using the pragmatic information (PI) which have been utilized in analyzing multimode laser, solar activity and neuronal systems. It is demonstrated that the dynamics of the PI for various oscillations can be characterized successfully by the Hyper-Gamma stochastic process.
Energy Technology Data Exchange (ETDEWEB)
Nicolaides, Cleanthes A; Constantoudis, Vasilios [Physics Department, National Technical University, Athens (Greece)], E-mail: caan@eie.gr, E-mail: vconst@imel.demokritos.gr
2009-11-15
In Planck's model of the harmonic oscillator (HO) a century ago, both the energy and the phase space were quantized according to {epsilon}{sub n} = nh{nu}, n = 0, 1, 2..., and {integral}{integral}dp{sub 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 quantum mechanical energy spectrum of the HO,
Landau damping via the harmonic sextupole
Directory of Open Access Journals (Sweden)
Lidia Tosi
2003-05-01
Full Text Available Multibunch instabilities of a storage ring electron beam occur due to coherent particle oscillations generated through a bunch to bunch coupling via the impedances, deteriorating the beam quality. One cure for multibunch instabilities is Landau damping, i.e., introducing a spread in the oscillation frequencies among the particles of the individual bunches in order to destroy the coherence of the coupled multibunch oscillation. Measurements at ELETTRA have shown that the harmonic sextupole provides Landau damping capable of suppressing transverse multibunch instabilities. The damping is induced by the nonlinear tune spread with amplitude among the electrons within the individual bunches.
Mathematical structure of Rabi oscillations in the strong coupling regime
International Nuclear Information System (INIS)
Fujii, Kazuyuki
2003-01-01
In this paper, we generalize the Jaynes-Cummings Hamiltonian by making use of some operators based on Lie algebras su(1, 1) and su(2), and study a mathematical structure of Rabi floppings of these models in the strong coupling regime. We show that Rabi frequencies are given by matrix elements of generalized coherent operators (Fujii K 2002 Preprint quant-ph/0202081) under the rotating-wave approximation. In the first half, we make a general review of coherent operators and generalized coherent ones based on Lie algebras su(1, 1) and su(2). In the latter half, we carry out a detailed examination of Frasca (Frasca M 2001 Preprint quant-ph/0111134) and generalize his method, and moreover present some related problems. We also apply our results to the construction of controlled unitary gates in quantum computation. Lastly, we make a brief comment on application to holonomic quantum computation
Soliton Properties of Coupled g-Mode Oscillations
Wolff, Charles L.
2007-01-01
Several features typical of solitons are also exhibited by stellar g-modes when coupled into "sets" that have unique rotation rates relative to the star. Enhanced nuclear burning due to weakly nonlinear amplitudes in a small portion of the stellar core holds each set together against dispersion. As the nonlinear regions of each set rotate past each other they have a complex interaction (shown in a video), yet emerge from this with their original wave forms. Other similarities with solitons we mentioned, including the physical origin of a phase shift. in longitude due to the interaction. These similarities suggest that a fully nonlinear derivation of g-mode sets may be able to show that their large amplitude regions approach true solitons.
Chimera states in coupled Kuramoto oscillators with inertia
Energy Technology Data Exchange (ETDEWEB)
Olmi, Simona, E-mail: simona.olmi@fi.isc.cnr.it [CNR - Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); INFN Sez. Firenze, via Sansone, 1 - I-50019 Sesto Fiorentino (Italy)
2015-12-15
The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.
Plexcitons: The Role of Oscillator Strengths and Spectral Widths in Determining Strong Coupling
Energy Technology Data Exchange (ETDEWEB)
Thomas, Reshmi [School; Thomas, Anoop [School; Pullanchery, Saranya [School; Joseph, Linta [School; Somasundaran, Sanoop Mambully [School; Swathi, Rotti Srinivasamurthy [School; Gray, Stephen K. [Center; Thomas, K. George [School
2018-01-05
Strong coupling interactions between plasmon and exciton-based excitations have been proposed to be useful in the design of optoelectronic systems. However, the role of various optical parameters dictating the plasmon-exciton (plexciton) interactions is less understood. Herein, we propose an inequality for achieving strong coupling between plasmons and excitons through appropriate variation of their oscillator strengths and spectral widths. These aspects are found to be consistent with experiments on two sets of free-standing plexcitonic systems obtained by (i) linking fluorescein isothiocyanate on Ag nanoparticles of varying sizes through silane coupling and (ii) electrostatic binding of cyanine dyes on polystyrenesulfonate-coated Au nanorods of varying aspect ratios. Being covalently linked on Ag nanoparticles, fluorescein isothiocyanate remains in monomeric state, and its high oscillator strength and narrow spectral width enable us to approach the strong coupling limit. In contrast, in the presence of polystyrenesulfonate, monomeric forms of cyanine dyes exist in equilibrium with their aggregates: Coupling is not observed for monomers and H-aggregates whose optical parameters are unfavorable. The large aggregation number, narrow spectral width, and extremely high oscillator strength of J-aggregates of cyanines permit effective delocalization of excitons along the linear assembly of chromophores, which in turn leads to efficient coupling with the plasmons. Further, the results obtained from experiments and theoretical models are jointly employed to describe the plexcitonic states, estimate the coupling strengths, and rationalize the dispersion curves. The experimental results and the theoretical analysis presented here portray a way forward to the rational design of plexcitonic systems attaining the strong coupling limits.
Coupled opto electronic oscillator with a passively mode locked extended cavity diode laser
Energy Technology Data Exchange (ETDEWEB)
Lee, Jeongmin; Jang, Gwang Hoon; Yoon, Duseong; Song, Minsoo; Yoon, Tai Hyun [Korea Univ., Seoul (Korea, Republic of)
2008-11-15
An opto electronic oscillator(OEO)has very unique properties compared to the conventional quartz based microwave oscillators in that its oscillation frequency is determined by the beat note frequency of a phase coherent optical frequency comb generated as a side bands to an optical single mode carrier by using an electro optic modulator (EOM)or a direct current modulation of a semiconductor laser. Recently, a different type of OEO called a COEO has been demonstrated, where the optical carrier in the OEO system has been replaced by a mode locked laser so that an EOM or a direct current modulation are no longer necessary, but has potentially a much lower phase noise thanks to the high Q value of the optical frequency comb due to the mode locking mechanism. In this paper, we propose and demonstrate a COEO based on a passively mode locked ECDL at 852nm in which the fourth harmonic of the repetition frequency of the ECDL matched exactly the ground state hyperfine splitting frequency of the Cs atoms.
Coupled opto electronic oscillator with a passively mode locked extended cavity diode laser
International Nuclear Information System (INIS)
Lee, Jeongmin; Jang, Gwang Hoon; Yoon, Duseong; Song, Minsoo; Yoon, Tai Hyun
2008-01-01
An opto electronic oscillator(OEO)has very unique properties compared to the conventional quartz based microwave oscillators in that its oscillation frequency is determined by the beat note frequency of a phase coherent optical frequency comb generated as a side bands to an optical single mode carrier by using an electro optic modulator (EOM)or a direct current modulation of a semiconductor laser. Recently, a different type of OEO called a COEO has been demonstrated, where the optical carrier in the OEO system has been replaced by a mode locked laser so that an EOM or a direct current modulation are no longer necessary, but has potentially a much lower phase noise thanks to the high Q value of the optical frequency comb due to the mode locking mechanism. In this paper, we propose and demonstrate a COEO based on a passively mode locked ECDL at 852nm in which the fourth harmonic of the repetition frequency of the ECDL matched exactly the ground state hyperfine splitting frequency of the Cs atoms
A weakly coupled semiconductor superlattice as a harmonic hypersonic-electrical transducer
International Nuclear Information System (INIS)
Poyser, C L; Akimov, A V; Campion, R P; Kent, A J; Balanov, A G
2015-01-01
We study experimentally and theoretically the effects of high-frequency strain pulse trains on the charge transport in a weakly coupled semiconductor superlattice. In a frequency range of the order of 100 GHz such excitation may be considered as single harmonic hypersonic excitation. While travelling along the axis of the SL, the hypersonic acoustic wavepacket affects the electron tunnelling, and thus governs the electrical current through the device. We reveal how the change of current depends on the parameters of the hypersonic excitation and on the bias applied to the superlattice. We have found that the changes in the transport properties of the superlattices caused by the acoustic excitation can be largely explained using the current–voltage relation of the unperturbed system. Our experimental measurements show multiple peaks in the dependence of the transferred charge on the repetition rate of the strain pulses in the train. We demonstrate that these resonances can be understood in terms of the spectrum of the applied acoustic perturbation after taking into account the multiple reflections in the metal film serving as a generator of hypersonic excitation. Our findings suggest an application of the semiconductor superlattice as a hypersonic-electrical transducer, which can be used in various microwave devices. (paper)
Antiresonant ring output-coupled continuous-wave optical parametric oscillator.
Devi, Kavita; Kumar, S Chaitanya; Esteban-Martin, A; Ebrahim-Zadeh, M
2012-08-13
We demonstrate the successful deployment of an antiresonant ring (ARR) interferometer for the attainment of optimum output coupling in a continuous-wave (cw) optical parametric oscillator (OPO). The cw OPO, configured as a singly-resonant oscillator (SRO), is based on a 50-mm-long MgO:PPLN crystal and pumped by cw Ytterbium-fiber laser at 1064 nm, with the ARR interferometer integrated into one arm of the standing-wave cavity. By fine adjustment of the ARR transmission, a continuously variable signal output coupling from 0.8% to 7.3% has been achieved, providing optimum output coupling for signal and optimum power extraction for the idler, at different input pumping levels. The experimental results are compared with theoretical calculations for conventional output-coupled cw SRO, and the study shows that by reducing the insertion loss of the ARR elements, the performance of the ARR-coupled cw SRO can be further enhanced. We also show that the use of the ARR does not lead to any degradation in the cw SRO output beam quality. The proof-of-principle demonstration confirms the effectiveness of the technique for continuous, in situ, and fine control of output coupling in cw OPOs to achieve maximum output power at any arbitrary pumping level above threshold.
Emergent organization of oscillator clusters in coupled self-regulatory chaotic maps
Ando, Hiroyasu; Sinha, Sudeshna; Aihara, Kazuyuki
2008-06-01
Here we introduce a model of parametrically coupled chaotic maps on a one-dimensional lattice. In this model, each element has its internal self-regulatory dynamics, whereby at fixed intervals of time the nonlinearity parameter at each site is adjusted by feedback from its past evolution. Additionally, the maps are coupled sequentially and unidirectionally, to their nearest neighbor, through the difference of their parametric variations. Interestingly we find that this model asymptotically yields clusters of superstable oscillators with different periods. We observe that the sizes of these oscillator clusters have a power-law distribution. Moreover, we find that the transient dynamics gives rise to a 1/f power spectrum. All these characteristics indicate self-organization and emergent scaling behavior in this system. We also interpret the power-law characteristics of the proposed system from an ecological point of view.
Teodorescu, Razvan
2009-10-01
Systems of oscillators coupled non-linearly (stochastically or not) are ubiquitous in nature and can explain many complex phenomena: coupled Josephson junction arrays, cardiac pacemaker cells, swarms or flocks of insects and birds, etc. They are know to have a non-trivial phase diagram, which includes chaotic, partially synchronized, and fully synchronized phases. A traditional model for this class of problems is the Kuramoto system of oscillators, which has been studied extensively for the last three decades. The model is a canonical example for non-equilibrium, dynamical phase transitions, so little understood in physics. From a stochastic analysis point of view, the transition is described by the large deviations principle, which offers little information on the scaling behavior near the critical point. I will discuss a special case of the model, which allows a rigorous analysis of the critical properties of the model, and reveals a new, anomalous scaling behavior in the vicinity of the critical point.
Robust synchronization of coupled circadian and cell cycle oscillators in single mammalian cells
Bieler, Jonathan; Cannavo, Rosamaria; Gustafson, Kyle; Gobet, Cedric; Gatfield, David; Naef, Felix
2014-01-01
Circadian cycles and cell cycles are two fundamental periodic processes with a period in the range of 1 day. Consequently, coupling between such cycles can lead to synchronization. Here, we estimated the mutual interactions between the two oscillators by time-lapse imaging of single mammalian NIH3T3 fibroblasts during several days. The analysis of thousands of circadian cycles in dividing cells clearly indicated that both oscillators tick in a 1:1 mode-locked state, with cell divisions occurring tightly 5 h before the peak in circadian Rev-Erbα-YFP reporter expression. In principle, such synchrony may be caused by either unidirectional or bidirectional coupling. While gating of cell division by the circadian cycle has been most studied, our data combined with stochastic modeling unambiguously show that the reverse coupling is predominant in NIH3T3 cells. Moreover, temperature, genetic, and pharmacological perturbations showed that the two interacting cellular oscillators adopt a synchronized state that is highly robust over a wide range of parameters. These findings have implications for circadian function in proliferative tissues, including epidermis, immune cells, and cancer. PMID:25028488
Ghoshal, Gourab; Muñuzuri, Alberto P.; Pérez-Mercader, Juan
2016-01-01
Oscillatory phenomena are ubiquitous in Nature. The ability of a large population of coupled oscillators to synchronize constitutes an important mechanism to express information and establish communication among members. To understand such phenomena, models and experimental realizations of globally coupled oscillators have proven to be invaluable in settings as varied as chemical, biological and physical systems. A variety of rich dynamical behavior has been uncovered, although usually in the context of a single state of synchronization or lack thereof. Through the experimental and numerical study of a large population of discrete chemical oscillators, here we report on the unexpected discovery of a new phenomenon revealing the existence of dynamically distinct synchronized states reflecting different degrees of communication. Specifically, we discover a novel large-amplitude super-synchronized state separated from the conventionally reported synchronized and quiescent states through an unusual sharp jump transition when sampling the strong coupling limit. Our results assume significance for further elucidating globally coherent phenomena, such as in neuropathologies, bacterial cell colonies, social systems and semiconductor lasers.
Coupled Oscillator Model of the Business Cycle withFluctuating Goods Markets
Ikeda, Y.; Aoyama, H.; Fujiwara, Y.; Iyetomi, H.; Ogimoto, K.; Souma, W.; Yoshikawa, H.
The sectoral synchronization observed for the Japanese business cycle in the Indices of Industrial Production data is an example of synchronization. The stability of this synchronization under a shock, e.g., fluctuation of supply or demand, is a matter of interest in physics and economics. We consider an economic system made up of industry sectors and goods markets in order to analyze the sectoral synchronization observed for the Japanese business cycle. A coupled oscillator model that exhibits synchronization is developed based on the Kuramoto model with inertia by adding goods markets, and analytic solutions of the stationary state and the coupling strength are obtained. We simulate the effects on synchronization of a sectoral shock for systems with different price elasticities and the coupling strengths. Synchronization is reproduced as an equilibrium solution in a nearest neighbor graph. Analysis of the order parameters shows that the synchronization is stable for a finite elasticity, whereas the synchronization is broken and the oscillators behave like a giant oscillator with a certain frequency additional to the common frequency for zero elasticity.
Coherent oscillation in a linear quantum system coupled to a thermal bath
International Nuclear Information System (INIS)
Bell, N.F.; Volkas, R.R.; Sawyer, R.F.
2000-01-01
We consider the time development of the density matrix for a system coupled to a thermal bath, in models that go beyond the standard two-level systems through addition of an energy excitation degree of freedom and through the possibility of the replacement of the spin algebra by a more complex algebra. We find conditions under which increasing the coupling to the bath above a certain level decreases the rate of entropy production, and in which the limiting behavior is a dissipationless sinusoidal oscillation that could be interpreted as the synchronization of many modes of the uncoupled system
Stace, A. J.
1995-01-01
A simple Monte Carlo model is presented for simulating the motion of a quantum harmonic oscillator trapped in a rare gas cluster or matrix which is treated as a classical heat bath. Preliminary results are present for the system I 2·Ar 11 where it would appear that the bond length of the molecule is sensitive to the temperature of the cluster. It is anticipated that the model may be used to study how vibrating molecules are accommodated by rare gas clusters and solids.
International Nuclear Information System (INIS)
Luo Jian; Lu Di; Du Chaoling; Liu Youwen; Shi Daning; Lai Wei; Guo Chunlei; Gong Shangqing
2012-01-01
We theoretically investigate how to control the Rabi oscillation of excitons of the coupling quantum dots by manipulating static electric fields. Our results show that, for a single-photon process, when direct excitons change into indirect excitons with a bias applied on the sample, the Rabi oscillation rarely alters. However, for the two-photon process, a pronounced enhancement of Rabi oscillation is observed, which can be utilized as the logic gate in quantum information. (paper)
Effects of a neutrino-dark energy coupling on oscillations of high-energy neutrinos
Klop, Niki; Ando, Shin'ichiro
2018-03-01
If dark energy (DE) is a dynamical field rather than a cosmological constant, an interaction between DE and the neutrino sector could exist, modifying the neutrino oscillation phenomenology and causing C P and apparent Lorentz violating effects. The terms in the Hamiltonian for flavor propagation induced by the DE-neutrino coupling do not depend on the neutrino energy, while the ordinary components decrease as Δ m2/Eν. Therefore, the DE-induced effects are absent at lower neutrino energies, but become significant at higher energies, allowing to be searched for by neutrino observatories. We explore the impact of the DE-neutrino coupling on the oscillation probability and the flavor transition in the three-flavor framework, and investigate the C P -violating and apparent Lorentz violating effects. We find that DE-induced effects become observable for Eνmeff˜10-20 GeV2, where meff is the effective mass parameter in the DE-induced oscillation probability, and C P is violated over a wide energy range. We also show that current and future experiments have the sensitivity to detect anomalous effects induced by a DE-neutrino coupling and probe the new mixing parameters. The DE-induced effects on neutrino oscillation can be distinguished from other new physics possibilities with similar effects, through the detection of the directional dependence of the interaction, which is specific to this interaction with DE. However, current experiments will not yet be able to measure the small changes of ˜0.03 % in the flavor composition due to this directional effect.
Quantum-coupled radial-breathing oscillations in double-walled carbon nanotubes.
Liu, Kaihui; Hong, Xiaoping; Wu, Muhong; Xiao, Fajun; Wang, Wenlong; Bai, Xuedong; Ager, Joel W; Aloni, Shaul; Zettl, Alex; Wang, Enge; Wang, Feng
2013-01-01
Van der Waals-coupled materials, ranging from multilayers of graphene and MoS(2) to superlattices of nanoparticles, exhibit rich emerging behaviour owing to quantum coupling between individual nanoscale constituents. Double-walled carbon nanotubes provide a model system for studying such quantum coupling mediated by van der Waals interactions, because each constituent single-walled nanotube can have distinctly different physical structures and electronic properties. Here we systematically investigate quantum-coupled radial-breathing mode oscillations in chirality-defined double-walled nanotubes by combining simultaneous structural, electronic and vibrational characterizations on the same individual nanotubes. We show that these radial-breathing oscillations are collective modes characterized by concerted inner- and outer-wall motions, and determine quantitatively the tube-dependent van der Waals potential governing their vibration frequencies. We also observe strong quantum interference between Raman scattering from the inner- and outer-wall excitation pathways, the relative phase of which reveals chirality-dependent excited-state potential energy surface displacement in different nanotubes.
Directory of Open Access Journals (Sweden)
M. Schulz
2007-01-01
Full Text Available Using a 3-dimensional climate model of intermediate complexity we show that the overturning circulation of the Atlantic Ocean can vary at multicentennial-to-millennial timescales for modern boundary conditions. A continuous freshwater perturbation in the Labrador Sea pushes the overturning circulation of the Atlantic Ocean into a bi-stable regime, characterized by phases of active and inactive deep-water formation in the Labrador Sea. In contrast, deep-water formation in the Nordic Seas is active during all phases of the oscillations. The actual timing of the transitions between the two circulation states occurs randomly. The oscillations constitute a 3-dimensional phenomenon and have to be distinguished from low-frequency oscillations seen previously in 2-dimensional models of the ocean. A conceptual model provides further insight into the essential dynamics underlying the oscillations of the large-scale ocean circulation. The model experiments indicate that the coupled climate system can exhibit unforced climate variability at multicentennial-to-millennial timescales that may be of relevance for Holocene climate variations.
Characteristic entanglement timescales of a qubit coupled to a quartic oscillator
Energy Technology Data Exchange (ETDEWEB)
Bosco de Magalhães, A.R., E-mail: magalhaes@des.cefetmg.br [Departamento de Física e Matemática, Centro Federal de Educação Tecnológica de Minas Gerais, Av. Amazonas 7675, Nova Gameleira, Belo Horizonte, MG, CEP 30510-000 (Brazil); Oliveira, Adélcio C., E-mail: adelcio@ufsj.edu.br [Departamento de Física e Matemática, Universidade Federal de São João Del Rei, Campus Alto Paraopeba, CP 131, Ouro Branco, MG, CEP 36420-000 (Brazil)
2016-02-05
The structure of the entanglement dynamics of a qubit coupled to a quartic oscillator is investigated through the calculation of timescales of visibility and predictability, and their relation with the concurrence dynamics. This model can describe a Rydberg atom in a Kerr medium. A method based on the analysis of the different interference processes of the terms that compose the physical quantities studied is proposed, and timescales related to decay, revivals and fast oscillations under the decay envelope are computed. The method showed to be effective for the vast majority of cases studied, even when the timescales vary several orders of magnitude. The conditions for expansions in power series to give correct decay timescales are analyzed. - Highlights: • A method for the calculation of different timescales is proposed. • It focuses on the interference of the terms that form the quantity of interest. • Entanglement timescales of a quartic oscillator coupled to a qubit are investigated. • This system can be used to model a Rydberg atom in a Kerr medium.
Coupled slow and fast surface dynamics in an electrocatalytic oscillator: Model and simulations
International Nuclear Information System (INIS)
Nascimento, Melke A.; Nagao, Raphael; Eiswirth, Markus; Varela, Hamilton
2014-01-01
The co-existence of disparate time scales is pervasive in many systems. In particular for surface reactions, it has been shown that the long-term evolution of the core oscillator is decisively influenced by slow surface changes, such as progressing deactivation. Here we present an in-depth numerical investigation of the coupled slow and fast surface dynamics in an electrocatalytic oscillator. The model consists of four nonlinear coupled ordinary differential equations, investigated over a wide parameter range. Besides the conventional bifurcation analysis, the system was studied by means of high-resolution period and Lyapunov diagrams. It was observed that the bifurcation diagram changes considerably as the irreversible surface poisoning evolves, and the oscillatory region shrinks. The qualitative dynamics changes accordingly and the chaotic oscillations are dramatically suppressed. Nevertheless, periodic cascades are preserved in a confined region of the resistance vs. voltage diagram. Numerical results are compared to experiments published earlier and the latter reinterpreted. Finally, the comprehensive description of the time-evolution in the period and Lyapunov diagrams suggests further experimental studies correlating the evolution of the system's dynamics with changes of the catalyst structure
A synthetic multi-cellular network of coupled self-sustained oscillators.
Directory of Open Access Journals (Sweden)
Miguel Fernández-Niño
Full Text Available Engineering artificial networks from modular components is a major challenge in synthetic biology. In the past years, single units, such as switches and oscillators, were successfully constructed and implemented. The effective integration of these parts into functional artificial self-regulated networks is currently on the verge of breakthrough. Here, we describe the design of a modular higher-order synthetic genetic network assembled from two independent self-sustained synthetic units: repressilators coupled via a modified quorum-sensing circuit. The isolated communication circuit and the network of coupled oscillators were analysed in mathematical modelling and experimental approaches. We monitored clustering of cells in groups of various sizes. Within each cluster of cells, cells oscillate synchronously, whereas the theoretical modelling predicts complete synchronization of the whole cellular population to be obtained approximately after 30 days. Our data suggest that self-regulated synchronization in biological systems can occur through an intermediate, long term clustering phase. The proposed artificial multicellular network provides a system framework for exploring how a given network generates a specific behaviour.
Coupled slow and fast surface dynamics in an electrocatalytic oscillator: Model and simulations
Nascimento, Melke A.; Nagao, Raphael; Eiswirth, Markus; Varela, Hamilton
2014-12-01
The co-existence of disparate time scales is pervasive in many systems. In particular for surface reactions, it has been shown that the long-term evolution of the core oscillator is decisively influenced by slow surface changes, such as progressing deactivation. Here we present an in-depth numerical investigation of the coupled slow and fast surface dynamics in an electrocatalytic oscillator. The model consists of four nonlinear coupled ordinary differential equations, investigated over a wide parameter range. Besides the conventional bifurcation analysis, the system was studied by means of high-resolution period and Lyapunov diagrams. It was observed that the bifurcation diagram changes considerably as the irreversible surface poisoning evolves, and the oscillatory region shrinks. The qualitative dynamics changes accordingly and the chaotic oscillations are dramatically suppressed. Nevertheless, periodic cascades are preserved in a confined region of the resistance vs. voltage diagram. Numerical results are compared to experiments published earlier and the latter reinterpreted. Finally, the comprehensive description of the time-evolution in the period and Lyapunov diagrams suggests further experimental studies correlating the evolution of the system's dynamics with changes of the catalyst structure.
Parihar, Abhinav; Shukla, Nikhil; Datta, Suman; Raychowdhury, Arijit
2015-02-01
Computing with networks of synchronous oscillators has attracted wide-spread attention as novel materials and device topologies have enabled realization of compact, scalable and low-power coupled oscillatory systems. Of particular interest are compact and low-power relaxation oscillators that have been recently demonstrated using MIT (metal-insulator-transition) devices using properties of correlated oxides. Further the computational capability of pairwise coupled relaxation oscillators has also been shown to outperform traditional Boolean digital logic circuits. This paper presents an analysis of the dynamics and synchronization of a system of two such identical coupled relaxation oscillators implemented with MIT devices. We focus on two implementations of the oscillator: (a) a D-D configuration where complementary MIT devices (D) are connected in series to provide oscillations and (b) a D-R configuration where it is composed of a resistor (R) in series with a voltage-triggered state changing MIT device (D). The MIT device acts like a hysteresis resistor with different resistances in the two different states. The synchronization dynamics of such a system has been analyzed with purely charge based coupling using a resistive (RC) and a capacitive (CC) element in parallel. It is shown that in a D-D configuration symmetric, identical and capacitively coupled relaxation oscillator system synchronizes to an anti-phase locking state, whereas when coupled resistively the system locks in phase. Further, we demonstrate that for certain range of values of RC and CC, a bistable system is possible which can have potential applications in associative computing. In D-R configuration, we demonstrate the existence of rich dynamics including non-monotonic flows and complex phase relationship governed by the ratios of the coupling impedance. Finally, the developed theoretical formulations have been shown to explain experimentally measured waveforms of such pairwise coupled
Coupled dipole oscillations of a mass-imbalanced Bose-Fermi superfluid mixture
Wu, Yu-Ping; Yao, Xing-Can; Liu, Xiang-Pei; Wang, Xiao-Qiong; Wang, Yu-Xuan; Chen, Hao-Ze; Deng, Youjin; Chen, Yu-Ao; Pan, Jian-Wei
2018-01-01
Recent experimental realizations of superfluid mixtures of Bose and Fermi quantum gases provide a unique platform for exploring diverse superfluid phenomena. We study dipole oscillations of a double superfluid in a cigar-shaped optical dipole trap, consisting of 41K and 6Li atoms with a large mass imbalance, where the oscillations of the bosonic and fermionic components are coupled via the Bose-Fermi interaction. In our high-precision measurements, the frequencies of both components are observed to be shifted from the single-species ones, and exhibit unusual features. The frequency shifts of the 41K component are upward (downward) in the radial (axial) direction, whereas the 6Li component has downshifted frequencies in both directions. Most strikingly, as the interaction strength is varied, the frequency shifts display a resonantlike behavior in both directions, for both species, and around a similar location at the BCS side of the fermionic superfluid. These rich phenomena challenge the theoretical understanding of superfluids.
Visualization of two-photon Rabi oscillations in evanescently coupled optical waveguides
Energy Technology Data Exchange (ETDEWEB)
Ornigotti, M; Valle, G Della; Fernandez, T Toney; Laporta, P; Longhi, S [Dipartimento di Fisica and Istituto di Fotonica e Nanotecnologie del CNR, Politecnico di Milano, Piazza L. da Vinci 32, I-20133 Milano (Italy); Coppa, A; Foglietti, V [Istituto di Fotonica e Nanotecnologie del CNR, sezione di Roma, Via Cineto Romano 42, 00156 Roma (Italy)], E-mail: longhi@fisi.polimi.it
2008-04-28
An optical analogue of two-photon Rabi oscillations, occurring in a three-level atomic or molecular system coherently driven by two detuned laser fields, is theoretically proposed and experimentally demonstrated using three evanescently coupled optical waveguides realized on an active glass substrate. The optical analogue stems from the formal analogy between spatial propagation of light waves in the three-waveguide structure and the coherent temporal evolution of populations in a three-level atomic medium driven by two laser fields under two-photon resonance. In our optical experiment, two-photon Rabi oscillations are thus visualized as a slow spatial oscillatory exchange of light power between the two outer waveguides of the structure with a small excitation of the central waveguide.
Visualization of two-photon Rabi oscillations in evanescently coupled optical waveguides
International Nuclear Information System (INIS)
Ornigotti, M; Valle, G Della; Fernandez, T Toney; Laporta, P; Longhi, S; Coppa, A; Foglietti, V
2008-01-01
An optical analogue of two-photon Rabi oscillations, occurring in a three-level atomic or molecular system coherently driven by two detuned laser fields, is theoretically proposed and experimentally demonstrated using three evanescently coupled optical waveguides realized on an active glass substrate. The optical analogue stems from the formal analogy between spatial propagation of light waves in the three-waveguide structure and the coherent temporal evolution of populations in a three-level atomic medium driven by two laser fields under two-photon resonance. In our optical experiment, two-photon Rabi oscillations are thus visualized as a slow spatial oscillatory exchange of light power between the two outer waveguides of the structure with a small excitation of the central waveguide
The Southern Oscillation in a coupled GCM: Implications for climate sensitivity and climate change
International Nuclear Information System (INIS)
Meehl, G.A.
1991-01-01
Results are presented from a global coupled ocean-atmosphere general circulation climate model developed at the National Center for Atmospheric Research. The atmospheric part of the coupled model is a global spectral (R15, 4.5 degree latitude by 7.5 degree longitude, 9 layers in the vertical) general circulation model. The ocean is coarse-grid (5 degree latitude by 5 degree longitude, 4 layers in the vertical) global general circulation model. The coupled model includes a simple thermodynamic sea-ice model. Due mainly to inherent limitations in the ocean model, the coupled model simulates sea surface temperatures that are too low in the tropics and too high in the extratropics in the mean. In spite of these limitations, the coupled model simulates active interannual variability of the global climate system involving signals in the tropical Pacific that resemble, in some respects, the observed Southern Oscillation. These signals in the tropics are associated with teleconnections to the extratropics of both hemispheres. The implications of this model-simulated interannual variability of the coupled system relating to climate sensitivity and climate change due to an increase of atmospheric carbon dioxide are discussed. 25 refs.; 9 figs
The Southern Oscillation in a coupled GCM: Implications for climate sensitivity and climate change
International Nuclear Information System (INIS)
Meehl, G.A.
1990-01-01
Results are presented from a global coupled ocean-atmosphere general circulation climate model developed at the National Center for Atmospheric Research. The atmospheric part of the coupled model is a global spectral (R15, 4.5 degree latitude by 7.5 degree longitude, 9 layers in the vertical) general circulation model. The ocean is coarse-grid (5 degree latitude by 5 degree longitude, 4 layers in the vertical) global general circulation model. The coupled model includes a simple thermodynamic sea-ice model. Due mainly to inherent limitations in the ocean model, the coupled model simulates sea surface temperatures that are too low in the tropics and too high in the extratropics in the mean. In spite of these limitations, the coupled model simulates active interannual variability of the global climate system involving signals in the tropical Pacific that resemble, in some respects, the observed Southern Oscillation. These signals in the tropics are associated with teleconnections to the extratropics of both hemispheres. The implications of this model-simulated interannual variability of the coupled system relating to climate sensitivity and climate change due to an increase of atmospheric carbon dioxide are discussed
Rigatos, Gerasimos
2014-12-01
A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of two coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie derivatives. For such a model it becomes possible to design a state feedback controller that assures the synchronization of the membrane's voltage variations for the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments.
Park, Jihoon; Mori, Hiroki; Okuyama, Yuji; Asada, Minoru
2017-01-01
Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the "information networks" different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.
Directory of Open Access Journals (Sweden)
Jihoon Park
Full Text Available Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random with a musculoskeletal model (i.e., a snake-like robot as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the "information networks" different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1 the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2 two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.
International Nuclear Information System (INIS)
Xu Xue-Xiang; Hu Li-Yun; Guo Qin; Fan Hong-Yi
2013-01-01
Following the spirit of thermo field dynamics initiated by Takahashi and Umezawa, we employ the technique of integration within an ordered product of operators to derive the thermal vacuum state (TVS) for the Hamiltonian H of the two-coupled-oscillator model. The ensemble averages of the system are derived conveniently by using the TVS. In addition, the entropy for this system is discussed based on the relation between the generalized Hellmann—Feynman theorem and the entroy variation in the context of the TVS. (general)
Robust autoassociative memory with coupled networks of Kuramoto-type oscillators
Heger, Daniel; Krischer, Katharina
2016-08-01
Uncertain recognition success, unfavorable scaling of connection complexity, or dependence on complex external input impair the usefulness of current oscillatory neural networks for pattern recognition or restrict technical realizations to small networks. We propose a network architecture of coupled oscillators for pattern recognition which shows none of the mentioned flaws. Furthermore we illustrate the recognition process with simulation results and analyze the dynamics analytically: Possible output patterns are isolated attractors of the system. Additionally, simple criteria for recognition success are derived from a lower bound on the basins of attraction.
Dynamics of a model of two delay-coupled relaxation oscillators
Ruelas, R. E.; Rand, R. H.
2010-08-01
This paper investigates the dynamics of a new model of two coupled relaxation oscillators. The model replaces the usual DDE (differential-delay equation) formulation with a discrete-time approach with jumps. Existence, bifurcation and stability of in-phase periodic motions is studied. Simple periodic motions, which involve exactly two jumps per period, are found to have large plateaus in parameter space. These plateaus are separated by regions of complicated dynamics, reminiscent of the Devil's Staircase. Stability of motions in the in-phase manifold are contrasted with stability of motions in the full phase space.
Linearly coupled oscillations in fully degenerate pair and warm pair-ion astrophysical plasmas
Khan, S. A.; Ilyas, M.; Wazir, Z.; Ehsan, Zahida
2014-08-01
In this paper we study the coexisting low frequency oscillations in strongly degenerate, magnetized, (electron-positron) pair and warm pair-ion plasma. The dispersion relations are obtained for both the cases in macroscopic quantum hydrodynamics approximation. In pair-ion case, the dispersion equation shows coupling of electrostatic and (shear) electromagnetic modes under certain circumstances with important role of ion temperature. Domain of existence of such waves and their relevance to dense degenerate astrophysical plasmas is pointed out. Results are analyzed numerically for typical systems with variation of ion concentration and ion temperature.
Choe, Chol-Ung; Kim, Ryong-Son; Ri, Ji-Song
2017-09-01
We consider a ring of phase oscillators with nonlocal coupling strength and heterogeneous phase lags. We analyze the effects of heterogeneity in the phase lags on the existence and stability of a variety of steady states. A nonlocal coupling with heterogeneous phase lags that allows the system to be solved analytically is suggested and the stability of solutions along the Ott-Antonsen invariant manifold is explored. We present a complete bifurcation diagram for stationary patterns including the uniform drift and modulated drift states as well as chimera state, which reveals that the stable modulated drift state and a continuum of metastable drift states could occur due to the heterogeneity of the phase lags. We verify our theoretical results using the direct numerical simulations of the model system.
Learning-enhanced coupling between ripple oscillations in association cortices and hippocampus.
Khodagholy, Dion; Gelinas, Jennifer N; Buzsáki, György
2017-10-20
Consolidation of declarative memories requires hippocampal-neocortical communication. Although experimental evidence supports the role of sharp-wave ripples in transferring hippocampal information to the neocortex, the exact cortical destinations and the physiological mechanisms of such transfer are not known. We used a conducting polymer-based conformable microelectrode array (NeuroGrid) to record local field potentials and neural spiking across the dorsal cortical surface of the rat brain, combined with silicon probe recordings in the hippocampus, to identify candidate physiological patterns. Parietal, midline, and prefrontal, but not primary cortical areas, displayed localized ripple (100 to 150 hertz) oscillations during sleep, concurrent with hippocampal ripples. Coupling between hippocampal and neocortical ripples was strengthened during sleep following learning. These findings suggest that ripple-ripple coupling supports hippocampal-association cortical transfer of memory traces. Copyright © 2017 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.
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.
El-Nashar, Hassan F.
2017-06-01
We consider a system of three nonidentical coupled phase oscillators in a ring topology. We explore the conditions that must be satisfied in order to obtain the phases at the transition to a synchrony state. These conditions lead to the correct mathematical expressions of phases that aid to find a simple analytic formula for critical coupling when the oscillators transit to a synchronization state having a common frequency value. The finding of a simple expression for the critical coupling allows us to perform a linear stability analysis at the transition to the synchronization stage. The obtained analytic forms of the eigenvalues show that the three coupled phase oscillators with periodic boundary conditions transit to a synchrony state when a saddle-node bifurcation occurs.
International Nuclear Information System (INIS)
Kretzschmar, Martin
1999-01-01
When a Penning trap is operated with an additional quadrupole driving field with a frequency that equals a suitable combination (sum or difference) of the frequencies of the fundamental modes of motion (modified cyclotron, magnetron and axial frequency), then a periodic conversion of the participating modes into each other is observed, strongly resembling the Rabi oscillations in a 2-level atom driven by a laser field tuned to the transition frequency. This investigation attempts to understand on a fundamental level how and why the motion of a classical particle in a macroscopic apparatus can be truely analogous to the oscillations of states of quantum mechanical 2-level systems (2-level atom or magnetic resonance). Ion motion in a Penning trap with an additional quadrupole driving field is described in a quantum mechanical frame work. The Heisenberg equations of motion for the creation and annihilation operators of the interacting oscillators have been explicitly solved, the time development operator of the Schroedinger picture has been determined. The driving field provides for two types of intermode interaction: Type I preserves the total number of excitation quanta present in the two interacting modes, the system oscillates between the modes with a frequency corresponding to the Rabi frequency in two-level systems. Type II preserves the difference of the numbers of excitation quanta present in the two interacting modes, it causes the ion motion to become unbounded. The two types of interaction are associated in a natural way with a SU(2) and a SU(1,1) Lie algebra. The three generators of these algebras form a vector operator that we denote as the Bloch vector operator. The Hilbert space decomposes in a natural way into invariant subspaces, finite dimensional in the case of type I interaction (SU(2)-algebra) and infinite dimensional in the case of type II interaction (SU(1,1)-algebra). The physics of the 2-level atom in the laser field can be described in the 2
Tunneling conductance oscillations in spin-orbit coupled metal-insulator-superconductor junctions
Kapri, Priyadarshini; Basu, Saurabh
2018-01-01
The tunneling conductance for a device consisting of a metal-insulator-superconductor (MIS) junction is studied in presence of Rashba spin-orbit coupling (RSOC) via an extended Blonder-Tinkham-Klapwijk formalism. We find that the tunneling conductance as a function of an effective barrier potential that defines the insulating layer and lies intermediate to the metallic and superconducting electrodes, displays an oscillatory behavior. The tunneling conductance shows high sensitivity to the RSOC for certain ranges of this potential, while it is insensitive to the RSOC for others. Additionally, when the period of oscillations is an odd multiple of a certain value of the effective potential, the conductance spectrum as a function of the biasing energy demonstrates a contrasting trend with RSOC, compared to when it is not an odd multiple. The explanations for the observation can be found in terms of a competition between the normal and Andreev reflections. Similar oscillatory behavior of the conductance spectrum is also seen for other superconducting pairing symmetries, thereby emphasizing that the insulating layer plays a decisive role in the conductance oscillations of a MIS junction. For a tunable Rashba coupling, the current flowing through the junction can be controlled with precision.
Moore, Keegan J.; Bunyan, Jonathan; Tawfick, Sameh; Gendelman, Oleg V.; Li, Shuangbao; Leamy, Michael; Vakakis, Alexander F.
2018-01-01
In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales—a linear large-scale oscillator coupled to a small scale by a nonlinear spring—and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.
International Nuclear Information System (INIS)
Suarez Antola, R.
2008-11-01
The cores of nuclear reactors, including its structural parts and cooling fluids, are complex mechanical systems able to vibrate in a set of normal modes and frequencies, if suitable perturbed. The cyclic variations in the strain state of the core materials may produce changes in density. Changes in density modify the reactivity. Changes in reactivity modify thermal power. Modifications in thermal power produce variations in temperature fields. Variations in temperature produce variations in strain due to thermal-elastic effects. If the variation of the temperature field is fast enough and if the Doppler Effect and other stabilizing prompt effects in the fuel are weak enough, a fast oscillatory instability could be produced, coupled with mechanical vibrations of small amplitude. A recently constructed, simple mathematical model of nuclear reactor kinetics, that improves the one due to A.S. Thompson, is reviewed. It was constructed in order to study, in a first approximation, the stability of the reactor: a nonlinear nuclear-thermal oscillator (that corresponds to reactor point kinetics with thermal-elastic feedback and with frozen delayed neutron effects) is coupled nonlinearly with a linear mechanical-thermal oscillator (that corresponds to the first normal mode of mechanical vibrations excited by thermo-elastic effects). This mathematical model is studied here from the standpoint of mechanical vibrations. It is shown how, under certain conditions, a suitable mechanical perturbation could elicit fast and growing oscillatory instabilities in the reactor power. Applying the asymptotic method due to Krylov, Bogoliubov and Mitropolsky, analytical formulae that may be used in the calculation of the time varying amplitude and phase of the mechanical oscillations are given, as functions of the mechanical, thermal and nuclear parameters of the reactor. The consequences for the mechanical integrity of the reactor are assessed. Some conditions, mainly, but not exclusively
Energy Technology Data Exchange (ETDEWEB)
dos Santos Coelho, Leandro [Pontifical Catholic University of Parana, PUCPR Industrial and Systems Engineering Graduate Program, PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil); Mariani, Viviana Cocco [Pontifical Catholic University of Parana, PUCPR Mechanical Engineering Graduate Program, PPGEM, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)
2008-11-15
Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature. (author)
Energy Technology Data Exchange (ETDEWEB)
Santos Coelho, Leandro dos [Pontifical Catholic University of Parana, PUCPR Industrial and Systems Engineering Graduate Program, PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)], E-mail: leandro.coelho@pucpr.br; Mariani, Viviana Cocco [Pontifical Catholic University of Parana, PUCPR Mechanical Engineering Graduate Program, PPGEM, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)], E-mail: viviana.mariani@pucpr.br
2008-11-15
Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature.
Lozano Soldevilla, D.; Huurne, N.P. ter; Oostenveld, R.
2016-01-01
Neuronal oscillations support cognitive processing. Modern views suggest that neuronal oscillations do not only reflect coordinated activity in spatially distributed networks, but also that there is interaction between the oscillations at different frequencies. For example, invasive recordings in
Aihara, Ikkyu; Tsumoto, Kunichika
2008-01-01
Synchronization has been observed in various systems, including living beings. In a previous study, we reported a new phenomenon with antisynchronization in calling behavior of two interacting Japanese tree frogs. In this paper, we theoretically analyse nonlinear dynamics in a system of three coupled oscillators, which models three interacting frogs, where the oscillators of each pair have the property of antisynchronization; in particular, we perform bifurcation analysis and Lyapunov function analysis.
Dynamics of 'quantumness' measures in the decohering harmonic ...
Indian Academy of Sciences (India)
We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of ...
Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure
Jiang, Hai-Bo; Zhang, Li-Ping; Yu, Jian-Jiang
2015-02-01
Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics. This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure. By constructing a proper Poincaré map of the non-smooth system, an analytical expression of the Jacobian matrix of Poincaré map is given. Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge-Kutta method. When the period is fixed and the coupling strength changes, the system undergoes stable, periodic, quasi-periodic, and hyper-chaotic solutions, etc. Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations. Project supported by the National Natural Science Foundation of China (Grant Nos. 11402224, 11202180, 61273106, and 11171290), the Qing Lan Project of the Jiangsu Higher Educational Institutions of China, and the Jiangsu Overseas Research and Training Program for University Prominent Young and Middle-aged Teachers and Presidents.
Directory of Open Access Journals (Sweden)
Andrew A Rouse
2016-06-01
Full Text Available Human capacity for entraining movement to external rhythms—i.e., beat keeping—is ubiquitous, but its evolutionary history and neural underpinnings remain a mystery. Recent findings of entrainment to simple and complex rhythms in non-human animals pave the way for a novel comparative approach to assess the origins and mechanisms of rhythmic behavior. The most reliable non-human beat keeper to date is a California sea lion, Ronan, who was trained to match head movements to isochronous repeating stimuli and showed spontaneous generalization of this ability to novel tempos and to the complex rhythms of music. Does Ronan’s performance rely on the same neural mechanisms as human rhythmic behavior? In the current study, we presented Ronan with simple rhythmic stimuli at novel tempos. On some trials, we introduced perturbations, altering either tempo or phase in the middle of a presentation. Ronan quickly adjusted her behavior following all perturbations, recovering her consistent phase and tempo relationships to the stimulus within a few beats. Ronan’s performance was consistent with predictions of mathematical models describing coupled oscillation: a model relying solely on phase coupling strongly matched her behavior, and the model was further improved with the addition of period coupling. These findings are the clearest evidence yet for parity in human and non-human beat keeping and support the view that the human ability to perceive and move in time to rhythm may be rooted in broadly conserved neural mechanisms.
Di Patti, Francesca; Fanelli, Duccio; Miele, Filippo; Carletti, Timoteo
2018-03-01
A normal form approximation for the evolution of a reaction-diffusion system hosted on a directed graph is derived, in the vicinity of a supercritical Hopf bifurcation. Weak diffusive couplings are assumed to hold between adjacent nodes. Under this working assumption, a Complex Ginzburg-Landau equation (CGLE) is obtained, whose coefficients depend on the parameters of the model and the topological characteristics of the underlying network. The CGLE enables one to probe the stability of the synchronous oscillating solution, as displayed by the reaction-diffusion system above Hopf bifurcation. More specifically, conditions can be worked out for the onset of the symmetry breaking instability that eventually destroys the uniform oscillatory state. Numerical tests performed for the Brusselator model confirm the validity of the proposed theoretical scheme. Patterns recorded for the CGLE resemble closely those recovered upon integration of the original Brussellator dynamics.
Driving-induced multistability in coupled chaotic oscillators: Symmetries and riddled basins
Energy Technology Data Exchange (ETDEWEB)
Ujjwal, Sangeeta Rani; Ramaswamy, Ram [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067 (India); Punetha, Nirmal; Prasad, Awadhesh [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India); Agrawal, Manish [Department of Physics, Sri Aurobindo College, University of Delhi, New Delhi 110017 (India)
2016-06-15
We study the multistability that results when a chaotic response system that has an invariant symmetry is driven by another chaotic oscillator. We observe that there is a transition from a desynchronized state to a situation of multistability. In the case considered, there are three coexisting attractors, two of which are synchronized and one is desynchronized. For large coupling, the asynchronous attractor disappears, leaving the system bistable. We study the basins of attraction of the system in the regime of multistability. The three attractor basins are interwoven in a complex manner, with extensive riddling within a sizeable region of (but not the entire) phase space. A quantitative characterization of the riddling behavior is made via the so–called uncertainty exponent, as well as by evaluating the scaling behavior of tongue–like structures emanating from the synchronization manifold.
Coupling of Thalamocortical Sleep Oscillations Are Important for Memory Consolidation in Humans.
Directory of Open Access Journals (Sweden)
Mohammad Niknazar
Full Text Available Sleep, specifically non-rapid eye movement (NREM sleep, is thought to play a critical role in the consolidation of recent memories. Two main oscillatory activities observed during NREM, cortical slow oscillations (SO, 0.5-1.0 Hz and thalamic spindles (12-15 Hz, have been shown to independently correlate with memory improvement. Yet, it is not known how these thalamocortical events interact, or the significance of this interaction, during the consolidation process. Here, we found that systemic administration of the GABAergic drug (zolpidem increased both the phase-amplitude coupling between SO and spindles, and verbal memory improvement in humans. These results suggest that thalamic spindles that occur during transitions to the cortical SO Up state are optimal for memory consolidation. Our study predicts that the timely interactions between cortical and thalamic events during consolidation, contribute to memory improvement and is mediated by the level of inhibitory neurotransmission.
Sidemode suppression for coupled optoelectronic oscillator by optical pulse power feedforward.
Dai, Yitang; Wang, Ruixin; Yin, Feifei; Dai, Jian; Yu, Lan; Li, Jianqiang; Xu, Kun
2015-10-19
Multiple sidemodes have been observed in a coupled optoelectronic oscillator (COEO) when the contained actively mode-locked fiber ring laser employs erbium-doped fiber (EDF). We propose that such sidemodes can be suppressed significantly by an optical pulse power feedforward scheme, through which the mode-locked optical pulse is reversely intensity-modulated by itself, resulting in a fast power limiting. Experimentally we show that sidemodes are suppressed as much as 40 dB in a 10-GHz COEO. The additional noise induced by the power feedforward technique is analyzed numerically. We show that for a COEO with a typical cavity length, the feedforward contribution to final single-side band (SSB) noise is minor and neglectable.
Energy Technology Data Exchange (ETDEWEB)
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.
Ajayamohan, R. S.; Annamalai, H.; Luo, Jing-Jia; Hafner, Jan; Yamagata, Toshio
2011-09-01
The study compares the simulated poleward migration characteristics of boreal summer intraseasonal oscillations (BSISO) in a suite of coupled ocean-atmospheric model sensitivity integrations. The sensitivity experiments are designed in such a manner to allow full coupling in specific ocean basins but forced by temporally varying monthly climatological sea surface temperature (SST) adopted from the fully coupled model control runs (ES10). While the local air-sea interaction is suppressed in the tropical Indian Ocean and allowed in the other oceans in the ESdI run, it is suppressed in the tropical Pacific and allowed in the other oceans in the ESdP run. Our diagnostics show that the basic mean state in precipitation and easterly vertical shear as well as the BSISO properties remain unchanged due to either inclusion or exclusion of local air-sea interaction. In the presence of realistic easterly vertical shear, the continuous emanation of Rossby waves from the equatorial convection is trapped over the monsoon region that enables the poleward propagation of BSISO anomalies in all the model sensitivity experiments. To explore the internal processes that maintain the tropospheric moisture anomalies ahead of BSISO precipitation anomalies, moisture and moist static energy budgets are performed. In all model experiments, advection of anomalous moisture by climatological winds anchors the moisture anomalies that in turn promote the northward migration of BSISO precipitation. While the results indicate the need for realistic simulation of all aspects of the basic state, our model results need to be taken with caution because in the ECHAM family of coupled models the internal variance at intraseasonal timescales is indeed very high, and therefore local air-sea interactions may not play a pivotal role.
Stankevich, N. V.; Kuznetsov, A. P.; Seleznev, E. P.
2017-06-01
Five van der Pol oscillators connected into a ring have been investigated numerically. We have considered different types of coupling: dissipative and active, as well as dissipative and active with a single coupling sign reversal. Bifurcations observed upon a transition from a five- to four-frequency torus have been investigated. The possibility of quasi-periodic Hopf bifurcation in this system has been established.
Yoshiki, Wataru; Chen-Jinnai, Akitoshi; Tetsumoto, Tomohiro; Tanabe, Takasumi
2015-11-30
We report the first experimental observation of an energy oscillation between two coupled ultra-high Q whispering gallery modes in the time domain. Two counter-propagating whispering gallery modes in a silica toroid microcavity were employed for this purpose. The combination of a large coupling coefficient between the two modes and an ultra-high Q factor, which creates a large Γ value of > 10, results in a clear energy oscillation. Our measurement is based on a drop-port measurement technique, which enables us to observe the light energy in the two modes directly. The oscillation period measured in the time domain precisely matched that inferred from mode splitting in the frequency domain, and the measured results showed excellent agreement with results calculated with the developed numerical model.
A simplified spherical harmonic method for coupled electron-photon transport calculations
Energy Technology Data Exchange (ETDEWEB)
Josef, J.A.
1997-12-01
In this thesis the author has developed a simplified spherical harmonic method (SP{sub N} method) and associated efficient solution techniques for 2-D multigroup electron-photon transport calculations. The SP{sub N} method has never before been applied to charged-particle transport. He has performed a first time Fourier analysis of the source iteration scheme and the P{sub 1} diffusion synthetic acceleration (DSA) scheme applied to the 2-D SP{sub N} equations. The theoretical analyses indicate that the source iteration and P{sub 1} DSA schemes are as effective for the 2-D SP{sub N} equations as for the 1-D S{sub N} equations. In addition, he has applied an angular multigrid acceleration scheme, and computationally demonstrated that it performs as well as for the 2-D SP{sub N} equations as for the 1-D S{sub N} equations. It has previously been shown for 1-D S{sub N} calculations that this scheme is much more effective than the DSA scheme when scattering is highly forward-peaked. The author has investigated the applicability of the SP{sub N} approximation to two different physical classes of problems: satellite electronics shielding from geomagnetically trapped electrons, and electron beam problems.
Chen, Xi; Jiang, Ruan-Lei; Li, Jing; Ban, Yue; Sherman, E. Ya.
2018-01-01
We investigate fast transport and spin manipulation of tunable spin-orbit-coupled Bose-Einstein condensates in a moving harmonic trap. Motivated by the concept of shortcuts to adiabaticity, we design inversely the time-dependent trap position and spin-orbit-coupling strength. By choosing appropriate boundary conditions we obtain fast transport and spin flip simultaneously. The nonadiabatic transport and relevant spin dynamics are illustrated with numerical examples and compared with the adiabatic transport with constant spin-orbit-coupling strength and velocity. Moreover, the influence of nonlinearity induced by interatomic interaction is discussed in terms of the Gross-Pitaevskii approach, showing the robustness of the proposed protocols. With the state-of-the-art experiments, such an inverse engineering technique paves the way for coherent control of spin-orbit-coupled Bose-Einstein condensates in harmonic traps.
Stankovski, Tomislav; Petkoski, Spase; Raeder, Johan; Smith, Andrew F.; McClintock, Peter V. E.; Stefanovska, Aneta
2016-05-01
The precise mechanisms underlying general anaesthesia pose important and still open questions. To address them, we have studied anaesthesia induced by the widely used (intravenous) propofol and (inhalational) sevoflurane anaesthetics, computing cross-frequency coupling functions between neuronal, cardiac and respiratory oscillations in order to determine their mutual interactions. The phase domain coupling function reveals the form of the function defining the mechanism of an interaction, as well as its coupling strength. Using a method based on dynamical Bayesian inference, we have thus identified and analysed the coupling functions for six relationships. By quantitative assessment of the forms and strengths of the couplings, we have revealed how these relationships are altered by anaesthesia, also showing that some of them are differently affected by propofol and sevoflurane. These findings, together with the novel coupling function analysis, offer a new direction in the assessment of general anaesthesia and neurophysiological interactions, in general.
A simplified spherical harmonic method for coupled electron-photon transport calculations
International Nuclear Information System (INIS)
Josef, J.A.
1996-12-01
In this thesis we have developed a simplified spherical harmonic method (SP N method) and associated efficient solution techniques for 2-D multigroup electron-photon transport calculations. The SP N method has never before been applied to charged-particle transport. We have performed a first time Fourier analysis of the source iteration scheme and the P 1 diffusion synthetic acceleration (DSA) scheme applied to the 2-D SP N equations. Our theoretical analyses indicate that the source iteration and P 1 DSA schemes are as effective for the 2-D SP N equations as for the 1-D S N equations. Previous analyses have indicated that the P 1 DSA scheme is unstable (with sufficiently forward-peaked scattering and sufficiently small absorption) for the 2-D S N equations, yet is very effective for the 1-D S N equations. In addition, we have applied an angular multigrid acceleration scheme, and computationally demonstrated that it performs as well for the 2-D SP N equations as for the 1-D S N equations. It has previously been shown for 1-D S N calculations that this scheme is much more effective than the DSA scheme when scattering is highly forward-peaked. We have investigated the applicability of the SP N approximation to two different physical classes of problems: satellite electronics shielding from geomagnetically trapped electrons, and electron beam problems. In the space shielding study, the SP N method produced solutions that are accurate within 10% of the benchmark Monte Carlo solutions, and often orders of magnitude faster than Monte Carlo. We have successfully modeled quasi-void problems and have obtained excellent agreement with Monte Carlo. We have observed that the SP N method appears to be too diffusive an approximation for beam problems. This result, however, is in agreement with theoretical expectations
Quantum energy teleportation with a linear harmonic chain
International Nuclear Information System (INIS)
Nambu, Yasusada; Hotta, Masahiro
2010-01-01
A protocol of quantum energy teleportation is proposed for a one-dimensional harmonic chain. A coherent-state positive operator-valued measure (POVM) measurement is performed on coupled oscillators of the chain in the ground state accompanied by energy infusion to the system. This measurement consumes a part of the ground-state entanglement. Depending on the measurement result, a displacement operation is performed on a distant oscillator accompanied by energy extraction from the zero-point fluctuation of the oscillator. We find that the amount of consumed entanglement is bounded from below by a positive value that is proportional to the amount of teleported energy.
Directory of Open Access Journals (Sweden)
Halimatus Sa’diyah
2017-12-01
Full Text Available The purpose of this research is to analyze of students' difficulties on the material elasticity and harmonic oscillation in the inquiry-based physics learning. It has eight stages. They are the orientation, the problem formulation, the formulation of hypotheses, the data obtaining, the testing hypotheses, conclusions, the implementation of the conclusions and generalizations, and the reflection stage. This research determines the student's learning difficulties on the each stage. The subject of this research is all of the students in X IPA 4 SMA N Sambungmacan Sragen. The amount of this research subject is thirty students. The method used in this research is descriptive qualitative. The data acquired with the learning process observation, the student's response questionnaire, and the student's cognitive tests. The results show that the student has difficulty in analyzing the elasticity and the force of deviation, speed, and acceleration concept, illustrates hooke law, and the matter's modulus elasticity. The difficult stages of the inquiry-based physics learning are the problem formulation, the formulation of hypotheses, the data obtaining, the testing hypotheses, conclusions, the implementation of the conclusions and generalizations, and the reflection stage.
Energy Technology Data Exchange (ETDEWEB)
Marquette, Ian, E-mail: i.marquette@uq.edu.au [School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072 (Australia); Quesne, Christiane, E-mail: cquesne@ulb.ac.be [Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)
2016-05-15
The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent P{sub IV}, obtained in the context of second-order supersymmetric quantum mechanics and third-order ladder operators, with a hierarchy of families of quantum systems called k-step rational extensions of the harmonic oscillator and related with multi-indexed X{sub m{sub 1,m{sub 2,…,m{sub k}}}} Hermite exceptional orthogonal polynomials of type III. The connection between these exactly solvable models is established at the level of the equivalence of the Hamiltonians using rational solutions of the fourth Painlevé equation in terms of generalized Hermite and Okamoto polynomials. We also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving Darboux-Crum and Krein-Adler supercharges, their zero modes and the corresponding energies. These results will demonstrate and clarify the relation observed for a particular case in previous papers.
Mouse hair cycle expression dynamics modeled as coupled mesenchymal and epithelial oscillators.
Directory of Open Access Journals (Sweden)
Ryan Tasseff
2014-11-01
Full Text Available The hair cycle is a dynamic process where follicles repeatedly move through phases of growth, retraction, and relative quiescence. This process is an example of temporal and spatial biological complexity. Understanding of the hair cycle and its regulation would shed light on many other complex systems relevant to biological and medical research. Currently, a systematic characterization of gene expression and summarization within the context of a mathematical model is not yet available. Given the cyclic nature of the hair cycle, we felt it was important to consider a subset of genes with periodic expression. To this end, we combined several mathematical approaches with high-throughput, whole mouse skin, mRNA expression data to characterize aspects of the dynamics and the possible cell populations corresponding to potentially periodic patterns. In particular two gene clusters, demonstrating properties of out-of-phase synchronized expression, were identified. A mean field, phase coupled oscillator model was shown to quantitatively recapitulate the synchronization observed in the data. Furthermore, we found only one configuration of positive-negative coupling to be dynamically stable, which provided insight on general features of the regulation. Subsequent bifurcation analysis was able to identify and describe alternate states based on perturbation of system parameters. A 2-population mixture model and cell type enrichment was used to associate the two gene clusters to features of background mesenchymal populations and rapidly expanding follicular epithelial cells. Distinct timing and localization of expression was also shown by RNA and protein imaging for representative genes. Taken together, the evidence suggests that synchronization between expanding epithelial and background mesenchymal cells may be maintained, in part, by inhibitory regulation, and potential mediators of this regulation were identified. Furthermore, the model suggests that
Tunable Coupling to a Mechanical Oscillator Circuit Using a Coherent Feedback Network
Directory of Open Access Journals (Sweden)
Joseph Kerckhoff
2013-06-01
Full Text Available We demonstrate a fully cryogenic microwave feedback network composed of modular superconducting devices connected by transmission lines and designed to control a mechanical oscillator that is coupled to one of the devices. The network features an electromechanical device and a tunable controller that coherently receives, processes, and feeds back continuous microwave signals that modify the dynamics and readout of the mechanical state. While previous electromechanical systems represent some compromise between efficient control and efficient readout of the mechanical state, as set by the electromagnetic decay rate, the tunable controller produces a closed-loop network that can be dynamically and continuously tuned between both extremes much faster than the mechanical response time. We demonstrate that the microwave decay rate may be modulated by at least a factor of 10 at a rate greater than 10^{4} times the mechanical response rate. The system is easy to build and suggests that some useful functions may arise most naturally at the network level of modular, quantum electromagnetic devices.
Stability and oscillation of two coupled Duffing equations with time delay state feedback
International Nuclear Information System (INIS)
El-Bassiouny, A F
2006-01-01
This paper presents an analytical study of the simultaneous principal parametric resonances of two coupled Duffing equations with time delay state feedback. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. The method of multiple scales is used to determine a set of ordinary differential equations governing the modulation of the amplitudes and phases of the two modes. The first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the frequency-response curves. We analyse the effect of time delay and the other different parameters on these oscillations. The stability of the fixed points is examined by using the variational method. Numerical solutions are carried out and graphical representations of the results are presented and discussed. Increasing in the time delay τ given decreasing and increasing in the regions of definition and stability respectively and the first mode has decreased magnitudes. The multivalued solutions disappear when decreasing the coefficients of cubic nonlinearities of the second mode α 3 and the detuning parameter σ 2 respectively. Both modes shift to the left for increasing linear feedback gain v 1 and the coefficient of parametric excitation f 1 respectively
Power harvesting by electromagnetic coupling from wind-induced limit cycle oscillations
Boccalero, G.; Olivieri, S.; Mazzino, A.; Boragno, C.
2017-09-01
Recent developments of low-power microprocessors open to new applications such as wireless sensor networks (WSN) with the consequent problem of autonomous powering. For this purpose, a possible strategy is represented by energy harvesting from wind or other flows exploiting fluid-structure interactions. In this work, we present an updated picture of a flutter-based device characterized by fully passive dynamics and a simple constructive layout, where limit cycle oscillations are undergone by an elastically bounded wing. In this case, the conversion from mechanical to electrical energy is performed by means of an electromagnetic coupling between a pair of coils and magnets. A centimetric-size prototype is shown to harvest energy from low wind velocities (between 2 and 4 m s-1), reaching a power peak of 14 mW, representing a valuable amount for applications related to WSN. A mathematical description of the nonlinear dynamics is then provided by a quasi-steady phenomenological model, revealing satisfactory agreement with the experimental framework within a certain parametric range and representing a useful tool for future optimizations.
Ih tunes theta/gamma oscillations and cross-frequency coupling in an in silico CA3 model.
Directory of Open Access Journals (Sweden)
Samuel A Neymotin
Full Text Available Ih channels are uniquely positioned to act as neuromodulatory control points for tuning hippocampal theta (4-12 Hz and gamma (25 Hz oscillations, oscillations which are thought to have importance for organization of information flow. contributes to neuronal membrane resonance and resting membrane potential, and is modulated by second messengers. We investigated oscillatory control using a multiscale computer model of hippocampal CA3, where each cell class (pyramidal, basket, and oriens-lacunosum moleculare cells, contained type-appropriate isoforms of . Our model demonstrated that modulation of pyramidal and basket allows tuning theta and gamma oscillation frequency and amplitude. Pyramidal also controlled cross-frequency coupling (CFC and allowed shifting gamma generation towards particular phases of the theta cycle, effected via 's ability to set pyramidal excitability. Our model predicts that in vivo neuromodulatory control of allows flexibly controlling CFC and the timing of gamma discharges at particular theta phases.
Cross-frequency coupling of brain oscillations in studying motivation and emotion
Schutter, Dennis J. L. G.; Knyazev, Gennady G.
2011-01-01
Research has shown that brain functions are realized by simultaneous oscillations in various frequency bands. In addition to examining oscillations in pre-specified bands, interactions and relations between the different frequency bandwidths is another important aspect that needs to be considered in unraveling the workings of the human brain and its functions. In this review we provide evidence that studying interdependencies between brain oscillations may be a valuable approach to study the ...
Theory and modelling of second harmonic ICRF coupling and heating in inhomogeneous plasmas
International Nuclear Information System (INIS)
Shokair, I.R.; Conn, R.W.; Mau, T.K.
1988-01-01
The combined theory of ion cyclotron wave coupling, mode conversion and absorption is developed for bounded inhomogeneous plasmas in slab geometry. The plasma response to the RF waves is described by the linearized Vlasov equation, with an equilibrium distribution function and a poloidal magnetic field profile which are self-consistent solutions of the equilibrium Vlasov and Maxwell's equations. A general form of the wave equation, valid to arbitrary order in Larmor radius and including first order gradient terms, is derived. Expressions are also derived for the plasma intrinsic impedance. The wave equation, keeping second order terms in Larmor radius, is solved numerically for a plasma bounded by two conducting walls using the INTOR tokamak design parameters. It was found that the effect of the one-dimensional poloidal field is small. Also, a rough estimate of the error due to truncation to second order in Larmor radius was made and was found to be very small except in the high temperature regions. The effects of plasma boundedness and reflections from the mode conversion region on the coupling of waves from the RF source as a function of the plasma parameters and antenna spectra are studied. It is found that, at certain values of the plasma and antenna parameters, eigenmodes are formed, resulting in an increase in the loading impedance. It is verified that the impedance is not symmetric with respect to the spectrum in the poloidal direction, with highly peaked resonances. As the plasma temperature is increased, the resonances broaden and eventually disappear at very high temperatures. This is attributed to increased single pass absorption and decreasing reflection from the mode conversion region. (author). 20 refs, 15 figs, 2 tabs
Coherent harmonic production using a two-section undulator FEL
Energy Technology Data Exchange (ETDEWEB)
Jaroszynski, D.A. [Commissariat a l`Energie, Bruyeres-le-Chatel (France); Prazeres, R.; Glotin, F. [Centre Universitaire Paris-Sud (France)] [and others
1995-12-31
We present measurements and a theoretical analysis of a new method of generating harmonic radiation in a free-electron laser oscillator with a two section undulator in a single optical cavity. To produce coherent harmonic radiation the undulator is arranged so that the downstream undulator section resonance frequency matches a harmonic of the upstream undulator. Both the fundamental and the harmonic optical fields evolve in the same optical cavity and are coupled out with different extraction fractions using a hole in one of the cavity mirrors. We present measurements that show that the optical power at the second and third harmonic can be enhanced by more than an order of magnitude in this fundamental/harmonic configuration. We compare the production of harmonic radiation of a two sectioned fundamental/harmonic undulator with that produced from a FEL operating at its highest efficiency with a step-tapered undulator, where the bunching at the end of the first section is very large. We examine, the dependence of the harmonic power on the intracavity power by adjusting the optical cavity desynchronism, {delta}L. We also examine the evolution of the fundamental and harmonic powers as a function of cavity roundtrip number to evaluate the importance of the small signal gain at the harmonic. We compare our measurements with predictions of a multi-electron numerical model that follows the evolution of fundamental and harmonic power to saturation. This fundamental/harmonic mode, of operation of the FEL may have useful applications in the production of coherent X-ray and VUV radiation, a spectral range where high reflectivity optical cavity mirrors are difficult or impossible to manufacture.
Huang, Yongjun; Flores, Jaime Gonzalo Flor; Cai, Ziqiang; Yu, Mingbin; Kwong, Dim-Lee; Wen, Guangjun; Churchill, Layne; Wong, Chee Wei
2017-06-29
For the sensitive high-resolution force- and field-sensing applications, the large-mass microelectromechanical system (MEMS) and optomechanical cavity have been proposed to realize the sub-aN/Hz 1/2 resolution levels. In view of the optomechanical cavity-based force- and field-sensors, the optomechanical coupling is the key parameter for achieving high sensitivity and resolution. Here we demonstrate a chip-scale optomechanical cavity with large mass which operates at ≈77.7 kHz fundamental mode and intrinsically exhibiting large optomechanical coupling of 44 GHz/nm or more, for both optical resonance modes. The mechanical stiffening range of ≈58 kHz and a more than 100 th -order harmonics are obtained, with which the free-running frequency instability is lower than 10 -6 at 100 ms integration time. Such results can be applied to further improve the sensing performance of the optomechanical inspired chip-scale sensors.
Kandil, Osama A.; Menzies, Margaret A.
1996-01-01
Unsteady, transonic vortex-breakdown flow over a 65 deg. sharp edged, cropped-delta wing of zero thickness undergoing forced coupled pitching and rolling oscillations is investigated computationally. The initial condition of the flow is characterized by a transverse terminating shock which induces of the leading edge vortex cores to breakdown. The computational investigation uses the time-accurate solution of the laminar, unsteady, compressible, full Navier-Stokes equations with the implicit, upwind, Roe flux-difference splitting, finite-volume scheme. The main focus is to analyze the effects of coupled motion on the wing response and vortex-breakdown flow by varying oscillation frequency and phase angle while keeping the maximum pitch and roll amplitude equal.
Ortiz, L.; Varona, S.; Viyuela, O.; Martin-Delgado, M. A.
2018-02-01
We study the localization and oscillation properties of the Majorana fermions that arise in a two-dimensional electron gas (2DEG) with spin-orbit coupling (SOC) and a Zeeman field coupled with a d -wave superconductor. Despite the angular dependence of the d -wave pairing, localization and oscillation properties are found to be similar to the ones seen in conventional s -wave superconductors. In addition, we study a microscopic lattice version of the previous system that can be characterized by a topological invariant. We derive its real space representation that involves nearest and next-to-nearest-neighbors pairing. Finally, we show that the emerging chiral Majorana fermions are indeed robust against static disorder. This analysis has potential applications to quantum simulations and experiments in high-Tc superconductors.
Cross-frequency coupling of brain oscillations in studying motivation and emotion
Schutter, D.J.L.G.; Knyazev, G.G.
2012-01-01
Research has shown that brain functions are realized by simultaneous oscillations in various frequency bands. In addition to examining oscillations in pre-specified bands, interactions and relations between the different frequency bandwidths is another important aspect that needs to be considered in
Corral, Álvaro; Pérez-Vicente, Conrado, 1962-; Díaz Guilera, Albert; Arenas, Àlex
1995-01-01
We introduce two coupled map lattice models with nonconservative interactions and a continuous nonlinear driving. Depending on both the degree of conservation and the convexity of the driving we find different behaviors, ranging from self-organized criticality, in the sense that the distribution of events (avalanches) obeys a power law, to a macroscopic synchronization of the population of oscillators, with avalanches of the size of the system.
Czech Academy of Sciences Publication Activity Database
Jamšek, J.; Paluš, Milan; Stefanovska, A.
2010-01-01
Roč. 81, č. 3 (2010), 036207:1-036207:10 ISSN 1539-3755 R&D Projects: GA MŠk 7E08027 EU Projects: European Commission(XE) 200728 - BRAINSYNC Institutional research plan: CEZ:AV0Z10300504 Keywords : interacting oscilators * wavelet bispectrum * coupling directionality * causality * information theory Subject RIV: FH - Neurology Impact factor: 2.352, year: 2010
International Nuclear Information System (INIS)
Eaker, C.W.; Schatz, G.C.; De Leon, N.; Heller, E.J.
1984-01-01
Two methods for calculating the good action variables and semiclassical eigenvalues for coupled oscillator systems are presented, both of which relate the actions to the coefficients appearing in the Fourier representation of the normal coordinates and momenta. The two methods differ in that one is based on the exact expression for the actions together with the EBK semiclassical quantization condition while the other is derived from the Sorbie--Handy (SH) approximation to the actions. However, they are also very similar in that the actions in both methods are related to the same set of Fourier coefficients and both require determining the perturbed frequencies in calculating actions. These frequencies are also determined from the Fourier representations, which means that the actions in both methods are determined from information entirely contained in the Fourier expansion of the coordinates and momenta. We show how these expansions can very conveniently be obtained from fast Fourier transform (FFT) methods and that numerical filtering methods can be used to remove spurious Fourier components associated with the finite trajectory integration duration. In the case of the SH based method, we find that the use of filtering enables us to relax the usual periodicity requirement on the calculated trajectory. Application to two standard Henon--Heiles models is considered and both are shown to give semiclassical eigenvalues in good agreement with previous calculations for nondegenerate and 1:1 resonant systems. In comparing the two methods, we find that although the exact method is quite general in its ability to be used for systems exhibiting complex resonant behavior, it converges more slowly with increasing trajectory integration duration and is more sensitive to the algorithm for choosing perturbed frequencies than the SH based method
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1985-01-01
This paper completes a descrption of the quantization procedure in the harmonic superspace approach. The Feynman rules for N=2 matter and Yang-Mills theories are derived and the various examples of harmonic supergraph calculations are given. Calculations appear to be not more difficult than those in the N=1 case. The integration over harmonic variables does not lead to any troubles, a non-locality in these disappears on-shell. The important property is that the quantum corrections are always writen as integrals over the full harmonic superspace even though the initial action is an integral over the analytic subspace. As a by-product our results imply a very simple proof of finiteness of a wide class of the N=4, d=2 non-linear Σ-models. The most general self-couplings of hypermultiplets including those with broken SU(2) are considered.The duality relations among the N=2 linear multiplet and both kinds of hypermultiplet are established
Kandil, Osama A.; Menzies, Margaret A.
1996-01-01
Unsteady, transonic vortex dominated flow over a 65 deg. sharp edged, cropped-delta wing of zero thickness undergoing forced coupled pitching and rolling oscillations is investigated computationally. The wing mean angle of attack is 20 deg. and the free stream Mach number and Reynolds number are 0.85 and 3.23 x 10(exp 6), respectively. The initial condition of the flow is characterized by a transverse terminating shock and vortex breakdown of the leading edge vortex cores. The computational investigation uses the time-accurate solution of the laminar, unsteady, compressible, full Navier-Stokes equations with the implicit, upwind, Roe flux-difference splitting, finite volume scheme. The main focus is to analyze the effects of coupled motion on the wing response and vortex breakdown flow by varying oscillation frequency and phase angle while the maximum pitch and roll amplitude is kept constant at 4.0 deg. Four cases demonstrate the following: simultaneous motion at a frequency of 1(pi), motion with a 90 deg. phase lead in pitch, motion with a rolling frequency of twice the pitching frequency, and simultaneous motion at a frequency of 2(pi). Comparisons with single mode motion at these frequencies complete this study and illustrate the effects of coupling the oscillations.
Sukharev, Maxim; Pachter, Ruth
2018-03-01
We study theoretically the optical response of a WS2 monolayer located near periodic metal nanostructured arrays in two and three dimensions. The emphasis of the simulations is on the strong coupling between excitons supported by WS2 and surface plasmon-polaritons supported by various periodic plasmonic interfaces. It is demonstrated that a monolayer of WS2 placed in close proximity of periodic arrays of either slits or holes results in a Rabi splitting of the corresponding surface plasmon-polariton resonance as revealed in calculated transmission and reflection spectra. The nonlinear regime, at which the few-layer WS2 exhibits experimentally third harmonic generation (THG), is studied in detail. Monolayer transition metal dichalcogenides (TMDs) do not exhibit THG because they are non-centrosymmetric, but here we use the monolayer as an approximation to a thin TMD nanostructure. We show that in the strong coupling regime the third harmonic signal is significantly affected by plasmon-polaritons and the symmetry of hybrid exciton-plasmon modes. It is also shown that the local electromagnetic field induced by plasmons is the major contributor to the enhancement of the third harmonic signal in three dimensions. The local electromagnetic fields resulting from the third harmonic generation are greatly localized and highly sensitive to the environment, thus making it a great tool for nano-probes.
Energy Technology Data Exchange (ETDEWEB)
Arzel, Olivier [The University of New South Wales, Climate Change Research Centre (CCRC), Sydney (Australia); Universite de Bretagne Occidentale, Laboratoire de Physique des Oceans (LPO), Brest (France); England, Matthew H. [The University of New South Wales, Climate Change Research Centre (CCRC), Sydney (Australia); Verdiere, Alain Colin de; Huck, Thierry [Universite de Bretagne Occidentale, Laboratoire de Physique des Oceans (LPO), Brest (France)
2012-07-15
The origin and bifurcation structure of abrupt millennial-scale climate transitions under steady external solar forcing and in the absence of atmospheric synoptic variability is studied by means of a global coupled model of intermediate complexity. We show that the origin of Dansgaard-Oeschger type oscillations in the model is caused by the weaker northward oceanic heat transport in the Atlantic basin. This is in agreement with previous studies realized with much simpler models, based on highly idealized geometries and simplified physics. The existence of abrupt millennial-scale climate transitions during glacial times can therefore be interpreted as a consequence of the weakening of the negative temperature-advection feedback. This is confirmed through a series of numerical experiments designed to explore the sensitivity of the bifurcation structure of the Atlantic meridional overturning circulation to increased atmospheric CO{sub 2} levels under glacial boundary conditions. Contrasting with the cold, stadial, phases of millennial oscillations, we also show the emergence of strong interdecadal variability in the North Atlantic sector during warm interstadials. The instability driving these interdecadal-interstadial oscillations is shown to be identical to that found in ocean-only models forced by fixed surface buoyancy fluxes, that is, a large-scale baroclinic instability developing in the vicinity of the western boundary current in the North Atlantic. Comparisons with modern observations further suggest a physical mechanism similar to that driving the 30-40 years time scale associated with the Atlantic multidecadal oscillation. (orig.)
Audouard, A.; Fortin, J.-Y.; Vignolles, D.; Lyubovskii, R. B.; Drigo, L.; Duc, F.; Shilov, G. V.; Ballon, G.; Zhilyaeva, E. I.; Lyubovskaya, R. N.; Canadell, E.
2012-03-01
Analytical formulae for de Haas-van Alphen (dHvA) oscillations in linear chain of coupled two-dimensional (2D) orbits (Pippard's model) are derived systematically taking into account the chemical potential oscillations in magnetic field. Although corrective terms are observed, basic (α) and magnetic-breakdown-induced (β and 2β-α) orbits can be accounted for by the Lifshits-Kosevich (LK) and Falicov-Stachowiak semiclassical models in the explored field and temperature ranges. In contrast, the "forbidden orbit"β-α amplitude is described by a non-LK equation involving a product of two classical orbit amplitudes. Furthermore, strongly non-monotonic field and temperature dependence may be observed for the second harmonics of basic frequencies such as 2α and the magnetic breakdown orbit β+α, depending on the value of the spin damping factors. These features are in agreement with the dHvA oscillation spectra of the strongly 2D organic metal θ-(ET)4CoBr4(C6H4Cl2).
International Nuclear Information System (INIS)
Khalafalla, M.A.H.; Durrani, Z.A.K.; Mizuta, H.; Ahmed, H.; Oda, S.
2005-01-01
Inter-grain electron-coupling effects are investigated at 4.2 K in dual-gated, point-contact, single-electron transistors fabricated in nanocrystalline silicon. The nanocrystalline silicon film is ∼40 nm thick, with grains ∼10-30 nm in size. The point-contact transistor channel is ∼30 nmx30 nmx40 nm in size, with two side-gates. Only a few grains exist within the channel and different grains contribute in varying degrees to the device conduction. By modifying the inter-grain coupling using selective oxidation of the grain boundaries, both electrostatic and wavefunction-coupling effects can be observed in the Coulomb oscillations vs. the two gate voltages
Energy Technology Data Exchange (ETDEWEB)
Ku, Wai Lim; Girvan, Michelle; Ott, Edward [Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742 (United States)
2015-12-15
In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is “extensive” in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.
Ganeev, Rashid A
2014-01-01
Preface; Why plasma harmonics? A very brief introduction Early stage of plasma harmonic studies - hopes and frustrations New developments in plasma harmonics studies: first successes Improvements of plasma harmonics; Theoretical basics of plasma harmonics; Basics of HHG Harmonic generation in fullerenes using few-cycle pulsesVarious approaches for description of observed peculiarities of resonant enhancement of a single harmonic in laser plasmaTwo-colour pump resonance-induced enhancement of odd and even harmonics from a tin plasmaCalculations of single harmonic generation from Mn plasma;Low-o
Lagrangian analysis of two-phase hydrodynamic and nuclear-coupled density-wave oscillations
International Nuclear Information System (INIS)
Lahey, R.T. Jr.; Yadigaroglu, G.
1974-01-01
The mathematical technique known as the ''method of characteristics'' has been used to construct an exact, analytical solution to predict the onset of density-wave oscillations in diabatic two-phase systems, such as Boiling Water Nuclear Reactors (BWR's). Specifically, heater wall dynamics, boiling boundary dynamics and nuclear kinetics have been accounted for in this analysis. Emphasis is placed on giving the reader a clear physical understanding of the phenomena of two-phase density-wave oscillations. Explanations are presented in terms of block diagram logic, and phasor representations of the various pressure drop perturbations are given. (U.S.)
Inducing and destruction of chimeras and chimera-like states by an external harmonic force
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.
DEFF Research Database (Denmark)
Isaeva, Olga B.; Kuznetsov, Sergey P.; Mosekilde, Erik
2011-01-01
The paper proposes an approach to constructing feasible examples of dynamical systems with hyperbolic chaotic attractors based on the successive transfer of excitation between two pairs of self-oscillators that are alternately active. An angular variable that measures the relations of the current...
Asymptotic solving method for sea-air coupled oscillator ENSO model
International Nuclear Information System (INIS)
Zhou Xian-Chun; Yao Jing-Sun; Mo Jia-Qi
2012-01-01
The ENSO is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interaction. In this article, we create an asymptotic solving method for the nonlinear system of the ENSO model. The asymptotic solution is obtained. And then we can furnish weather forecasts theoretically and other behaviors and rules for the atmosphere-ocean oscillator of the ENSO. (general)
An exactly solvable model of an oscillator with nonlinear coupling and zeros of Bessel functions
Dodonov, V. V.; Klimov, A. B.
1993-01-01
We consider an oscillator model with nonpolynomial interaction. The model admits exact solutions for two situations: for energy eigenvalues in terms of zeros of Bessel functions, that were considered as functions of the continuous index; and for the corresponding eigenstates in terms of Lommel polynomials.
Directory of Open Access Journals (Sweden)
Yufei Liu
2015-01-01
Full Text Available This paper investigates the dynamic of a flexible robotic manipulator (FRM which consists of rigid driving base, flexible links, and flexible joints. With considering the motion fluctuations caused by the coupling effect, such as the motor parameters and mechanism inertias, as harmonic disturbances, the system investigated in this paper remains a parametrically excited system. An elastic restraint model of the FRM with elastic joints (FRMEJ is proposed, which considers the elastic properties of the connecting joints between the flexible arm and the driving base, as well as the harmonic disturbances aroused by the electromechanical coupling effect. As a consequence, the FRMEJ accordingly remains a flexible multibody system which conveys the effects of rigid-flexible couple and electromechanical couple. The Lagrangian function and Hamilton’s principle are used to establish the dynamic model of the FRMEJ. Based on the dynamic model proposed, the vibration power flow is introduced to show the vibration energy distribution. Numerical simulations are conducted to investigate the effect of the joint elasticities and the disturbance excitations, and the influences of the structure parameters and motion parameters on the vibration power flow are studied. The results obtained in this paper contribute to the structure design, motion optimization, and vibration control of FRMs.
Duan, Pengshuo; Liu, Genyou; Hu, Xiaogang; Zhao, Jin; Huang, Chengli
2018-01-01
A significant 6 yr oscillation exists in the length of day (LOD) on the interannual scales. There are mainly two models currently to explain this oscillation, i.e., mantle-inner core gravitational (MICG) coupling mode and the fast torsional waves within the fluid outer core. The former has been doubted, while the source of the excitation of the latter is not yet understood. Therefore, the mechanism of the 6 yr oscillation is still not clear. Here, by considering the mantle and inner core angular momentum, we investigate the MICG coupling mode and its natural period (T0). Given that the strength of gravitational core-mantle coupling (Γ bar) within a recently constrained range is quite weaker than that estimated previously, the mechanism of the 6 yr oscillation still can be attributed to MICG coupling mode (i.e., T0 equals to 6 yrs), but, we require the inertia moment of fluid within the tangent cylinder involved in the 6 yr oscillation to be smaller than 1.23 ×1035 kgm2. This interpretation can be used to constrain the electromagnetic (EM) coupling at the inner core boundary (ICB). In order to study quantitatively the constraints on the EM coupling at the core-mantle boundary (CMB) from the observed 6 yr oscillation with a quality factor Q (∼51.6), we further develop the mathematical expression between the Q value based on the observations and EM coupling at the CMB. According to the Γ bar value from recent estimates and assuming that the 6 yr oscillation is in a free decay, we can obtain the radial magnetic field at the CMB is 0.52 mT∼0.62 mT when conductance at the CMB is 108 S.
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.)
Sakaguchi, Hidetsugu; Malomed, Boris A.
2017-10-01
We analyze the possibility of macroscopic quantum effects in the form of coupled structural oscillations and shuttle motion of bright two-component spin-orbit-coupled striped (one-dimensional, 1D) and semivortex (two-dimensional, 2D) matter-wave solitons, under the action of linear mixing (Rabi coupling) between the components. In 1D, the intrinsic oscillations manifest themselves as flippings between spatially even and odd components of striped solitons, while in 2D the system features periodic transitions between zero-vorticity and vortical components of semivortex solitons. The consideration is performed by means of a combination of analytical and numerical methods.
Strange attractors and synchronization dynamics of coupled Van der Pol-Duffing oscillators
International Nuclear Information System (INIS)
Yamapi, R.; Filatrella, G.
2006-07-01
We consider in this paper the dynamics and synchronization of coupled chaotic Van der Pol-Duffing systems. The stability of the synchronization process between two coupled autonomous Van der Pol model is first analyzed analytically and numerically, before following the problem of synchronizing chaos both on the same and different chaotic orbits of two coupled Van der Pol-Duffing systems. The stability boundaries of the synchronization process are derived and the effects of the amplitude of the periodic perturbation of the coupling parameter on these boundaries are analyzed. The results are provided on the stability map in the (q, K) plane. (author)
Minati, Ludovico
2014-12-01
In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties.
Nagashima, Yoshihiko; Oosako, Takuya; Takase, Yuichi; Ejiri, Akira; Watanabe, Osamu; Kobayashi, Hiroaki; Adachi, Yuuki; Tojo, Hiroshi; Yamaguchi, Takashi; Kurashina, Hiroki; Yamada, Kotaro; An, Byung Il; Kasahara, Hiroshi; Shimpo, Fujio; Kumazawa, Ryuhei; Hayashi, Hiroyuki; Matsuzawa, Haduki; Hiratsuka, Junichi; Hanashima, Kentaro; Kakuda, Hidetoshi; Sakamoto, Takuya; Wakatsuki, Takuma
2010-06-18
We present an observation of beat oscillation generation by coupled modes associated with parametric decay instability (PDI) during radio frequency (rf) wave heating experiments on the Tokyo Spherical Tokamak-2. Nearly identical PDI spectra, which are characterized by the coexistence of the rf pump wave, the lower-sideband wave, and the low-frequency oscillation in the ion-cyclotron range of frequency, are observed at various locations in the edge plasma. A bispectral power analysis was used to experimentally discriminate beat oscillation from the resonant mode for the first time. The pump and lower-sideband waves have resonant mode components, while the low-frequency oscillation is exclusively excited by nonlinear coupling of the pump and lower-sideband waves. Newly discovered nonlocal transport channels in spectral space and in real space via PDI are described.
Espinosa, Ismael; Gonzalez, Hortensia; Quiza, Jorge; Gonazalez, J. Jesus; Arroyo, Ruben; Lara, Ritaluz
1995-01-01
Oscillation of electrical activity has been found in many nervous systems, from invertebrates to vertebrates including man. There exists experimental evidence of very simple circuits with the capability of oscillation. Neurons with intrinsic oscillation have been found and also neural circuits where oscillation is a property of the network. These two types of oscillations coexist in many instances. It is nowadays hypothesized that behind synchronization and oscillation there is a system of coupled oscillators responsible for activities that range from locomotion and feature binding in vision to control of sleep and circadian rhythms. The huge knowledge that has been acquired on oscillators from the times of Lord Rayleigh has made the simulation of neural oscillators a very active endeavor. This has been enhanced with more recent physiological findings about small neural circuits by means of intracellular and extracellular recordings as well as imaging methods. The future of this interdisciplinary field looks very promising; some researchers are going into quantum mechanics with the idea of trying to provide a quantum description of the brain. In this work we describe some simulations using neuron models by means of which we form simple neural networks that have the capability of oscillation. We analyze the oscillatory activity with root locus method, cross-correlation histograms, and phase planes. In the more complicated neural network models there is the possibility of chaotic oscillatory activity and we study that by means of Lyapunov exponents. The companion paper shows an example of that kind.
Chlis, Ilias
2014-01-01
This paper reports comparative analyses of phase noise in Hartley, Colpitts, and common-source cross-coupled differential pair LC oscillator topologies in 28 nm CMOS technology. The impulse sensitivity function is used to carry out both qualitative and quantitative analyses of the phase noise exhibited by each circuit component in each circuit topology with oscillation frequency ranging from 1 to 100 GHz. The comparative analyses show the existence of four distinct frequency regions in which the three oscillator topologies rank unevenly in terms of best phase noise performance, due to the combined effects of device noise and circuit node sensitivity. PMID:24683340
Chlis, Ilias; Pepe, Domenico; Zito, Domenico
2014-01-01
This paper reports comparative analyses of phase noise in Hartley, Colpitts, and common-source cross-coupled differential pair LC oscillator topologies in 28 nm CMOS technology. The impulse sensitivity function is used to carry out both qualitative and quantitative analyses of the phase noise exhibited by each circuit component in each circuit topology with oscillation frequency ranging from 1 to 100 GHz. The comparative analyses show the existence of four distinct frequency regions in which the three oscillator topologies rank unevenly in terms of best phase noise performance, due to the combined effects of device noise and circuit node sensitivity.
Efficiency of conscious access improves with coupling of slow and fast neural oscillations.
Nakatani, Chie; Raffone, Antonino; van Leeuwen, Cees
2014-05-01
Global workspace access is considered as a critical factor for the ability to report a visual target. A plausible candidate mechanism for global workspace access is coupling of slow and fast brain activity. We studied coupling in EEG data using cross-frequency phase-amplitude modulation measurement between delta/theta phases and beta/gamma amplitudes from two experimental sessions, held on different days, of a typical attentional blink (AB) task, implying conscious access to targets. As the AB effect improved with practice between sessions, theta-gamma and theta-beta coupling increased generically. Most importantly, practice effects observed in delta-gamma and delta-beta couplings were specific to performance on the AB task. In particular, delta-gamma coupling showed the largest increase in cases of correct target detection in the most challenging AB conditions. All these practice effects were observed in the right temporal region. Given that the delta band is the main frequency of the P3 ERP, which is a marker of global workspace activity for conscious access, and because the gamma band is involved in visual object processing, the current results substantiate the role of phase-amplitude modulation in conscious access to visual target representations.
Michiels, Wim; Nijmeijer, Henk
2009-09-01
We consider the synchronization problem of an arbitrary number of coupled nonlinear oscillators with delays in the interconnections. The network topology is described by a directed graph. Unlike the conventional approach of deriving directly sufficient synchronization conditions, the approach of the paper starts from an exact stability analysis in a (gain, delay) parameter space of a synchronized equilibrium and extracts insights from an analysis of its bifurcations and from the corresponding emerging behavior. Instrumental to this analysis a factorization of the characteristic equation is employed that not only facilitates the analysis and reduces computational cost but also allows to determine the precise role of the individual agents and the topology of the network in the (in)stability mechanisms. The study provides an algorithm to perform a stability and bifurcation analysis of synchronized equilibria. Furthermore, it reveals fundamental limitations to synchronization and it explains under which conditions on the topology of the network and on the characteristics of the coupling the systems are expected to synchronize. In the second part of the paper the results are applied to coupled Lorenz systems. The main results show that for sufficiently large coupling gains, delay-coupled Lorenz systems exhibit a generic behavior that does not depend on the number of systems and the topology of the network, as long as some basic assumptions are satisfied, including the strong connectivity of the graph. Here the linearized stability analysis is strengthened by a nonlinear stability analysis which confirms the predictions based on the linearized stability and bifurcation analysis. This illustrates the usefulness of the exact linearized analysis in a situation where a direct nonlinear stability analysis is not possible or where it yields conservative conditions from which it is hard to get qualitative insights in the synchronization mechanisms and their scaling properties
International Nuclear Information System (INIS)
Aniel-Buchheit, Sylvie; Podowski, Michael Z.
2006-01-01
The purpose of this paper is to discuss the development in progress of a complete space- and time-dependent model of the coupled neutron kinetic and reactor thermal-hydraulics. The neutron kinetics model is based on two-group diffusion equations with Doppler and void reactivity feedback effects. This model is coupled with the model of two-phase flow and heat transfer in parallel coolant channels. The modeling concepts considered for this purpose include one-dimensional drift flux and two-fluid models, as well a CFD model implemented in the NPHASE advanced computational multiphase fluid dynamics (CMFD) computer code. Two methods of solution for the overall model are proposed. One is based on direct numerical integration of the spatially-discretized governing equations. The other approach is based on a quasi-analytical modal approach to the neutronics model, in which a complete set of eigenvectors is found for step-wise temporal changes of the cross-sections of core materials (fuel and coolant/moderator). The issues investigated in the paper include details of model formulation, as well as the results of calculations for neutronically-coupled density-wave oscillations. (authors)
Allen-Perkins, Alfonso; de Assis, Thiago Albuquerque; Pastor, Juan Manuel; Andrade, Roberto F. S.
2017-10-01
This work considers the time scales associated with the global order parameter and the interlayer synchronization of coupled Kuramoto oscillators on multiplexes. For two-layer multiplexes with an initially high degree of synchronization in each layer, the difference between the average phases in each layer is analyzed from two different perspectives: the spectral analysis and the nonlinear Kuramoto model. Both viewpoints confirm that the prior time scales are inversely proportional to the interlayer coupling strength. Thus, increasing the interlayer coupling always shortens the transient regimes of both the global order parameter and the interlayer synchronization. Surprisingly, the analytical results show that the convergence of the global order parameter is faster than the interlayer synchronization, and the latter is generally faster than the global synchronization of the multiplex. The formalism also outlines the effects of frequencies on the difference between the average phases of each layer, and it identifies the conditions for an oscillatory behavior. Computer simulations are in fairly good agreement with the analytical findings, and they reveal that the time scale of the global order parameter is half the size of the time scale of the multiplex, if not smaller.
Directory of Open Access Journals (Sweden)
Holger eFinger
2014-01-01
Full Text Available Synchronization has been suggested as a mechanism of binding distributed feature representations facilitating segmentation of visual stimuli. Here we investigate this concept based on unsupervised learning using natural visual stimuli. We simulate dual-variable neural oscillators with separate activation and phase variables. The binding of a set of neurons is coded by synchronized phase variables. The network of tangential synchronizing connections learned from the induced activations exhibits small-world properties and allows binding even over larger distances. We evaluate the resulting dynamic phase maps using segmentation masks labeled by human experts. Our simulation results show a continuously increasing phase synchrony between neurons within the labeled segmentation masks. The evaluation of the network dynamics shows that the synchrony between network nodes establishes a relational coding of the natural image inputs. This demonstrates that the concept of binding by synchrony is applicable in the context of unsupervised learning using natural visual stimuli.
International Nuclear Information System (INIS)
Song Yongli; Tadé, Moses O; Zhang Tonghua
2009-01-01
In this paper, a delayed neural network with unidirectional coupling is considered which consists of two two-dimensional nonlinear differential equation systems with exponential decay where one system receives a delayed input from the other system. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using the theory of functional differential equations. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the centre manifold theorem. We also investigate the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay-differential equations combined with representation theory of Lie groups. Then the global continuation of phase-locked periodic solutions is investigated. Numerical simulations are given to illustrate the results obtained
Optimum Design of a Nonlinear Vibration Absorber Coupled to a Resonant Oscillator: A Case Study
Directory of Open Access Journals (Sweden)
H. F. Abundis-Fong
2018-01-01
Full Text Available This paper presents the optimal design of a passive autoparametric cantilever beam vibration absorber for a linear mass-spring-damper system subject to harmonic external force. The design of the autoparametric vibration absorber is obtained by using an approximation of the nonlinear frequency response function, computed via the multiple scales method. Based on the solution given by the perturbation method mentioned above, a static optimization problem is formulated in order to determine the optimum parameters (mass and length of the nonlinear absorber which minimizes the steady state amplitude of the primary mass under resonant conditions; then, a PZT actuator is cemented to the base of the beam, so the nonlinear absorber is made active, thus enabling the possibility of controlling the effective stiffness associated with the passive absorber and, as a consequence, the implementation of an active vibration control scheme able to preserve, as possible, the autoparametric interaction as well as to compensate varying excitation frequencies and parametric uncertainty. Finally, some simulations and experimental results are included to validate and illustrate the dynamic performance of the overall system.
Oscillation death in a coupled van der Pol–Mathieu system
Indian Academy of Sciences (India)
phenomena in physical, chemical, biological, and other systems including social sciences. Out of the various dynamical behaviours of coupled nonlinear system, the ..... In the top panel, the thick blue (left) and red (right) circles represent two limit cycles of the systems. In the bottom panel, the annihilation of the limit cycles to ...
Oscillation death in a coupled van der Pol–Mathieu system
Indian Academy of Sciences (India)
Research Articles Volume 81 Issue 4 October 2013 pp 677-690 ... We have shown that the system arrives at an OD regime when coupling strength crosses a threshold value at which the system undergoes saddle-node bifurcation and two limit cycles coalesce onto a fixed point of the system. We have further shown that this ...
Coupling of Surface and Volume Dipole Oscillations in C60 Molecules
Brack, M.; Winkler, P.; Murthy, M. V. N.
We first give a short review of the "local-current approximation" (LCA), derived from a general variation principle, which serves as a semiclassical description of strongly collective excitations in finite fermion systems starting from their quantum-mechanical mean-field ground state. We illustrate it for the example of coupled translational and compressional dipole excitations in metal clusters. We then discuss collective electronic dipole excitations in C60 molecules (Buckminster fullerenes). We show that the coupling of the pure translational mode ("surface plasmon") with compressional volume modes in the semiclasscial LCA yields semi-quantitative agreement with microscopic time-dependent density functional (TDLDA) calculations, while both theories yield qualitative agreement with the recent experimental observation of a "volume plasmon".
Coupling of surface and volume dipole oscillations in C60 molecules
International Nuclear Information System (INIS)
Brack, M.; Winkler, P.; Murthy, M.V.N.
2008-01-01
We first give a short review of the "local-current approximation" (LCA), derived from a general variation principle, which serves as a semiclassical description of strongly collective excitations in finite fermion systems starting from their quantum-mechanical mean-field ground state. We illustrate it for the example of coupled translational and compressional dipole excitations in metal clusters. We then discuss collective electronic dipole excitations in C 60 molecules (Buckminster fullerenes). We show that the coupling of the pure translational mode ("surface plasmon") with compressional volume modes in the semiclasscial LCA yields semi-quantitative agreement with microscopic time-dependent density functional (TDLDA) calculations, while both theories yield qualitative agreement with the recent experimental observation of a "volume plasmon". (author)
The effect of temperature on the coupled slow and fast dynamics of an electrochemical oscillator
Zülke, Alana A.; Varela, Hamilton
2016-04-01
The coupling among disparate time-scales is ubiquitous in many chemical and biological systems. We have recently investigated the effect of fast and, long-term, slow dynamics in surface processes underlying some electrocatalytic reactions. Herein we report on the effect of temperature on the coupled slow and fast dynamics of a model system, namely the electro-oxidation of formic acid on platinum studied at five temperatures between 5 and 45 °C. The main result was a turning point found at 25 °C, which clearly defines two regions for the temperature dependency on the overall kinetics. In addition, the long-term evolution allowed us to compare reaction steps related to fast and slow evolutions. Results were discussed in terms of the key role of PtO species, which chemically couple slow and fast dynamics. In summary we were able to: (a) identify the competition between two reaction steps as responsible for the occurrence of two temperature domains; (b) compare the relative activation energies of these two steps; and (c) suggest the role of a given reaction step on the period-increasing set of reactions involved in the oscillatory dynamics. The introduced methodology could be applied to other systems to uncover the temperature dependence of complex chemical networks.
Anterior Thalamic High Frequency Band Activity Is Coupled with Theta Oscillations at Rest
Directory of Open Access Journals (Sweden)
Catherine M. Sweeney-Reed
2017-07-01
Full Text Available Cross-frequency coupling (CFC between slow and fast brain rhythms, in the form of phase–amplitude coupling (PAC, is proposed to enable the coordination of neural oscillatory activity required for cognitive processing. PAC has been identified in the neocortex and mesial temporal regions, varying according to the cognitive task being performed and also at rest. PAC has also been observed in the anterior thalamic nucleus (ATN during memory processing. The thalamus is active during the resting state and has been proposed to be involved in switching between task-free cognitive states such as rest, in which attention is internally-focused, and externally-focused cognitive states, in which an individual engages with environmental stimuli. It is unknown whether PAC is an ongoing phenomenon during the resting state in the ATN, which is modulated during different cognitive states, or whether it only arises during the performance of specific tasks. We analyzed electrophysiological recordings of ATN activity during rest from seven patients who received thalamic electrodes implanted for treatment of pharmacoresistant focal epilepsy. PAC was identified between theta (4–6 Hz phase and high frequency band (80–150 Hz amplitude during rest in all seven patients, which diminished during engagement in tasks involving an external focus of attention. The findings are consistent with the proposal that theta–gamma coupling in the ATN is an ongoing phenomenon, which is modulated by task performance.
Himeoka, Yusuke; Kaneko, Kunihiko
2016-04-01
Cells generally convert nutrient resources to products via energy transduction. Accordingly, the thermodynamic efficiency of this conversion process is one of the most essential characteristics of living organisms. However, although these processes occur under conditions of dynamic metabolism, most studies of cellular thermodynamic efficiency have been restricted to examining steady states; thus, the relevance of dynamics to this efficiency has not yet been elucidated. Here, we develop a simple model of metabolic reactions with anabolism-catabolism coupling catalyzed by enzymes. Through application of external oscillation in the enzyme abundances, the thermodynamic efficiency of metabolism was found to be improved. This result is in strong contrast with that observed in the oscillatory input, in which the efficiency always decreased with oscillation. This improvement was effectively achieved by separating the anabolic and catabolic reactions, which tend to disequilibrate each other, and taking advantage of the temporal oscillations so that each of the antagonistic reactions could progress near equilibrium. In this case, anti-phase oscillation between the reaction flux and chemical affinity through oscillation of enzyme abundances is essential. This improvement was also confirmed in a model capable of generating autonomous oscillations in enzyme abundances. Finally, the possible relevance of the improvement in thermodynamic efficiency is discussed with respect to the potential for manipulation of metabolic oscillations in microorganisms.
Komarov, M.; Pikovsky, A.
2015-12-01
The author would like to inform the readers that the Acknowledgements in the above article should be read as "MK thanks Alexander von Humboldt Foundation for support. AP and MK have been supported by the grant No 02.49.21.0003 (the agreement of August 27, 2013 between the Ministry of Education and Science of the Russian Federation and Lobachevsky State University of Nizhni Novgorod). Also Section 5 of this work was supported in part by
Strong-coupling approximations
International Nuclear Information System (INIS)
Abbott, R.B.
1984-03-01
Standard path-integral techniques such as instanton calculations give good answers for weak-coupling problems, but become unreliable for strong-coupling. Here we consider a method of replacing the original potential by a suitably chosen harmonic oscillator potential. Physically this is motivated by the fact that potential barriers below the level of the ground-state energy of a quantum-mechanical system have little effect. Numerically, results are good, both for quantum-mechanical problems and for massive phi 4 field theory in 1 + 1 dimensions. 9 references, 6 figures
From two competing oscillators to one coupled-clock pacemaker cell system
Yaniv, Yael; Lakatta, Edward G.; Maltsev, Victor A.
2015-01-01
At the beginning of this century, debates regarding “what are the main control mechanisms that ignite the action potential (AP) in heart pacemaker cells” dominated the electrophysiology field. The original theory which prevailed for over 50 years had advocated that the ensemble of surface membrane ion channels (i.e., “M-clock”) is sufficient to ignite rhythmic APs. However, more recent experimental evidence in a variety of mammals has shown that the sarcoplasmic reticulum (SR) acts as a “Ca2+-clock” rhythmically discharges diastolic local Ca2+ releases (LCRs) beneath the cell surface membrane. LCRs activate an inward current (likely that of the Na+/Ca2+ exchanger) that prompts the surface membrane “M-clock” to ignite an AP. Theoretical and experimental evidence has mounted to indicate that this clock “crosstalk” operates on a beat-to-beat basis and determines both the AP firing rate and rhythm. Our review is focused on the evolution of experimental definition and numerical modeling of the coupled-clock concept, on how mechanisms intrinsic to pacemaker cell determine both the heart rate and rhythm, and on future directions to develop further the coupled-clock pacemaker cell concept. PMID:25741284
Bills, Bruce G.; James, Thomas S.; Mengel, John G.
1999-01-01
Precessional motion of Earth's rotation axis relative to its orbit is a well-known source of long-period climatic variation. It is less well appreciated that growth and decay of polar ice sheets perturb the symmetry of the global mass distribution enough that the geographic location of the rotation axis will change by at least 15 km and possibly as much as 100 km during a single glacial cycle. This motion of the pole will change the seasonal and latitudinal pattern of temperatures. We present calculations, based on a diurnal average energy balance, which compare the summer and winter temperature anomalies due to a 1° decrease in obliquity with those due to a 1° motion of the rotation pole toward Hudson Bay. Both effects result in peak temperature perturbations of about 1° Celsius. The obliquity change primarily influences the amplitude of the seasonal cycle, while the polar motion primarily changes the annual mean temperatures. The polar motion induced temperature anomaly is such that it will act as a powerful negative feedback on ice sheet growth. We also explore the evolution of the coupled system composed of ice sheet mass and pole position. Oscillatory solutions result from the conflicting constraints of rotational and thermal stability. A positive mass anomaly on an otherwise featureless Earth is in rotational equilibrium only at the poles or the equator. The two polar equilibria are rotationally unstable, and the equatorial equilibrium, though rotationally stable, is thermally unstable. We find that with a plausible choice for the strength of coupling between the thermal and rotational systems, relatively modest external forcing can produce significant response at periods of 104–106 years, but it strongly attenuates polar motion at longer periods. We suggest that these coupled oscillations may contribute to the observed dominance of 100 kyr glacial cycles since the mid-Pleistocene and will tend to stabilize geographic patterns that are suitable to
Ladenbauer, Julia; Ladenbauer, Josef; Külzow, Nadine; de Boor, Rebecca; Avramova, Elena; Grittner, Ulrike; Flöel, Agnes
2017-07-26
Alzheimer's disease (AD) not only involves loss of memory functions, but also prominent deterioration of sleep physiology, which is already evident at the stage of mild cognitive impairment (MCI). Cortical slow oscillations (SO; 0.5-1 Hz) and thalamocortical spindle activity (12-15 Hz) during sleep, and their temporal coordination, are considered critical for memory formation. We investigated the potential of slow oscillatory transcranial direct current stimulation (so-tDCS), applied during a daytime nap in a sleep-state-dependent manner, to modulate these activity patterns and sleep-related memory consolidation in nine male and seven female human patients with MCI. Stimulation significantly increased overall SO and spindle power, amplified spindle power during SO up-phases, and led to stronger synchronization between SO and spindle power fluctuations in EEG recordings. Moreover, visual declarative memory was improved by so-tDCS compared with sham stimulation and was associated with stronger synchronization. These findings indicate a well-tolerated therapeutic approach for disordered sleep physiology and memory deficits in MCI patients and advance our understanding of offline memory consolidation. SIGNIFICANCE STATEMENT In the light of increasing evidence that sleep disruption is crucially involved in the progression of Alzheimer's disease (AD), sleep appears as a promising treatment target in this pathology, particularly to counteract memory decline. This study demonstrates the potential of a noninvasive brain stimulation method during sleep in patients with mild cognitive impairment (MCI), a precursor of AD, and advances our understanding of its mechanism. We provide first time evidence that slow oscillatory transcranial stimulation amplifies the functional cross-frequency coupling between memory-relevant brain oscillations and improves visual memory consolidation in patients with MCI. Copyright © 2017 the authors 0270-6474/17/377111-14$15.00/0.
Harmonically excited orbital variations
International Nuclear Information System (INIS)
Morgan, T.
1985-01-01
Rephrasing the equations of motion for orbital maneuvers in terms of Lagrangian generalized coordinates instead of Newtonian rectangular cartesian coordinates can make certain harmonic terms in the orbital angular momentum vector more readily apparent. In this formulation the equations of motion adopt the form of a damped harmonic oscillator when torques are applied to the orbit in a variationally prescribed manner. The frequencies of the oscillator equation are in some ways unexpected but can nonetheless be exploited through resonant forcing functions to achieve large secular variations in the orbital elements. Two cases are discussed using a circular orbit as the control case: (1) large changes in orbital inclination achieved by harmonic excitation rather than one impulsive velocity change, and (2) periodic and secular changes to the longitude of the ascending node using both stable and unstable excitation strategies. The implications of these equations are also discussed for both artificial satellites and natural satellites. For the former, two utilitarian orbits are suggested, each exploiting a form of harmonic excitation. 5 refs
Zamani, A.; Azargoshasb, T.; Niknam, E.; Mohammadhosseini, E.
2017-06-01
In this work, effects of external electric and magnetic fields in the presence of both Rashba and Dresselhaus spin-orbit couplings on the second and third harmonic generations (SHG and THG) of a lens-shaped GaAs quantum dot are studied. Energy eigenvalues and eigenvectors are calculated numerically and optical properties are obtained using the compact density matrix approach. Our results reveal that, an increase in the magnetic field, leads to both red and blue shifts in resonant peaks of both SHG and THG. On the other hand, augmentation of electric field leads to blue shift in all resonant peaks except the first peak related to lowest transition. Also the dipole moment matrix elements increase by enhancing both electric and magnetic fields. Finally the effect of dot size is studied and results illustrate that increment in size reduces the transition energies except the lowest one and thus leads to red shift in resonant peaks while the first peak remains constant.
International Nuclear Information System (INIS)
Taneichi, T.; Kobayashi, T.
2007-01-01
Discussion on wavelength dependent 'anharmonic' effects in a pump-probe signal for a system of wavepacket on one- and two-dimensional harmonic potentials was given. The Fourier power spectrum of the signal, calculated for a model composed of a three-state electronic system coupled to a set of displaced harmonic oscillators, depends on the pulse duration. Condition under which the wavepacket motion in the harmonic potential substantially deviates from that of the classical point mass is derived. The Fourier power spectrum has enhanced components with frequencies of harmonics even in a system composed of ideally harmonic potentials. Utility of the Fourier analysis of the spectrum for clarification of the squeezed molecular vibrational state is discussed. Calculated oscillatory behavior in phase of a pump-probe signal, as a function of probe frequency, was discussed in terms of a two-dimensional effect on a pump-probe signal
Eliazar, Iddo
2017-05-01
The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their 'public relations' for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford's law, and 1/f noise.
Oscillations of a spring-magnet system damped by a conductive plate
Ladera, C. L.; Donoso, G.
2013-09-01
We study the motion of a spring-magnet system that oscillates with very low frequencies above a circular horizontal non-magnetizable conductive plate. The magnet oscillations couple with the plate via the Foucault currents induced therein. We develop a simple theoretical model for this magneto-mechanical oscillator, a model that leads to the equation of a damped harmonic oscillator, whose weak attenuation constant depends upon the system parameters, e.g. the electrical conductivity of the constituent material of the plate and its thickness. We present a set of validating experiments, the results of which are predicted with good accuracy by our analytical model. Additional experiments can be performed with this oscillating system or its variants. This oscillator is simple and low-cost, easy to assemble, and can be used in experiments or project works in physics teaching laboratories at the undergraduate level.
Oscillations of a spring–magnet system damped by a conductive plate
International Nuclear Information System (INIS)
Ladera, C L; Donoso, G
2013-01-01
We study the motion of a spring–magnet system that oscillates with very low frequencies above a circular horizontal non-magnetizable conductive plate. The magnet oscillations couple with the plate via the Foucault currents induced therein. We develop a simple theoretical model for this magneto-mechanical oscillator, a model that leads to the equation of a damped harmonic oscillator, whose weak attenuation constant depends upon the system parameters, e.g. the electrical conductivity of the constituent material of the plate and its thickness. We present a set of validating experiments, the results of which are predicted with good accuracy by our analytical model. Additional experiments can be performed with this oscillating system or its variants. This oscillator is simple and low-cost, easy to assemble, and can be used in experiments or project works in physics teaching laboratories at the undergraduate level. (paper)
Rérat, Michel; Maschio, Lorenzo; Kirtman, Bernard; Civalleri, Bartolomeo; Dovesi, Roberto
2016-01-12
The electronic second harmonic generation (SHG) tensor, d, of crystalline urea and potassium dihydrogen phosphate (KDP) is evaluated as a function of frequency using a Gaussian type basis set and the Coupled Perturbed Hartree-Fock (CPHF) and Kohn-Sham (CPKS) schemes as implemented in the CRYSTAL code. The results of various functionals, including LDA, GGA (PBE), and global and range-separated hybrids (B3LYP, PBE0, LC-BLYP), as well as Hartree-Fock, are compared. It is found that the calculated SHG intensity always decreases as the percentage of exact exchange increases. The hybrid functionals turn out to provide results that agree well with experiment. For urea and KDP the percentage of exact exchange determined by the inverse dielectric constant is too large. At 1064 nm the vibrational contribution for urea is found to be less than 5% of the total value. To the authors' knowledge, this is the first coupled (self-consistent) calculation of SHG for any periodic system.
Directory of Open Access Journals (Sweden)
P. De Vita
2012-05-01
Full Text Available Thus far, studies on climate change have focused mainly on the variability of the atmospheric and surface components of the hydrologic cycle, investigating the impact of this variability on the environment, especially with respect to the risks of desertification, droughts and floods. Conversely, the impacts of climate change on the recharge of aquifers and on the variability of groundwater flow have been less investigated, especially in Mediterranean karst areas whose water supply systems depend heavily upon groundwater exploitation.
In this paper, long-term climatic variability and its influence on groundwater recharge were analysed by examining decadal patterns of precipitation, air temperature and spring discharges in the Campania region (southern Italy, coupled with the North Atlantic Oscillation (NAO.
The time series of precipitation and air temperature were gathered over 90 yr, from 1921 to 2010, using 18 rain gauges and 9 air temperature stations with the most continuous functioning. The time series of the winter NAO index and of the discharges of 3 karst springs, selected from those feeding the major aqueducts systems, were collected for the same period.
Regional normalised indexes of the precipitation, air temperature and karst spring discharges were calculated, and different methods were applied to analyse the related time series, including long-term trend analysis using smoothing numerical techniques, cross-correlation and Fourier analysis.
The investigation of the normalised indexes highlighted the existence of long-term complex periodicities, from 2 to more than 30 yr, with differences in average values of up to approximately ±30% for precipitation and karst spring discharges, which were both strongly correlated with the winter NAO index.
Although the effects of the North Atlantic Oscillation (NAO had already been demonstrated in the long-term precipitation and streamflow patterns of
Berger, Birk; Steinberger, Thomas; Schüngel, Edmund; Koepke, Mark; Mussenbrock, Thomas; Awakowicz, Peter; Schulze, Julian
2017-11-01
Inductive discharges with radio-frequency (RF) substrate bias are frequently used for various technological applications. We operate such a hybrid discharge with a phase-locked RF substrate bias at twice the frequency of the inductive coupling with fixed but adjustable phase between both RF sources in neon at low pressures of a few Pa. The ion flux to the substrate is found to be a function of this relative phase in the H-mode at constant RF powers as long as some residual capacitive coupling of the planar coil is present. For distinct choices of the phase, Phase Resolved Optical Emission Spectroscopy measurements show that energetic beam electrons generated by the expanding boundary sheaths (i) are well confined, (ii) are accelerated efficiently, and (iii) propagate vertically through the inductive skin layer at the times of maximum azimuthal induced electric field within the fundamental RF period. This enhances the inductive stochastic electron heating, the power coupling efficiency, and finally the ion flux.
Bozkaya, Uǧur; Sherrill, C. David
2013-08-01
Orbital-optimized coupled-electron pair theory [or simply "optimized CEPA(0)," OCEPA(0), for short] and its analytic energy gradients are presented. For variational optimization of the molecular orbitals for the OCEPA(0) method, a Lagrangian-based approach is used along with an orbital direct inversion of the iterative subspace algorithm. The cost of the method is comparable to that of CCSD [O(N6) scaling] for energy computations. However, for analytic gradient computations the OCEPA(0) method is only half as expensive as CCSD since there is no need to solve the λ2-amplitude equation for OCEPA(0). The performance of the OCEPA(0) method is compared with that of the canonical MP2, CEPA(0), CCSD, and CCSD(T) methods, for equilibrium geometries, harmonic vibrational frequencies, and hydrogen transfer reactions between radicals. For bond lengths of both closed and open-shell molecules, the OCEPA(0) method improves upon CEPA(0) and CCSD by 25%-43% and 38%-53%, respectively, with Dunning's cc-pCVQZ basis set. Especially for the open-shell test set, the performance of OCEPA(0) is comparable with that of CCSD(T) (ΔR is 0.0003 Å on average). For harmonic vibrational frequencies of closed-shell molecules, the OCEPA(0) method again outperforms CEPA(0) and CCSD by 33%-79% and 53%-79%, respectively. For harmonic vibrational frequencies of open-shell molecules, the mean absolute error (MAE) of the OCEPA(0) method (39 cm-1) is fortuitously even better than that of CCSD(T) (50 cm-1), while the MAEs of CEPA(0) (184 cm-1) and CCSD (84 cm-1) are considerably higher. For complete basis set estimates of hydrogen transfer reaction energies, the OCEPA(0) method again exhibits a substantially better performance than CEPA(0), providing a mean absolute error of 0.7 kcal mol-1, which is more than 6 times lower than that of CEPA(0) (4.6 kcal mol-1), and comparing to MP2 (7.7 kcal mol-1) there is a more than 10-fold reduction in errors. Whereas the MAE for the CCSD method is only 0.1 kcal
Kanao, Taro; Suto, Hirofumi; Kudo, Kiwamu; Nagasawa, Tazumi; Mizushima, Koichi; Sato, Rie
2018-01-01
We study the magnetization dynamics of a spin-torque oscillator (STO) and a magnetic dot coupled by a magnetic dipolar field using micromagnetic simulation with the aim of developing a read method in magnetic recording that uses magnetic resonance. We propose an STO with a perpendicularly magnetized free layer and an in-plane-magnetized fixed layer as a suitable STO for this resonance read method. When the oscillation frequency of the STO is near the ferromagnetic resonance (FMR) frequency of the magnetic dot, the oscillation amplitude of the STO decreases because FMR excited in the magnetic dot causes additional dissipation. To estimate the read rate of the resonance read method, we study the transient magnetization dynamics to the coupled oscillation state from an initial state where the STO is in a free-running state and the magnetic dot is in a stationary stable state. The STO shows transient dynamics within a time scale of 1 ns, which means that the STO can perform resonance reading with a response time within this time scale. This response time is shorter when the separation length between the STO and the magnetic dot is shorter, which indicates that the response speed can become faster by increasing the strength of the interaction between the STO and the magnetic dot. Successive reads are demonstrated by moving the STO over an array of magnetic dots.
Qian, Youhua; Chen, Shengmin
2010-10-01
In this paper, the homotopy analysis method (HAM) is presented to establish the accurate approximate analytical solutions for multi-degree-of-freedom (MDOF) nonlinear coupled oscillators. The periodic solutions for the three-degree-of-freedom (3DOF) coupled van der Pol-Duffing oscillators are applied to illustrate the validity and great potential of this method. For given physical parameters of nonlinear systems and with different initial conditions, the frequency ω , displacements x1 (t),x2 (t) and x3 (t) can be explicitly obtained. In addition, comparisons are conducted between the results obtained by the HAM and the numerical integration (i.e. Runge-Kutta) method. It is shown that the analytical solutions of the HAM are in excellent agreement with respect to the numerical integration solutions, even if time t progresses to a certain large domain in the time history responses. Finally, the homotopy Pade technique is used to accelerate the convergence of the solutions.
Oscillators from nonlinear realizations
Kozyrev, N.; Krivonos, S.
2018-02-01
We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of nonlinear realizations. We prove that it is always possible to choose time and the fields within this formalism in such a way that the equations of motion become linear and, therefore, reduce to ones of ordinary harmonic and Pais-Uhlenbeck oscillators. The first-order actions, that produce these equations, can also be provided. As particular examples of this construction, we discuss the so(2, 3) and G 2(2) algebras.
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il
2017-05-15
The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.
Exact complex integrals in two dimensions for shifted harmonic ...
Indian Academy of Sciences (India)
With a view of constructing complex integral for some cases here, in this section we use methods discussed in the previous section. To start with, we first consider the case of shifted harmonic oscillator systems within the framework of rationalization method. Note that for shifted harmonic oscillator in complex plane. H = 1. 2.
The homotopic method of travelling wave solution for El Niño tropic sea–air coupled oscillator
International Nuclear Information System (INIS)
Mo Jiaqi; Lin Wantao
2008-01-01
The EI Niño and Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific sea–air interactions. In this paper, an asymptotic method of solving nonlinear equations for the ENSO model is proposed. And based on a class of oscillator of the ENSO model and by employing the method of homotopic mapping, the approximate solution of equations for the corresponding ENSO model is studied. It is proved from the results that homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial Pacific of the sea–air oscillator for the ENSO model