Covariant harmonic oscillators and coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, Daesoo; Kim, Young S.; Noz, Marilyn E.
1995-01-01
It is shown that the system of two coupled harmonic oscillators shares the basic symmetry properties with the covariant harmonic oscillator formalism which provides a concise description of the basic features of relativistic hadronic features observed in high-energy laboratories. It is shown also that the coupled oscillator system has the SL(4,r) symmetry in classical mechanics, while the present formulation of quantum mechanics can accommodate only the Sp(4,r) portion of the SL(4,r) symmetry. The possible role of the SL(4,r) symmetry in quantum mechanics is discussed.
Symmetries of coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, D.; Kim, Y. S.
1993-01-01
It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).
Markovian evolution of strongly coupled harmonic oscillators
NASA Astrophysics Data System (ADS)
Joshi, Chaitanya; Öhberg, Patrik; Cresser, James D.; Andersson, Erika
2014-12-01
We investigate how to model Markovian evolution of coupled harmonic oscillators, each of them interacting with a local environment. When the coupling between the oscillators is weak, dissipation may be modeled using local Lindblad terms for each of the oscillators in the master equation, as is commonly done. When the coupling between oscillators is strong, this model may become invalid. We derive a master equation for two coupled harmonic oscillators that are subject to individual heat baths modeled by a collection of harmonic oscillators and show that this master equation in general contains nonlocal Lindblad terms. We compare the resulting time evolution with that obtained for dissipation through local Lindblad terms for each individual oscillator and show that the evolution is different in the two cases. In particular, the two descriptions give different predictions for the steady state and for the entanglement between strongly coupled oscillators. This shows that when describing strongly coupled harmonic oscillators, one must take great care in how dissipation is modeled and that a description using local Lindblad terms may fail. This may be particularly relevant when attempting to generate entangled states of strongly coupled quantum systems.
Edge Event-Triggered Synchronization in Networks of Coupled Harmonic Oscillators.
Wei, Bo; Xiao, Feng; Dai, Ming-Zhe
2016-08-30
The synchronization problems of networks of coupled harmonic oscillators are addressed by the edge event-triggered approach in this paper. The network dynamics with respect to edge states are presented and a new edge event-triggered control protocol is designed. Combined with the periodic event-detecting and edge event-triggered approach, sufficient conditions that guarantee the synchronization of coupled harmonic oscillators are presented. Two event-detecting rules are given to achieve the synchronization of coupled harmonic oscillators with low resource consumption. Finally, simulations are conducted to illustrate the effectiveness of the edge event-triggered control algorithm.
Chou, Chung-Hsien; Yu, Ting; Hu, B L
2008-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to N, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations, and dissipation of mesoscopic objects toward the construction of a theoretical framework for macroscopic quantum phenomena.
Containment control for coupled harmonic oscillators with multiple leaders under directed topology
NASA Astrophysics Data System (ADS)
Xu, Chengjie; Zheng, Ying; Su, Housheng; Wang, Hua O.
2015-02-01
This paper investigates the problem of containment control for coupled harmonic oscillators with multiple leaders under directed topology. Using tools from matrix, graph and stability theories, necessary and sufficient conditions are obtained for coupled harmonic oscillators under continuous-time and sampled-data-based protocols, respectively. When the continuous-time protocol is used, it is proved that every follower will ultimately converge to the convex hull spanned by the leaders if and only if there exists at least one leader that has a directed path to that follower at any time. When the sampled-data-based protocol is used, it is shown that the containment can be achieved if and only if: (1) an appropriate sampling period is chosen and (2) for every follower, there exists at least one leader that has a directed path to that follower at any time. And we also give the containment conditions for coupled harmonic oscillators under undirected topology as a special case. Finally, numerical simulations are presented to illustrate the theoretical findings.
Hwang, Myung-Joong; Choi, Mahn-Soo
2010-08-15
The nonclassical behavior of a two-level system coupled to a harmonic oscillator is investigated in the ultrastrong coupling regime. We revisit the variational solution of the ground state and find that the existing solutions do not account accurately for nonclassical effects such as squeezing. We suggest a trial wave function and demonstrate that it has an excellent accuracy for the quantum correlation effects as well as for the energy.
Workshop on Harmonic Oscillators
NASA Technical Reports Server (NTRS)
Han, D. (Editor); Kim, Y. S. (Editor); Zachary, W. W. (Editor)
1993-01-01
Proceedings of a workshop on Harmonic Oscillators held at the College Park Campus of the University of Maryland on March 25 - 28, 1992 are presented. The harmonic oscillator formalism is playing an important role in many branches of physics. This is the simplest mathematical device which can connect the basic principle of physics with what is observed in the real world. The harmonic oscillator is the bridge between pure and applied physics.
Fourth-order master equation for a charged harmonic oscillator coupled to an electromagnetic field
NASA Astrophysics Data System (ADS)
Kurt, Arzu; Eryigit, Resul
Using Krylov averaging method, we have derived a fourth-order master equation for a charged harmonic oscillator weakly coupled to an electromagnetic field. Interaction is assumed to be of velocity coupling type which also takes into account the diagmagnetic term. Exact analytical expressions have been obtained for the second, the third and the fourth-order corrections to the diffusion and the drift terms of the master equation. We examined the validity range of the second order master equation in terms of the coupling constant and the bath cutoff frequency and found that for the most values of those parameters, the contribution from the third and the fourth order terms have opposite signs and cancel each other. Inclusion of the third and the fourth-order terms is found to not change the structure of the master equation. Bolu, Turkey.
Floquet topological system based on frequency-modulated classical coupled harmonic oscillators
NASA Astrophysics Data System (ADS)
Salerno, Grazia; Ozawa, Tomoki; Price, Hannah M.; Carusotto, Iacopo
2016-02-01
We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time. Making use of Floquet theory in the high-frequency limit, we identify a regime in which the system is accurately described by a Harper-Hofstadter model where the synthetic magnetic field can be externally tuned via the phase of the frequency modulation of the different oscillators. We illustrate how the topologically protected chiral edge states, as well as the Hofstadter butterfly of bulk bands, can be observed in the driven-dissipative steady state under a monochromatic drive. In analogy with the integer quantum Hall effect, we show how the topological Chern numbers of the bands can be extracted from the mean transverse shift of the steady-state oscillation amplitude distribution. Finally, we discuss the regime where the analogy with the Harper-Hofstadter model breaks down.
NASA Astrophysics Data System (ADS)
Zhao, Liyun; Zhou, Jin; Wu, Quanjun
2016-01-01
This paper considers the sampled-data synchronisation problems of coupled harmonic oscillators with communication and input delays subject to controller failure. A synchronisation protocol is proposed for such oscillator systems over directed network topology, and then some general algebraic criteria on exponential convergence for the proposed protocol are established. The main features of the present investigation include: (1) both the communication and input delays are simultaneously addressed, and the directed network topology is firstly considered and (2) the effects of time delays on synchronisation performance are theoretically and numerically investigated. It is shown that in the absence of communication delays, coupled harmonic oscillators can achieve synchronisation oscillatory motion. Whereas if communication delays are nonzero at infinite multiple sampled-data instants, its synchronisation (or consensus) state is zero. This conclusion can be used as an effective control strategy to stabilise coupled harmonic oscillators in practical applications. Furthermore, it is interesting to find that increasing either communication or input delays will enhance the synchronisation performance of coupled harmonic oscillators. Subsequently, numerical examples illustrate and visualise theoretical results.
Rodriguez-Gallardo, M.; Arias, J. M.; Gomez-Camacho, J.; Moro, A. M.; Johnson, R. C.; Tostevin, J. A.; Thompson, I. J.
2008-06-15
The scattering of a weakly bound three-body system by a target is discussed. A transformed harmonic oscillator basis is used to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum of the projectile. The continuum-discretized coupled-channels framework is used for the scattering calculations. The formalism is applied to different reactions, {sup 6}He+{sup 12}C at 229.8 MeV, {sup 6}He+{sup 64}Zn at 10 and 13.6 MeV, and {sup 6}He+{sup 208}Pb at 22 MeV, induced by the Borromean nucleus {sup 6}He. Both the Coulomb and nuclear interactions with a target are taken into account.
Moro, A. M.; Arias, J. M.; Gomez-Camacho, J.; Perez-Bernal, F.
2009-11-15
A new method for continuum discretization in continuum-discretized coupled-channels calculations is proposed. The method is based on an analytic local-scale transformation of the harmonic-oscillator wave functions proposed for other purposes in a recent work [Karatagladis et al., Phys. Rev. C 71, 064601 (2005)]. The new approach is compared with the standard method of continuum discretization in terms of energy bins for the reactions d+{sup 58}Ni at 80 MeV, {sup 6}Li+{sup 40}Ca at 156 MeV, and {sup 6}He+{sup 208}Pb at 22 MeV and 240 MeV/nucleon. In all cases very good agreement between both approaches is found.
Entanglement in a continuously measured two-level system coupled to a harmonic oscillator
Hernandez-Concepcion, E.; Alonso, D.; Brouard, S.
2009-05-15
The dynamics of a two-level system (TLS) coupled to a harmonic oscillator (HO) is studied under the combined effect of a thermal bath acting on the HO and of a detector continuously measuring one of the components of the spinlike TLS. The analysis focuses on the dynamics of the 'relative entropy of entanglement' (REE) in the one-energy-excitation manifold of the reduced TLS+HO system. For this model system, a stationary state is shown to be reached for which the relative entropy of entanglement is in general nonzero, even though, under certain approximations, the separate effects of bath and detector would be to remove any trace of this resource from the system. Analytical as well as numerical results are obtained for the REE as a function of the different parameters involved in the model definition.
Relativistic harmonic oscillator revisited
Bars, Itzhak
2009-02-15
The familiar Fock space commonly used to describe the relativistic harmonic oscillator, for example, as part of string theory, is insufficient to describe all the states of the relativistic oscillator. We find that there are three different vacua leading to three disconnected Fock sectors, all constructed with the same creation-annihilation operators. These have different spacetime geometric properties as well as different algebraic symmetry properties or different quantum numbers. Two of these Fock spaces include negative norm ghosts (as in string theory), while the third one is completely free of ghosts. We discuss a gauge symmetry in a worldline theory approach that supplies appropriate constraints to remove all the ghosts from all Fock sectors of the single oscillator. The resulting ghost-free quantum spectrum in d+1 dimensions is then classified in unitary representations of the Lorentz group SO(d,1). Moreover, all states of the single oscillator put together make up a single infinite dimensional unitary representation of a hidden global symmetry SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these new results in string theory and other areas of physics and mathematics are briefly mentioned.
On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress
Bocko, M.F.; Onofrio, R.
1996-07-01
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 {ital et} {ital al}., 1980, Rev. Mod. Phys. {bold 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} {ital 1996 The American Physical Society.}
Harmonic Oscillators as Bridges between Theories
NASA Astrophysics Data System (ADS)
Kim, Y. S.; Noz, Marilyn E.
2005-03-01
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. It is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called SL(2, c). Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics.
Synchronous Discrete Harmonic Oscillator
Antippa, Adel F.; Dubois, Daniel M.
2008-10-17
We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2{pi} in phase space, is an integral multiple N of the discrete time step {delta}t. It is fully synchronous when N is even. It is pseudo-synchronous when T/{delta}t is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is ''blue shifted'' relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval {delta}t. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.
Synchronous Discrete Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Antippa, Adel F.; Dubois, Daniel M.
2008-10-01
We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2π in phase space, is an integral multiple N of the discrete time step Δt. It is fully synchronous when N is even. It is pseudo-synchronous when T/Δt is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is "blue shifted" relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval Δt. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.
Galilean covariant harmonic oscillator
NASA Technical Reports Server (NTRS)
Horzela, Andrzej; Kapuscik, Edward
1993-01-01
A Galilean covariant approach to classical mechanics of a single particle is described. Within the proposed formalism, all non-covariant force laws defining acting forces which become to be defined covariantly by some differential equations are rejected. Such an approach leads out of the standard classical mechanics and gives an example of non-Newtonian mechanics. It is shown that the exactly solvable linear system of differential equations defining forces contains the Galilean covariant description of harmonic oscillator as its particular case. Additionally, it is demonstrated that in Galilean covariant classical mechanics the validity of the second Newton law of dynamics implies the Hooke law and vice versa. It is shown that the kinetic and total energies transform differently with respect to the Galilean transformations.
NASA Astrophysics Data System (ADS)
Xu, Shi-Min; Xu, Xing-Lei; Li, Hong-Qi
2008-06-01
The intermediate representation (namely intermediate coordinate-momentum representation) | x> λ, ν are introduced and employed to research the expression of the operator tauhat{p}+σhat{x} in intermediate representation | x> λ, ν . The systematic Hamilton operator hat{H} of 3D cross coupling quantum harmonic oscillator was diagonalized by virtue of quadratic form theory. The quantity of λ, ν, τand σ were figured out. The dynamic problems of 3D cross coupling quantum harmonic oscillator are researched by virtue of intermediate representation. The energy eigen-value and eigenwave function of 3D cross coupling quantum harmonic oscillator were obtained in intermediate representation. The importance of intermediate representation was discussed. The results show that the Radon transformation of Wigner operator is just the projectional operator | x> λ, ν λ, ν < x|, and the Radon transformation of Wigner function is just a margin distribution.
Quantum wormholes and harmonic oscillators
NASA Technical Reports Server (NTRS)
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.
Quantum harmonic oscillator in a thermal bath
NASA Technical Reports Server (NTRS)
Zhang, Yuhong
1993-01-01
The influence functional path-integral treatment of quantum Brownian motion is briefly reviewed. A newly derived exact master equation of a quantum harmonic oscillator coupled to a general environment at arbitrary temperature is discussed. It is applied to the problem of loss of quantum coherence.
Braun, J; Buntkowsky, G; Bernarding, J; Tolxdorff, T; Sack, I
2001-06-01
New methods for simulating and analyzing Magnetic Resonance Elastography (MRE) images are introduced. To simulate a two-dimensional shear wave pattern, the wave equation is solved for a field of coupled harmonic oscillators with spatially varying coupling and damping coefficients in the presence of an external force. The spatial distribution of the coupling and the damping constants are derived from an MR image of the investigated object. To validate the simulation as well as to derive the elasticity modules from experimental MRE images, the wave patterns are analyzed using a Local Frequency Estimation (LFE) algorithm based on Gauss filter functions with variable bandwidths. The algorithms are tested using an Agar gel phantom with spatially varying elasticity constants. Simulated wave patterns and LFE results show a high agreement with experimental data. Furthermore, brain images with estimated elasticities for gray and white matter as well as for exemplary tumor tissue are used to simulate experimental MRE data. The calculations show that already small distributions of pathologically changed brain tissue should be detectable by MRE even within the limit of relatively low shear wave excitation frequency around 0.2 kHz.
Covariant harmonic oscillators: 1973 revisited
NASA Technical Reports Server (NTRS)
Noz, M. E.
1993-01-01
Using the relativistic harmonic oscillator, a physical basis is given to the phenomenological wave function of Yukawa which is covariant and normalizable. It is shown that this wave function can be interpreted in terms of the unitary irreducible representations of the Poincare group. The transformation properties of these covariant wave functions are also demonstrated.
Demonstration of Double EIT Using Coupled Harmonic Oscillators and RLC Circuits
ERIC Educational Resources Information Center
Harden, Joshua; Joshi, Amitabh; Serna, Juan D.
2011-01-01
Single and double electromagnetically induced transparencies (EIT) in a medium, consisting of four-level atoms in the inverted-Y configuration, are discussed using mechanical and electrical analogies. A three-coupled spring-mass system subject to damping and driven by an external force is used to represent the four-level atom mechanically. The…
Saturation in coupled oscillators
NASA Astrophysics Data System (ADS)
Roman, Ahmed; Hanna, James
2015-03-01
We consider a weakly nonlinear system consisting of a resonantly forced oscillator coupled to an unforced oscillator. It has long been known that, for quadratic nonlinearities and a 2:1 resonance between the oscillators, a perturbative solution of the dynamics exhibits a phenomenon known as saturation. At low forcing, the forced oscillator responds, while the unforced oscillator is quiescent. Above a critical value of the forcing, the forced oscillator's steady-state amplitude reaches a plateau, while that of the unforced oscillator increases without bound. We show that, contrary to established folklore, saturation is not unique to quadratically nonlinear systems. We present conditions on the form of the nonlinear couplings and resonance that lead to saturation. Our results elucidate a mechanism for localization or diversion of energy in systems of coupled oscillators, and suggest new approaches for the control or suppression of vibrations in engineered systems.
Relation of squeezed states between damped harmonic and simple harmonic oscillators
NASA Technical Reports Server (NTRS)
Um, Chung-In; Yeon, Kyu-Hwang; George, Thomas F.; Pandey, Lakshmi N.
1993-01-01
The minimum uncertainty and other relations are evaluated in the framework of the coherent states of the damped harmonic oscillator. It is shown that the coherent states of the damped harmonic oscillator are the squeezed coherent states of the simple harmonic oscillator. The unitary operator is also constructed, and this connects coherent states with damped harmonic and simple harmonic oscillators.
Pure Gaussian states from quantum harmonic oscillator chains with a single local dissipative process
NASA Astrophysics Data System (ADS)
Ma, Shan; Woolley, Matthew J.; Petersen, Ian R.; Yamamoto, Naoki
2017-03-01
We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of (2\\aleph +1) quantum harmonic oscillators where the central oscillator of the chain is coupled to a single reservoir. We then completely parametrize the class of (2\\aleph +1) -mode pure Gaussian states that can be prepared by this type of quantum harmonic oscillator chain. This parametrization allows us to determine the steady-state entanglement properties of such quantum harmonic oscillator chains.
The harmonic oscillator and nuclear physics
NASA Technical Reports Server (NTRS)
Rowe, D. J.
1993-01-01
The three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It is shown that the three-dimensional harmonic oscillator features a rich variety of coherent states, including vibrations of the monopole, dipole, and quadrupole types, and rotations of the rigid flow, vortex flow, and irrotational flow types. Nuclear collective states exhibit all of these flows. It is also shown that the coherent state representations, which have their origins in applications to the dynamical groups of the simple harmonic oscillator, can be extended to vector coherent state representations with a much wider range of applicability. As a result, coherent state theory and vector coherent state theory become powerful tools in the application of algebraic methods in physics.
Second International Workshop on Harmonic Oscillators
NASA Technical Reports Server (NTRS)
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.
Quantum harmonic oscillator with superoscillating initial datum
Buniy, R. V.; Struppa, D. C.; Colombo, F.; Sabadini, I.
2014-11-15
In this paper, we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the harmonic potential and that the analytic solution develops a singularity in finite time. We also show that for a large class of solutions of the Schrödinger equation, superoscillating behavior at any given time implies superoscillating behavior at any other time.
Improving Density Functionals with Quantum Harmonic Oscillators
NASA Astrophysics Data System (ADS)
Tkatchenko, Alexandre
2013-03-01
Density functional theory (DFT) is the most widely used and successful approach for electronic structure calculations. However, one of the pressing challenges for DFT is developing efficient functionals that can accurately capture the omnipresent long-range electron correlations, which determine the structure and stability of many molecules and materials. Here we show that, under certain conditions, the problem of computing the long-range correlation energy of interacting electrons can be mapped to a system of coupled quantum harmonic oscillators (QHOs). The proposed model allows us to synergistically combine concepts from DFT, quantum chemistry, and the widely discussed random-phase approximation for the correlation energy. In the dipole limit, the interaction energy for a system of coupled QHOs can be calculated exactly, thereby leading to an efficient and accurate model for the many-body dispersion energy of complex molecules and materials. The studied examples include intermolecular binding energies, the conformational hierarchy of DNA structures, the geometry and stability of molecular crystals, and supramolecular host-guest complexes (A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012); R. A. DiStasio Jr., A. von Lilienfeld, A. Tkatchenko, PNAS 109, 14791 (2012); A. Tkatchenko, D. Alfe, K. S. Kim, J. Chem. Theory and Comp. (2012), doi: 10.1021/ct300711r; A. Tkatchenko, A. Ambrosetti, R. A. DiStasio Jr., arXiv:1210.8343v1).
Quantum nondemolition measurements of harmonic oscillators
NASA Technical Reports Server (NTRS)
Thorne, K. S.; Caves, C. M.; Zimmermann, M.; Sandberg, V. D.; Drever, R. W. P.
1978-01-01
Measuring systems to determine the real component of the complex amplitude of a harmonic oscillator are described. This amplitude is constant in the absence of driving forces, and the uncertainty principle accounts for the fact that only the real component can be measured precisely and continuously ('quantum nondemolition measurement'). Application of the measuring systems to the detection of gravitational waves is considered.
Group Theory of Covariant Harmonic Oscillators
ERIC Educational Resources Information Center
Kim, Y. S.; Noz, Marilyn E.
1978-01-01
A simple and concrete example for illustrating the properties of noncompact groups is presented. The example is based on the covariant harmonic-oscillator formalism in which the relativistic wave functions carry a covariant-probability interpretation. This can be used in a group theory course for graduate students who have some background in…
Reaching Synchronization in Networked Harmonic Oscillators With Outdated Position Data.
Song, Qiang; Yu, Wenwu; Cao, Jinde; Liu, Fang
2016-07-01
This paper studies the synchronization problem for a network of coupled harmonic oscillators by proposing a distributed control algorithm based only on delayed position states, i.e., outdated position states stored in memory. The coupling strength of the network is conveniently designed according to the absolute values and the principal arguments of the nonzero eigenvalues of the network Laplacian matrix. By analyzing a finite number of stability switches of the network with respect to the variation in the time delay, some necessary and sufficient conditions are derived for reaching synchronization in networked harmonic oscillators with positive and negative coupling strengths, respectively, and it is shown that the time delay should be taken from a set of intervals bounded by some critical values. Simulation examples are given to illustrate the effectiveness of the theoretical analysis.
Finite quantum kinematics of the harmonic oscillator
Shiri-Garakani, Mohsen; Finkelstein, David Ritz
2006-03-15
Arbitrarily small changes in the commutation relations suffice to transform the usual singular quantum theories into regular quantum theories. This process is an extension of canonical quantization that we call general quantization. Here we apply general quantization to the time-independent linear harmonic oscillator. The unstable Heisenberg group becomes the stable group SO(3). This freezes out the zero-point energy of very soft or very hard oscillators, like those responsible for the infrared or ultraviolet divergencies of usual field theories, without much changing the medium oscillators. It produces pronounced violations of equipartition and of the usual uncertainty relations for soft or hard oscillators, and interactions between the previously uncoupled excitation quanta of the oscillator, weakly attractive for medium quanta, strongly repulsive for soft or hard quanta.
Caligiuri, Luigi Maxmilian
2015-01-01
The question regarding the potential biological and adverse health effects of non-ionizing electromagnetic fields on living organisms is of primary importance in biophysics and medicine. Despite the several experimental evidences showing such occurrence in a wide frequency range from extremely low frequency to microwaves, a definitive theoretical model able to explain a possible mechanism of interaction between electromagnetic fields and living matter, especially in the case of weak and very weak intensities, is still missing. In this paper it has been suggested a possible mechanism of interaction involving the resonant absorption of electromagnetic radiation by microtubules. To this aim these have been modeled as non-dissipative forced harmonic oscillators characterized by two coupled "macroscopic" degrees of freedom, respectively describing longitudinal and transversal vibrations induced by the electromagnetic field. We have shown that the proposed model, although at a preliminary stage, is able to explain the ability of even weak electromagnetic radiating electromagnetic fields to transfer high quantities of energy to living systems by means of a resonant mechanism, so capable to easily damage microtubules structure.
Enhancing energy harvesting by coupling monostable oscillators
NASA Astrophysics Data System (ADS)
Peña Rosselló, Julián I.; Wio, Horacio S.; Deza, Roberto R.; Hänggi, Peter
2017-02-01
The performance of a ring of linearly coupled, monostable nonlinear oscillators is optimized towards its goal of acting as energy harvester - through piezoelectric transduction - of mesoscopic fluctuations, which are modeled as Ornstein-Uhlenbeck noises. For a single oscillator, the maximum output voltage and overall efficiency are attained for a soft piecewise-linear potential (providing a weak attractive constant force) but they are still fairly large for a harmonic potential. When several harmonic springs are linearly and bidirectionally coupled to form a ring, it is found that counter-phase coupling can largely improve the performance while in-phase coupling worsens it. Moreover, it turns out that few (two or three) coupled units perform better than more.
Harmonic oscillator interaction with squeezed radiation
NASA Technical Reports Server (NTRS)
Dodonov, V. V.; Nikonov, D. E.
1993-01-01
Although the problem of electromagnetic radiation by a quantum harmonic oscillator is considered in textbooks on quantum mechanics, some of its aspects have remained unclear until now. By this, we mean that usually the initial quantum states of both the oscillator and the field are assumed to be characterized by a definite energy level of the oscillator and definite occupation numbers of the field modes. In connection with growing interest in squeezed states, it would be interesting to analyze the general case when the initial states of both subsystems are arbitrary superpositions of energy eigenstates. This problem was considered in other work, where the power of the spontaneous emission was calculated in the case of an arbitrary oscillator's initial state, but the field was initially in a vacuum state. In the present article, we calculate the rate of the oscillator average energy, squeezing, and correlation parameter change under the influence of an arbitrary external radiation field. Some other problems relating to the interaction between quantum particles (atoms) or oscillators where the electromagnetic radiation is an arbitrary (in particular squeezed) state were investigated.
Finite quantum theory of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Shiri-Garakani, Mohsen
We apply the Segal process of group simplification to the linear harmonic oscillator. The result is a finite quantum theory with three quantum constants h, h', h″ instead of the usual one. We compare the classical (CLHO), quantum (QLHO), and finite (FLHO) linear harmonic oscillators and their canonical or unitary groups. The FLHO is isomorphic to a dipole rotator with N = l(l + 1) ˜ 1/(h ' h″) states and Hamiltonian H = A(Lx)2 + B(Ly)2, and the physically interesting case has N ≫ 1. The position and momentum variables are quantized with uniform finite spectra. For fixed quantum constants and large N ≫ 1 there are three broad classes of FLHO: soft, medium, and hard, with B/A ≪ 1, B/A ˜ 1, and B/A ≫ 1 respectively. The field oscillators responsible for infra-red and ultraviolet divergences are soft and hard respectively. Medium oscillators have B/A ˜ 1 and approximate the QLHO. They have ˜ N low-lying states with nearly the same zero-point energy and level spacing as the QLHO, and nearly obeying the Heisenberg uncertainty principle and the equipartition principle. The corresponding rotators are nearly polarized along the z axis with Lz ˜ +/-l. The soft and hard FLHO's have infinitesimal 0-point energy and grossly violate equipartition and the Heisenberg uncertainty principle. They do not resemble the QLHO at all. Their low-lying energy states correspond to rotators with Lx ˜ 0 or Ly ˜ 0 instead of Lz ˜ +/-l. Soft oscillators have frozen momentum, because their maximum potential energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to excite one quantum of position.
Avoiding dissipation in a system of three quantum harmonic oscillators
NASA Astrophysics Data System (ADS)
Manzano, Gonzalo; Galve, Fernando; Zambrini, Roberta
2013-03-01
We analyze the symmetries in an open quantum system composed by three coupled and detuned harmonic oscillators in the presence of a common heat bath. It is shown analytically how to engineer the couplings and frequencies of the system so as to have several degrees of freedom unaffected by decoherence, irrespective of the specific spectral density or initial state of the bath. This partial thermalization allows observing asymptotic entanglement at moderate temperatures, even in the nonresonant case. This latter feature cannot be seen in the simpler situation of only two oscillators, highlighting the richer structural variety of the three-body case. When departing from the strict conditions for partial thermalization, a hierarchical structure of dissipation rates for the normal modes is observed, leading to a long transient where quantum correlations such as the quantum discord are largely preserved, as well as to synchronous dynamics of the oscillators quadratures.
Coupled opto-electronic oscillator
NASA Technical Reports Server (NTRS)
Yao, X. Steve (Inventor); Maleki, Lute (Inventor)
1999-01-01
A coupled opto-electronic oscillator that directly couples a laser oscillation with an electronic oscillation to simultaneously achieve a stable RF oscillation at a high frequency and ultra-short optical pulsation by mode locking with a high repetition rate and stability. Single-mode selection can be achieved even with a very long opto-electronic loop. A multimode laser can be used to pump the electronic oscillation, resulting in a high operation efficiency. The optical and the RF oscillations are correlated to each other.
Classical and revival time periods of confined harmonic oscillator
NASA Astrophysics Data System (ADS)
Ghosh, P.; Ghosh, S.; Bera, N.
2015-02-01
We have used perturbation theory to compute energy eigenvalues, classical and the revival time periods for a one-dimensional harmonic oscillator confined in a box. First we have considered a simple harmonic oscillator as the unperturbed problem and boundary as perturbation. In next case, free particle in a box is considered as unperturbed problem that has been perturbed by a parabolic potential. We have used Fourier Grid Hamiltonian method to estimate classical and revival time period for the confined harmonic oscillator, which crosses smoothly from free particle in a box to a simple harmonic oscillator.
Effective field theory in the harmonic oscillator basis
Binder, S.; Ekström, Jan A.; Hagen, Gaute; ...
2016-04-25
In this paper, we develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leadingmore » order. Finally, many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.« less
Effective field theory in the harmonic oscillator basis
Binder, S.; Ekström, Jan A.; Hagen, Gaute; Papenbrock, Thomas F.; Wendt, Kyle A.
2016-04-25
In this paper, we develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Finally, many-body coupled-cluster calculations of nuclei up to ^{132}Sn converge fast for the ground-state energies and radii in feasible model spaces.
NASA Astrophysics Data System (ADS)
Tay, Buang Ann
The eigenvalue problem of Kossakowski-Linblad's kinetic equation associated with the reduced density matrix of a harmonic oscillator interacting with a thermal bath in equilibrium is solved. The solution gives rise to a complete orthogonal eigenbasis endowed with Hilbert space structure that has a weighted norm. We find that the eigenfunctions at finite temperature can be obtained from the eigenfunction at zero temperature through a hyperbolic rotation on the position variables. This transformation enables the extension of the simple harmonic oscillator density matrix to that of a finite temperature. We further investigate the decay of these extended states under our dissipative kinetic equation. Furthermore, the Hilbert space structure enables the proof of a H -theorem in this system. We apply the eigenbasis expansion of an initial state to analyze decoherence as well as coherence processes. We find that coherence process occurs at a longer time scale compared to decoherence process. The time scales of both processes are estimated with the eigenbasis expansion. In the same way we analyze the evolution of the coherent state. We show that in addition to the ordinary decay time, we found another time scale which is defined by the time when the motion of the peak of the coherent state become comparative to the width of the coherent state. In contrast to the ordinary decay time this new relaxation time depends on the initial value of the momentum of the oscillator. We also find that our eigenbasis is applicable to a class of non-linear interactions, with a slight extension of the form of transport coefficients due to the non-linear interactions.
Non-Markovian quantum Brownian motion of a harmonic oscillator
Tang, J.
1994-02-01
We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.
A possible generalization of the harmonic oscillator potential
NASA Technical Reports Server (NTRS)
Levai, Geza
1995-01-01
A four-parameter potential is analyzed, which contains the three-dimensional harmonic oscillator as a special case. This potential is exactly solvable and retains several characteristics of the harmonic oscillator, and also of the Coulomb problem. The possibility of similar generalizations of other potentials is also pointed out.
Coherent states for the relativistic harmonic oscillator
NASA Technical Reports Server (NTRS)
Aldaya, Victor; Guerrero, J.
1995-01-01
Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.
A Look at Damped Harmonic Oscillators through the Phase Plane
ERIC Educational Resources Information Center
Daneshbod, Yousef; Latulippe, Joe
2011-01-01
Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the…
Hamiltonian of mean force and a damped harmonic oscillator in an anisotropic medium
NASA Astrophysics Data System (ADS)
Jafari, Marjan; Kheirandish, Fardin
2017-01-01
The quantum dynamics of a damped harmonic oscillator is investigated in the presence of an anisotropic heat bath. The medium is modeled by a continuum of three dimensional harmonic oscillators and anisotropic coupling is treated by introducing tensor coupling functions. Starting from a classical Lagrangian, the total system is quantized in the framework of the canonical quantization. Following the Fano technique, the Hamiltonian of the system is diagonalized in terms of creation and annihilation operators that are linear combinations of the basic dynamical variables. Using the diagonalized Hamiltonian, the mean force internal energy, free energy and entropy of the damped oscillator are calculated.
Driven harmonic oscillator as a quantum simulator for open systems
Piilo, Jyrki; Maniscalco, Sabrina
2006-09-15
We show theoretically how a driven harmonic oscillator can be used as a quantum simulator for the non-Markovian damped harmonic oscillator. In the general framework, our results demonstrate the possibility to use a closed system as a simulator for open quantum systems. The quantum simulator is based on sets of controlled drives of the closed harmonic oscillator with appropriately tailored electric field pulses. The non-Markovian dynamics of the damped harmonic oscillator is obtained by using the information about the spectral density of the open system when averaging over the drives of the closed oscillator. We consider single trapped ions as a specific physical implementation of the simulator, and we show how the simulator approach reveals physical insight into the open system dynamics, e.g., the characteristic quantum mechanical non-Markovian oscillatory behavior of the energy of the damped oscillator, usually obtained by the non-Lindblad-type master equation, can have a simple semiclassical interpretation.
Coupled oscillators on evolving networks
NASA Astrophysics Data System (ADS)
Singh, R. K.; Bagarti, Trilochan
2016-12-01
In this work we study coupled oscillators on evolving networks. We find that the steady state behavior of the system is governed by the relative values of the spread in natural frequencies and the global coupling strength. For coupling strong in comparison to the spread in frequencies, the system of oscillators synchronize and when coupling strength and spread in frequencies are large, a phenomenon similar to amplitude death is observed. The network evolution provides a mechanism to build inter-oscillator connections and once a dynamic equilibrium is achieved, oscillators evolve according to their local interactions. We also find that the steady state properties change by the presence of additional time scales. We demonstrate these results based on numerical calculations studying dynamical evolution of limit-cycle and van der Pol oscillators.
Isar, A.; Sandulescu, A. ); Scheid, W. )
1990-05-01
In the frame of the Lindblad theory of open quantum systems, the spherical harmonic oscillator with opening operators linear in the coordinates and the momenta of the considered system is analyzed. Explicit expressions for the damping of the energy, angular momentum and its projection, including the coupling of the harmonic oscillator due to the environment, are obtained.
Heat and work fluctuations for a harmonic oscillator.
Sabhapandit, Sanjib
2012-02-01
The formalism of Kundu et al. [J. Stat. Mech. P03007 (2011)], for computing the large deviations of heat flow in harmonic systems, is applied to the case of single Brownian particle in a harmonic trap and coupled to two heat baths at different temperatures. The large-τ form of the moment generating function
Harmonic and Anharmonic Behaviour of a Simple Oscillator
ERIC Educational Resources Information Center
O'Shea, Michael J.
2009-01-01
We consider a simple oscillator that exhibits harmonic and anharmonic regimes and analyse its behaviour over the complete range of possible amplitudes. The oscillator consists of a mass "m" fixed at the midpoint of a horizontal rope. For zero initial rope tension and small amplitude the period of oscillation, tau, varies as tau is approximately…
Entanglement dynamics for a conditionally kicked harmonic oscillator
NASA Astrophysics Data System (ADS)
Arrais, Eric G.; Sales, J. S.; de Almeida, N. G.
2016-08-01
The time evolution of the quantum kicked harmonic oscillator (KHO) is described by the Floquet operator which maps the state of the system immediately before one kick onto the state at a time immediately after the next. Quantum KHO is characterized by three parameters: the coupling strength V 0, the so-called Lamb-Dicke parameter η whose square is proportional to the effective Planck constant {{\\hslash }}{{eff}}, and the ratio T of the natural frequency of the oscillator and the kick frequency. To a given coupling strength and depending on T being a natural or irrational number, the phase space of the classical kicked oscillator can display different behaviors, as for example, stochastic webs or quasicrystal structures, thus showing a chaotic or localized behavior that is mirrored in the quantum phase space. On the other hand, the classical limit is studied letting {{\\hslash }}{{eff}} become negligible. In this paper we investigate how the ratio T, considered as integer, rational or irrational, influences the entanglement dynamics of the quantum KHO and study how the entanglement dynamics behaves when varying either V 0 or {{\\hslash }}{{eff}} parameters.
Harmonic oscillator in quantum rotational spectra: Molecules and nuclei
NASA Technical Reports Server (NTRS)
Pavlichenkov, Igor M.
1995-01-01
The mapping of a rotational dynamics on a harmonic oscillator is considered. The method used for studying the stabilization of the rigid top rotation around the intermediate moment of inertial axix by orbiting particle is described.
A harmonic oscillator having “volleyball damping”
NASA Astrophysics Data System (ADS)
Mickens, R. E.; Oyedeji, K.; Rucker, S. A.
2006-05-01
Volleyball damping corresponds to linear damping up to a certain critical velocity, with zero damping above this value. The dynamics of a linear harmonic oscillator is investigated with this damping mechanism.
Harmonic coupling of steady-state visual evoked potentials.
Krusienski, Dean J; Allison, Brendan Z
2008-01-01
Steady-state visual evoked potentials (SSVEPs) are oscillating components of the electroencephalogram (EEG) that are detected over the occipital areas, having frequencies corresponding to visual stimulus frequencies. SSVEPs have been demonstrated to be reliable control signals for operating a brain-computer interface (BCI). This study uses offline analyses to investigate the characteristics of SSVEP harmonic amplitude and phase coupling and the impact of using this information to construct a matched filter for continuously tracking the signal.
Experimental demonstration of a technique for generation of arbitrary harmonic oscillator states.
NASA Astrophysics Data System (ADS)
Ben-Kish, A.; Demarco, B.; Rowe, M.; Meyer, V.; Britton, J.; Itano, W. M.; Jelenković, B. M.; Langer, C.; Leibfried, D.; Rosenband, T.; Wineland, D. J.
2002-05-01
Synthesizing arbitrary quantum states is at the heart of such diverse fields as quantum computation and reaction control in chemistry. For harmonic oscillator states, particular interactions (in general, non-linear) can be used to generate special states such as squeezed states. However, it is usually intractable to realize the interactions required to create arbitrary states. Law and Eberly [1] have devised a technique for arbitrary harmonic oscillator state generation that couples the oscillator to a two-level atomic or spin system and applies a sequence of operations that use simple interactions. We demonstrate the general features of this technique on the harmonic motion of a single trapped ^9Be^+ ion and extend it to the generation of arbitrary spin-oscillator states [2]. [1] C. K. Law and J. H. Eberly, Phys. Rev. Lett. 76, 1055 (1996). [2] B. Kneer and C. K. Law, Phys. Rev. A 57, 2096 (1998).
The Study of Damped Harmonic Oscillations Using an Electronic Counter
ERIC Educational Resources Information Center
Wadhwa, Ajay
2009-01-01
We study damped harmonic oscillations in mechanical systems like the loaded spring and simple pendulum with the help of an oscillation measuring electronic counter. The experimental data are used in a software program that solves the differential equation for damped vibrations of any system and determines its position, velocity and acceleration as…
On the moment of inertia of a quantum harmonic oscillator
Khamzin, A. A. Sitdikov, A. S.; Nikitin, A. S.; Roganov, D. A.
2013-04-15
An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.
Coupled harmonic systems as quantum buses in thermal environments
NASA Astrophysics Data System (ADS)
Nicacio, F.; Semião, F. L.
2016-09-01
In this work, we perform a careful study of a special arrangement of coupled systems that consists of two external harmonic oscillators weakly coupled to an arbitrary network (data bus) of strongly interacting oscillators. Our aim is to establish simple effective Hamiltonians and Liouvillians allowing an accurate description of the dynamics of the external oscillators regardless of the topology of the network. By simple, we mean an effective description using just a few degrees of freedom. With the methodology developed here, we are able to treat general topologies and, under certain structural conditions, to also include the interaction with external environments. In order to illustrate the predictability of the simplified dynamics, we present a comparative study with the predictions of the numerically obtained exact description in the context of propagation of energy through the network.
Magnetically Coupled Magnet-Spring Oscillators
ERIC Educational Resources Information Center
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…
Time-dependent Hartree approximation and time-dependent harmonic oscillator model
NASA Astrophysics Data System (ADS)
Blaizot, J. P.; Schulz, H.
1982-03-01
We present an analytically soluble model for studying nuclear collective motion within the framework of the time-dependent Hartree (TDH) approximation. The model reduces the TDH equations to the Schrödinger equation of a time-dependent harmonic oscillator. Using canonical transformations and coherent states we derive a few properties of the time-dependent harmonic oscillator which are relevant for applications. We analyse the role of the normal modes in the time evolution of a system governed by TDH equations. We show how these modes couple together due to the anharmonic terms generated by the non-linearity of the theory.
Coupled oscillators and Feynman's three papers
NASA Astrophysics Data System (ADS)
Kim, Y. S.
2007-05-01
According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the "rest of the universe" contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators.
An algebraic cluster model based on the harmonic oscillator basis
NASA Technical Reports Server (NTRS)
Levai, Geza; Cseh, J.
1995-01-01
We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.
Predicting charmonium and bottomonium spectra with a quark harmonic oscillator
NASA Technical Reports Server (NTRS)
Norbury, J. W.; Badavi, F. F.; Townsend, L. W.
1986-01-01
The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.
Violation of smooth observable macroscopic realism in a harmonic oscillator.
Leshem, Amir; Gat, Omri
2009-08-14
We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. We demonstrate a breakdown of dynamical realism in a wide parameter range that is maximized in a scaling limit of extreme squeezing, where it is based on measurements of smooth observables, implying that macroscopic realism is not valid in the harmonic oscillator. We propose an indirect experimental test of these predictions with entangled photons by demonstrating that local realism in a composite system implies dynamical realism in a subsystem.
Quantum kicked harmonic oscillator in contact with a heat bath
NASA Astrophysics Data System (ADS)
Prado Reynoso, M. Á.; López Vázquez, P. C.; Gorin, T.
2017-02-01
We consider the quantum harmonic oscillator in contact with a finite-temperature bath, modeled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system in different dynamical regimes between classical integrability and chaos, on the one hand, and ballistic or diffusive energy absorption, on the other. We then investigate the influence of the heat bath on the oscillator in each case. Phase-space techniques allow us to simulate the evolution of the system efficiently. In this way, we calculate high-resolution Wigner functions at long times, where the system approaches a quasistationary cyclic evolution. Thereby, we perform an accurate study of the thermodynamic properties of a nonintegrable, quantum chaotic system in contact with a heat bath at finite temperature. In particular, we find that the heat transfer between harmonic oscillator and heat bath is governed by Fourier's law.
Observations of Harmonic Oscillations and ELM Magnetic Precursors in NSTX
NASA Astrophysics Data System (ADS)
Kelly, F.; Fredrickson, E.; Bell, R.; Tritz, K.; Maingi, R.; Takahashi, H.
2010-11-01
Recent experiments in the National Spherical Torus Experiment (NSTX) demonstrated the progressive suppression of edge localized modes (ELMs) with increasing lithium deposition. Sufficient lithium suppressed ELMs and made the occurrence of low-frequency, low-n harmonics more frequent. Signatures of these harmonic oscillations with a significant edge component were observed in both the high-n Mirnov magnetic and soft X-ray diagnostics of NSTX. Two distinct sets of harmonic oscillations can be observed during some ELM-free periods. The harmonic oscillations are consistent with modes localized in the edge with the frequency of the n = 1 harmonic near the rotation frequency of the edge plasma. NSTX magnetic diagnostics also observe distinctive signatures of ELMs. Transient n = 1 and n = 2 mode bursts and occasional higher n modes with frequency in the 30 to 90 kHz range occurred simultaneous with the increase in fast Da signal. These bursts of n = 1 and n = 2 modes resemble a model simulation of ELMs by T. Evans in which a bifurcation of magnetic topology is driven by nonlinear feedback amplification of thermoelectric currents from linear peeling-ballooning modes.
Symmetry algebra of a generalized anisotropic harmonic oscillator
NASA Technical Reports Server (NTRS)
Castanos, O.; Lopez-Pena, R.
1993-01-01
It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.
The One-Dimensional Damped Forced Harmonic Oscillator Revisited
ERIC Educational Resources Information Center
Flores-Hidalgo, G.; Barone, F. A.
2011-01-01
In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.
Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps
ERIC Educational Resources Information Center
Pendrill, Ann-Marie; Eager, David
2015-01-01
Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…
A Simple Mechanical Model for the Isotropic Harmonic Oscillator
ERIC Educational Resources Information Center
Nita, Gelu M.
2010-01-01
A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)
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.
Equity prices as a simple harmonic oscillator with noise
NASA Astrophysics Data System (ADS)
Ataullah, Ali; Tippett, Mark
2007-08-01
The centred return on the London Stock Exchange's FTSE All Share Index is modelled as a simple harmonic oscillator with noise over the period from 1 January, 1994 until 30 June 2006. Our empirical results are compatible with the hypothesis that there is a period in the FTSE All Share Index of between two and two and one half years. This means the centred return will on average continue to increase for about a year after reaching the minimum in its oscillatory cycle; alternatively, it will continue on average to decline for about a year after reaching a maximum. Our analysis also shows that there is potential to exploit the harmonic nature of the returns process to earn abnormal profits. Extending our analysis to the low energy states of a quantum harmonic oscillator is also suggested.
Nonsingular parametric oscillators Darboux-related to the classical harmonic oscillator
NASA Astrophysics Data System (ADS)
Rosu, H. C.; Cornejo-Pérez, O.; Chen, P.
2012-12-01
Interesting nonsingular parametric oscillators which are Darboux-related to the classical harmonic oscillator and have periodic dissipative/gain features are identified through a modified factorization method. The same method is applied to the upside-down (hyperbolic) “oscillator” for which the obtained Darboux partners show transient underdamped features.
Probing deformed commutators with macroscopic harmonic oscillators
Bawaj, Mateusz; Biancofiore, Ciro; Bonaldi, Michele; Bonfigli, Federica; Borrielli, Antonio; Di Giuseppe, Giovanni; Marconi, Lorenzo; Marino, Francesco; Natali, Riccardo; Pontin, Antonio; Prodi, Giovanni A.; Serra, Enrico; Vitali, David; Marin, Francesco
2015-01-01
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters have just been extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high-quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass mP (≈22 μg). The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation. PMID:26088965
Equilibrium and stationary nonequilibrium states in a chain of colliding harmonic oscillators
Sano
2000-02-01
Equilibrium and nonequilibrium properties of a chain of colliding harmonic oscillators (ding-dong model) are investigated. Our chain is modeled as harmonically bounded particles that can only interact with neighboring particles by hard-core interaction. Between the collisions, particles are just independent harmonic oscillators. We are especially interested in the stationary nonequilibrium state of the ding-dong model coupled with two stochastic heat reservoirs (not thermostated) at the ends, whose temperature is different. We check the Gallavotti-Cohen fluctuation theorem [G. Gallavoti and E. G. D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)] and also the Evans-Searles identity [D. Evans and D. Searles, Phys. Rev. E. 50, 1994 (1994)] numerically. It is verified that the former theorem is satisfied for this system, although the system is not a thermostated system.
Random reverse-cyclic matrices and screened harmonic oscillator
NASA Astrophysics Data System (ADS)
Srivastava, Shashi C. L.; Jain, Sudhir R.
2012-04-01
We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an N-body exactly solvable model. We refer to this well-known model potential as a screened harmonic oscillator. The connection enables us to obtain all the correlations among the particle positions moving in a screened harmonic potential. The density of nontrivial eigenvalues of this ensemble is found to be of the Wigner form and admits a hole at the origin, in contrast to the semicircle law of the Gaussian orthogonal ensemble of random matrices. The spacing distributions assume different forms ranging from Gaussian-like to Wigner.
Quantum harmonic oscillator: an elementary derivation of the energy spectrum
NASA Astrophysics Data System (ADS)
Borghi, Riccardo
2017-03-01
An elementary treatment of the quantum harmonic oscillator is proposed. No previous knowledge of linear differential equation theory or Fourier analysis are required, but rather only a few basics of elementary calculus. The pivotal role in our analysis is played by the sole particle localization constraint, which implies square integrability of stationary-state wavefunctions. The oscillator ground-state characterization is then achieved in a way that could be grasped, in principle, even by first-year undergraduates. A very elementary approach to build up and to characterize all higher-level energy eigenstates completes our analysis.
Pisot q-coherent states quantization of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Gazeau, J. P.; del Olmo, M. A.
2013-03-01
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 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.
BAYESIAN ANALYSIS OF MULTIPLE HARMONIC OSCILLATIONS IN THE SOLAR CORONA
Arregui, I.; Asensio Ramos, A.; Diaz, A. J.
2013-03-01
The detection of multiple mode harmonic kink oscillations in coronal loops enables us to obtain information on coronal density stratification and magnetic field expansion using seismology inversion techniques. The inference is based on the measurement of the period ratio between the fundamental mode and the first overtone and theoretical results for the period ratio under the hypotheses of coronal density stratification and magnetic field expansion of the wave guide. We present a Bayesian analysis of multiple mode harmonic oscillations for the inversion of the density scale height and magnetic flux tube expansion under each of the hypotheses. The two models are then compared using a Bayesian model comparison scheme to assess how plausible each one is given our current state of knowledge.
Free fall and harmonic oscillations: analyzing trampoline jumps
NASA Astrophysics Data System (ADS)
Pendrill, Ann-Marie; Eager, David
2015-01-01
Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is obtained in terms of maximum normalized force from the trampoline and the harmonic frequency. A simple expression is obtained for the ratio between air-time and harmonic period, and the maximum g-factor. The results are compared to experimental results, including accelerometer data showing 7g during bounces on a small trampoline in an amusement park play area. Similar results are obtained on a larger garden trampoline, and even larger accelerations have been measured for gymnastic trampolines.
An analogue of the Berry phase for simple harmonic oscillators
NASA Astrophysics Data System (ADS)
Suslov, S. K.
2013-03-01
We evaluate a variant of Berry's phase for a ‘missing’ family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables (in a natural way). Instead, it is obtained by the action of the maximal kinematical invariance group on the standard solutions. A simple closed formula for the phase (in terms of elementary functions) is found here by integration with the help of a computer algebra system.
Coherent and squeezed states for the 3D harmonic oscillator
NASA Astrophysics Data System (ADS)
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.
High gain amplifiers: Power oscillations and harmonic generation
Dattoli, G.; Ottaviani, P. L.; Pagnutti, S.
2007-08-01
We discuss the power oscillations in saturated high gain free electron laser amplifiers and show that the relevant period can be written in terms of the gain length. We use simple arguments following from the solution of the pendulum equation in terms of Jacobi elliptic functions. Nontrivial effects due to nonlinear harmonic generation and inhomogeneous broadening are discussed too, as well as the saturated dynamics of short pulses.
Collision-induced squeezing in a harmonic oscillator
NASA Technical Reports Server (NTRS)
Lee, Hai-Woong
1993-01-01
The concept of squeezing has so far been applied mainly to light, as is evidenced by the number of research works on the subject of squeezed light. Since, in quantum mechanics, both light and the simple harmonic oscillator are described within the same mathematical framework, there is of course no difficulty in applying the concept to the simple harmonic oscillator as well. In fact, the theoretical development of squeezed states and squeezed light owes much to the physical insights that one obtains as the analogy between light and the harmonic oscillator is exploited. The example presented shows clearly that two states with different phases in general have different degrees of squeezing, even if they have the same state distribution. This means that, even if one considers collision processes that produce the same state distribution, the degree of squeezing obtained during and after the collisions can be quite different, depending on how the phases phi(sub n) of the probability amplitudes develop in time as the collisions proceed. It is therefore evident that, for a detailed study of collision-induced squeezing, further study on the time development of the phases in collisions and its relation to collision parameters such as potential energy surfaces and collision energy is needed.
Teaching from a Microgravity Environment: Harmonic Oscillator and Pendulum
NASA Astrophysics Data System (ADS)
Benge, Raymond; Young, Charlotte; Davis, Shirley; Worley, Alan; Smith, Linda; Gell, Amber
2009-04-01
This presentation reports on an educational experiment flown in January 2009 as part of NASA's Microgravity University program. The experiment flown was an investigation into the properties of harmonic oscillators in reduced gravity. Harmonic oscillators are studied in every introductory physics class. The equation for the period of a harmonic oscillator does not include the acceleration due to gravity, so the period should be independent of gravity. However, the equation for the period of a pendulum does include the acceleration due to gravity, so the period of a pendulum should appear longer under reduced gravity (such as lunar or Martian gravity) and shorter under hyper-gravity. These environments can be simulated aboard an aircraft. Video of the experiments being performed aboard the aircraft is to be used in introductory physics classes. Students will be able to record information from watching the experiment performed aboard the aircraft in a similar manner to how they collect data in the laboratory. They can then determine if the experiment matches theory. Video and an experimental procedure are being prepared based upon this flight, and these materials will be available for download by faculty anywhere with access to the internet who wish to use the experiment in their own classrooms.
Coupled oscillators with parity-time symmetry
NASA Astrophysics Data System (ADS)
Tsoy, Eduard N.
2017-02-01
Different models of coupled oscillators with parity-time (PT) symmetry are studied. Hamiltonian functions for two and three linear oscillators coupled via coordinates and accelerations are derived. Regions of stable dynamics for two coupled oscillators are obtained. It is found that in some cases, an increase of the gain-loss parameter can stabilize the system. A family of Hamiltonians for two coupled nonlinear oscillators with PT-symmetry is obtained. An extension to high-dimensional PT-symmetric systems is discussed.
Emergence of a negative resistance in noisy coupled linear oscillators
NASA Astrophysics Data System (ADS)
Quiroz-Juárez, M. A.; Aragón, J. L.; León-Montiel, R. de J.; Vázquez-Medina, R.; Domínguez-Juárez, J. L.; Quintero-Torres, R.
2016-12-01
We report on the experimental observation of an emerging negative resistance in a system of coupled linear electronic RLC harmonic oscillators under the influence of multiplicative noise with long correlation time. When two oscillators are coupled by a noisy inductor, an analysis in the Fourier space of the electrical variables unveils the presence of an effective negative resistance, which acts as an energy transport facilitator. This might constitute a simple explanation of the now fashionable problem of energy transport assisted by noise in classical systems. The experimental setup is based on the working principle of an analog computer and by itself constitutes a versatile platform for studying energy transport in noisy systems by means of coupled electrical oscillator systems.
Entanglement dynamics of quantum oscillators nonlinearly coupled to thermal environments
NASA Astrophysics Data System (ADS)
Voje, Aurora; Croy, Alexander; Isacsson, Andreas
2015-07-01
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing, and coupling strength, is compared to results for systems with linear system-reservoir coupling. We find that, due to the parity-conserving nature of the coupling, the asymptotic entanglement is considerably more robust than for the linearly damped cases. In contrast to linearly damped systems, the asymptotic behavior of entanglement is similar for the two bath configurations in the nonlinearly damped case. This is due to the two-phonon system-bath exchange causing a suppression of information exchange between the oscillators via the bath in the common-bath configuration at low temperatures.
Pisot q-coherent states quantization of the harmonic oscillator
Gazeau, J.P.; Olmo, M.A. del
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.
Emergence of amplitude and oscillation death in identical coupled oscillators.
Zou, Wei; Senthilkumar, D V; Duan, Jinqiao; Kurths, Jürgen
2014-09-01
We deduce rigorous conditions for the onset of amplitude death (AD) and oscillation death (OD) in a system of identical coupled paradigmatic Stuart-Landau oscillators. A nonscalar coupling and high frequency are beneficial for the onset of AD. In strong contrast, scalar diffusive coupling and low intrinsic frequency are in favor of the emergence of OD. Our finding contributes to clearly distinguish intrinsic geneses for AD and OD, and further substantially corroborates that AD and OD are indeed two dynamically distinct oscillation quenching phenomena due to distinctly different mechanisms.
Manipulating Fock states of a harmonic oscillator while preserving its linearity
NASA Astrophysics Data System (ADS)
Juliusson, K.; Bernon, S.; Zhou, X.; Schmitt, V.; le Sueur, H.; Bertet, P.; Vion, D.; Mirrahimi, M.; Rouchon, P.; Esteve, D.
2016-12-01
We present a scheme for controlling the quantum state of a harmonic oscillator by coupling it to an anharmonic multilevel system (MLS) with first- to second-excited-state transition on resonance with the oscillator. In this scheme, which we call ef-resonant, the spurious oscillator Kerr nonlinearity inherited from the MLS is very small, while its Fock states can still be selectively addressed via an MLS transition at a frequency that depends on the number of photons. We implement this concept in a circuit-QED setup with a microwave three-dimensional cavity (the oscillator, with frequency 6.4 GHz and quality factor QO=2 ×106 ) embedding a frequency tunable transmon qubit (the MLS). We characterize the system spectroscopically and demonstrate selective addressing of Fock states and a Kerr nonlinearity below 350 Hz. At times much longer than the transmon coherence times, a nonlinear cavity response with driving power is also observed and explained.
Nonlinear harmonic generation in finite amplitude black hole oscillations
NASA Astrophysics Data System (ADS)
Papadopoulos, Philippos
2002-04-01
The nonlinear generation of harmonics in gravitational perturbations of black holes is explored using numerical relativity based on an ingoing light-cone framework. Localized, finite, perturbations of an isolated black hole are parametrized by amplitude and angular harmonic form. The response of the black hole spacetime is monitored and its harmonic content analyzed to identify the strength of the nonlinear generation of harmonics as a function of the initial data amplitude. It is found that overwhelmingly the black hole responds at the harmonic mode perturbed, even for spacetimes with 10% of the black hole mass radiated. The coefficients for down and up scattering in harmonic space are computed for a range of couplings. Down scattering, leading to smoothing out of angular structure, is found to be equally as or more efficient than the up scatterings that would lead to increased rippling. The details of this nonlinear balance may form the quantitative mechanism by which black holes avoid fission even for arbitrary strong distortions.
Information theories for time-dependent harmonic oscillator
Choi, Jeong Ryeol; Kim, Min-Soo; Kim, Daeyeoul; Maamache, Mustapha; Menouar, Salah; Nahm, In Hyun
2011-06-15
Highlights: > Information theories for the general time-dependent harmonic oscillator based on invariant operator method. > Time dependence of entropies and entropic uncertainty relation. > Characteristics of Shannon information and Fisher information. > Application of information theories to particular systems that have time-dependent behavior. - Abstract: Information theories for the general time-dependent harmonic oscillator are described on the basis of invariant operator method. We obtained entropic uncertainty relation of the system and discussed whether it is always larger than or equal to the physically allowed minimum value. Shannon information and Fisher information are derived by means of density operator that satisfies Liouville-von Neumann equation and their characteristics are investigated. Shannon information is independent of time, but Fisher information is explicitly dependent on time as the time functions of the Hamiltonian vary. We can regard that the Fisher information is a local measure since its time behavior is largely affected by local arrangements of the density, whilst the Shannon information plays the role of a global measure of the spreading of density. To promote the understanding, our theory is applied to special systems, the so-called quantum oscillator with time-dependent frequency and strongly pulsating mass system.
NASA Astrophysics Data System (ADS)
Kurt, Arzu; Eryigit, Resul
2015-12-01
The master equation for a charged harmonic oscillator coupled to an electromagnetic reservoir is investigated up to fourth order in the interaction strength by using Krylov averaging method. The interaction is in the velocity-coupling form and includes a diamagnetic term. Exact analytical expressions for the second-, the third-, and the fourth-order contributions to mass renormalization, decay constant, normal and anomalous diffusion coefficients are obtained for the blackbody type environment. It is found that, generally, the third- and the fourth-order contributions have opposite signs when their magnitudes are comparable to that of the second-order one.
Kraus representation of a damped harmonic oscillator and its application
Liu Yuxi; Oezdemir, Sahin K.; Miranowicz, Adam; Imoto, Nobuyuki
2004-10-01
By definition, the Kraus representation of a harmonic oscillator suffering from the environment effect, modeled as the amplitude damping or the phase damping, is directly given by a simple operator algebra solution. As examples and applications, we first give a Kraus representation of a single qubit whose computational basis states are defined as bosonic vacuum and single particle number states. We further discuss the environment effect on qubits whose computational basis states are defined as the bosonic odd and even coherent states. The environment effects on entangled qubits defined by two different kinds of computational basis are compared with the use of fidelity.
Harmonic Oscillator Model for Radin's Markov-Chain Experiments
NASA Astrophysics Data System (ADS)
Sheehan, D. P.; Wright, J. H.
2006-10-01
The conscious observer stands as a central figure in the measurement problem of quantum mechanics. Recent experiments by Radin involving linear Markov chains driven by random number generators illuminate the role and temporal dynamics of observers interacting with quantum mechanically labile systems. In this paper a Lagrangian interpretation of these experiments indicates that the evolution of Markov chain probabilities can be modeled as damped harmonic oscillators. The results are best interpreted in terms of symmetric equicausal determinism rather than strict retrocausation, as posited by Radin. Based on the present analysis, suggestions are made for more advanced experiments.
Harmonic Oscillator Model for Radin's Markov-Chain Experiments
Sheehan, D. P.; Wright, J. H.
2006-10-16
The conscious observer stands as a central figure in the measurement problem of quantum mechanics. Recent experiments by Radin involving linear Markov chains driven by random number generators illuminate the role and temporal dynamics of observers interacting with quantum mechanically labile systems. In this paper a Lagrangian interpretation of these experiments indicates that the evolution of Markov chain probabilities can be modeled as damped harmonic oscillators. The results are best interpreted in terms of symmetric equicausal determinism rather than strict retrocausation, as posited by Radin. Based on the present analysis, suggestions are made for more advanced experiments.
Elementary derivation of the quantum propagator for the harmonic oscillator
NASA Astrophysics Data System (ADS)
Shao, Jiushu
2016-10-01
Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.
Analysis of transonic flow about harmonically oscillating airfoils and wings
NASA Technical Reports Server (NTRS)
Weatherill, W. H.; Ehlers, F. E.
1980-01-01
A finite difference method for analyzing the unsteady transonic flow about harmonically oscillating wings is discussed. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting partial differential equations for small disturbances. Initial solutions were obtained using relaxation procedures, but the solution range proved to be limited in terms of Mach number and reduced frequency. Recent two-dimensional results are presented which have been obtained with direct solution procedures in which the difference equations are solved 'all at once' and these provide reasonable correlation for practical values of Mach number and reduced frequency.
Generalized Energy Equipartition in Harmonic Oscillators Driven by Active Baths
NASA Astrophysics Data System (ADS)
Maggi, Claudio; Paoluzzi, Matteo; Pellicciotta, Nicola; Lepore, Alessia; Angelani, Luca; Di Leonardo, Roberto
2014-12-01
We study experimentally and numerically the dynamics of colloidal beads confined by a harmonic potential in a bath of swimming E. coli bacteria. The resulting dynamics is well approximated by a Langevin equation for an overdamped oscillator driven by the combination of a white thermal noise and an exponentially correlated active noise. This scenario leads to a simple generalization of the equipartition theorem resulting in the coexistence of two different effective temperatures that govern dynamics along the flat and the curved directions in the potential landscape.
A method of solving simple harmonic oscillator Schroedinger equation
NASA Technical Reports Server (NTRS)
Maury, Juan Carlos F.
1995-01-01
A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.
Reentrant transition in coupled noisy oscillators
NASA Astrophysics Data System (ADS)
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.
Paal, Eugen; Virkepu, Jueri
2009-05-15
Operadic Lax representations for the harmonic oscillator are used to construct the dynamical deformations of three-dimensional (3D) real Lie algebras in the Bianchi classification. It is shown that the energy conservation of the harmonic oscillator is related to the Jacobi identities of the dynamically deformed algebras. Based on this observation, it is proved that the dynamical deformations of 3D real Lie algebras in the Bianchi classification over the harmonic oscillator are Lie algebras.
On quantum harmonic oscillator being subjected to absolute potential state
NASA Astrophysics Data System (ADS)
Nityayogananda, Swami
2017-01-01
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 frequencies becomes gradually subtler to transform into a very high dormant potential energy. This very high dormant potential energy is referred to as `like-potential' energy in this paper. In the process a new wave function is generated. This new function, which corresponds to new sets of particles, has scope to raise the quantum oscillator energy (QOE) up to infinity. It is proposed to show that this high energy does not get cancelled but remains dormant. Further, it is proposed that the displacement about the equilibrium goes to zero when the vibration of the oscillator stops and then the QOE becomes infinity - this needs further research. The more the QOE, the greater will be the degree of dormancy. A simple mathematical model has been derived here to discuss the possibilities that are involved in the QHO under the above-mentioned boundary conditions.
Transients in the synchronization of asymmetrically coupled oscillator arrays
NASA Astrophysics Data System (ADS)
Cantos, C. E.; Hammond, D. K.; Veerman, J. J. P.
2016-09-01
We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a certain parameter regime Ω. As corollaries we show that minimizing the transients requires considering non-symmetric coupling, and that within Ω the computed linear growth in N of the transients is independent of (reasonable) boundary conditions.
NASA Astrophysics Data System (ADS)
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.
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
NASA Astrophysics Data System (ADS)
Chou, Chia-Chun
2016-10-01
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton-Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Observations of ELM Magnetic Precursors and Harmonic Oscillations in NSTX
NASA Astrophysics Data System (ADS)
Kelly, F.; Frederickson, E.; Bell, R.; Tritz, K.; Takahashi, H.; Maingi, R.; NSTX Collaboration
2011-10-01
Recent experiments on NSTX have shown n=1 dominant and n=2 mode ELM magnetic precursors with mode frequency in the 30 to 90 kHz range. The growing magnetic oscillations measured with the NSTX high-n Mirnov diagnostic occurred simultaneous with the onset of the increase in fast D α signal. These bursts of dominantly n=1, some n=2 and fewer higher modes resemble the predictions of a model simulation of ELMs by T. Evans in which a feedback amplification mechanism causes explosive growth of the separatrix topology driven by thermoelectric currents in flux tubes connecting the divertor plates. The n=1 mode remained dominant as wall recycling was reduced with lithium conditioning and n=3 RMP was applied, suggesting the trigger mechanism remained the same. Sufficient lithium suppressed ELMs and made the occurrence of low-frequency, low-n Harmonics Oscillations (HOs) more frequent. The HOs are consistent with modes localized in the edge with the frequency of the n = 1 harmonic near the rotation frequency of the edge plasma. Work supported in part by US DOE contract no. DE-AC02-09CH11466.
1-GHz harmonically pumped femtosecond optical parametric oscillator frequency comb.
Balskus, K; Leitch, S M; Zhang, Z; McCracken, R A; Reid, D T
2015-01-26
We present the first example of a femtosecond optical parametric oscillator frequency comb harmonically-pumped by a 333-MHz Ti:sapphire laser to achieve a stabilized signal comb at 1-GHz mode spacing in the 1.1-1.6-µm wavelength band. Simultaneous locking of the comb carrier-envelope-offset and repetition frequencies is achieved with uncertainties over 1 s of 0.27 Hz and 5 mHz respectively, which are comparable with those of 0.27 Hz and 1.5 mHz achieved for 333-MHz fundamental pumping. The phase-noise power-spectral density of the CEO frequency integrated from 1 Hz-64 kHz was 2.8 rad for the harmonic comb, 1.0 rad greater than for fundamental pumping. The results show that harmonic operation does not substantially compromise the frequency-stability of the comb, which is shown to be limited only by the Rb atomic frequency reference used.
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
2016-01-01
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies. PMID:27886252
NASA Astrophysics Data System (ADS)
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
2016-11-01
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies.
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
2016-11-25
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies.
Fox, Ronald F.; Vela-Arevalo, Luz V.
2002-11-01
The problem of multiphoton processes for intense, long-wavelength irradiation of atomic and molecular electrons is presented. The recently developed method of quasiadiabatic time evolution is used to obtain a nonperturbative analysis. When applied to the standard vector potential coupling, an exact auxiliary equation is obtained that is in the electric dipole coupling form. This is achieved through application of the Goeppert-Mayer gauge. While the analysis to this point is general and aimed at microwave irradiation of Rydberg atoms, a Floquet analysis of the auxiliary equation is presented for the special case of the periodically driven harmonic oscillator. Closed form expressions for a complete set of Floquet states are obtained. These are used to demonstrate that for the oscillator case there are no multiphoton resonances.
Coupling functions in networks of oscillators
NASA Astrophysics Data System (ADS)
Stankovski, Tomislav; Ticcinelli, Valentina; McClintock, Peter V. E.; Stefanovska, Aneta
2015-03-01
Networks of interacting oscillators abound in nature, and one of the prevailing challenges in science is how to characterize and reconstruct them from measured data. We present a method of reconstruction based on dynamical Bayesian inference that is capable of detecting the effective phase connectivity within networks of time-evolving coupled phase oscillators subject to noise. It not only reconstructs pairwise, but also encompasses couplings of higher degree, including triplets and quadruplets of interacting oscillators. Thus inference of a multivariate network enables one to reconstruct the coupling functions that specify possible causal interactions, together with the functional mechanisms that underlie them. The characteristic features of the method are illustrated by the analysis of a numerically generated example: a network of noisy phase oscillators with time-dependent coupling parameters. To demonstrate its potential, the method is also applied to neuronal coupling functions from single- and multi-channel electroencephalograph recordings. The cross-frequency δ, α to α coupling function, and the θ, α, γ to γ triplet are computed, and their coupling strengths, forms of coupling function, and predominant coupling components, are analysed. The results demonstrate the applicability of the method to multivariate networks of oscillators, quite generally.
NASA Astrophysics Data System (ADS)
Deymier, P. A.; Runge, K.; Vasseur, J. O.
2016-12-01
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.
Pulse-coupled BZ oscillators with unequal coupling strengths.
Horvath, Viktor; Kutner, Daniel J; Chavis, John T; Epstein, Irving R
2015-02-14
Coupled chemical oscillators are usually studied with symmetric coupling, either between identical oscillators or between oscillators whose frequencies differ. Asymmetric connectivity is important in neuroscience, where synaptic strength inequality in neural networks commonly occurs. While the properties of the individual oscillators in some coupled chemical systems may be readily changed, enforcing inequality between the connection strengths in a reciprocal coupling is more challenging. We recently demonstrated a novel way of coupling chemical oscillators, which allows for manipulation of individual connection strengths. Here we study two identical, pulse-coupled Belousov-Zhabotinsky (BZ) oscillators with unequal connection strengths. When the pulse perturbations contain KBr (inhibitor), this system exhibits simple out-of-phase and complex oscillations, oscillatory-suppressed states as well as temporally periodic patterns (N : M) in which the two oscillators exhibit different numbers of peaks per cycle. The N : M patterns emerge due to the long-term effect of the inhibitory pulse-perturbations, a feature that has not been considered in earlier works. Time delay was previously shown to have a profound effect on the system's behaviour when pulse coupling was inhibitory and the coupling strengths were equal. When the coupling is asymmetric, however, delay produces no qualitative change in behaviour, though the 1 : 2 temporal pattern becomes more robust. Asymmetry in instantaneous excitatory coupling via AgNO3 injection produces a previously unseen temporal pattern (1 : N patterns starting with a double peak) with time delay and high [AgNO3]. Numerical simulations of the behaviour agree well with theoretical predictions in asymmetrical pulse-coupled systems.
Entrainment in coupled salt-water oscillators
NASA Astrophysics Data System (ADS)
Miyakawa, Kenji; Yamada, Kazuhiko
1999-03-01
The properties of coupling between two salt-water oscillators were studied. Two salt-water oscillators were coupled through the window of the partition wall. With an increase of the area of the window, the quasi-periodic mode, the in-phase mode, the bistable mode, and the out-of-phase mode appeared successively. A phase diagram of coupling was obtained in the plane of the area of the window and the diameter of the orifice of the cup. Furthermore, the effect of viscosity on coupling behaviors was investigated. In the boundary region between quasi-periodic coupling and in-phase coupling, the mode coupled with the phase difference of approximately π/4 was found. The experimental results were reproduced by the numerical simulation using coupled non-linear differential equations.
Quantum optics. Quantum harmonic oscillator state synthesis by reservoir engineering.
Kienzler, D; Lo, H-Y; Keitch, B; de Clercq, L; Leupold, F; Lindenfelser, F; Marinelli, M; Negnevitsky, V; Home, J P
2015-01-02
The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to generate squeezed, coherent, and displaced-squeezed states as steady states in the presence of noise. We verify the created state by generating two-state correlated spin-motion Rabi oscillations, resulting in high-contrast measurements. For both cooling and measurement, we use spin-oscillator couplings that provide transitions between oscillator states in an engineered Fock state basis. Our approach should facilitate studies of entanglement, quantum computation, and open-system quantum simulations in a wide range of physical systems.
Period variability of coupled noisy oscillators
NASA Astrophysics Data System (ADS)
Mori, Fumito; Kori, Hiroshi
2013-03-01
Period variability, quantified by the standard deviation (SD) of the cycle-to-cycle period, is investigated for noisy phase oscillators. We define the checkpoint phase as the beginning or end point of one oscillation cycle and derive an expression for the SD as a function of this phase. We find that the SD is dependent on the checkpoint phase only when oscillators are coupled. The applicability of our theory is verified using a realistic model. Our work clarifies the relationship between period variability and synchronization from which valuable information regarding coupling can be inferred.
Arrays of coupled chemical oscillators
NASA Astrophysics Data System (ADS)
Forrester, Derek Michael
2015-11-01
Oscillating chemical reactions result from complex periodic changes in the concentration of the reactants. In spatially ordered ensembles of candle flame oscillators the fluctuations in the ratio of oxygen atoms with respect to that of carbon, hydrogen and nitrogen produces an oscillation in the visible part of the flame related to the energy released per unit mass of oxygen. Thus, the products of the reaction vary in concentration as a function of time, giving rise to an oscillation in the amount of soot and radiative emission. Synchronisation of interacting dynamical sub-systems occurs as arrays of flames that act as master and slave oscillators, with groups of candles numbering greater than two, creating a synchronised motion in three-dimensions. In a ring of candles the visible parts of each flame move together, up and down and back and forth, in a manner that appears like a “worship”. Here this effect is shown for rings of flames which collectively empower a central flame to pulse to greater heights. In contrast, situations where the central flames are suppressed are also found. The phenomena leads to in-phase synchronised states emerging between periods of anti-phase synchronisation for arrays with different columnar sizes of candle and positioning.
Arrays of coupled chemical oscillators
Forrester, Derek Michael
2015-01-01
Oscillating chemical reactions result from complex periodic changes in the concentration of the reactants. In spatially ordered ensembles of candle flame oscillators the fluctuations in the ratio of oxygen atoms with respect to that of carbon, hydrogen and nitrogen produces an oscillation in the visible part of the flame related to the energy released per unit mass of oxygen. Thus, the products of the reaction vary in concentration as a function of time, giving rise to an oscillation in the amount of soot and radiative emission. Synchronisation of interacting dynamical sub-systems occurs as arrays of flames that act as master and slave oscillators, with groups of candles numbering greater than two, creating a synchronised motion in three-dimensions. In a ring of candles the visible parts of each flame move together, up and down and back and forth, in a manner that appears like a “worship”. Here this effect is shown for rings of flames which collectively empower a central flame to pulse to greater heights. In contrast, situations where the central flames are suppressed are also found. The phenomena leads to in-phase synchronised states emerging between periods of anti-phase synchronisation for arrays with different columnar sizes of candle and positioning. PMID:26582365
Adaptive coupling and enhanced synchronization in coupled phase oscillators
NASA Astrophysics Data System (ADS)
Ren, Quansheng; Zhao, Jianye
2007-07-01
We study the dynamics of an adaptive coupled array of phase oscillators. The adaptive law is designed in such a way that the coupling grows stronger for the pairs which have larger phase incoherence. The proposed scheme enhances the synchronization and achieves a more reasonable coupling dynamics for the network of oscillators with different intrinsic frequencies. The synchronization speed and the steady-state phase difference can be adjusted by the parameters of the adaptive law. Besides global coupling, nearest-neighbor ring coupling is also considered to demonstrate the generality of the method.
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
ERIC Educational Resources Information Center
Lee, Keeyung
2009-01-01
The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…
Exact solution of a quantum forced time-dependent harmonic oscillator
NASA Technical Reports Server (NTRS)
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
1992-01-01
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
ERIC Educational Resources Information Center
Earl, Boyd L.
2008-01-01
A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…
The Acoustic Simple Harmonic Oscillator: Experimental Verification and Applications
NASA Astrophysics Data System (ADS)
Matteson, Sam
2009-04-01
In his famous volume, The Sensations of Tone, published in 1877, Hermann Helmholtz introduced a resonator that was central to his investigations of acoustics. This talk revisits the device that Helmholtz described and examines it as a manifestation of an acoustic simple harmonic oscillator (SHO). The presentation demonstrates that an enclosed volume which communicates with the outside world via a narrow tube exhibits a single strong frequency response in analogy to a mechanical SHO, along with weaker resonances of the air in the short pipe that comprises the ``neck.'' The investigations, furthermore, report results of a straightforward experiment that confirms the SHO model (with damping) and that is very accessible to undergraduate students using inexpensive equipment and internet-obtainable freeware. The current work also extends the analysis to include applications of the Helmholtz Resonator to several folk instruments, namely, the ocarina, whistling, and the ``bottle band.''
Phase-space treatment of the driven quantum harmonic oscillator
NASA Astrophysics Data System (ADS)
Campos, Diógenes
2017-03-01
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 standard position and momentum wave functions, together with expressions for the ηth derivatives with respect to q and p, respectively. Afterwards, general formulae for momentum, position and energy expectation values are obtained, and the Ehrenfest theorem is verified. Subsequently, general expressions for the cross-Wigner functions are deduced. Finally, a specific example is considered to numerically and graphically illustrate some results.
A Perturbation of the Dunkl Harmonic Oscillator on the Line
NASA Astrophysics Data System (ADS)
Álvarez López, Jesús A.; Calaza, Manuel
2015-07-01
Let J_σ be the Dunkl harmonic oscillator on R (σ>-1/2). For 00, it is proved that, if σ>u-1/2, then the operator U=J_σ+ξ|x|^{-2u}, with appropriate domain, is essentially self-adjoint in L^2({R},|x|^{2σ} dx), the Schwartz space S is a core of overline U^{1/2}, and overline U has a discrete spectrum, which is estimated in terms of the spectrum of overline{J_σ}. A generalization J_{σ,τ} of J_σ is also considered by taking different parameters σ and τ on even and odd functions. Then extensions of the above result are proved for J_{σ,τ}, where the perturbation has an additional term involving, either the factor x^{-1} on odd functions, or the factor x on even functions. Versions of these results on R_+ are derived.
Excitation with quantum light. I. Exciting a harmonic oscillator
NASA Astrophysics Data System (ADS)
Carreño, J. C. López; Laussy, F. P.
2016-12-01
We present a two-part study of the excitation of an optical target by quantum light. In this first part, we introduce the problematic and address the first case of interest, that of exciting the quantum harmonic oscillator, corresponding to, e.g., a single-mode passive cavity or a noninteracting bosonic field. We introduce a mapping of the Hilbert space that allows to chart usefully the accessible regions. We then consider the quantum excitation from single-photon sources in the form of a two-level system under various regimes of (classical) pumping: incoherent, coherent, and in the Mollow triplet regime. We close this first part with an overview of the material to be covered in the subsequent work.
Ecological optimization of an irreversible harmonic oscillators Carnot heat engine
NASA Astrophysics Data System (ADS)
Liu, Xiaowei; Chen, Lingen; Wu, Feng; Sun, Fengrui
2009-12-01
A model of an irreversible quantum Carnot heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting harmonic oscillators is established in this paper. Based on the quantum master equation and semi-group approach, equations of some important performance parameters, such as power output, efficiency, exergy loss rate and ecological function for the irreversible quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. Effects of internal irreversibility and heat leakage on the ecological performance are discussed. A performance comparison of the quantum heat engine under maximum ecological function and maximum power conditions is also performed.
Quantum Harmonic Oscillator Subjected to Quantum Vacuum Fluctuations
Gevorkyan, A. S.; Burdik, C.; Oganesyan, K. B.
2010-05-04
Spontaneous transitions between bound states of an atomic system, 'Lamb Shift' of energy level, as well as many other phenomena in real nonrelativistic quantum systems are connected with the influence of quantum vacuum fluctuations which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system 'quantum harmonic oscillator (QHO)+ environment' is described in terms of complex probabilistic processes (CPP) which satisfies a stochastic differential equation (SDE) of Langevin-Schroedinger (L-Sch) type. On the basis of orthogonal CPP, the method of stochastic density matrix (SDM) is developed. The energy spectrum of QHO and a possibility of infringement of detailed balance of transitions between quantum levels including spontaneous decay of <
Chiral potential renormalized in harmonic-oscillator space
NASA Astrophysics Data System (ADS)
Yang, C.-J.
2016-12-01
We renormalize the chiral effective field theory potential in harmonic-oscillator (HO) model space. The low energy constants (LECs) are utilized to absorb not just the ultraviolet part of the physics due to the cutoff, but also the infrared part due to the truncation of model space. We use the inverse J -matrix method to reproduce the nucleon-nucleon scattering phase shifts in the given model space. We demonstrate that by including the NLO correction, the nucleon-nucleon scattering in the continuum could be well reproduced in the truncated HO trap space up to laboratory energy Tlab=100 MeV with number of HO basis nmax as small as 10. A perturbative power counting starts at subleading order is adopted in this work, and how to extract the perturbative contribution is demonstrated. This work serves as the input to perform ab initio calculations.
Explosive oscillation death in coupled Stuart-Landau oscillators
NASA Astrophysics Data System (ADS)
Bi, Hongjie; Hu, Xin; Zhang, Xiyun; Zou, Yong; Liu, Zonghua; Guan, Shuguang
2014-12-01
Recently, explosive phase transitions, such as explosive percolation and explosive synchronization, have attracted extensive research interest. So far, most existing works have investigated Kuramoto-type models, where only phase variables are involved. Here, we report the occurrence of explosive oscillation quenching in a system of coupled Stuart-Landau oscillators that incorporates both phase and amplitude dynamics. We observe three typical scenarios with distinct microscopic mechanism of occurrence, i.e., ordinary, hierarchical, and cluster explosive oscillation death, corresponding to different frequency distributions of oscillators. We carry out theoretical analyses and obtain the backward transition point, which is shown to be independent of the specific frequency distributions. Numerical results are consistent with the theoretical predictions.
Dynamical Recurrence and the Quantum Control of Coupled Oscillators
NASA Astrophysics Data System (ADS)
Genoni, Marco G.; Serafini, Alessio; Kim, M. S.; Burgarth, Daniel
2012-04-01
Controllability—the possibility of performing any target dynamics by applying a set of available operations—is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, such as spin systems, precise criteria to establish controllability, such as the so-called rank criterion, are well known. However, most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems—encompassing quantum light, ensembles of bosonic atoms, motional degrees of freedom of ions, and nanomechanical oscillators—governed by quadratic Hamiltonians (such that their evolution is analogous to coupled harmonic oscillators). After having highlighted the intimate connection between controllability and recurrence in the Hilbert space, we prove that, for coupled oscillators, a simple extra condition has to be fulfilled to extend the rank criterion to infinite-dimensional quadratic systems. Further, we present a useful application of our finding, by proving indirect controllability of a chain of harmonic oscillators.
Entanglement prethermalization in an interaction quench between two harmonic oscillators
NASA Astrophysics Data System (ADS)
Ikeda, Tatsuhiko N.; Mori, Takashi; Kaminishi, Eriko; Ueda, Masahito
2017-02-01
Entanglement prethermalization (EP) refers to a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble exactly describes the total system if we take into account nonlocal conserved quantities that act nontrivially on both subsystems. In the presence of a symmetry-breaking perturbation, the relaxation dynamics of the system exhibits a quasi-stationary EP plateau and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.
Entanglement prethermalization in an interaction quench between two harmonic oscillators.
Ikeda, Tatsuhiko N; Mori, Takashi; Kaminishi, Eriko; Ueda, Masahito
2017-02-01
Entanglement prethermalization (EP) refers to a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble exactly describes the total system if we take into account nonlocal conserved quantities that act nontrivially on both subsystems. In the presence of a symmetry-breaking perturbation, the relaxation dynamics of the system exhibits a quasi-stationary EP plateau and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.
Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Singh, Manu Pratap; Rajput, B. S.
2016-10-01
Realization of qudit quantum computation has been presented in terms of number operator and phase operators associated with one-dimensional harmonic oscillator and it has been demonstrated that the representations of generalized Pauli group, viewed in harmonic oscillator operators, allow the qudits to be explicitly encoded in such systems. The non-Hermitian quantum phase operators contained in decomposition of the annihilation and creation operators associated with harmonic oscillator have been analysed in terms of semi unitary transformations (SUT) and it has been shown that the non-vanishing analytic index for harmonic oscillator leads to an alternative class of quantum anomalies. Choosing unitary transformation and the Hermitian phase operator free from quantum anomalies, the truncated annihilation and creation operators have been obtained for harmonic oscillator and it has been demonstrated that any attempt of removal of quantum anomalies leads to absence of minimum uncertainty.
Synchronization of coupled Boolean phase oscillators
NASA Astrophysics Data System (ADS)
Rosin, David P.; Rontani, Damien; Gauthier, Daniel J.
2014-04-01
We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged. Specifically, increasing the coupling strength via the range of state-dependent delay leads to larger locking ranges in uni- and bidirectional coupling of oscillators in both experiment and numerical simulation with a piecewise switching model. In the unidirectional coupling scheme, we unveil asymmetric triangular-shaped locking regions (Arnold tongues) that appear at multiples of the natural frequency of the oscillators. This extends observations of a single locking region reported in previous studies. In the bidirectional coupling scheme, we map out a symmetric locking region in the parameter space of frequency detuning and coupling strength. Because of the large scalability of our setup, our observations constitute a first step towards realizing large-scale networks of coupled oscillators to address fundamental questions on the dynamical properties of networks in a new experimental setting.
Double Fourier Harmonic Balance Method for Nonlinear Oscillators by Means of Bessel Series
2014-10-16
Double Fourier harmonic balance method for nonlinear oscillators by means of Bessel series T.C. Lipscombe∗1 and C.E. Mungan†2 1Catholic University of... harmonic balance method consists in expanding the displacement of an oscillator as a Fourier cosine series in time. A key modification is proposed here, in...than the exact value. Even better, the predicted frequency for the V-ramp case turns out to be exact. Keywords: Fourier expansion, harmonic balance
Feinberg-Horodecki states of a time-dependent mass distribution harmonic oscillator
NASA Astrophysics Data System (ADS)
Eshghi, M.; Sever, R.; Ikhdair, S. M.
2016-07-01
The solution of the Feinberg-Horodecki (FH) equation for a time-dependent mass (TDM) harmonic oscillator quantum system is studied. A certain interaction is applied to a mass m(t) to provide a particular spectrum of stationary energies. The related spectrum of the harmonic oscillator potential V(t) acting on the TDM m(t) oscillators is found. We apply the time version of the asymptotic iteration method (AIM) to calculate analytical expressions of the TDM stationary state energies and their wave functions. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the time-dependent mass reduces to m0.
Damping of a harmonic oscillator in a squeezed vacuum without rotating-wave approximation
NASA Astrophysics Data System (ADS)
Hassan, S. S.; Joshi, A.; Frege, O. M.; Emam, W.
2007-09-01
A single harmonic oscillator interacting with a broadband squeezed reservoir is analyzed within the framework of master equation without invoking the rotating-wave approximation. The dynamical evolution and photon statistics of the system are investigated by studying mean photon number and second order intensity-intensity correlation function, respectively, under resonance condition which show transient oscillations at twice the harmonic oscillator frequency. The transient fluorescent spectrum reveals asymmetric features. Inclusion of vacuum and field-dependent frequency shifts affects the thermal equilibrium value of the average photon number of the harmonic oscillator.
Cooper pair of superconductivity in the coordinate representation and q-deformed harmonic oscillator
NASA Astrophysics Data System (ADS)
Van Ngu, Man; Gia Vinh, Ngo; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Viet, Nguyen Ai
2016-06-01
In this work we study the similarity between the wave functions of q -deformed harmonic oscillator and wave functions of Cooper pair. The wave functions of Cooper pairs in coordinate-space have an “onion-like” layered structure with exponent decay (Boltzmann) envelope modulation. The ground state wave function of q -deform harmonic oscillator has the form of oscillate functions with Gaussian decay envelope modulation. The corresponding between Boltzmann and Gaussian forms of envelope functions and their quantum similarity are discussed.
Synchronization of coupled nonidentical genetic oscillators
NASA Astrophysics Data System (ADS)
Li, Chunguang; Chen, Luonan; Aihara, Kazuyuki
2006-03-01
The study of the collective dynamics of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic oscillators are biochemical networks, which can generally be modelled as nonlinear dynamic systems. We show in this paper that many genetic oscillators can be transformed into Lur'e form by exploiting the special structure of biological systems. By using a control theory approach, we provide a theoretical method for analysing the synchronization of coupled nonidentical genetic oscillators. Sufficient conditions for the synchronization as well as the estimation of the bound of the synchronization error are also obtained. To demonstrate the effectiveness of our theoretical results, a population of genetic oscillators based on the Goodwin model are adopted as numerical examples.
Mode coupling in spin torque oscillators
Zhang, Steven S. -L.; Zhou, Yan; Li, Dong; Heinonen, Olle
2016-09-15
A number of recent experimental works have shown that the dynamics of a single spin torque oscillator can exhibit complex behavior that stems from interactions between two or more modes of the oscillator, such as observed mode-hopping or 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 the present work, we rigorously derive such a theory starting with the Landau–Lifshitz–Gilbert equation for magnetization dynamics by expanding up to third-order terms in deviation from equilibrium. Here, our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. In conclusion, the acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature.
Mode coupling in spin torque oscillators
Zhang, Steven S. -L.; Zhou, Yan; Li, Dong; ...
2016-09-15
A number of recent experimental works have shown that the dynamics of a single spin torque oscillator can exhibit complex behavior that stems from interactions between two or more modes of the oscillator, such as observed mode-hopping or 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 the present work, we rigorously derive such a theory starting with the Landau–Lifshitz–Gilbert equation for magnetization dynamics by expanding up to third-order terms in deviation from equilibrium. Here, our resultsmore » show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. In conclusion, the acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature.« less
Oscillator death induced by amplitude-dependent coupling in repulsively coupled oscillators.
Liu, Weiqing; Xiao, Guibao; Zhu, Yun; Zhan, Meng; Xiao, Jinghua; Kurths, Jürgen
2015-05-01
The effects of amplitude-dependent coupling on oscillator death (OD) are investigated for two repulsively coupled Lorenz oscillators. Based on numerical simulations, it is shown that as constraint strengths on the amplitude-dependent coupling change, an oscillatory state may undergo a transition to an OD state. The parameter regimes of the OD domain are theoretically determined, which coincide well with the numerical results. An electronic circuit is set up to exhibit the transition process to the OD state with an amplitude-dependent coupling. These findings may have practical importance on chaos control and oscillation depression.
Oscillator death induced by amplitude-dependent coupling in repulsively coupled oscillators
NASA Astrophysics Data System (ADS)
Liu, Weiqing; Xiao, Guibao; Zhu, Yun; Zhan, Meng; Xiao, Jinghua; Kurths, Jürgen
2015-05-01
The effects of amplitude-dependent coupling on oscillator death (OD) are investigated for two repulsively coupled Lorenz oscillators. Based on numerical simulations, it is shown that as constraint strengths on the amplitude-dependent coupling change, an oscillatory state may undergo a transition to an OD state. The parameter regimes of the OD domain are theoretically determined, which coincide well with the numerical results. An electronic circuit is set up to exhibit the transition process to the OD state with an amplitude-dependent coupling. These findings may have practical importance on chaos control and oscillation depression.
Novel Approach for Solving the Equation of Motion of a Simple Harmonic Oscillator. Classroom Notes
ERIC Educational Resources Information Center
Gauthier, N.
2004-01-01
An elementary method, based on the use of complex variables, is proposed for solving the equation of motion of a simple harmonic oscillator. The method is first applied to the equation of motion for an undamped oscillator and it is then extended to the more important case of a damped oscillator. It is finally shown that the method can readily be…
Susceptibility of large populations of coupled oscillators
NASA Astrophysics Data System (ADS)
Daido, Hiroaki
2015-01-01
It is an important and interesting problem to elucidate how the degree of phase order in a large population of coupled oscillators responds to a synchronizing periodic force from the outside. Here this problem is studied analytically as well as numerically by introducing the concept of susceptibility for globally coupled phase oscillators with either nonrandom or random interactions. It is shown that the susceptibility diverges at the critical point in the nonrandom case with Widom's equality satisfied, while it exhibits a cusp in the most random case.
Calorimetric measurement of work for a driven harmonic oscillator
NASA Astrophysics Data System (ADS)
Sampaio, Rui; Suomela, Samu; Ala-Nissila, Tapio
2016-12-01
A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.
Calorimetric measurement of work for a driven harmonic oscillator.
Sampaio, Rui; Suomela, Samu; Ala-Nissila, Tapio
2016-12-01
A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.
NASA Astrophysics Data System (ADS)
De Rosis, Alessandro
2014-11-01
In this paper, the fluid dynamics induced by a rigid lamina undergoing harmonic oscillations in a non-Newtonian calm fluid is investigated. The fluid is modelled through the lattice Boltzmann method and the flow is assumed to be nearly incompressible. An iterative viscosity-correction based procedure is proposed to properly account for the non-Newtonian fluid feature and its accuracy is evaluated. In order to handle the mutual interaction between the lamina and the encompassing fluid, the Immersed Boundary method is adopted. A numerical campaign is performed. In particular, the effect of the non-Newtonian feature is highlighted by investigating the fluid forces acting on a harmonically oscillating lamina for different values of the Reynolds number. The findings prove that the non-Newtonian feature can drastically influence the behaviour of the fluid and, as a consequence, the forces acting upon the lamina. Several considerations are carried out on the time history of the drag coefficient and the results are used to compute the added mass through the hydrodynamic function. Moreover, the computational cost involved in the numerical simulations is discussed. Finally, two applications concerning water resources are investigated: the flow through an obstructed channel and the particle sedimentation. Present findings highlight a strong coupling between the body shape, the Reynolds number, and the flow behaviour index.
Mode coupling in solar spicule oscillations
NASA Astrophysics Data System (ADS)
Fazel, Zahra
2016-01-01
In a real medium which has oscillations, the perturbations can cause an energy transfer between different modes. A perturbation, which is interpreted as an interaction between the modes, is inferred to be mode coupling. The mode coupling process in an inhomogeneous medium such as solar spicules may lead to the coupling of kink waves to local Alfvén waves. This coupling occurs in practically any conditions when there is smooth variation in density in the radial direction. This process is seen as the decay of transverse kink waves in the medium. To study the damping of kink waves due to mode coupling, a 2.5-dimensional numerical simulation of the initial wave is considered in spicules. The initial perturbation is assumed to be in a plane perpendicular to the spicule axis. The considered kink wave is a standing wave which shows an exponential damping in the inhomogeneous layer after the mode coupling occurs.
NASA Technical Reports Server (NTRS)
Yeon, Kyu-Hwang; Um, Chung-In; George, Thomas F.; Pandey, Lakshmi N.
1993-01-01
Starting with evaluations of propagator and wave function for the damped harmonic oscillator with time-dependent frequency, exact coherent states are constructed. These coherent states satisfy the properties which coherent states should generally have.
Locally and globally coupled oscillators in muscle.
Sato, Katsuhiko; Kuramoto, Yoshiki; Ohtaki, Masako; Shimamoto, Yuta; Ishiwata, Shin'ichi
2013-09-06
At an intermediate activation level, striated muscle exhibits autonomous oscillations called SPOC, in which the basic contractile units, sarcomeres, oscillate in length, and various oscillatory patterns such as traveling waves and their disrupted forms appear in a myofibril. Here we show that these patterns are reproduced by mechanically connecting in series the unit model that explains characteristics of SPOC at the single-sarcomere level. We further reduce the connected model to phase equations, revealing that the combination of local and global couplings is crucial to the emergence of these patterns.
Locally and Globally Coupled Oscillators in Muscle
NASA Astrophysics Data System (ADS)
Sato, Katsuhiko; Kuramoto, Yoshiki; Ohtaki, Masako; Shimamoto, Yuta; Ishiwata, Shin'ichi
2013-09-01
At an intermediate activation level, striated muscle exhibits autonomous oscillations called SPOC, in which the basic contractile units, sarcomeres, oscillate in length, and various oscillatory patterns such as traveling waves and their disrupted forms appear in a myofibril. Here we show that these patterns are reproduced by mechanically connecting in series the unit model that explains characteristics of SPOC at the single-sarcomere level. We further reduce the connected model to phase equations, revealing that the combination of local and global couplings is crucial to the emergence of these patterns.
Phase of the quantum harmonic oscillator with applications to optical polarization
NASA Technical Reports Server (NTRS)
Shepard, Scott R.
1993-01-01
The phase of the quantum harmonic oscillator, the temporal distribution of a particle in a square-well potential, and a quantum theory of angles are derived from a general theory of complementarity. Schwinger's harmonic oscillator model of angular momenta is modified for the case of photons. Angular distributions for systems of identical and distinguishable particles are discussed. Unitary and antiunitary time reversal operators are then presented and applied to optical polarization states in birefringent media.
Amplitude and phase representation of quantum invariants for the time-dependent harmonic oscillator
Fernandez Guasti, M.; Moya-Cessa, H.
2003-06-01
The correspondence between classical and quantum invariants is established. The Ermakov-Lewis quantum invariant of the time-dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase operators. In doing so, Turski's phase operator as well as Susskind-Glogower operators are generalized to the time-dependent harmonic-oscillator case. A quantum derivation of the Manley-Rowe relations is shown as an example.
Brownian motion of a harmonic oscillator in a noninertial reference frame.
Jiménez-Aquino, J I; Romero-Bastida, M
2013-08-01
The Brownian motion of a charged harmonic oscillator in the presence of additional force fields, such as a constant magnetic field and arbitrary time-dependent electric and mechanical forces, is studied in a rotational reference frame under uniform motion. By assuming an isotropic surrounding medium (a scalar friction constant), we solve explicitly the Smoluchowski equation associated with the Langevin equation for the charged harmonic oscillator and calculate the mean square displacements along and orthogonal to the rotation axis.
Discrete Excitation Spectrum of a Classical Harmonic Oscillator in Zero-Point Radiation
NASA Astrophysics Data System (ADS)
Huang, Wayne Cheng-Wei; Batelaan, Herman
2015-03-01
We report that upon excitation by a single pulse, a classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation exhibits a discrete harmonic spectrum in agreement with that of its quantum counterpart. This result is interesting in view of the fact that the vacuum field is needed in the classical calculation to obtain the agreement.
Synchronization Dynamics of Coupled Chemical Oscillators
NASA Astrophysics Data System (ADS)
Tompkins, Nathan
The synchronization dynamics of complex networks have been extensively studied over the past few decades due to their ubiquity in the natural world. Prominent examples include cardiac rhythms, circadian rhythms, the flashing of fireflies, predator/prey population dynamics, mammalian gait, human applause, pendulum clocks, the electrical grid, and of the course the brain. Detailed experiments have been done to map the topology of many of these systems and significant advances have been made to describe the mathematics of these networks. Compared to these bodies of work relatively little has been done to directly test the role of topology in the synchronization dynamics of coupled oscillators. This Dissertation develops technology to examine the dynamics due to topology within networks of discrete oscillatory components. The oscillatory system used here consists of the photo-inhibitable Belousov-Zhabotinsky (BZ) reaction water-in-oil emulsion where the oscillatory drops are diffusively coupled to one another and the topology is defined by the geometry of the diffusive connections. Ring networks are created from a close-packed 2D array of drops using the Programmable Illumination Microscope (PIM) in order to test Turing's theory of morphogenesis directly. Further technology is developed to create custom planar networks of BZ drops in more complicated topologies which can be individually perturbed using illumination from the PIM. The work presented here establishes the validity of using the BZ emulsion system with a PIM to study the topology induced effects on the synchronization dynamics of coupled chemical oscillators, tests the successes and limitations of Turing's theory of morphogenesis, and develops new technology to further probe the effects of network topology on a system of coupled oscillators. Finally, this Dissertation concludes by describing ongoing experiments which utilize this new technology to examine topology induced transitions of synchronization
Synchronization in Networks of Coupled Chemical Oscillators
NASA Astrophysics Data System (ADS)
Showalter, Kenneth; Tinsley, Mark; Nkomo, Simbarashe; Ke, Hua
2014-03-01
We have studied networks of coupled photosensitive chemical oscillators. Experiments and simulations are carried out on networks with different topologies and modes of coupling. We describe experimental and modeling studies of chimera and phase-cluster states and their relation to other synchronization states. Networks of integrate-and-fire oscillators are also studied in which sustained coordinated activity is exhibited. Individual nodes display incoherent firing events; however, a dominant frequency within the collective signal is exhibited. The introduction of spike-timing-dependent plasticity allows the network to evolve and leads to a stable unimodal link-weight distribution. M. R. Tinsley et al., Nature Physics 8, 662 (2012); S. Nkomo et al., Phys. Rev. Lett. 110, 244102 (2013); H. Ke et al., in preparation.
NASA Astrophysics Data System (ADS)
Gaiko, Nick V.; van Horssen, Wim T.
2016-11-01
In this paper, the free transverse vibrations of a vertically moving string with a harmonically time-varying length are studied. The string length variations are assumed to be small. By using the multiple-timescales perturbation method in conjunction with a Fourier series approach, we determine the resonance frequencies and derive the non-secularity conditions in the form of an infinite dimensional system of coupled ordinary differential equations. This system describes the long time behavior of the amplitudes of the oscillations. Then, the eigenvalues of the obtained system are studied by the Galerkin truncation method, and applicability of this method is discussed. Apart from this, the dynamic stability of the solution is investigated by an energy analysis. Additionally, resonance detuning is considered.
Harmonic oscillator representation in the theory of scattering and nuclear reactions
NASA Technical Reports Server (NTRS)
Smirnov, Yuri F.; Shirokov, A. M.; Lurie, Yuri, A.; Zaitsev, S. A.
1995-01-01
The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.
The Adiabatic Invariant of the n-Degree-of-Freedom Harmonic Oscillator
ERIC Educational Resources Information Center
Devaud, M.; Leroy, V.; Bacri, J.-C.; Hocquet, T.
2008-01-01
In this graduate-level theoretical paper, we propose a general derivation of the adiabatic invariant of the n-degree-of-freedom harmonic oscillator, available whichever the physical nature of the oscillator and of the parametrical excitation it undergoes. This derivation is founded on the use of the classical Glauber variables and ends up with…
Nicu, Valentin Paul
2016-08-03
Motivated by the renewed interest in the coupled oscillator (CO) model for VCD, in this work a generalised coupled oscillator (GCO) expression is derived by introducing the concept of a coupled oscillator origin. Unlike the standard CO expression, the GCO expression is exact within the harmonic approximation. Using two illustrative example molecules, the theoretical concepts introduced here are demonstrated by performing a GCO decomposition of the rotational strengths computed using DFT. This analysis shows that: (1) the contributions to the rotational strengths that are normally neglected in the standard CO model can be comparable to or larger than the CO contribution, and (2) the GCO mechanism introduced here can affect the VCD intensities of all types of modes in symmetric and asymmetric molecules.
NASA Astrophysics Data System (ADS)
Schmidt, Lennart; Krischer, Katharina
2015-06-01
We study an oscillatory medium with a nonlinear global coupling that gives rise to a harmonic mean-field oscillation with constant amplitude and frequency. Two types of cluster states are found, each undergoing a symmetry-breaking transition towards a related chimera state. We demonstrate that the diffusional coupling is non-essential for these complex dynamics. Furthermore, we investigate localized turbulence and discuss whether it can be categorized as a chimera state.
Predicting synchrony in heterogeneous pulse coupled oscillators
NASA Astrophysics Data System (ADS)
Talathi, Sachin S.; Hwang, Dong-Uk; Miliotis, Abraham; Carney, Paul R.; Ditto, William L.
2009-08-01
Pulse coupled oscillators (PCOs) represent an ubiquitous model for a number of physical and biological systems. Phase response curves (PRCs) provide a general mathematical framework to analyze patterns of synchrony generated within these models. A general theoretical approach to account for the nonlinear contributions from higher-order PRCs in the generation of synchronous patterns by the PCOs is still lacking. Here, by considering a prototypical example of a PCO network, i.e., two synaptically coupled neurons, we present a general theory that extends beyond the weak-coupling approximation, to account for higher-order PRC corrections in the derivation of an approximate discrete map, the stable fixed point of which can predict the domain of 1:1 phase locked synchronous states generated by the PCO network.
Four mass coupled oscillator guitar model.
Popp, John E
2012-01-01
Coupled oscillator models have been used for the low frequency response (50 to 250 Hz) of a guitar. These 2 and 3 mass models correctly predict measured resonance frequency relationships under various laboratory boundary conditions, but did not always represent the true state of a guitar in the players' hands. The model presented has improved these models in three ways, (1) a fourth oscillator includes the guitar body, (2) plate stiffnesses and other fundamental parameters were measured directly and effective areas and masses used to calculate the responses, including resonances and phases, directly, and (3) one of the three resultant resonances varies with neck and side mass and can also be modeled as a bar mode of the neck and body. The calculated and measured resonances and phases agree reasonably well.
Switching dynamics of single and coupled VO2-based oscillators as elements of neural networks
NASA Astrophysics Data System (ADS)
Velichko, Andrey; Belyaev, Maksim; Putrolaynen, Vadim; Pergament, Alexander; Perminov, Valentin
2017-01-01
In the present paper, we report on the switching dynamics of both single and coupled VO2-based oscillators, with resistive and capacitive coupling, and explore the capability of their application in oscillatory neural networks. Based on these results, we further select an adequate SPICE model to describe the modes of operation of coupled oscillator circuits. Physical mechanisms influencing the time of forward and reverse electrical switching, that determine the applicability limits of the proposed model, are identified. For the resistive coupling, it is shown that synchronization takes place at a certain value of the coupling resistance, though it is unstable and a synchronization failure occurs periodically. For the capacitive coupling, two synchronization modes, with weak and strong coupling, are found. The transition between these modes is accompanied by chaotic oscillations. A decrease in the width of the spectrum harmonics in the weak-coupling mode, and its increase in the strong-coupling one, is detected. The dependences of frequencies and phase differences of the coupled oscillatory circuits on the coupling capacitance are found. Examples of operation of coupled VO2 oscillators as a central pattern generator are demonstrated.
On harmonic oscillators and their Kemmer relativistic forms
NASA Technical Reports Server (NTRS)
Debergh, Nathalie; Beckers, Jules
1993-01-01
It is shown that Dirac (Kemmer) equations are intimately connected with (para)supercharges coming from (para)supersymmetric quantum mechanics, a nonrelativistic theory. The dimensions of the irreducible representations of Clifford (Kemmer) algebras play a fundamental role in such an analysis. These considerations are illustrated through oscillator like interactions, leading to (para)relativistic oscillators.
Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Plyushchay, Mikhail S.
2016-11-01
Ladder operators for the simplest version of a rationally extended quantum harmonic oscillator (REQHO) are constructed by applying a Darboux transformation to the quantum harmonic oscillator system. It is shown that the physical spectrum of the REQHO carries a direct sum of a trivial and an infinite-dimensional irreducible representation of the polynomially deformed bosonized osp (1 |2 ) superalgebra. In correspondence with this the ground state of the system is isolated from other physical states but can be reached by ladder operators via nonphysical energy eigenstates, which belong to either an infinite chain of similar eigenstates or to the chains with generalized Jordan states. We show that the discrete chains of the states generated by ladder operators and associated with physical energy levels include six basic generalized Jordan states, in comparison with the two basic Jordan states entering in analogous discrete chains for the quantum harmonic oscillator.
The finite harmonic oscillator and its associated sequences
Gurevich, Shamgar; Hadani, Ronny; Sochen, Nir
2008-01-01
A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication theory are explained. PMID:18635684
Application of Elliott's SU(3) model to the triaxially deformed harmonic oscillators
NASA Astrophysics Data System (ADS)
Sugawara-Tanabe, Kazuko
2011-05-01
We have introduced new bosons corresponding to the integral ratio of three frequencies for a harmonic oscillator potential, by means of a non-linear transformation which realizes the SU(3) group as a dynamical symmetry group, and which leaves the anisotropic harmonic oscillator Hamiltonian invariant. The classification of the single-particle levels based on this covering group predicts magic numbers depending on the deformation parameters δ and γ. The special cases with tan γ = 1/√3 (γ = 30°) and √3 /5(γ˜19°) are discussed.
Application of Elliott's SU(3) model to the triaxially deformed harmonic oscillators
Sugawara-Tanabe, Kazuko
2011-05-06
We have introduced new bosons corresponding to the integral ratio of three frequencies for a harmonic oscillator potential, by means of a non-linear transformation which realizes the SU(3) group as a dynamical symmetry group, and which leaves the anisotropic harmonic oscillator Hamiltonian invariant. The classification of the single-particle levels based on this covering group predicts magic numbers depending on the deformation parameters {delta} and {gamma}. The special cases with tan {gamma} = 1/{radical}(3)({gamma} = 30 deg.) and {radical}(3)/5({gamma}{approx}19 deg.) are discussed.
On the effects of a screw dislocation and a linear potential on the harmonic oscillator
NASA Astrophysics Data System (ADS)
Bueno, M. J.; Furtado, C.; Bakke, K.
2016-09-01
Quantum effects on the harmonic oscillator due to the presence of a linear scalar potential and a screw dislocation are investigated. By searching for bound states solutions, it is shown that an Aharonov-Bohm-type effect for bound states and a restriction of the values of the angular frequency of the harmonic oscillator can be obtained, where the allowed values are determined by the topology of the screw dislocation and the quantum numbers associated with the radial modes and the angular momentum. As particular cases, the angular frequency and the energy levels associated with the ground state and the first excited state of the system are obtained.
NASA Astrophysics Data System (ADS)
Mandal, Swapan
2017-03-01
The classical harmonic oscillator with time dependent mass and frequency is investigated to obtain a closed form exact analytical solution. It is found that the closed form analytical solutions are indeed possible if the time dependent mass of the oscillator is inversely proportional to the time dependent frequency. The scaled wronskian obtained from the linearly independent solutions of the equation of motion of the classical oscillator is used to obtain the solution corresponding to its quantum mechanical counterpart. The analytical solution of the present oscillator is used to obtain the squeezing effects of the input coherent light. In addition to the possibilities of getting the squeezed states, the present solution will be of use for investigating various quantum statistical properties of the radiation fields. As an example, we investigate the antibunching of the input thermal (chaotic) light coupled to the oscillator. Therefore, the appearance of the photon antibunching does not warrant the squeezing and vice-versa. The exact solution is obtained at the cost of the stringent condition where the product of time dependent mass and frequency of the oscillator is time invariant.
Active Coupled Oscillators in the Inner Ear
NASA Astrophysics Data System (ADS)
Strimbu, Clark Elliott
Auditory and vestibular systems are endowed with an active process that enables them to detect signals as small as a few Angstroms; they also exhibit frequency selectivity; show strong nonlinearities; and can exhibit as spontaneous activity. Much of this active process comes from the sensory hair cells at the periphery of the auditory and vestibular systems. Each hair cell is capped by an eponymous hair bundle, a specialized structure that transduces mechanical forces into electrical signals. Experiments on mechanically decoupled cells from the frog sacculus have shown that individual hair bundles behave in an active manner analogous to an intact organ suggesting a common cellular basis for the active processes seen in many species. In particular, mechanically decoupled hair bundles show rapid active movements in response to transient stimuli and exhibit spontaneous oscillations. However, a single mechanosensitive hair cell is unable to match the performance of an entire organ. In vivo, hair bundles are often coupled to overlying membranes, gelatinous extracellular matrices. We used an in vitro preparation of the frog sacculus in which the otolithic membrane has been left intact. Under natural coupling conditions, there is a strong degree of correlation across the saccular epithelium, suggesting that the collective response of many cells contributes to the extreme sensitivity of this organ. When the membrane is left intact, the hair bundles do not oscillate spontaneously, showing that the natural coupling and loading tunes them into a quiescent regime. However, when stimulated by a pulse, the bundles show a rapid biphasic response that is abolished when the transduction channels are blocked. The active forces generated by the bundles are sufficient to move the overlying membrane.
Harmonic and anharmonic oscillations investigated by using a microcomputer-based Atwood's machine
NASA Astrophysics Data System (ADS)
Pecori, Barbara; Torzo, Giacomo; Sconza, Andrea
1999-03-01
We describe how the Atwood's machine, interfaced to a personal computer through a rotary encoder, is suited for investigating harmonic and anharmonic oscillations, exploiting the buoyancy force acting on a body immersed in water. We report experimental studies of oscillators produced by driving forces of the type F=-kxn with n=1,2,3, and F=-k sgn(x). Finally we suggest how this apparatus can be used for showing to the students a macroscopic model of interatomic forces.
Synchronization using environmental coupling in mercury beating heart oscillators
NASA Astrophysics Data System (ADS)
Singla, Tanu; Montoya, Fernando; Rivera, M.; Tajima, Shunsuke; Nakabayashi, Seiichiro; Parmananda, P.
2016-06-01
We report synchronization of Mercury Beating Heart (MBH) oscillators using the environmental coupling mechanism. This mechanism involves interaction of the oscillators with a common medium/environment such that the oscillators do not interact among themselves. In the present work, we chose a modified MBH system as the common environment. In the absence of coupling, this modified system does not exhibit self sustained oscillations. It was observed that, as a result of the coupling of the MBH oscillators with this common environment, the electrical and the mechanical activities of both the oscillators synchronized simultaneously. Experimental results indicate the emergence of both lag and the complete synchronization in the MBH oscillators. Simulations of the phase oscillators were carried out in order to better understand the experimental observations.
The impact damped harmonic oscillator in free decay
NASA Technical Reports Server (NTRS)
Brown, G. V.; North, C. M.
1987-01-01
The impact-damped oscillator in free decay is studied by using time history solutions. A large range of oscillator amplitude is covered. The amount of damping is correlated with the behavior of the impacting mass. There are three behavior regimes: (1) a low amplitude range with less than one impact per cycle and very low damping, (2) a useful middle amplitude range with a finite number of impacts per cycle, and (3) a high amplitude range with an infinite number of impacts per cycle and progressively decreasing damping. For light damping the impact damping in the middle range is: (1) proportional to impactor mass, (2) additive to proportional damping, (3) a unique function of vibration amplitude, (4) proportional to 1-epsilon, where epsilon is the coefficient of restitution, and (5) very roughly inversely proportional to amplitude. The system exhibits jump phenomena and period doublings. An impactor with 2 percent of the oscillator's mass can produce a loss factor near 0.1.
Synchronization in arrays of coupled self-induced friction oscillators
NASA Astrophysics Data System (ADS)
Marszal, Michał; Saha, Ashesh; Jankowski, Krzysztof; Stefański, Andrzej
2016-11-01
We investigate synchronization phenomena in systems of self-induced dry friction oscillators with kinematic excitation coupled by linear springs. Friction force is modelled according to exponential model. Initially, a single degree of freedom mass-spring system on a moving belt is considered to check the type of motion of the system (periodic, non-periodic). Then the system is coupled in chain of identical oscillators starting from two, up to four oscillators. A reference probe of two coupled oscillators is applied in order to detect synchronization thresholds for both periodic and non-periodic motion of the system. The master stability function is applied to predict the synchronization thresholds for longer chains of oscillators basing on two oscillator probe. It is shown that synchronization is possible both for three and four coupled oscillators under certain circumstances. Our results confirmed that this technique can be also applied for the systems with discontinuities.
ERIC Educational Resources Information Center
Parnis, J. Mark; Thompson, Matthew G. K.
2004-01-01
An introductory undergraduate physical organic chemistry exercise that introduces the harmonic oscillator's use in vibrational spectroscopy is developed. The analysis and modeling exercise begins with the students calculating the stretching modes of common organic molecules with the help of the quantum mechanical harmonic oscillator (QMHO) model.
Constructing quantum logic gates using q-deformed harmonic oscillator algebras
NASA Astrophysics Data System (ADS)
Altintas, Azmi Ali; Ozaydin, Fatih; Yesilyurt, Can; Bugu, Sinan; Arik, Metin
2014-04-01
We study two-level q-deformed angular momentum states, and using q-deformed harmonic oscillators, we provide a framework for constructing qubits and quantum gates. We also present the construction of some basic one-qubit and two-qubit quantum logic gates.
Generalized uncertainty principle corrections to the simple harmonic oscillator in phase space
NASA Astrophysics Data System (ADS)
Das, Saurya; Robbins, Matthew P. G.; Walton, Mark A.
2016-01-01
We compute Wigner functions for the harmonic oscillator including corrections from generalized uncertainty principles (GUPs), and study the corresponding marginal probability densities and other properties. We show that the GUP corrections to the Wigner functions can be significant, and comment on their potential measurability in the laboratory.
Convergence for Fourier Series Solutions of the Forced Harmonic Oscillator II
ERIC Educational Resources Information Center
Fay, Temple H.
2002-01-01
This paper compliments two recent articles by the author in this journal concerning solving the forced harmonic oscillator equation when the forcing is periodic. The idea is to replace the forcing function by its Fourier series and solve the differential equation term-by-term. Herein the convergence of such series solutions is investigated when…
Note on the Time-Dependent Damped and Forced Harmonic Oscillator.
ERIC Educational Resources Information Center
Leach, P. G. L.
1978-01-01
A Hamiltonian for the time-dependent damped and forced harmonic oscillator is derived. A simple time-dependent linear canonical transformation transforms the Hamiltonian to one whose solution is readily obtained. The wave function for the corresponding quantum mechanical problem is given. (Author/GA)
Morales, J.; Ovando, G.; Pena, J. J.
2010-12-23
One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.
Damped harmonic oscillator model for analyzing the dynamic characteristics of STM system
NASA Astrophysics Data System (ADS)
Liu, A. P.; Yao, X. X.; Wang, X.; Yang, D. X.; Zhang, X. M.
2015-09-01
Recognizing and distinguishing the dynamic characteristics of scanning tunneling microscopy (STM) system is fatal for studying STM image. In this paper, a method for analyzing system’s characteristics by using a damped harmonic oscillator model is presented. The model is driven by random force and all of its properties are described by damping and periodic. For the general solution of such harmonic oscillator’s Langevin equation is deduced and the auto-correlation function (ACF) is obtained for fitting curve. It is shown that damping and periodic property of the two curves have a good agreement by comparing the fitting curve with the auto-correlation curve of time series dates which are acquired by STM. It could be concluded that the damped harmonic oscillator model and auto-correlation method are feasible for analyzing the dynamic characteristics of STM system.
Harmonic mode competition in a terahertz gyrotron backward-wave oscillator
Kao, S. H.; Chiu, C. C.; Chang, P. C.; Wu, K. L.; Chu, K. R.
2012-10-15
Electron cyclotron maser interactions at terahertz (THz) frequencies require a high-order-mode structure to reduce the wall loss to a tolerable level. To generate THz radiation, it is also essential to employ cyclotron harmonic resonances to reduce the required magnetic field strength to a value within the capability of the superconducting magnets. However, much weaker harmonic interactions in a high-order-mode structure lead to serious mode competition problems. The current paper addresses harmonic mode competition in the gyrotron backward wave oscillator (gyro-BWO). We begin with a comparative study of the mode formation and oscillation thresholds in the gyro-BWO and gyromonotron. Differences in linear features result in far fewer 'windows' for harmonic operation of the gyro-BWO. Nonlinear consequences of these differences are examined in particle simulations of the multimode competition processes in the gyro-BWO, which shed light on the competition criteria between modes of different as well as the same cyclotron harmonic numbers. The viability of a harmonic gyro-BWO is assessed on the basis of the results obtained.
NASA Astrophysics Data System (ADS)
Vignat, C.; Lamberti, P. W.
2009-10-01
Recently, Cariñena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.
NASA Astrophysics Data System (ADS)
Gautam, Kumar; Chauhan, Garv; Rawat, Tarun Kumar; Parthasarathy, Harish; Sharma, Navneet
2015-09-01
This paper presents the design of a given quantum unitary gate by perturbing a three-dimensional (3-D) quantum harmonic oscillator with a time-varying but spatially constant electromagnetic field. The idea is based on expressing the radiation- perturbed Hamiltonian as the sum of the unperturbed Hamiltonian and O( e) and perturbations and then solving the Schrödinger equation to obtain the evolution operator at time T up to , and this is a linear-quadratic function of the perturbing electromagnetic field values over the time interval [0, T]. Setting the variational derivative of the error energy with respect to the electromagnetic field values with an average electromagnetic field energy constraint leads to the optimal electromagnetic field solution, a linear integral equation. The reliability of such a gate design procedure in the presence of heat bath coupling is analysed, and finally, an example illustrating how atoms and molecules can be approximated using oscillators is presented.
Amplitude death in coupled robust-chaos oscillators
NASA Astrophysics Data System (ADS)
Palazzi, M. J.; Cosenza, M. G.
2014-12-01
We investigate the synchronization behavior of a system of globally coupled, continuous-time oscillators possessing robust chaos. The local dynamics corresponds to the Shimizu-Morioka model where the occurrence of robust chaos in a region of its parameter space has been recently discovered. We show that the global coupling can drive the oscillators to synchronization into a fixed point created by the coupling, resulting in amplitude death in the system. The existence of robust chaos allows to introduce heterogeneity in the local parameters, while guaranteeing the functioning of all the oscillators in a chaotic mode. In this case, the system reaches a state of oscillation death, with coexisting clusters of oscillators in different steady states. The phenomena of amplitude death or oscillation death in coupled robust-chaos flows could be employed as mechanisms for stabilization and control in systems that require reliable operation under chaos.
Phase patterns of coupled oscillators with application to wireless communication
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
NASA Astrophysics Data System (ADS)
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.
Surprises of the Transformer as a Coupled Oscillator System
ERIC Educational Resources Information Center
Silva, J. P.; Silvestre, A. J.
2008-01-01
We study a system of two RLC oscillators coupled through a variable mutual inductance. The system is interesting because it exhibits some peculiar features of coupled oscillators: (i) there are two natural frequencies; (ii) in general, the resonant frequencies do not coincide with the natural frequencies; (iii) the resonant frequencies of both…
Gluing Bifurcations in Coupled Spin Torque Nano-Oscillators
2013-01-01
REPORT Gluing bifurcations in coupled spin torque nano -oscillators 14. ABSTRACT 16. SECURITY CLASSIFICATION OF: Over the past few years it has been...shown, through theory and experiments, that the AC current produced by spin torque nano -oscillators (STNO), coupled in an array, can lead to feedback...Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 15. SUBJECT TERMS Nano -oscillators, symmetry, bifurcations Katherine
Entangling Qubits in a One-Dimensional Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Owen, Edmund; Dean, Matthew; Barnes, Crispin
2012-02-01
We present a method for generating entanglement between qubits associated with a pair of particles interacting in a one-dimensional harmonic potential. By considering the effect of the interaction on the energy spectrum of the system, we show that, under certain approximations, a ``power-of-SWAP" operation is performed on the initial two-qubit quantum state without requiring any time-dependent control. Initialization errors and deviations from our approximation are shown to have a negligible effect on the final state. Using a GPU-accelerated iteration scheme to find numerical solutions to the two-particle time-dependent Schr"odinger equation, we demonstrate that it is possible to generate maximally entangled Bell states between the two qubits with high fidelity for a range of possible interaction potentials.
Whitfield, Troy W; Martyna, Glenn J
2007-02-21
In the effort to develop atomistic models capable of accurately describing nanoscale systems with complex interfaces, it has become clear that simple treatments with rigid charge distributions and dispersion coefficients selected to generate bulk properties are insufficient to predict important physical properties. The quantum Drude oscillator model, a system of one-electron pseudoatoms whose "pseudoelectrons" are harmonically bound to their respective "pseudonuclei," is capable of treating many-body polarization and dispersion interactions in molecular systems on an equal footing due to the ability of the pseudoatoms to mimic the long-range interactions that characterize real materials. Using imaginary time path integration, the Drude oscillator model can, in principle, be solved in computer operation counts that scale linearly with the number of atoms in the system. In practice, however, standard expressions for the energy and pressure, including the commonly used virial estimator, have extremely large variances that require untenably long simulation times to generate converged averages. In this paper, low-variance estimators for the internal energy are derived, in which the large zero-point energy of the oscillators does not contribute to the variance. The new estimators are applicable to any system of harmonic oscillators coupled to one another (or to the environment) via an arbitrary set of anharmonic interactions. The variance of the new estimators is found to be much smaller than standard estimators in three example problems, a one-dimensional anharmonic oscillator and quantum Drude models of the xenon dimer and solid (fcc) xenon, respectively, yielding 2-3 orders of magnitude improvement in computational efficiency.
Fidler, Andrew F; Engel, Gregory S
2013-10-03
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.
Harmonic Oscillations in Homeostatic Controllers: Dynamics of the p53 Regulatory System
Jolma, Ingunn W.; Ni, Xiao Yu; Rensing, Ludger; Ruoff, Peter
2010-01-01
Abstract Homeostatic mechanisms are essential for the protection and adaptation of organisms in a changing and challenging environment. Previously, we have described molecular mechanisms that lead to robust homeostasis/adaptation under inflow or outflow perturbations. Here we report that harmonic oscillations occur in models of such homeostatic controllers and that a close relationship exists between the control of the p53/Mdm2 system and that of a homeostatic inflow controller. This homeostatic control model of the p53 system provides an explanation why large fluctuations in the amplitude of p53/Mdm2 oscillations may arise as part of the homeostatic regulation of p53 by Mdm2 under DNA-damaging conditions. In the presence of DNA damage p53 is upregulated, but is subject to a tight control by Mdm2 and other factors to avoid a premature apoptotic response of the cell at low DNA damage levels. One of the regulatory steps is the Mdm2-mediated degradation of p53 by the proteasome. Oscillations in the p53/Mdm2 system are considered to be part of a mechanism by which a cell decides between cell cycle arrest/DNA repair and apoptosis. In the homeostatic inflow control model, harmonic oscillations in p53/Mdm2 levels arise when the binding strength of p53 to degradation complexes increases. Due to the harmonic character of the oscillations rapid fluctuating noise can lead, as experimentally observed, to large variations in the amplitude of the oscillation but not in their period, a behavior which has been difficult to simulate by deterministic limit-cycle models. In conclusion, the oscillatory response of homeostatic controllers may provide new insights into the origin and role of oscillations observed in homeostatically controlled molecular networks. PMID:20197027
Spin Number Coherent States and the Problem of Two Coupled Oscillators
NASA Astrophysics Data System (ADS)
Ojeda-Guillén, D.; Mota, R. D.; Granados, V. D.
2015-07-01
From the definition of the standard Perelomov coherent states we introduce the Perelomov number coherent states for any su(2) Lie algebra. With the displacement operator we apply a similarity transformation to the su(2) generators and construct a new set of operators which also close the su(2) Lie algebra, being the Perelomov number coherent states the new basis for its unitary irreducible representation. We apply our results to obtain the energy spectrum, the eigenstates and the partition function of two coupled oscillators. We show that the eigenstates of two coupled oscillators are the SU(2) Perelomov number coherent states of the two-dimensional harmonic oscillator with an appropriate choice of the coherent state parameters. Supported by SNI-México, COFAA-IPN, EDD-IPN, EDI-IPN, SIP-IPN Project No. 20150935
Robustness and fragility in coupled oscillator networks under targeted attacks
NASA Astrophysics Data System (ADS)
Yuan, Tianyu; Aihara, Kazuyuki; Tanaka, Gouhei
2017-01-01
The dynamical tolerance of coupled oscillator networks against local failures is studied. As the fraction of failed oscillator nodes gradually increases, the mean oscillation amplitude in the entire network decreases and then suddenly vanishes at a critical fraction as a phase transition. This critical fraction, widely used as a measure of the network robustness, was analytically derived for random failures but not for targeted attacks so far. Here we derive the general formula for the critical fraction, which can be applied to both random failures and targeted attacks. We consider the effects of targeting oscillator nodes based on their degrees. First we deal with coupled identical oscillators with homogeneous edge weights. Then our theory is applied to networks with heterogeneous edge weights and to those with nonidentical oscillators. The analytical results are validated by numerical experiments. Our results reveal the key factors governing the robustness and fragility of oscillator networks.
Collective phase response curves for heterogeneous coupled oscillators
NASA Astrophysics Data System (ADS)
Hannay, Kevin M.; Booth, Victoria; Forger, Daniel B.
2015-08-01
Phase response curves (PRCs) have become an indispensable tool in understanding the entrainment and synchronization of biological oscillators. However, biological oscillators are often found in large coupled heterogeneous systems and the variable of physiological importance is the collective rhythm resulting from an aggregation of the individual oscillations. To study this phenomena we consider phase resetting of the collective rhythm for large ensembles of globally coupled Sakaguchi-Kuramoto oscillators. Making use of Ott-Antonsen theory we derive an asymptotically valid analytic formula for the collective PRC. A result of this analysis is a characteristic scaling for the change in the amplitude and entrainment points for the collective PRC compared to the individual oscillator PRC. We support the analytical findings with numerical evidence and demonstrate the applicability of the theory to large ensembles of coupled neuronal oscillators.
Spectra of delay-coupled heterogeneous noisy nonlinear oscillators
NASA Astrophysics Data System (ADS)
Vüllings, Andrea; Schöll, Eckehard; Lindner, Benjamin
2014-02-01
Nonlinear oscillators that are subject to noise and delayed interaction have been used to describe a number of dynamical phenomena in Physics and beyond. Here we study the spectral statistics (power and cross-spectral densities) of a small number of noisy nonlinear oscillators and derive analytical approximations for these spectra. In our paper, individual oscillators are described by the normal form of a supercritical or subcritical Hopf bifurcation supplemented by Gaussian white noise. Oscillators can be distinguished from each other by their frequency, bifurcation parameter, and noise intensity. Extending previous results from the literature, we first calculate in linear response theory the power spectral density and response function of the single oscillator in both super- and subcritical parameter regime and test them against numerical simulations. For small heterogeneous groups of oscillators (N = 2 or 3), which are coupled by a delayed linear term, we use a linear response ansatz to derive approximations for the power and cross-spectral densities of the oscillators within this small network. These approximations are confirmed by comparison with extensive numerical simulations. Using the theory we relate the peaks in the spectra of the homogeneous system (identical oscillators) to periodic solutions of the deterministic (noiseless) system. For two delay-coupled subcritical Hopf oscillators, we show that the coupling can enhance the coherence resonance effect, which is known to occur for the single subcritical oscillator. In the case of heterogeneous oscillators, we find that the delay-induced characteristic profile of the spectra is conserved for moderate frequency detuning.
Non-Heisenberg states of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Dechoum, K.; França, H. M.
1995-11-01
The effects of the vacuum electromagnetic fluctuations and the radiation reaction fields on the time development of a simple microscopic system are identified using a new mathematical method. This is done by studying a charged mechanical oscillator (frequency Ω 0) within the realm of stochastic electrodynamics, where the vacuum plays the role of an energy reservoir. According to our approach, which may be regarded as a simple mathematical exercise, we show how the oscillator Liouville equation is transformed into a Schrödinger-like stochastic equation with a free parameter h' with dimensions of action. The role of the physical Planck's constant h is introduced only through the zero-point vacuum electromagnetic fields. The perturbative and the exact solutions of the stochastic Schrödinger-like equation are presented for h'>0. The exact solutions for which h'
Basin stability measure of different steady states in coupled oscillators
Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-01-01
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis. PMID:28378760
Symmetry-broken states on networks of coupled oscillators
NASA Astrophysics Data System (ADS)
Jiang, Xin; Abrams, Daniel M.
2016-05-01
When identical oscillators are coupled together in a network, dynamical steady states are often assumed to reflect network symmetries. Here, we show that alternative persistent states may also exist that break the symmetries of the underlying coupling network. We further show that these symmetry-broken coexistent states are analogous to those dubbed "chimera states," which can occur when identical oscillators are coupled to one another in identical ways.
Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator
NASA Astrophysics Data System (ADS)
Mahdifar, A.; Roknizadeh, R.; Naderi, M. H.
2006-06-01
In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using the nonlinear coherent states approach. For this purpose, we study two-dimensional harmonic oscillators on the flat surface and on a sphere by applying the Higgs model. With the use of their algebras, we show that the two-dimensional oscillator algebra on a surface can be considered as a deformed one-dimensional oscillator algebra where the effect of the curvature of the surface appears as a deformation function. We also show that the curvature of the physical space plays the role of deformation parameter. Then we construct the associated coherent states on the flat surface and on a sphere and compare their quantum statistical properties, including quadrature squeezing and antibunching effect.
Harmonically pumped femtosecond optical parametric oscillator with multi-gigahertz repetition rate.
Tian, Wenlong; Wang, Zhaohua; Zhu, Jiangfeng; Wei, Zhiyi
2016-12-26
We report a multi-gigahertz (GHz) repetition-rate femtosecond MgO:PPLN optical parametric oscillator (OPO) harmonically pumped by a 75.6 MHz Kerr-lens mode-locked Yb:KGW laser. By fractionally increasing the OPO cavity length, we obtained OPO operation up to the 493rd harmonic of the pump laser repetition rate, corresponding to a repetition rate as high as 37.3 GHz. Using a 1.5% output coupler, we are able to extract signal pulses with up to 260 mW average power at the 102nd harmonic (7.7 GHz) and 90 mW at the 493rd harmonic (37.3 GHz) under 2 W pump power. The measured relative standard deviations of the fundamental and the 102nd harmonic signal power were recorded to be 0.5% and 2.1%, respectively. The signal pulse durations at different harmonics were measured in the range of 160-230 fs.
Laser cooling of a harmonic oscillator's bath with optomechanics
NASA Astrophysics Data System (ADS)
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.
Form of the effective interaction in harmonic-oscillator-based effective theory
NASA Astrophysics Data System (ADS)
Haxton, W. C.
2008-03-01
I explore the form of the effective interaction in harmonic-oscillator-based effective theory (HOBET) in leading order (LO) through next-to-next-to-next-to-leading order (NLO3). Because the included space in a HOBET (as in the shell model) is defined by the oscillator energy, both long-distance (low-momentum) and short-distance (high-momentum) degrees of freedom reside in the high-energy excluded space. A HOBET effective interaction is developed in which a short-range contact-gradient expansion, free of operator mixing and corresponding to a systematic expansion in nodal quantum numbers, is combined with an exact summation of the relative kinetic energy. By this means the very strong coupling of the included (P) and excluded (Q) spaces by the kinetic energy is removed. One finds a simple and rather surprising result, that the interplay of QT and QV is governed by a single parameter κ, the ratio of an observable, the binding energy |E|, to a parameter in the effective theory, the oscillator energy ℏω. Once the functional dependence on κ is identified, the remaining order-by-order subtraction of the short-range physics residing in Q becomes systematic and rapidly converging. Numerical calculations are used to demonstrate how well the resulting expansion reproduces the running of Heff from high scales to a typical shell-model scale of 8ℏω. At NLO3 various global properties of Heff are reproduced to a typical accuracy of 0.01%, or about 1 keV, at 8ℏω. Channel-by-channel variations in convergence rates are similar to those found in effective field theory approaches. The state dependence of the effective interaction has been a troubling problem in nuclear physics and is embodied in the energy dependence of Heff(|E|) in the Bloch-Horowitz formalism. It is shown that almost all of this state dependence is also extracted in the procedures followed here, isolated in the analytic dependence of Heff on κ. Thus there exists a simple, Hermitian Heff that can be use
Oscillator Seeding of a High Gain Harmonic Generation FEL in a Radiator-First Configuration
Gandhi, P.; Wurtele, J.; Penn, G.; Reinsch, M.
2012-05-20
A longitudinally coherent X-ray pulse from a high repetition rate free electron laser (FEL) is desired for a wide variety of experimental applications. However, generating such a pulse with a repetition rate greater than 1 MHz is a significant challenge. The desired high repetition rate sources, primarily high harmonic generation with intense lasers in gases or plasmas, do not exist now, and, for the multi-MHz bunch trains that superconducting accelerators can potentially produce, are likely not feasible with current technology. In this paper, we propose to place an oscillator downstream of a radiator. The oscillator generates radiation that is used as a seed for a high gain harmonic generation (HGHG) FEL which is upstream of the oscillator. For the first few pulses the oscillator builds up power and, until power is built up, the radiator has no HGHG seed. As power in the oscillator saturates, the HGHG is seeded and power is produced. The dynamics and stability of this radiator-first scheme is explored analytically and numerically. A single-pass map is derived using a semi-analytic model for FEL gain and saturation. Iteration of the map is shown to be in good agreement with simulations. A numerical example is presented for a soft X-ray FEL.
Coherent states for nonlinear harmonic oscillator and some of its properties
Amir, Naila E-mail: naila.amir@sns.nust.edu.pk; Iqbal, Shahid E-mail: siqbal@sns.nust.edu.pk
2015-06-15
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
Study of the harmonic oscillation on EAST by an eight-channel Doppler Backscattering (DBS) system
NASA Astrophysics Data System (ADS)
Zhou, C.; Liu, A. D.; Wang, M. Y.; Hu, J. Q.; Zhang, J.; Li, H.; Lan, T.; Xie, J. L.; Liu, W. D.; Yu, C. X.; Doyle, E. J.; University of California, Los Angeles Collaboration; University of Science; Technology of China Team
2016-10-01
The eight-channel DBS system has been installed for turbulence measurements in such plasmas. The frequency range is 55 to 75 GHz, covering the entire H-mode pedestal, with a turbulence wavenumber range of 4-12/cm. A harmonic oscillation has been observed by DBS on EAST during ELMy-free H mode. The fundamental frequency of the coherent oscillation is 12-20 kHz and 2nd-8th harmonic are observed, and the radial coverage is from the edge to rho 0.85. Work supported by the Natural Science Foundation of China (NSFC) under 11475173, 11505184, National Magnetic Confinement Fusion Energy Development Program of China under 2013GB106002 and 2014GB109002, and DOE Grants DE- SC0010424 and DE-SC0010469.
Transformations of the perturbed two-body problem to unperturbed harmonic oscillators
NASA Technical Reports Server (NTRS)
Szebehely, V.; Bond, V.
1983-01-01
Singular, nonlinear, and Liapunov unstable equations are made regular and linear through transformations that change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients, so that the stable solution may be immediately written in terms of the new variables. The use of arbitrary and special functions for the transformations allows the systematic discussion of previously introduced and novel anomalies. For the case of the unperturbed two-body problem, it is proved that if transformations are power functions of the radial variable, only the eccentric and the true anomalies (with the corresponding transformations of the radial variable) will result in harmonic oscillators. The present method significantly reduces computation requirements in autonomous space operations.
Bound States Energies of a Harmonic Oscillator Perturbed by Point Interactions
NASA Astrophysics Data System (ADS)
Ferkous, N.; Boudjedaa, T.
2017-03-01
We determine explicitly the exact transcendental bound states energies equation for a one-dimensional harmonic oscillator perturbed by a single and a double point interactions via Green’s function techniques using both momentum and position space representations. The even and odd solutions of the problem are discussed. The corresponding limiting cases are recovered. For the harmonic oscillator with a point interaction in more than one dimension, divergent series appear. We use to remove this divergence an exponential regulator and we obtain a transcendental equation for the energy bound states. The results obtained here are consistent with other investigations using different methods. Supported by the Algerian Ministry of Higher Education and Scientific Research under the CNEPRU project No. D01720140001
The mutual synchronization of coupled delayed feedback klystron oscillators
NASA Astrophysics Data System (ADS)
Emel'yanov, V. V.; Emelianova, Yu. P.; Ryskin, N. M.
2016-08-01
We report on the results of a numerical investigation of the synchronization of two coupled klystron oscillators with an external feedback circuit. Simulation has been carried out using the particle-in-cell method. We have also considered the results of a numerical analysis of an amplifier klystron and an isolated klystron oscillator, which make it possible to choose the optimal values of parameters of coupled klystrons. The structure of the synchronization domain for various parameters has been analyzed. The possibility of increasing the total output power with an appropriate choice of parameter of coupling between the oscillators has been revealed.
Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator
Chen Xi; Muga, J. G.
2010-11-15
We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes ('shortcuts to adiabaticity') designed to reproduce the initial populations at some predetermined final frequency and time. We provide lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.
NASA Astrophysics Data System (ADS)
Hamerly, Ryan; Marandi, Alireza; Jankowski, Marc; Fejer, M. M.; Yamamoto, Yoshihisa; Mabuchi, Hideo
2016-12-01
We develop reduced models that describe half-harmonic generation in a synchronously pumped optical parametric oscillator above threshold, where nonlinearity, dispersion, and group-velocity mismatch are all relevant. These models are based on (1) an eigenmode expansion for low pump powers, (2) a simultonlike sech-pulse ansatz for intermediate powers, and (3) dispersionless box-shaped pulses for high powers. Analytic formulas for pulse compression, degenerate vs nondegenerate operation, and stability are derived and compared to numerical and experimental results.
Parallel-path biquad active-RC oscillator with enhanced harmonic rejection
NASA Astrophysics Data System (ADS)
Vosper, J. V.; Heima, M.; Cryan, R. A.
1995-04-01
A biquad active-RC oscillator is described and a linear analysis given which shows that harmonics injected within the feedback loop are multiplied by a factor which is inversely proportional to the effective open-loop Q-factor Q(sub 0). Experimental results show that distortion is low at high Q(sub 0) values even when saturated operation of the main gain-producing opamp is allowed.
Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise
NASA Astrophysics Data System (ADS)
Jara, Milton; Komorowski, Tomasz; Olla, Stefano
2015-10-01
We consider a one dimensional infinite chain of harmonic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to the solution of the fractional diffusion equation . For a pinned system we prove that its energy evolves diffusively, generalizing some results of Basile and Olla (J. Stat. Phys. 155(6):1126-1142, 2014).
Dynamics of SU(1,1) coherent states for the damped harmonic oscillator
Choi, Jeong Ryeol; Yeon, Kyu Hwang
2009-05-15
Gerry, Ma, and Vrscay [Phys. Rev. A 39, 668 (1989)] studied the time evolution of SU(1,1) coherent states for the damped harmonic oscillator by introducing the Kanai-Caldirola Hamiltonian. The purposes of this Brief Report are to demonstrate that there are somewhat serious errors on their results and to correct them. Most of the figures given in their work are reproduced with correction in order to facilitate our explanation of results.
A common lag scenario in quenching of oscillation in coupled oscillators
NASA Astrophysics Data System (ADS)
Suresh, K.; Sabarathinam, S.; Thamilmaran, K.; Kurths, Jürgen; Dana, Syamal K.
2016-08-01
A large parameter mismatch can induce amplitude death in two instantaneously coupled oscillators. Alternatively, a time delay in the coupling can induce amplitude death in two identical oscillators. We unify the mechanism of quenching of oscillation in coupled oscillators, either by a large parameter mismatch or a delay coupling, by a common lag scenario that is, surprisingly, different from the conventional lag synchronization. We present numerical as well as experimental evidence of this unknown kind of lag scenario when the lag increases with coupling and at a critically large value at a critical coupling strength, amplitude death emerges in two largely mismatched oscillators. This is analogous to amplitude death in identical systems with increasingly large coupling delay. In support, we use examples of the Chua oscillator and the Bonhoeffer-van der Pol system. Furthermore, we confirm this lag scenario during the onset of amplitude death in identical Stuart-Landau system under various instantaneous coupling forms, repulsive, conjugate, and a type of nonlinear coupling.
Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.
Li, Haifeng; Shao, Jiushu; Wang, Shikuan
2011-11-01
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.
Brownian motion of a classical harmonic oscillator in a magnetic field.
Jiménez-Aquino, J I; Velasco, R M; Uribe, F J
2008-05-01
In this paper, the stochastic diffusion process of a charged classical harmonic oscillator in a constant magnetic field is exactly described through the analytical solution of the associated Langevin equation. Due to the presence of the magnetic field, stochastic diffusion takes place across and along the magnetic field. Along the magnetic field, the Brownian motion is exactly the same as that of the ordinary one-dimensional classical harmonic oscillator, which was very well described in Chandrasekhar's celebrated paper [Rev. Mod. Phys. 15, 1 (1943)]. Across the magnetic field, the stochastic process takes place on a plane, perpendicular to the magnetic field. For internally Gaussian white noise, this planar-diffusion process is exactly described through the first two moments of the positions and velocities and their corresponding cross correlations. In the absence of the magnetic field, our analytical results are the same as those calculated by Chandrasekhar for the ordinary harmonic oscillator. The stochastic planar diffusion is also well characterized in the overdamped approximation, through the solutions of the Langevin equation.
The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Rañada, Manuel F.; Santander, Mariano
2008-03-01
The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and metric of any signature, either Riemannian (definite positive) or Lorentzian (indefinite). In this paper we study the main properties of these "curved" harmonic oscillators simultaneously on any such configuration space, using a Cayley-Klein (CK)-type approach, with two free parameters κ1,κ2 which altogether correspond to the possible values for curvature and signature type: the generic Riemannian and Lorentzian spaces of constant curvature (sphere S2, hyperbolic plane H2, AntiDeSitter sphere AdS1+1, and DeSitter sphere dS1+1) appear in this family, with Euclidean and Minkowski spaces as flat particular cases. We solve the equations of motion for the curved harmonic oscillator and obtain explicit expressions for the orbits by using three different methods: by direct integration, by obtaining the general CK version of Binet's equation, and finally as a consequence of its superintegrable character. The orbits are conics with center at the potential origin on any CK space, thereby extending this well known Euclidean property to any constant curvature configuration space. The final part of the article, that has a more geometric character, presents pertinent results of the theory of conics on spaces of constant curvature.
Classification of attractors for systems of identical coupled Kuramoto oscillators
Engelbrecht, Jan R.; Mirollo, Renato
2014-03-15
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For N≠3 oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
Classification of attractors for systems of identical coupled Kuramoto oscillators.
Engelbrecht, Jan R; Mirollo, Renato
2014-03-01
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For [Formula: see text] oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
Collective Dipole Oscillations of a Spin-Orbit Coupled Bose-Einstein Condensate
NASA Astrophysics Data System (ADS)
Zhang, Jin-Yi; Ji, Si-Cong; Chen, Zhu; Zhang, Long; Du, Zhi-Dong; Yan, Bo; Pan, Ge-Sheng; Zhao, Bo; Deng, You-Jin; Zhai, Hui; Chen, Shuai; Pan, Jian-Wei
2012-09-01
In this Letter, we present an experimental study of the collective dipole oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. The dynamics of the center-of-mass dipole oscillation is studied in a broad parameter region as a function of spin-orbit coupling parameters as well as the oscillation amplitude. The anharmonic properties beyond the effective-mass approximation are revealed, such as the amplitude-dependent frequency and finite oscillation frequency at a place with a divergent effective mass. These anharmonic behaviors agree quantitatively with variational wave-function calculations. Moreover, we experimentally demonstrate a unique feature of the spin-orbit coupled system predicted by a sum-rule approach, stating that spin polarization susceptibility—a static physical quantity—can be measured via the dynamics of dipole oscillation. The divergence of polarization susceptibility is observed at the quantum phase transition that separates the magnetic nonzero-momentum condensate from the nonmagnetic zero-momentum phase. The good agreement between the experimental and theoretical results provides a benchmark for recently developed theoretical approaches.
ERIC Educational Resources Information Center
Andrews, David L.; Romero, Luciana C. Davila
2009-01-01
The dynamical behaviour of simple harmonic motion can be found in numerous natural phenomena. Within the quantum realm of atomic, molecular and optical systems, two main features are associated with harmonic oscillations: a finite ground-state energy and equally spaced quantum energy levels. Here it is shown that there is in fact a one-to-one…
The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
NASA Astrophysics Data System (ADS)
Quintela, T. S.; Fabris, J. C.; Nogueira, J. A.
2016-12-01
In this work, we explicitly solve the problem of the harmonic oscillator in the classical limit of a minimal-length scenario. We show that (i) the motion equation of the oscillator is not linear anymore because the presence of a minimal length introduces an anarmonic term and (ii) its motion is described by a Jacobi sine elliptic function. Therefore, the motion is periodic with the same amplitude and with the new period depending on the minimal length. This result (the change in the period of oscillation) is very important since it enables us to find in a quite simple way the most relevant effect of the presence of a minimal length and consequently traces of the Planck-scale physics. We show applications of our results in spectroscopy and gravity.
NASA Astrophysics Data System (ADS)
Stepšys, A.; Mickevicius, S.; Germanas, D.; Kalinauskas, R. K.
2014-11-01
This new version of the HOTB program for calculation of the three and four particle harmonic oscillator transformation brackets provides some enhancements and corrections to the earlier version (Germanas et al., 2010) [1]. In particular, new version allows calculations of harmonic oscillator transformation brackets be performed in parallel using MPI parallel communication standard. Moreover, higher precision of intermediate calculations using GNU Quadruple Precision and arbitrary precision library FMLib [2] is done. A package of Fortran code is presented. Calculation time of large matrices can be significantly reduced using effective parallel code. Use of Higher Precision methods in intermediate calculations increases the stability of algorithms and extends the validity of used algorithms for larger input values. Catalogue identifier: AEFQ_v4_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFQ_v4_0.html Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 Number of lines in programs, including test data, etc.: 1711 Number of bytes in distributed programs, including test data, etc.: 11667 Distribution format: tar.gz Program language used: FORTRAN 90 with MPI extensions for parallelism Computer: Any computer with FORTRAN 90 compiler Operating system: Windows, Linux, FreeBSD, True64 Unix Has the code been vectorized of parallelized?: Yes, parallelism using MPI extensions. Number of CPUs used: up to 999 RAM(per CPU core): Depending on allocated binomial and trinomial matrices and use of precision; at least 500 MB Catalogue identifier of previous version: AEFQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181, Issue 2, (2010) 420-425 Does the new version supersede the previous version? Yes Nature of problem: Calculation of matrices of three-particle harmonic oscillator brackets (3HOB) and four-particle harmonic oscillator brackets (4HOB) in a more
Hopf bifurcation with dihedral group symmetry - Coupled nonlinear oscillators
NASA Technical Reports Server (NTRS)
Golubitsky, Martin; Stewart, Ian
1986-01-01
The theory of Hopf bifurcation with symmetry developed by Golubitsky and Stewart (1985) is applied to systems of ODEs having the symmetries of a regular polygon, that is, whose symmetry group is dihedral. The existence and stability of symmetry-breaking branches of periodic solutions are considered. In particular, these results are applied to a general system of n nonlinear oscillators coupled symmetrically in a ring, and the generic oscillation patterns are described. It is found that the symmetry can force some oscillators to have twice the frequency of others. The case of four oscillators has exceptional features.
Coupling between ion-acoustic waves and neutrino oscillations.
Haas, Fernando; Pascoal, Kellen Alves; Mendonça, José Tito
2017-01-01
The work investigates the coupling between ion-acoustic waves and neutrino flavor oscillations in a nonrelativistic electron-ion plasma under the influence of a mixed neutrino beam. Neutrino oscillations are mediated by the flavor polarization vector dynamics in a material medium. The linear dispersion relation around homogeneous static equilibria is developed. When resonant with the ion-acoustic mode, the neutrino flavor oscillations can transfer energy to the plasma exciting a new fast unstable mode in extreme astrophysical scenarios. The growth rate and the unstable wavelengths are determined in typical type II supernova parameters. The predictions can be useful for a new indirect probe on neutrino oscillations in nature.
Coupling between ion-acoustic waves and neutrino oscillations
NASA Astrophysics Data System (ADS)
Haas, Fernando; Pascoal, Kellen Alves; Mendonça, José Tito
2017-01-01
The work investigates the coupling between ion-acoustic waves and neutrino flavor oscillations in a nonrelativistic electron-ion plasma under the influence of a mixed neutrino beam. Neutrino oscillations are mediated by the flavor polarization vector dynamics in a material medium. The linear dispersion relation around homogeneous static equilibria is developed. When resonant with the ion-acoustic mode, the neutrino flavor oscillations can transfer energy to the plasma exciting a new fast unstable mode in extreme astrophysical scenarios. The growth rate and the unstable wavelengths are determined in typical type II supernova parameters. The predictions can be useful for a new indirect probe on neutrino oscillations in nature.
The vertical oscillations of coupled magnets
NASA Astrophysics Data System (ADS)
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.
Energetics of synchronization in coupled oscillators rotating on circular trajectories
NASA Astrophysics Data System (ADS)
Izumida, Yuki; Kori, Hiroshi; Seifert, Udo
2016-11-01
We derive a concise and general expression of the energy dissipation rate for coupled oscillators rotating on circular trajectories by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics. In the framework of phase oscillator models, it is known that the even and odd parts of the coupling function express the effect on collective and relative dynamics, respectively. We reveal that the odd part always decreases the dissipation upon synchronization, while the even part yields a characteristic square-root change of the dissipation near the bifurcation point whose sign depends on the specific system parameters. We apply our theory to hydrodynamically coupled Stokes spheres rotating on circular trajectories that can be interpreted as a simple model of synchronization of coupled oscillators in a biophysical system. We show that the coupled Stokes spheres gain the ability to do more work on the surrounding fluid as the degree of phase synchronization increases.
Coupling a Bose condensate to micromechanical oscillators
NASA Astrophysics Data System (ADS)
Kemp, Chandler; Fox, Eli; Flanz, Scott; Vengalattore, Mukund
2011-05-01
We describe the construction of a compact apparatus to investigate the interaction of a spinor Bose-Einstein condensate and a micromechanical oscillator. The apparatus uses a double magneto-optical trap, Raman sideband cooling, and evaporative cooling to rapidly produce a 87Rb BEC in close proximity to a high Q membrane. The micromotion of the membrane results in small Zeeman shifts at the location of the BEC due to a magnetic domain attached to the oscillator. Detection of this micromotion by the condensate results in a backaction on the membrane. We investigate prospects of using this backaction to generate nonclassical states of the mechanical oscillator. This work was funded by the DARPA ORCHID program.
Coupled Harmonic Bases for Longitudinal Characterization of Brain Networks.
Hwang, Seong Jae; Adluru, Nagesh; Collins, Maxwell D; Ravi, Sathya N; Bendlin, Barbara B; Johnson, Sterling C; Singh, Vikas
2016-01-01
There is a great deal of interest in using large scale brain imaging studies to understand how brain connectivity evolves over time for an individual and how it varies over different levels/quantiles of cognitive function. To do so, one typically performs so-called tractography procedures on diffusion MR brain images and derives measures of brain connectivity expressed as graphs. The nodes correspond to distinct brain regions and the edges encode the strength of the connection. The scientific interest is in characterizing the evolution of these graphs over time or from healthy individuals to diseased. We pose this important question in terms of the Laplacian of the connectivity graphs derived from various longitudinal or disease time points - quantifying its progression is then expressed in terms of coupling the harmonic bases of a full set of Laplacians. We derive a coupled system of generalized eigenvalue problems (and corresponding numerical optimization schemes) whose solution helps characterize the full life cycle of brain connectivity evolution in a given dataset. Finally, we show a set of results on a diffusion MR imaging dataset of middle aged people at risk for Alzheimer's disease (AD), who are cognitively healthy. In such asymptomatic adults, we find that a framework for characterizing brain connectivity evolution provides the ability to predict cognitive scores for individual subjects, and for estimating the progression of participant's brain connectivity into the future.
NASA Astrophysics Data System (ADS)
Laguna, Humberto; Sagar, Robin
2013-03-01
The confined quantum harmonic oscillator (CHO) is an intermediate model which lies between the particle-in-a-box (PIAB), where the free particle is confined, and the quantum harmonic oscillator (HO) where the particle is not confined but is under the influence of a harmonic potential. Position and momentum space densities, and phase-space Wigner functions, are obtained for this system and analyzed using tools from information theory. Shannon entropies are used to gain insights into the localization of the particle in position, momentum and phase-space. The statistical correlation between the position and momentum of the particle is examined using the Wigner function and its mutual information. The analysis is performed as a function of the quantum number and of the box length, and the calculated quantities are compared to those of the PIAB and HO models. Our interests lie in determining similarities or differences among the different models and if there are regimes where the behavior of the CHO model more closely resembles either that of the PIAB or HO model. Departamento de Quimica
NASA Technical Reports Server (NTRS)
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.
Use of videos for students to see the effect of changing gravity on harmonic oscillators
NASA Astrophysics Data System (ADS)
Benge, Raymond; Young, Charlotte; Worley, Alan; Davis, Shirley; Smith, Linda; Gell, Amber
2010-03-01
In introductory physics classes, students are introduced to harmonic oscillators such as masses on springs and the simple pendulum. In derivation of the equations describing these systems, the term ``g'' for the acceleration due to gravity cancels in the equation for the period of a mass oscillating on a spring, but it remains in the equation for the period of a pendulum. Frequently there is a homework problem asking how the system described would behave on the Moon, Mars, etc. Students have to have faith in the equations. In January, 2009, a team of community college faculty flew an experiment aboard an aircraft in conjunction with NASA's Microgravity University program. The experiment flown was a study in harmonic oscillator and pendulum behavior under various gravity situations. The aircraft simulated zero gravity, Martian, Lunar, and hypergravity conditions. The experiments were video recorded for students to study the behavior of the systems in varying gravity conditions. These videos are now available on the internet for anyone to use in introductory physics classes.
Resonant behavior of a harmonic oscillator with fluctuating mass driven by a Mittag-Leffler noise
NASA Astrophysics Data System (ADS)
Zhong, Suchuan; Yang, Jianqiang; Zhang, Lu; Ma, Hong; Luo, Maokang
2017-02-01
The resonant behavior of a generalized Langevin equation (GLE) in the presence of a Mittag-Leffler noise is studied analytically in this paper. Considering that a GLE with a Mittag-Leffler friction kernel is very useful for modeling anomalous diffusion processes with long-memory and long-range dependence, and the surrounding molecules do not only collide with the Brownian particle but also adhere to the Brownian particle for random time. Thus, we consider the Brownian particle with fluctuating mass, and the fluctuations of the mass are modelled as a dichotomous noise. Applying the stochastic averaging method, we obtain the exact expression of the output amplitude gain of the system. By studying the impact of the driving frequency and the noise parameters, we find the non-monotonic behaviors of the output amplitude gain. The results indicate that the bona fide SR, the wide sense SR and the conventional SR phenomena occur in the proposed harmonic oscillator with fluctuating mass driven by Mittag-Leffler noise. It is found that when we consider the output amplitude gain versus the driving frequency, the phenomena of stochastic multi-resonance (SMR) with two, three and four peaks are observed, and the quadruple-peaks SR phenomenon had never been observed in previous literature. Besides, when we investigate the dependence of output amplitude gain on the memory exponent, the inverse stochastic resonance (ISR) phenomenon takes place, in contrast to the well-known phenomenon of stochastic resonance. Furthermore, we compare the corresponding ordinary harmonic oscillator without memory to our generalized model, and found that the properties of long-memory and long-range dependence endows our generalized model with more abundant dynamic behaviors than the ordinary harmonic oscillator without memory.
An Agile Beam Transmit Array Using Coupled Oscillator Phase Control
NASA Technical Reports Server (NTRS)
Pogorzelski, Ronald S.; Scaramastra, Rocco P.; Huang, John; Beckon, Robert J.; Petree, Steve M.; Chavez, Cosme
1993-01-01
A few years ago York and colleagues suggested that injection locking of voltage controlled oscillators could be used to implement beam steering in a phased array [I]. The scheme makes use of the fact that when an oscillator is injection locked to an external signal, the phase difference between the output of the oscillator and the injection signal is governed by the difference between the injection frequency and the free running frequency of the oscillator (the frequency to which the oscillator is tuned). Thus, if voltage controlled oscillators (VCOs) are used, this phase difference is controlled by an applied voltage. Now, if a set of such oscillators are coupled to nearest neighbors, they can be made to mutually injection lock and oscillate as an ensemble. If they are all tuned to the same frequency, they will all oscillate in phase. Thus, if the outputs are connected to radiating elements forming a linear array, the antenna will radiate normal to the line of elements. Scanning is accomplished by antisymmetrically detuning the end oscillators in the array by application of a pair of appropriate voltages to their tuning ports. This results in a linear phase progression across the array which is just the phasing required to scan the beam. The scan angle is determined by the degree of detuning. We have constructed a seven element one dimensional agile beam array at S-band based on the above principle. Although, a few such arrays have been built in the past, this array possesses two unique features. First, the VCO MMICs have buffer amplifiers which isolate the output from the tuning circuit, and second, the oscillators are weakly coupled to each other at their resonant circuits rather than their outputs. This results in a convenient isolation between the oscillator array design and the radiating aperture design. An important parameter in the design is the so called coupling phase which determines the phase shift of the signals passing from one oscillator to its
Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons
Menikoff, Ralph
2014-09-02
A complete equation of state (EOS) for a molecular solid is derived utilizing a Helmholtz free energy. Assuming that the solid is nonconducting, phonon excitations dominate the specific heat. Phonons are approximated as independent quasi-harmonic oscillators with vibrational frequencies depending on the specific volume. The model is suitable for calibrating an EOS based on isothermal compression data and infrared/Raman spectroscopy data from high pressure measurements utilizing a diamond anvil cell. In contrast to a Mie-Gruneisen EOS developed for an atomic solid, the specific heat and Gruneisen coefficient depend on both density and temperature.
NASA Astrophysics Data System (ADS)
Afshar, Davood; Motamedinasab, Amin; Anbaraki, Azam; Jafarpour, Mojtaba
2016-02-01
In this paper, we have constructed even and odd superpositions of supercoherent states, similar to the standard even and odd coherent states of the harmonic oscillator. Then, their nonclassical properties, that is, squeezing and entanglement have been studied. We have observed that even supercoherent states show squeezing behavior for some values of parameters involved, while odd supercoherent states do not show squeezing at all. Also sub-Poissonian statistics have been observed for some ranges of the parameters in both states. We have also shown that these states may be considered as logical qubits which reduce to the Bell states at a limit, with concurrence equal to 1.
Step potential problem and harmonic oscillator problem in the minimum length quantum mechanics
NASA Astrophysics Data System (ADS)
Park, Soyeon; Woo, Byeong Hyo; Jung, Min; Jang, Eun Ji; Chung, Won Sang
2015-05-01
In this paper, we use the quasi-position representation of the minimum length quantum mechanics (MLQM) to study the effects of minimum length uncertainty principle (MLUP) on the quantum mechanical system up to a first-order in β. We introduce the probability density and the probability flux to discuss two problems such as particle in a box and step potential problem. For the step potential, we compute the transmission coefficient and the reflection coefficient and compare them with those of the ordinary quantum mechanics. We also discuss the harmonic oscillator problem in MLQM.
Sonic horizon formation for oscillating Bose-Einstein condensates in isotropic harmonic potential
Wang, Ying; Zhou, Yu; Zhou, Shuyu
2016-01-01
We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study. PMID:27922129
Comment on 'Wave functions of a time-dependent harmonic oscillator in a static magnetic field'
Maamache, M.; Bounames, A.; Ferkous, N.
2006-01-15
We show that the procedure used by Ferreira et al. [Phys. Rev. A 66, 024103 (2002)] is not correct for the following reasons: (i) the invariant I(t) they derived does not satisfy the Liouville-Von Neuman equation. (ii) They found that the eigenvalues of I(t) are time dependent which should not be the case according to the Lewis-Riesenfeld theory. We give a correct procedure to find the solution of the system they considered, i.e., the Schroedinger equation for a two-dimensional harmonic oscillator with time-dependent mass and frequency in the presence of a static magnetic field.
Sonic horizon formation for oscillating Bose-Einstein condensates in isotropic harmonic potential.
Wang, Ying; Zhou, Yu; Zhou, Shuyu
2016-12-06
We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study.
NASA Astrophysics Data System (ADS)
Guo, Feng; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Li, Heng
2016-10-01
Stochastic resonance in a fractional harmonic oscillator with random mass and signal-modulated noise is investigated. Applying linear system theory and the characteristics of the noises, the analysis expression of the mean output-amplitude-gain (OAG) is obtained. It is shown that the OAG varies non-monotonically with the increase of the intensity of the multiplicative dichotomous noise, with the increase of the frequency of the driving force, as well as with the increase of the system frequency. In addition, the OAG is a non-monotonic function of the system friction coefficient, as a function of the viscous damping coefficient, as a function of the fractional exponent.
Harmonic oscillators and resonance series generated by a periodic unstable classical orbit
NASA Technical Reports Server (NTRS)
Kazansky, A. K.; Ostrovsky, Valentin N.
1995-01-01
The presence of an unstable periodic classical orbit allows one to introduce the decay time as a purely classical magnitude: inverse of the Lyapunov index which characterizes the orbit instability. The Uncertainty Relation gives the corresponding resonance width which is proportional to the Planck constant. The more elaborate analysis is based on the parabolic equation method where the problem is effectively reduced to the multidimensional harmonic oscillator with the time-dependent frequency. The resonances form series in the complex energy plane which is equidistant in the direction perpendicular to the real axis. The applications of the general approach to various problems in atomic physics are briefly exposed.
Coupled domain wall oscillations in magnetic cylindrical nanowires
Murapaka, Chandrasekhar; Goolaup, S.; Purnama, I.; Lew, W. S.
2015-02-07
We report on transverse domain wall (DW) dynamics in two closely spaced cylindrical nanowires. The magnetostatically coupled DWs are shown to undergo an intrinsic oscillatory motion along the nanowire length in addition to their default rotational motion. In the absence of external forces, the amplitude of the DW oscillation is governed by the change in the frequency of the DW rotation. It is possible to sustain the DW oscillations by applying spin-polarized current to the nanowires to balance the repulsive magnetostatic coupling. The current density required to sustain the DW oscillation is found to be in the order of 10{sup 5 }A/cm{sup 2}. Morover, our analysis of the oscillation reveals that the DWs in cylindrical nanowires possess a finite mass.
Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators.
Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong
2016-03-10
Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO.
Pyragas, Viktoras; Pyragas, Kestutis
2015-08-01
In a recent paper [Phys. Rev. E 91, 012920 (2015)] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.
NASA Astrophysics Data System (ADS)
Pyragas, Viktoras; Pyragas, Kestutis
2015-08-01
In a recent paper [Phys. Rev. E 91, 012920 (2015), 10.1103/PhysRevE.91.012920] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.
A time-discrete harmonic oscillator model of human car-following
NASA Astrophysics Data System (ADS)
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.
Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators
Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong
2016-01-01
Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO. PMID:26961962
NASA Astrophysics Data System (ADS)
Yu, Da-ren; Wei, Li-qiu; Ding, Yong-jie; Han, Ke; Yan, Guo-jun; Qi, Feng-yan
2007-11-01
In order to study the physical mechanism of an oscillation newly discovered by the Harbin Institute of Technology Plasma Propulsion Lab (HPPL) in the range of hundreds of kHz to several MHz, Hall thrusters with different magnetic coils are studied by changing one of the following three parameters: discharge voltage, anode flow and coil current, directly measuring the coil current and measuring plasma oscillations related to coil current oscillation with the Langmuir probe. Experimental results indicated that in the discharge process of a Hall thruster the broadband turbulence of the Hall current causes an unstable spatial magnetic field and this field causes the magnetic circuit to resonate as an equivalent high level resistance-inductance-capacitance (RLC) network. As the response of the network, the oscillation of the coil current has a large oscillating component at the natural frequencies of the network. Also, the oscillation of coil current has an effect on the discharge process at the same time, so that they reach a self-consistent equilibrium state. As a result of such a coupling, both coil current and the discharge current exhibit their oscillating component at the natural frequencies of the magnetic circuit. It is therefore concluded that the newly discovered oscillation is caused by the coupling between the magnetic circuit and the discharge circuit.
Birth of oscillation in coupled non-oscillatory Rayleigh-Duffing oscillators
NASA Astrophysics Data System (ADS)
Guin, A.; Dandapathak, M.; Sarkar, S.; Sarkar, B. C.
2017-01-01
We have studied the dynamics of two bilaterally-coupled non-oscillatory Rayleigh-Duffing oscillators (RDOs). With the increase of coupling factor (CF) between RDOs, birth of periodic oscillations observed. For increased values of CF, dynamics becomes chaotic through a quasi-periodicroute but for even higher CF, synchronized stable periodic oscillations in RDOs are found. Taking direct and anti-diffusive coupling cases into consideration, we derive conditions for periodic bifurcation in parameter space analytically and verified them through numerical solution of system equations. Numerical simulation is also used to predict system states in two parameter space involving CF and linear damping parameter of RDOs. It indicates non-oscillatory, periodic, quasi-periodic and chaotic zones of system dynamics. Qualitative explanation of the simulated dynamics is given using homoclinic perturbation theory. Hardware experiment is performed on analog circuits simulating RDO model and obtained results confirm the predictions regarding birth of periodic oscillation and other features of system dynamics. Experimental results examining onset of oscillations in two under-biased bi-laterally coupled X-band Gunn oscillators (which are modelled as RDOs) is presented in support of the analysis.
Link weight evolution in a network of coupled chemical oscillators
NASA Astrophysics Data System (ADS)
Ke, Hua; Tinsley, Mark R.; Steele, Aaron; Wang, Fang; Showalter, Kenneth
2014-05-01
Link weight evolution is studied in a network of coupled chemical oscillators. Oscillators are perturbed by adjustments in imposed light intensity based on excitatory or inhibitory links to other oscillators undergoing excitation. Experimental and modeling studies demonstrate that the network is capable of producing sustained coordinated activity. The individual nodes of the network exhibit incoherent firing events; however, a dominant frequency can be discerned within the collective signal by Fourier analysis. The introduction of spike-timing-dependent plasticity yields a network that evolves to a stable unimodal link weight distribution.
NASA Astrophysics Data System (ADS)
Guseinov, I. I.; Mamedov, B. A.
2017-04-01
In this paper, the physical nature of quantum usual and self-friction (SF) harmonic oscillators is presented. The procedure for studying these harmonic oscillators is identical; therefore, we can benefit from the theory of the usual harmonic oscillator. To study the SF harmonic oscillator, using analytical formulae for the L^{{(pl^{ * } )}}-SF Laguerre polynomials (L^{{(pl^{ * } )}}-SFLPs) and L^{{(α^{*} )}}-modified SFLPs (L^{{(α^{*} )}}-MSFLPs) in standard convention, the V^{{(pl^{ * } )}}-SF potentials (V^{{(pl^{ * } )}}-SFPs), V^{{(α^{*} )}}-modified SFPs (V^{{(α^{*} )}}-MSFPs), F^{{(pl^{ * } )}}-SF forces (F^{{(pl^{ * } )}}-SFFs) and F^{{(α^{*} )}}-modified SFFs (F^{{(α^{*} )}}-MSFFs) are investigated, where pl^{ * } = 2l + 2 - α^{*} and α^{*} is the integer (α^{*} = α, - ∞ < α ≤ 2) or non-integer (α^{*} ≠ α, - ∞ < α < 3) SF quantum number. We note that the potentials (V^{{(pl^{ * } )}}-SFPs and V^{{(α^{*} )}}-MSFPs), and forces (F^{{(pl^{ * } )}}-SFFs and F^{{(α^{*} )}}-MSFFs), respectively, are independent functions. It is shown that the numerical values of these independent functions are the same, i.e., V_{num}^{{(pl^{ * } )}} = V_{num}^{{(α^{*} )}} and F_{num}^{{(pl^{ * } )}} = F_{num}^{{(α^{*} )}}. The dependence of the SF harmonic oscillator as a function of the distance is analyzed. The presented relationships are valid for arbitrary values of parameters.
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.
Skardal, Per Sebastian; Arenas, Alex
2015-08-01
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.
Enhancing the stability of the synchronization of multivariable coupled oscillators
NASA Astrophysics Data System (ADS)
Sevilla-Escoboza, R.; Gutiérrez, R.; Huerta-Cuellar, G.; Boccaletti, S.; Gómez-Gardeñes, J.; Arenas, A.; Buldú, J. M.
2015-09-01
Synchronization processes in populations of identical networked oscillators are the focus of intense studies in physical, biological, technological, and social systems. Here we analyze the stability of the synchronization of a network of oscillators coupled through different variables. Under the assumption of an equal topology of connections for all variables, the master stability function formalism allows assessing and quantifying the stability properties of the synchronization manifold when the coupling is transferred from one variable to another. We report on the existence of an optimal coupling transference that maximizes the stability of the synchronous state in a network of Rössler-like oscillators. Finally, we design an experimental implementation (using nonlinear electronic circuits) which grounds the robustness of the theoretical predictions against parameter mismatches, as well as against intrinsic noise of the system.
Dynamics of phase oscillators with generalized frequency-weighted coupling
NASA Astrophysics Data System (ADS)
Xu, Can; Gao, Jian; Xiang, Hairong; Jia, Wenjing; Guan, Shuguang; Zheng, Zhigang
2016-12-01
Heterogeneous coupling patterns among interacting elements are ubiquitous in real systems ranging from physics, chemistry to biology communities, which have attracted much attention during recent years. In this paper, we extend the Kuramoto model by considering a particular heterogeneous coupling scheme in an ensemble of phase oscillators, where each oscillator pair interacts with different coupling strength that is weighted by a general function of the natural frequency. The Kuramoto theory for the transition to synchronization can be explicitly generalized, such as the expression for the critical coupling strength. Also, a self-consistency approach is developed to predict the stationary states in the thermodynamic limit. Moreover, Landau damping effects are further revealed by means of linear stability analysis and resonance poles theory below the critical threshold, which turns to be far more generic. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the synchronization transition in general networks with heterogenous couplings.
Clustering and phase synchronization in populations of coupled phase oscillators
NASA Astrophysics Data System (ADS)
Cascallares, Guadalupe; Gleiser, Pablo M.
2015-10-01
In many species daily rhythms are endogenously generated by groups of coupled neurons that play the role of a circadian pacemaker. The adaptation of the circadian clock to environmental and seasonal changes has been proposed to be regulated by a dual oscillator system. In order to gain insight into this model, we analyzed the synchronization properties of two fully coupled groups of Kuramoto oscillators. Each group has an internal coupling parameter and the interaction between the two groups can be controlled by two parameters allowing for symmetric or non-symmetric coupling. We show that even for such a simple model counterintuitive behaviours take place, such as a global decrease in synchrony when the coupling between the groups is increased. Through a detailed analysis of the local synchronization processes we explain this behaviour.
Chimera states in purely local delay-coupled oscillators.
Bera, Bidesh K; Ghosh, Dibakar
2016-05-01
We study the existence of chimera states in a network of locally coupled chaotic and limit-cycle oscillators. The necessary condition for chimera state in purely local coupled oscillators is discussed. At first, we numerically observe the existence of chimera or multichimera states in the locally coupled Hindmarsh-Rose neuron model. We find that delay time in the nonlinear local coupling reduces the domain of the coherent island in the parameter space of the synaptic coupling strength and time delay, and thus the coherent region can be completely eliminated once the time delay exceeds a certain threshold. We then consider another form of nonlinearity in the local coupling, and the existence of chimera states is observed in the time-delayed Mackey-Glass system and in a Van der Pol oscillator. We also discuss the effect of time delay in local coupling for the existence of chimera states in Mackey-Glass systems. The nonlinearity present in the coupling function plays a key role in the emergence of chimera or multichimera states. A phase diagram for the chimera state is identified over a wide parameter space.
Chimera states in purely local delay-coupled oscillators
NASA Astrophysics Data System (ADS)
Bera, Bidesh K.; Ghosh, Dibakar
2016-05-01
We study the existence of chimera states in a network of locally coupled chaotic and limit-cycle oscillators. The necessary condition for chimera state in purely local coupled oscillators is discussed. At first, we numerically observe the existence of chimera or multichimera states in the locally coupled Hindmarsh-Rose neuron model. We find that delay time in the nonlinear local coupling reduces the domain of the coherent island in the parameter space of the synaptic coupling strength and time delay, and thus the coherent region can be completely eliminated once the time delay exceeds a certain threshold. We then consider another form of nonlinearity in the local coupling, and the existence of chimera states is observed in the time-delayed Mackey-Glass system and in a Van der Pol oscillator. We also discuss the effect of time delay in local coupling for the existence of chimera states in Mackey-Glass systems. The nonlinearity present in the coupling function plays a key role in the emergence of chimera or multichimera states. A phase diagram for the chimera state is identified over a wide parameter space.
NASA Astrophysics Data System (ADS)
Wang, Zhiguo; Liang, Zhenguo
2017-04-01
In this paper we prove an infinite dimensional KAM theorem, in which the assumptions on the derivatives of the perturbation in [24] are weakened from polynomial decay to logarithmic decay. As a consequence, we can apply it to 1D quantum harmonic oscillators and prove the reducibility of the linear harmonic oscillator, T=-\\frac{{{\\text{d}}2}}{\\text{d}{{x}2}}+{{x}2} , on {{L}2}≤ft({R}\\right) perturbed by the quasi-periodic in the time potential V(x,ω t;ω ) with logarithmic decay. This proves the pure-point nature of the spectrum of the Floquet operator K, where K:=‑i∑k=1nωk∂∂θk‑d2dx2+x2+εV(x,θω) is defined on {{L}2}≤ft({R}\\right)\\otimes {{L}2}≤ft({{{T}}n}\\right) , and the potential V(x,θ ;ω ) has logarithmic decay as well as its gradient in ω.
Coupled, Active Oscillators and Lizard Otoacoustic Emissions
NASA Astrophysics Data System (ADS)
Bergevin, Christopher; Velenovsky, David S.; Bonine, Kevin E.
2011-11-01
The present study empirically explores the relationship between spontaneous otoacoustic emissions (SOAEs) and stimulus-frequency emissions (SFOAEs) in lizards, an ideal group for such research given their relatively simple inner ear (e.g., lack of basilar membrane traveling waves), diverse morphology across species/families (e.g., tectorial membrane structure) and robust emissions. In a nutshell, our results indicate that SFOAEs evoked using low-level tones are intimately related to underlying SOAE activity, and appear to represent the entrained response of active oscillators closely tuned to the probe frequency. The data described here indicate several essential features that are desirable to capture in theoretical models for auditory transduction in lizards, and potentially represent generic properties at work in many different classes of "active" ears.
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
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
Coupling among three chemical oscillators: Synchronization, phase death, and frustration
NASA Astrophysics Data System (ADS)
Yoshimoto, Minoru; Yoshikawa, Kenichi; Mori, Yoshihito
1993-02-01
Various modes in three coupled chemical oscillators in a triangular arrangement were observed. As a well-defined nonlinear oscillator, the Belousov-Zhabotinsky reaction was studied in a continuous-flow stirred tank reactor (CSTR). Coupling among CSTR's was performed by mass exchange. The coupling strength was quantitatively controlled by changing the flow rate of reacting solutions among the three CSTR's using peristaltic pumps between each pair of the reactors. As a key parameter to control the model of coupling, we changed the symmetry of the interaction between the oscillators. In the case of the symmetric coupling, a quasiperiodic state or a biperiodic mode, an all-death mode and two kinds of synchronized modes appeared, depending on the coupling strength. On the other hand, under the asymmetric coupling, a quasiperiodic state or a biperiodic mode, an all death mode and four kinds of synchronized modes appeared. Those modes have been discussed in relation to the idea of ``frustration'' in the Ising spin system, where the three-phase mode appears as a transition from the Ising spin system to the XY spin system.
Dynamics of learning in coupled oscillators tutored with delayed reinforcements.
Trevisan, M A; Bouzat, S; Samengo, I; Mindlin, G B
2005-07-01
In this work we analyze the solutions of a simple system of coupled phase oscillators in which the connectivity is learned dynamically. The model is inspired by the process of learning of birdsongs by oscine birds. An oscillator acts as the generator of a basic rhythm and drives slave oscillators which are responsible for different motor actions. The driving signal arrives at each driven oscillator through two different pathways. One of them is a direct pathway. The other one is a reinforcement pathway, through which the signal arrives delayed. The coupling coefficients between the driving oscillator and the slave ones evolve in time following a Hebbian-like rule. We discuss the conditions under which a driven oscillator is capable of learning to lock to the driver. The resulting phase difference and connectivity are a function of the delay of the reinforcement. Around some specific delays, the system is capable of generating dramatic changes in the phase difference between the driver and the driven systems. We discuss the dynamical mechanism responsible for this effect and possible applications of this learning scheme.
Dynamics of learning in coupled oscillators tutored with delayed reinforcements
NASA Astrophysics Data System (ADS)
Trevisan, M. A.; Bouzat, S.; Samengo, I.; Mindlin, G. B.
2005-07-01
In this work we analyze the solutions of a simple system of coupled phase oscillators in which the connectivity is learned dynamically. The model is inspired by the process of learning of birdsongs by oscine birds. An oscillator acts as the generator of a basic rhythm and drives slave oscillators which are responsible for different motor actions. The driving signal arrives at each driven oscillator through two different pathways. One of them is a direct pathway. The other one is a reinforcement pathway, through which the signal arrives delayed. The coupling coefficients between the driving oscillator and the slave ones evolve in time following a Hebbian-like rule. We discuss the conditions under which a driven oscillator is capable of learning to lock to the driver. The resulting phase difference and connectivity are a function of the delay of the reinforcement. Around some specific delays, the system is capable of generating dramatic changes in the phase difference between the driver and the driven systems. We discuss the dynamical mechanism responsible for this effect and possible applications of this learning scheme.
A generalized harmonic balance method for forced non-linear oscillations: the subharmonic cases
NASA Astrophysics Data System (ADS)
Wu, J. J.
1992-12-01
This paper summarizes and extends results in two previous papers, published in conference proceedings, on a variant of the generalized harmonic balance method (GHB) and its application to obtain subharmonic solutions of forced non-linear oscillation problems. This method was introduced as an alternative to the method of multiple scales, and it essentially consists of two parts. First, the part of the multiple scales method used to reduce the problem to a set of differential equations is used to express the solution as a sum of terms of various harmonics with unknown, time dependent coefficients. Second, the form of solution so obtained is substituted into the original equation and the coefficients of each harmonic are set to zero. Key equations of approximations for a subharmonic case are derived for the cases of both "small" damping and excitations, and "Large" damping and excitations, which are shown to be identical, in the intended order of approximation, to those obtained by Nayfeh using the method of multiple scales. Detailed numerical formulations, including the derivation of the initial conditions, are presented, as well as some numerical results for the frequency-response relations and the time evolution of various harmonic components. Excellent agreement is demonstrated between results by GHB and by integrating the original differential equation directly. The improved efficiency in obtaining numerical solutions using GHB as compared with integrating the original differential equation is demonstrated also. For the case of large damping and excitations and for non-trivial solutions, it is noted that there exists a threshold value of the force beyond which no subharmonic excitations are possible.
Efficiency at maximum power of a quantum heat engine based on two coupled oscillators.
Wang, Jianhui; Ye, Zhuolin; Lai, Yiming; Li, Weisheng; He, Jizhou
2015-06-01
We propose and theoretically investigate a system of two coupled harmonic oscillators as a heat engine. We show how these two coupled oscillators within undamped regime can be controlled to realize an Otto cycle that consists of two adiabatic and two isochoric processes. During the two isochores the harmonic system is embedded in two heat reservoirs at constant temperatures T(h) and T(c)(
Efficiency at maximum power of a quantum heat engine based on two coupled oscillators
NASA Astrophysics Data System (ADS)
Wang, Jianhui; Ye, Zhuolin; Lai, Yiming; Li, Weisheng; He, Jizhou
2015-06-01
We propose and theoretically investigate a system of two coupled harmonic oscillators as a heat engine. We show how these two coupled oscillators within undamped regime can be controlled to realize an Otto cycle that consists of two adiabatic and two isochoric processes. During the two isochores the harmonic system is embedded in two heat reservoirs at constant temperatures Th and Tc(
Internal wave--vorticity coupling for an oscillating disk
NASA Astrophysics Data System (ADS)
Voisin, Bruno; Joubaud, Sylvain; Dauxois, Thierry
2011-11-01
In a density-stratified fluid, viscosity couples internal waves with vertical vorticity. So far this coupling used to be neglected in analytical studies and only the viscous attenuation and spreading of the waves was taken into account, except in a very recent study of the oscillations of a horizontal circular disk. We investigate the relations between the previous analytical approaches of the disk, considering either inviscid or viscous propagation of the waves and either free- or no-slip conditions at the disk, and compare their output with an original approach based on the boundary integral method. In particular, the role of the Stokes number is clarified. The analytical predictions are compared with contact measurements for vertical oscillations and with original PIV measurements and visualizations for both vertical and horizontal oscillations. Supported by grant PIWO of the ANR (France).
Experimental Evidence on Intermittent Lag Synchronization in Coupled Chua's Oscillators
NASA Astrophysics Data System (ADS)
Roy, P. K.; Dana, S. K.
2003-08-01
Phase synchronization (PS) in coupled chaotic oscillators has been investigated numerically in Lorenz, Rossler models and also experimentally in cardiorespiratory systems by many researchers. In non-identical oscillators, which is a reality, complete synchronization (CS) of amplitude and phase is difficult to arrive at. Lag synchronization (LS) is an intermediate step between complete (CS) and PS. PS shows promises in communication, in the context of pulse position modulation, in homoclinic chaotic systems. As has been observed earlier by others in numerical experiments that there is an intermittent region between PS and LS. This intermediate region is defined as the intermittent lag synchronization (ILS). Experimental evidence on both PS and ILS using two coupled Chua's oscillator (non-identical) is reported here.
Raman-Suppressing Coupling for Optical Parametric Oscillator
NASA Technical Reports Server (NTRS)
Savchenkov, Anatoliy; Maleki, Lute; Matsko, Andrey; Rubiola, Enrico
2007-01-01
A Raman-scattering-suppressing input/ output coupling scheme has been devised for a whispering-gallery-mode optical resonator that is used as a four-wave-mixing device to effect an all-optical parametric oscillator. Raman scattering is undesired in such a device because (1) it is a nonlinear process that competes with the desired nonlinear four-wave conversion process involved in optical parametric oscillation and (2) as such, it reduces the power of the desired oscillation and contributes to output noise. The essence of the present input/output coupling scheme is to reduce output loading of the desired resonator modes while increasing output loading of the undesired ones.
NASA Technical Reports Server (NTRS)
Defacio, B.; Vannevel, Alan; Brander, O.
1993-01-01
A formulation is given for a collection of phonons (sound) in a fluid at a non-zero temperature which uses the simple harmonic oscillator twice; one to give a stochastic thermal 'noise' process and the other which generates a coherent Glauber state of phonons. Simple thermodynamic observables are calculated and the acoustic two point function, 'contrast' is presented. The role of 'coherence' in an equilibrium system is clarified by these results and the simple harmonic oscillator is a key structure in both the formulation and the calculations.
On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on ℝ
NASA Astrophysics Data System (ADS)
Alvarez-Nodarse, R.; Atakishiyeva, M. K.; Atakishiyev, N. M.
2005-11-01
We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics based on a q-extension of the classical Hermite polynomials H n ( x) recently introduced by us in R. Alvarez-Nodarse et al.: Boletin de la Sociedad Matematica Mexicana (3) 8 (2002) 127. The wave functions in this q-model of the quantum harmonic oscillator possess the continuous orthogonality property on the whole real line ℝ with respect to a positive weight function. A detailed description of the corresponding q-system is carried out.
Cold atoms coupled with mechanical oscillators
NASA Astrophysics Data System (ADS)
Valencia, Jose; Montoya, Cris; Ranjit, Gambhir; Geraci, Andrew; Eardley, Matt; Kitching, John
2015-05-01
Mechanical resonators can be used to probe and manipulate atomic spins with nanometer spatial resolution and single-spin sensitivity, ultimately enabling new approaches in neutral-atom quantum computation, quantum simulation, or precision sensing. We describe our experiment that manipulates the spin of trapped, cold Rb atoms using magnetic material on a cantilever. Cold atoms can also be used as a coolant for mechanical resonators: we estimate that ground state cooling of an optically trapped nano-sphere is achievable when starting at room temperature, by sympathetic cooling of a cold atomic gas optically coupled to the nanoparticle.
Dynamics of globally coupled oscillators: Progress and perspectives
NASA Astrophysics Data System (ADS)
Pikovsky, Arkady; Rosenblum, Michael
2015-09-01
In this paper, we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as interrelations between different approaches.
Dynamics of finite-size networks of coupled oscillators
NASA Astrophysics Data System (ADS)
Buice, Michael; Chow, Carson
2010-03-01
Mean field models of coupled oscillators do not adequately capture the dynamics of large but finite size networks. For example, the incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the population is not synchronous. This demonstration is facilitated by the construction of a non-equilibrium statistical field theoretic formulation of a generic model of coupled oscillators. This theory is consistent with previous results. In the all-to-all case, the fluctuations in this theory are due completely to finite size corrections, which can be calculated in an expansion in 1/N, where N is the number of oscillators. The N -> infinity limit of this theory is what is traditionally called mean field theory for the Kuramoto model. We also demonstrate this approach with a system of pulse coupled theta neurons and describe the stability of the population activity.
Golden Ratio in a Coupled-Oscillator Problem
ERIC Educational Resources Information Center
Moorman, Crystal M.; Goff, John Eric
2007-01-01
The golden ratio appears in a classical mechanics coupled-oscillator problem that many undergraduates may not solve. Once the symmetry is broken in a more standard problem, the golden ratio appears. Several student exercises arise from the problem considered in this paper.
String-Coupled Pendulum Oscillators: Theory and Experiment.
ERIC Educational Resources Information Center
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)
Wu, Wei; Chen, Tianping
2009-12-01
Fireflies, as one of the most spectacular examples of synchronization in nature, have been investigated widely. In 1990, Mirollo and Strogatz proposed a pulse-coupled oscillator model to explain the synchronization of South East Asian fireflies (Pteroptyx malaccae). However, transmission delays were not considered in their model. In fact, when transmission delays are introduced, the dynamic behaviors of pulse-coupled networks change a lot. In this paper, pulse-coupled oscillator networks with delayed excitatory coupling are studied. A concept of synchronization, named weak asymptotic synchronization, which is weaker than asymptotic synchronization, is proposed. We prove that for pulse-coupled oscillator networks with delayed excitatory coupling, weak asymptotic synchronization cannot occur.
Nonlinear Coupling between Cortical Oscillations and Muscle Activity during Isotonic Wrist Flexion
Yang, Yuan; Solis-Escalante, Teodoro; van de Ruit, Mark; van der Helm, Frans C. T.; Schouten, Alfred 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 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 (ICA) 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 (SMA), prefrontal area (PFA) and posterior parietal cortex (PPC). For all these areas, linear coupling between electroencephalogram (EEG) and electromyogram (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 (SMA, PFA) compared to the sensory association area (PPC); 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. PMID:27999537
Nonlinear Coupling between Cortical Oscillations and Muscle Activity during Isotonic Wrist Flexion.
Yang, Yuan; Solis-Escalante, Teodoro; van de Ruit, Mark; van der Helm, Frans C T; Schouten, Alfred 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 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 (ICA) 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 (SMA), prefrontal area (PFA) and posterior parietal cortex (PPC). For all these areas, linear coupling between electroencephalogram (EEG) and electromyogram (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 (SMA, PFA) compared to the sensory association area (PPC); 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.
Revised calculation of four-particle harmonic-oscillator transformation brackets matrix
NASA Astrophysics Data System (ADS)
Mickevičius, S.; Germanas, D.; Kalinauskas, R. K.
2013-02-01
In this article we present a new, considerably enhanced and more rapid method for calculation of the matrix of four-particle harmonic-oscillator transformation brackets (4HOB). The new method is an improved version of 4HOB matrix calculations which facilitates the matrix calculation by finding the eigenvectors of the 4HOB matrix explicitly. Using this idea the new Fortran code for fast and 4HOB matrix calculation is presented. The calculation time decreases more than a few hundred times for large matrices. As many problems of nuclear and hadron physics structure are modeled on the harmonic oscillator (HO) basis our presented method can be useful for large-scale nuclear structure and many-particle identical fermion systems calculations. Program summaryTitle of program: HOTB_M Catalogue identifier: AEFQ_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFQ_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 2149 No. of bytes in distributed program, including test data, etc.: 17576 Distribution format: tar.gz Programming language: Fortran 90. Computer: Any computer with Fortran 90 compiler. Operating system: Windows, Linux, FreeBSD, True64 Unix. RAM: Up to a few Gigabytes (see Tables 1 and 2 included in the distribution package) Classification: 17.16, 17.17. Catalogue identifier of previous version: AEFQ_v2_0 Journal reference of previous version: Comput. Phys. Comm. 182(2011)1377 Does the new version supersede the previous version?: Yes Nature of problem: Calculation of the matrix of the 4HOB in a more effective way, which allows us to calculate the matrix of the brackets up to a few hundred times more rapidly than in a previous version. Solution method: The method is based on compact expressions of 4HOB, presented in [1] and its simplifications presented in this paper. Reasons for new version
Three People Can Synchronize as Coupled Oscillators during Sports Activities
Yokoyama, Keiko; Yamamoto, Yuji
2011-01-01
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. PMID:21998570
Speech encoding by coupled cortical theta and gamma oscillations
Hyafil, Alexandre; Fontolan, Lorenzo; Kabdebon, Claire; Gutkin, Boris; Giraud, Anne-Lise
2015-01-01
Many environmental stimuli present a quasi-rhythmic structure at different timescales that the brain needs to decompose and integrate. Cortical oscillations have been proposed as instruments of sensory de-multiplexing, i.e., the parallel processing of different frequency streams in sensory signals. Yet their causal role in such a process has never been demonstrated. Here, we used a neural microcircuit model to address whether coupled theta–gamma oscillations, as observed in human auditory cortex, could underpin the multiscale sensory analysis of speech. We show that, in continuous speech, theta oscillations can flexibly track the syllabic rhythm and temporally organize the phoneme-level response of gamma neurons into a code that enables syllable identification. The tracking of slow speech fluctuations by theta oscillations, and its coupling to gamma-spiking activity both appeared as critical features for accurate speech encoding. These results demonstrate that cortical oscillations can be a key instrument of speech de-multiplexing, parsing, and encoding. DOI: http://dx.doi.org/10.7554/eLife.06213.001 PMID:26023831
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
Cyanobacterial clock, a stable phase oscillator with negligible intercellular coupling
Amdaoud, M.; Vallade, M.; Weiss-Schaber, C.; Mihalcescu, I.
2007-01-01
Accuracy in cellular function has to be achieved despite random fluctuations (noise) in the concentrations of different molecular constituents inside and outside the cell. The circadian oscillator in cyanobacteria is an example of resilience to noise. This resilience could be either the consequence of intercellular communication or the intrinsic property of the built-in biochemical network. Here we investigate the intercellular coupling hypothesis. A short theoretical depiction of interacting noisy phase oscillators, confirmed by numerical simulations, allows us to discriminate the effect of coupling from noise. Experimentally, by studying the phase of concurrent populations of different initial phases, we evaluate a very small upper limit of the intercellular coupling strength. In addition, in situ entrainment experiments confirm our ability to detect a coupling of the circadian oscillator to an external force and to describe explicitly the dynamic change of the mean phase. We demonstrate, therefore, that the cyanobacterial clock stability is a built-in property as the intercellular coupling effect is negligible. PMID:17438272
ERIC Educational Resources Information Center
Viana-Gomes, J.; Peres, N. M. R.
2011-01-01
We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…
Collective cell movement promotes synchronization of coupled genetic oscillators.
Uriu, Koichiro; Morelli, Luis G
2014-07-15
Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somitogenesis, where short-range correlated movement of cells has been observed. We describe the segmentation clock tissue by a Voronoi diagram, cell movement by the force balance of self-propelled and repulsive forces between cells, the dynamics of the direction of self-propelled motion, and the synchronization of genetic oscillators by locally coupled phase oscillators. We find that movement with a correlation length of about 2 ∼ 3 cell diameters is optimal for the synchronization of coupled oscillators. Quantification of cell mixing reveals that this short-range correlation of cell movement allows cells to exchange neighbors most efficiently. Moreover, short-range correlated movement strongly destabilizes nonuniform spatial phase patterns, further promoting global synchronization. Our theoretical results suggest that collective cell movement may enhance the synchronization of the segmentation clock in zebrafish somitogenesis. More generally, collective cell movement may promote information flow in tissues by enhancing cell mixing and destabilizing spurious patterns.
Collective Cell Movement Promotes Synchronization of Coupled Genetic Oscillators
Uriu, Koichiro; Morelli, Luis G.
2014-01-01
Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somitogenesis, where short-range correlated movement of cells has been observed. We describe the segmentation clock tissue by a Voronoi diagram, cell movement by the force balance of self-propelled and repulsive forces between cells, the dynamics of the direction of self-propelled motion, and the synchronization of genetic oscillators by locally coupled phase oscillators. We find that movement with a correlation length of about 2 ∼ 3 cell diameters is optimal for the synchronization of coupled oscillators. Quantification of cell mixing reveals that this short-range correlation of cell movement allows cells to exchange neighbors most efficiently. Moreover, short-range correlated movement strongly destabilizes nonuniform spatial phase patterns, further promoting global synchronization. Our theoretical results suggest that collective cell movement may enhance the synchronization of the segmentation clock in zebrafish somitogenesis. More generally, collective cell movement may promote information flow in tissues by enhancing cell mixing and destabilizing spurious patterns. PMID:25028893
NASA Astrophysics Data System (ADS)
Marengo, Edwin A.; Khodja, Mohamed R.
2006-09-01
The nonrelativistic Larmor radiation formula, giving the power radiated by an accelerated charged point particle, is generalized for a spatially extended particle in the context of the classical charged harmonic oscillator. The particle is modeled as a spherically symmetric rigid charge distribution that possesses both translational and spinning degrees of freedom. The power spectrum obtained exhibits a structure that depends on the form factor of the particle, but reduces, in the limit of an infinitesimally small particle and for the charge distributions considered, to Larmor’s familiar result. It is found that for finite-duration small-enough accelerations as well as perpetual uniform accelerations the power spectrum of the spatially extended particle reduces to that of a point particle. It is also found that when the acceleration is violent or the size parameter of the particle is very large compared to the wavelength of the emitted radiation the power spectrum is highly suppressed. Possible applications are discussed.
Song, Yongli; Zhang, Tonghua; Tadé, Moses O
2008-12-01
We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov-Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved.
Alternative descriptions of wave and particle aspects of the harmonic oscillator
NASA Technical Reports Server (NTRS)
Schuch, Dieter
1993-01-01
The dynamical properties of the wave and particle aspects of the harmonic oscillator can be studied with the help of the time-dependent Schroedinger equation (SE). Especially the time-dependence of maximum and width of Gaussian wave packet solutions allow to show the evolution and connections of those two complementary aspects. The investigation of the relations between the equations describing wave and particle aspects leads to an alternative description of the considered systems. This can be achieved by means of a Newtonian equation for a complex variable in connection with a conservation law for a nonclassical angular momentum-type quantity. With the help of this complex variable, it is also possible to develop a Hamiltonian formalism for the wave aspect contained in the SE, which allows to describe the dynamics of the position and momentum uncertainties. In this case the Hamiltonian function is equivalent to the difference between the mean value of the Hamiltonian operator and the classical Hamiltonian function.
LETTER TO THE EDITOR: Exact energy distribution function in a time-dependent harmonic oscillator
NASA Astrophysics Data System (ADS)
Robnik, Marko; Romanovski, Valery G.; Stöckmann, Hans-Jürgen
2006-09-01
Following a recent work by Robnik and Romanovski (2006 J. Phys. A: Math. Gen. 39 L35, 2006 Open Syst. Inf. Dyn. 13 197-222), we derive an explicit formula for the universal distribution function of the final energies in a time-dependent 1D harmonic oscillator, whose functional form does not depend on the details of the frequency ω(t) and is closely related to the conservation of the adiabatic invariant. The normalized distribution function is P(x) = \\pi^{-1} (2\\mu^2 - x^2)^{-\\frac{1}{2}} , where x=E_1- \\skew3\\bar{E}_1 ; E1 is the final energy, \\skew3\\bar{E}_1 is its average value and µ2 is the variance of E1. \\skew3\\bar{E}_1 and µ2 can be calculated exactly using the WKB approach to all orders.
The quantum fidelity for the time-periodic singular harmonic oscillator
NASA Astrophysics Data System (ADS)
Combescure, Monique
2006-03-01
In this paper we perform an exact study of "quantum fidelity" (also called Loschmidt echo) for the time-periodic quantum harmonic oscillator of the following Hamiltonian: Ĥg(t)≔(P2/2)+f(t)(Q2/2)+(g2/Q2), when compared with the quantum evolution induced by Ĥ0(t) (g=0), in the case where f is a T-periodic function and g a real constant. The reference (initial) state is taken to be an arbitrary "generalized coherent state" in the sense of Perelomov. We show that, starting with a quadratic decrease in time in the neighborhood of t =0, this quantum fidelity may recur to its initial value 1 at an infinite sequence of times tk. We discuss the result when the classical motion induced by Hamiltonian Ĥ0(t) is assumed to be stable versus unstable.
NASA Astrophysics Data System (ADS)
Xiong, Huai; Kong, Xianren; Li, Haiqin; Yang, Zhenguo
2017-01-01
This paper considers dynamics of bilinear hysteretic systems, which are widely used for vibration control and vibration absorption such as magneto-rheological damper, metal-rubber. The method of incremental harmonic balance (IHB) technique that hysteresis is considered in the corrective term is improved in order to determine periodic solutions of bilinear hysteretic systems. The improved continuation method called two points tracing algorithm which is stable to the turning point makes the calculation more efficient for tracing amplitude-frequency response. Precise Hsu's method for analysing the stability of periodic solutions is introduced. The effects of different parameters of bilinear hysteretic oscillator on the response are discussed numerically. Some numerical simulations of considered bilinear hysteretic systems, including a single DOF and a 2DOF system, are effectively obtained by the modified IHB method and the results compare very well with the 4-oder Runge-Kutta method.
Some properties of an infinite family of deformations of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Quesne, Christiane
2010-12-01
In memory of Marcos Moshinsky, who promoted the algebraic study of the harmonic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed. This set, which was introduced by Tremblay, Turbiner, and Winternitz, consists in some Hamiltonians Hk on the plane, depending on a positive real parameter k. Two algebraic extensions of Hk are described. The first one, based on the elements of the dihedral group D2k and a Dunkl operator formalism, provides a convenient tool to prove the superintegrability of Hk for odd integer k. The second one, employing two pairs of fermionic operators, leads to a supersymmetric extension of Hk of the same kind as the familiar Freedman and Mende super-Calogero model. Some connection between both extensions is also outlined.
Rigatos, Gerasimos G.
2007-09-06
Neural computation based on principles of quantum mechanics can provide improved models of memory processes and brain functioning and is of importance for the realization of quantum computing machines. To this end, this paper studies neural structures with weights that follow the model of the quantum harmonic oscillator. These weights correspond to diffusing particles, which interact to each other as the theory of Brownian motion predicts. The learning of the stochastic weights (convergence of the diffusing particles to an equilibrium) is analyzed. In the case of associative memories the proposed neural model results in an exponential increase of the number of attractors. Spectral analysis shows that the stochastic weights satisfy an equation which is analogous to the principle of uncertainty.
Coupled Self-Oscillating Systems:. Theory and Applications
NASA Astrophysics Data System (ADS)
Guerra, Francesco
We review the structure of self-oscillating dynamical systems, and point out the numerous applications that they can have. In the case of coupled self-oscillating systems, the typical features of complexity show up, in a completely dynamical setting. This general scheme goes well beyond Fourier analysis, and allows to consider modes at the various time scale levels in a frame where non-linearity plays an essential role. We discuss some basic applications to speech generation, hydrodynamic instabilities, volcanic tremor. Possible lines of development are pointed out.
Phase Synchronization of Coupled Rossler Oscillators: Amplitude Effect
NASA Astrophysics Data System (ADS)
Li, Xiao-Wen; Zheng, Zhi-Gang
2007-02-01
Phase synchronization of two linearly coupled Rossler oscillators with parameter misfits is explored. It is found that depending on parameter mismatches, the synchronization of phases exhibits different manners. The synchronization regime can be divided into three regimes. For small mismatches, the amplitude-insensitive regime gives the phase-dominant synchronization; When the parameter misfit increases, the amplitudes and phases of oscillators are correlated, and the amplitudes will dominate the synchronous dynamics for very large mismatches. The lag time among phases exhibits a power law when phase synchronization is achieved.
Time Correlations in Mode Hopping of Coupled Oscillators
NASA Astrophysics Data System (ADS)
Heltberg, Mathias L.; Krishna, Sandeep; Jensen, Mogens H.
2017-02-01
We study the dynamics in a system of coupled oscillators when Arnold Tongues overlap. By varying the initial conditions, the deterministic system can be attracted to different limit cycles. Adding noise, the mode hopping between different states become a dominating part of the dynamics. We simplify the system through a Poincare section, and derive a 1D model to describe the dynamics. We explain that for some parameter values of the external oscillator, the time distribution of occupancy in a state is exponential and thus memoryless. In the general case, on the other hand, it is a sum of exponential distributions characteristic of a system with time correlations.
Coupled Langmuir oscillations in 2-dimensional quantum plasmas
Akbari-Moghanjoughi, M.
2014-03-15
In this work, we present a hydrodynamic model to study the coupled quantum electron plasma oscillations (QEPO) for two dimensional (2D) degenerate plasmas, which incorporates all the essential quantum ingredients such as the statistical degeneracy pressure, electron-exchange, and electron quantum diffraction effect. Effects of diverse physical aspects like the electronic band-dispersion effect, the electron exchange-correlations and the quantum Bohm-potential as well as other important plasma parameters such as the coupling parameter (plasma separation) and the plasma electron number-densities on the linear response of the coupled system are investigated. By studying three different 2D plasma coupling types, namely, graphene-graphene, graphene-metalfilm, and metalfilm-metalfilm coupling configurations, it is remarked that the collective quantum effects can influence the coupled modes quite differently, depending on the type of the plasma configuration. It is also found that the slow and fast QEPO frequency modes respond very differently to the change in plasma parameters. Current findings can help in understanding of the coupled density oscillations in multilayer graphene, graphene-based heterojunctions, or nanofabricated integrated circuits.
Spherical harmonic stacking for the singlets of Earth's normal modes of free oscillation
NASA Astrophysics Data System (ADS)
Chao, Benjamin F.; Ding, Hao
2014-08-01
We extend the spherical harmonic stacking (SHS) method of Buland et al. (1979) for the radial (vertical) component in the seismogram to the transverse (horizontal) components of the displacement field. Taking advantage of the orthogonality of the spherical harmonic functions (scalar and vectorial), SHS isolates and accentuates the signals of individual singlets of the Earth's normal modes of free oscillation. We apply the SHS on the broadband Incorporated Research Institutions for Seismology (IRIS) seismograms from up to 97 IRIS seismic stations for the 2004 Sumatra-Andaman earthquake, in experiments targeted to spheroidal as well as toroidal modes—2S1, 0S3, 2S2, 3S1, 1S3, 0T2, and 0T3. We report the complete resolution of the singlet frequencies of these multiplets, some for the first time, and estimate the singlets' complex frequencies using the frequency domain autoregressive method of Chao and Gilbert (1980). The latter contain useful information to be used in inversions for the 3-D structure of the Earth's interior.
NASA Technical Reports Server (NTRS)
Ehlers, F. E.; Weatherill, W. H.; Yip, E. L.
1984-01-01
A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.
NASA Astrophysics Data System (ADS)
Tong, Zhengrong; Wang, Zhiyong; En, De; Chen, Caihe; Li, Xuejiao; Xie, Xiaofang
2008-03-01
A kind of photo-electronic integrated acceleration seismic detecting technology, which is novel and precise based on waveguide M-Z interference, is presented. It provieds modern geologic prospect with a novel detection technology. The principle of the photo-electronic integrated acceleration seismic geophone is introduced in this paper. The core of the photo-electronic integrated acceleration is the silicon harmonic oscillator, which is supported by four silicon beams and integrated on the signal beam of the M-Z interferometer. When the seismic mass is subjected to a normal acceleration a z, the acceleration a z, will result in an inertial force F z, causing the mass to move up or down like the piston, until the counter force of the beam suspension equals this inertial force. The principle of the harmonic oscillator is briefly introduced, the factors influencing the anisotropic etching quality of the harmonic oscillator are analyzed in detail. In experiment, the fabrication technology was studied and improved. The high quality harmonic oscillator has been successfully fabricated. It has been applied in the integrated optical chip of "the theory and experiment research of photoelectric integrated acceleration seismic geophone technology".
Cari, C. Suparmi, A.
2014-09-30
Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.
ERIC Educational Resources Information Center
Nicolaides, Cleanthes A.; Constantoudis, Vasilios
2009-01-01
In Planck's model of the harmonic oscillator (HO) a century ago, both the energy and the phase space were quantized according to epsilon[subscript n] = nhv, n = 0, 1, 2..., and [double integral]dp[subscript x] dx = h. By referring to just these two relations, we show how the adoption of "cycle-averaged phase-space states" (CAPSSs) leads to the…
Synchronization of two memristively coupled van der Pol oscillators
NASA Astrophysics Data System (ADS)
Ignatov, M.; Hansen, M.; Ziegler, M.; Kohlstedt, H.
2016-02-01
The objective of this letter is to convey two essential principles of biological computing—synchronization and memory—in an electronic circuit with two van der Pol (vdP) oscillators coupled via a memristive device. The coupling was mediated by connecting the gate terminals of two programmable unijunction transistors through a resistance-capacitance network comprising an Ag-TiOx-Al memristive device. In the high resistance state the memristance was in the order of MΩ, which leads to two independent self-sustained oscillators characterized by the different frequencies f1 and f2 and no phase relation between the oscillations. Depending on the mediated pulse amplitude, the memristive device switched to the low resistance state after a few cycles and a frequency adaptation and phase locking were observed. The experimental results are underlined by theoretically considering a system of two coupled vdP equations. This experiment may pave the way to larger neuromorphic networks in which the coupling parameters (through memristive devices) can vary in time and strength and are able to remember the history of applied electrical potentials.
Coexistence of Quantized, Time Dependent, Clusters in Globally Coupled Oscillators
NASA Astrophysics Data System (ADS)
Bi, Hongjie; Hu, Xin; Boccaletti, S.; Wang, Xingang; Zou, Yong; Liu, Zonghua; Guan, Shuguang
2016-11-01
We report on a novel collective state, occurring in globally coupled nonidentical oscillators in the proximity of the point where the transition from the system's incoherent to coherent phase converts from explosive to continuous. In such a state, the oscillators form quantized clusters, where neither their phases nor their instantaneous frequencies are locked. The oscillators' instantaneous speeds are different within the clusters, but they form a characteristic cusped pattern and, more importantly, they behave periodically in time so that their average values are the same. Given its intrinsic specular nature with respect to the recently introduced Chimera states, the phase is termed the Bellerophon state. We provide an analytical and numerical description of Bellerophon states, and furnish practical hints on how to seek them in a variety of experimental and natural systems.
Experimental observation of a transition from amplitude to oscillation death in coupled oscillators
NASA Astrophysics Data System (ADS)
Banerjee, Tanmoy; Ghosh, Debarati
2014-06-01
We report the experimental evidence of an important transition scenario, namely the transition from amplitude death (AD) to oscillation death (OD) state in coupled limit cycle oscillators. We consider two Van der Pol oscillators coupled through mean-field diffusion and show that this system exhibits a transition from AD to OD, which was earlier shown for Stuart-Landau oscillators under the same coupling scheme [T. Banerjee and D. Ghosh, Phys. Rev. E 89, 052912 (2014), 10.1103/PhysRevE.89.052912]. We show that the AD-OD transition is governed by the density of mean-field and beyond a critical value this transition is destroyed; further, we show the existence of a nontrivial AD state that coexists with OD. Next, we implement the system in an electronic circuit and experimentally confirm the transition from AD to OD state. We further characterize the experimental parameter zone where this transition occurs. The present study may stimulate the search for the practical systems where this important transition scenario can be observed experimentally.
Non-Sticking Oscillation Formulae for Coulomb Friction Under Harmonic Loading
NASA Astrophysics Data System (ADS)
HONG, H.-K.; LIU, C.-S.
2001-07-01
In this paper, a new estimate for periodic non-sticking (i.e., zero stop per cycle) solutions is presented for the steady state responses of the Coulomb friction oscillator subjected to harmonic loading. Compared with the Den Hartog (1931 Transactions of the American Society of Mechanical Engineers53, 107-115 [1]) estimate, the new estimate leads to the same formulae for the maximum displacement and its time lag, but only the new estimate offers the closed-form formulae for the maximum velocity and its time lag. More importantly, a simple formula is derived for estimating the minimum driving force amplitude needed to prevent an oscillating object from sticking to the friction surface on which it slides. The validity of the assumptions made for the new estimate and the accuracy of the formulae developed are confirmed by comparing with the exact solutions (Hong and Liu 2000 Journal of Sound and Vibration229, 1171-1192 [2]). It is also found that there exists the best driving force amplitude for maximum dissipation efficiency.
On the nonlinear electromagnetic coupling between a coil and an oscillating magnet
NASA Astrophysics Data System (ADS)
Sneller, Adam J.; Mann, Brian P.
2010-07-01
The electromagnetic induction of voltage across a coil due to the motion of a magnet is among the fundamental problems of physics, and it has a broad range of practical applications. While Maxwell's equations exactly describe this phenomenon, the physical complexity inherent in most realistic situations often prevents the generation of closed-form expressions for the electromagnetic coupling. This paper uses basic principles to develop an approximate analytical expression for the induced voltage in terms of a set of physical parameters, and experimental results demonstrate a high level of validity in the model over the parameter values tested. For oscillatory magnet motion about a point on a coil's axis, it is shown that the induced voltage is an infinite sum of harmonics at integer multiples of the oscillation frequency; the relative amplitudes of these harmonics vary as the magnet's equilibrium position migrates along the coil's axis, causing the odd and even harmonics to vanish, reappear and reach peak values at predictable locations. Several simplifications to the model are considered, and their validity is investigated analytically over a range of parameters.
Plykin-type attractor in nonautonomous coupled oscillators
NASA Astrophysics Data System (ADS)
Kuznetsov, Sergey P.
2009-03-01
A system of two coupled nonautonomous oscillators is considered. Dynamics of complex amplitudes is governed by differential equations with periodic piecewise continuous dependence of the coefficients on time. The Poincaré map is derived explicitly. With the exclusion of the overall phase, on which the evolution of other variables does not depend, the Poincaré map is reduced to three-dimensional (3D) mapping. It possesses an attractor of Plykin-type located on an invariant sphere. Computer verification of the cone criterion confirms the hyperbolic nature of the attractor in the 3D map. Some results of numerical studies of the dynamics for the coupled oscillators are presented, including the attractor portraits, Lyapunov exponents, and the power spectral density.
Spiral wave chimeras in locally coupled oscillator systems
NASA Astrophysics Data System (ADS)
Li, Bing-Wei; Dierckx, Hans
2016-02-01
The recently discovered chimera state involves the coexistence of synchronized and desynchronized states for a group of identical oscillators. In this work, we show the existence of (inwardly) rotating spiral wave chimeras in the three-component reaction-diffusion systems where each element is locally coupled by diffusion. A transition from spiral waves with the smooth core to spiral wave chimeras is found as we change the local dynamics of the system or as we gradually increase the diffusion coefficient of the activator. Our findings on the spiral wave chimera in the reaction-diffusion systems suggest that spiral chimera states may be found in chemical and biological systems that can be modeled by a large population of oscillators indirectly coupled via a diffusive environment.
On cross-frequency phase-phase coupling between theta and gamma oscillations in the hippocampus
Scheffer-Teixeira, Robson; Tort, Adriano BL
2016-01-01
Phase-amplitude coupling between theta and multiple gamma sub-bands is a hallmark of hippocampal activity and believed to take part in information routing. More recently, theta and gamma oscillations were also reported to exhibit phase-phase coupling, or n:m phase-locking, suggesting an important mechanism of neuronal coding that has long received theoretical support. However, by analyzing simulated and actual LFPs, here we question the existence of theta-gamma phase-phase coupling in the rat hippocampus. We show that the quasi-linear phase shifts introduced by filtering lead to spurious coupling levels in both white noise and hippocampal LFPs, which highly depend on epoch length, and that significant coupling may be falsely detected when employing improper surrogate methods. We also show that waveform asymmetry and frequency harmonics may generate artifactual n:m phase-locking. Studies investigating phase-phase coupling should rely on appropriate statistical controls and be aware of confounding factors; otherwise, they could easily fall into analysis pitfalls. DOI: http://dx.doi.org/10.7554/eLife.20515.001 PMID:27925581
Environmental coupling in ecosystems: From oscillation quenching to rhythmogenesis
NASA Astrophysics Data System (ADS)
Arumugam, Ramesh; Dutta, Partha Sharathi; Banerjee, Tanmoy
2016-08-01
How landscape fragmentation affects ecosystems diversity and stability is an important and complex question in ecology with no simple answer, as spatially separated habitats where species live are highly dynamic rather than just static. Taking into account the species dispersal among nearby connected habitats (or patches) through a common dynamic environment, we model the consumer-resource interactions with a ring type coupled network. By characterizing the dynamics of consumer-resource interactions in a coupled ecological system with three fundamental mechanisms such as the interaction within the patch, the interaction between the patches, and the interaction through a common dynamic environment, we report the occurrence of various collective behaviors. We show that the interplay between the dynamic environment and the dispersal among connected patches exhibits the mechanism of generation of oscillations, i.e., rhythmogenesis, as well as suppression of oscillations, i.e., amplitude death and oscillation death. Also, the transition from homogeneous steady state to inhomogeneous steady state occurs through a codimension-2 bifurcation. Emphasizing a network of a spatially extended system, the coupled model exposes the collective behavior of a synchrony-stability relationship with various synchronization occurrences such as in-phase and out-of-phase.
Chimera and phase-cluster states in populations of coupled chemical oscillators
NASA Astrophysics Data System (ADS)
Tinsley, Mark R.; Nkomo, Simbarashe; Showalter, Kenneth
2012-09-01
Populations of coupled oscillators may exhibit two coexisting subpopulations, one with synchronized oscillations and the other with unsynchronized oscillations, even though all of the oscillators are coupled to each other in an equivalent manner. This phenomenon, discovered about ten years ago in theoretical studies, was then further characterized and named the chimera state after the Greek mythological creature made up of different animals. The highly counterintuitive coexistence of coherent and incoherent oscillations in populations of identical oscillators, each with an equivalent coupling structure, inspired great interest and a flurry of theoretical activity. Here we report on experimental studies of chimera states and their relation to other synchronization states in populations of coupled chemical oscillators. Our experiments with coupled Belousov-Zhabotinsky oscillators and corresponding simulations reveal chimera behaviour that differs significantly from the behaviour found in theoretical studies of phase-oscillator models.
Wu, Wei; Liu, Bo; Chen, Tianping
2010-09-01
In this paper, we investigate the firing behaviors in networks of pulse-coupled oscillators with delayed excitatory coupling according to the coupling strength epsilon and delay tau. We find out that the parameter space A={(epsilon,tau)|0
Synchronization of phase oscillators with frequency-weighted coupling
Xu, Can; Sun, Yuting; Gao, Jian; Qiu, Tian; Zheng, Zhigang; Guan, Shuguang
2016-01-01
Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all couplings. A rigorous mean-field analysis is implemented to predict the possible steady states. Furthermore, a detailed linear stability analysis proves that the incoherent state is only neutrally stable below the synchronization threshold. Nevertheless, interestingly, the amplitude of the order parameter decays exponentially (at least for short time) in this regime, resembling the Landau damping effect in plasma physics. Moreover, the explicit expression for the critical coupling strength is determined by both the mean-field method and linear operator theory. The mechanism of bifurcation for the incoherent state near the critical point is further revealed by the amplitude expansion theory, which shows that the oscillating standing wave state could also occur in this model for certain frequency distributions. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the synchronization transition in general networks with heterogenous couplings. PMID:26903110
Different kinds of chimera death states in nonlocally coupled oscillators
NASA Astrophysics Data System (ADS)
Premalatha, K.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2016-05-01
We investigate the significance of nonisochronicity parameter in a network of nonlocally coupled Stuart-Landau oscillators with symmetry breaking form. We observe that the presence of nonisochronicity parameter leads to structural changes in the chimera death region while varying the strength of the interaction. This gives rise to the existence of different types of chimera death states such as multichimera death state, type I periodic chimera death (PCD) state, and type II periodic chimera death state. We also find that the number of periodic domains in both types of PCD states decreases exponentially with an increase of coupling range and obeys a power law under nonlocal coupling. Additionally, we also analyze the structural changes of chimera death states by reducing the system of dynamical equations to a phase model through the phase reduction. We also briefly study the role of nonisochronicity parameter on chimera states, where the existence of a multichimera state with respect to the coupling range is pointed out. Moreover, we also analyze the robustness of the chimera death state to perturbations in the natural frequencies of the oscillators.
Different kinds of chimera death states in nonlocally coupled oscillators.
Premalatha, K; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M
2016-05-01
We investigate the significance of nonisochronicity parameter in a network of nonlocally coupled Stuart-Landau oscillators with symmetry breaking form. We observe that the presence of nonisochronicity parameter leads to structural changes in the chimera death region while varying the strength of the interaction. This gives rise to the existence of different types of chimera death states such as multichimera death state, type I periodic chimera death (PCD) state, and type II periodic chimera death state. We also find that the number of periodic domains in both types of PCD states decreases exponentially with an increase of coupling range and obeys a power law under nonlocal coupling. Additionally, we also analyze the structural changes of chimera death states by reducing the system of dynamical equations to a phase model through the phase reduction. We also briefly study the role of nonisochronicity parameter on chimera states, where the existence of a multichimera state with respect to the coupling range is pointed out. Moreover, we also analyze the robustness of the chimera death state to perturbations in the natural frequencies of the oscillators.
Synchronization of phase oscillators with frequency-weighted coupling
NASA Astrophysics Data System (ADS)
Xu, Can; Sun, Yuting; Gao, Jian; Qiu, Tian; Zheng, Zhigang; Guan, Shuguang
2016-02-01
Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all couplings. A rigorous mean-field analysis is implemented to predict the possible steady states. Furthermore, a detailed linear stability analysis proves that the incoherent state is only neutrally stable below the synchronization threshold. Nevertheless, interestingly, the amplitude of the order parameter decays exponentially (at least for short time) in this regime, resembling the Landau damping effect in plasma physics. Moreover, the explicit expression for the critical coupling strength is determined by both the mean-field method and linear operator theory. The mechanism of bifurcation for the incoherent state near the critical point is further revealed by the amplitude expansion theory, which shows that the oscillating standing wave state could also occur in this model for certain frequency distributions. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the synchronization transition in general networks with heterogenous couplings.
Quantization and instability of the damped harmonic oscillator subject to a time-dependent force
Majima, H. Suzuki, A.
2011-12-15
We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity (-{gamma}x) and a time-dependent external force (K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman's system, which is described by the Lagrangian: L=mxy-U(x+1/2 y)+U(x-1/2 y)+({gamma})/2 (xy-yx)-xK(t)+yK(t), which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting U(x{+-}y/2)=1/2 k(x{+-}y/2){sup 2} specifically for a dual extended damped-amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman's Hamiltonian H. The Heisenberg equations of motion utilizing the quantized Hamiltonian H surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped-amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force. - Highlights: > A method of quantizing dissipative systems is presented. > In order to obtain the method, we apply Bateman's dual system approach. > A formula for a transition amplitude is derived. > We use the formula to study the instability of the dissipative systems.
Anti-resonance in a one-dimensional chain of driven coupled oscillators
NASA Astrophysics Data System (ADS)
Belbasi, Somayyeh; Ebrahim Foulaadvand, M.; Joe, Yong S.
2014-01-01
We investigate a driven system of N one-dimensional coupled oscillators with identical masses. The first mass is connected to a sinusoidal driving force of frequency ω. In the steady state, when all the masses perform simple harmonic motion, we analytically obtain the dependence of their amplitudes on ω and show that there are resonance and anti-resonance frequencies. At an anti-resonance frequency, the amplitude of one of the masses becomes exactly zero. The mass directly connected to the driving force has the largest number of anti-resonance frequencies, N - 1. The phase of each mass's motion is either 0 or π with respect to the driving force. The case where damping forces are present is also considered, and the amplitude dependence on driving frequency is analytically obtained. In the presence of damping, there is no anti-resonance.
Fluid powered linear piston motor with harmonic coupling
Raymond, David W.
2016-09-20
A motor is disclosed that includes a module assembly including a piston that is axially cycled. The piston axial motion is coupled to torque couplers that convert the axial motion into rotary motion. The torque couplers are coupled to a rotor to rotate the rotor.
Pacemakers in large arrays of oscillators with nonlocal coupling
NASA Astrophysics Data System (ADS)
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.
Coupled Oscillations and Circadian Rhythms in Molecular Replication Networks.
Wagner, Nathaniel; Alasibi, Samaa; Peacock-Lopez, Enrique; Ashkenasy, Gonen
2015-01-02
Living organisms often display rhythmic and oscillatory behavior. We investigate here a challenge in contemporary Systems Chemistry, that is, to construct "bottom-up" molecular networks that display such complex behavior. We first describe oscillations during self-replication by applying kinetic parameters relevant to peptide replication in an open environment. Small networks of coupled oscillators are then constructed in silico, producing various functions such as logic gates, integrators, counters, triggers, and detectors. These networks are finally utilized to simulate the connectivity and network topology of the Kai proteins circadian clocks from the S. elongatus cyanobacteria, thus producing rhythms whose constant frequency is independent of the input intake rate and robust toward concentration fluctuations. We suggest that this study helps further reveal the underlying principles of biological clocks and may provide clues into their emergence in early molecular evolution.
Enhanced second harmonic generation in coupled semiconductor whispering gallery mode microresonators
NASA Astrophysics Data System (ADS)
Dumeige, Yannick
2009-02-01
It has been shown that doubly resonant microcavities can be used to obtain miniaturized parametric devices leading for example to efficient second-harmonic generation (SHG). First we will briefly recall the basic properties of SHG in III-V semiconductor whispering gallery mode microdisks or microrings. Then we will show theoretically that by coupling such microresonators and by using the artificial dispersion of a side-coupled integrated spaced sequence of resonators (SCISSOR) it is possible to adapt the Fresnel phase-matching technique to the case of highly confining waveguides or to enhance the second order nonlinear properties of a semiconductor waveguide by slowing fundamental and second-harmonic waves.
Multistable states in a system of coupled phase oscillators with inertia
Yuan, Di; Lin, Fang; Wang, Limei; Liu, Danyang; Yang, Junzhong; Xiao, Yi
2017-01-01
We investigate the generalized Kuramoto model of globally coupled oscillators with inertia, in which oscillators with positive coupling strength are conformists and oscillators with negative coupling strength are contrarians. We consider the correlation between the coupling strengths of oscillators and the distributions of natural frequencies. Two different types of correlations are studied. It is shown that the model supports multistable synchronized states such as different types of travelling wave states, π state and another type of nonstationary state: an oscillating π state. The phase distribution oscillates in a confined region and the phase difference between conformists and contrarians oscillates around π periodically in the oscillating π state. The different types of travelling wave state may be characterized by the speed of travelling wave and the effective frequencies of oscillators. Finally, the bifurcation diagrams of the model in the parameter space are presented. PMID:28176829
Multistable states in a system of coupled phase oscillators with inertia
NASA Astrophysics Data System (ADS)
Yuan, Di; Lin, Fang; Wang, Limei; Liu, Danyang; Yang, Junzhong; Xiao, Yi
2017-02-01
We investigate the generalized Kuramoto model of globally coupled oscillators with inertia, in which oscillators with positive coupling strength are conformists and oscillators with negative coupling strength are contrarians. We consider the correlation between the coupling strengths of oscillators and the distributions of natural frequencies. Two different types of correlations are studied. It is shown that the model supports multistable synchronized states such as different types of travelling wave states, π state and another type of nonstationary state: an oscillating π state. The phase distribution oscillates in a confined region and the phase difference between conformists and contrarians oscillates around π periodically in the oscillating π state. The different types of travelling wave state may be characterized by the speed of travelling wave and the effective frequencies of oscillators. Finally, the bifurcation diagrams of the model in the parameter space are presented.
NASA Astrophysics Data System (ADS)
Butet, Jérémy; Dutta-Gupta, Shourya; Martin, Olivier J. F.
2014-06-01
The surface second-harmonic generation from interacting spherical plasmonic nanoparticles building different clusters (symmetric and asymmetric dimers, trimers) is theoretically investigated. The plasmonic eigenmodes of the nanoparticle clusters are first determined using an ab initio approach based on the Green's functions method. This method provides the properties, such as the resonant wavelengths, of the modes sustained by a given cluster. The fundamental and second-harmonic responses of the corresponding clusters are then calculated using a surface integral method. The symmetry of both the linear and nonlinear responses is investigated, as well as their relationship. It is shown that the second-harmonic generation can be significantly enhanced when the fundamental field is such that its second harmonic matches modes with suitable symmetry. The role played by the nanogaps in second-harmonic generation is also underlined. The results presented in this article demonstrate that the properties of the second-harmonic generation from coupled metallic nanoparticles cannot be fully predicted from their linear response only, while, on the other hand, a detailed knowledge of the underlying modal structure can be used to optimize the generation of the second harmonic.
Thomas, Gareth E; Bass, Stephen F; Grainger, Roy G; Lambert, Alyn
2005-03-01
A new method for the retrieval of the spectral refractive indices of micrometer-sized particles from infrared aerosol extinction spectra has been developed. With this method we use a classical damped harmonic-oscillator model of molecular absorption in conjunction with Mie scattering to model extinction spectra, which we then fit to the measurements using a numerical optimal estimation algorithm. The main advantage of this method over the more traditional Kramers-Kronig approach is that it allows the full complex refractive-index spectra, along with the parameters of the particle size distribution, to be retrieved from a single extinction spectrum. The retrieval scheme has been extensively characterized and has been found to provide refractive indices with a maximum uncertainty of approximately 10% (with a minimum of approximately 0.1%). Comparison of refractive indices calculated from measurements of a ternary solution of HNO3, H2SO4, and H2O with those published in J. Phys. Chem. A 104, 783 (2000) show similar differences as found by other authors.
Are There Signatures of Harmonic Oscillator Shells Far from Stability? First Spectroscopy of 110Zr
NASA Astrophysics Data System (ADS)
Paul, N.; Corsi, A.; Obertelli, A.; Doornenbal, P.; Authelet, G.; Baba, H.; Bally, B.; Bender, M.; Calvet, D.; Château, F.; Chen, S.; Delaroche, J.-P.; Delbart, A.; Gheller, J.-M.; Giganon, A.; Gillibert, A.; Girod, M.; Heenen, P.-H.; Lapoux, V.; Libert, J.; Motobayashi, T.; Niikura, M.; Otsuka, T.; Rodríguez, T. R.; Roussé, J.-Y.; Sakurai, H.; Santamaria, C.; Shimizu, N.; Steppenbeck, D.; Taniuchi, R.; Togashi, T.; Tsunoda, Y.; Uesaka, T.; Ando, T.; Arici, T.; Blazhev, A.; Browne, F.; Bruce, A. M.; Carroll, R.; Chung, L. X.; Cortés, M. L.; Dewald, M.; Ding, B.; Flavigny, F.; Franchoo, S.; Górska, M.; Gottardo, A.; Jungclaus, A.; Lee, J.; Lettmann, M.; Linh, B. D.; Liu, J.; Liu, Z.; Lizarazo, C.; Momiyama, S.; Moschner, K.; Nagamine, S.; Nakatsuka, N.; Nita, C.; Nobs, C. R.; Olivier, L.; Patel, Z.; Podolyák, Zs.; Rudigier, M.; Saito, T.; Shand, C.; Söderström, P.-A.; Stefan, I.; Orlandi, R.; Vaquero, V.; Werner, V.; Wimmer, K.; Xu, Z.
2017-01-01
The first measurement of the low-lying states of the neutron-rich 110Zr and 112Mo was performed via in-beam γ -ray spectroscopy after one proton removal on hydrogen at ˜200 MeV /nucleon . The 21+ excitation energies were found at 185(11) keV in 110Zr, and 235(7) keV in 112Mo, while the R42=E (41+)/E (21+) ratios are 3.1(2), close to the rigid rotor value, and 2.7(1), respectively. These results are compared to modern energy density functional based configuration mixing models using Gogny and Skyrme effective interactions. We conclude that first levels of 110Zr exhibit a rotational behavior, in agreement with previous observations of lighter zirconium isotopes as well as with the most advanced Monte Carlo shell model predictions. The data, therefore, do not support a harmonic oscillator shell stabilization scenario at Z =40 and N =70 . The present data also invalidate predictions for a tetrahedral ground state symmetry in 110Zr.
Generalized su(1,1) coherent states for pseudo harmonic oscillator and their nonclassical properties
NASA Astrophysics Data System (ADS)
Mojaveri, B.; Dehghani, A.
2013-08-01
In this paper we define a non-unitary displacement operator, which by acting on the vacuum state of the pseudo harmonic oscillator (PHO), generates new class of generalized coherent states (GCSs). An interesting feature of this approach is that, contrary to the Klauder-Perelomov and Barut-Girardello approaches, it does not require the existence of dynamical symmetries associated with the system under consideration. These states admit a resolution of the identity through positive definite measures on the complex plane. We have shown that the realization of these states for different values of the deformation parameters leads to the well-known Klauder-Perelomov and Barut-Girardello CSs associated with the su(1,1) Lie algebra. This is why we call them the generalized su(1,1) CSs for the PHO. Finally, study of some statistical characters such as squeezing, anti-bunching effect and sub-Poissonian statistics reveals that the constructed GCSs have indeed nonclassical features.
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators.
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
2016-07-01
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators
NASA Astrophysics Data System (ADS)
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
2016-07-01
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.
NASA Technical Reports Server (NTRS)
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
NASA Astrophysics Data System (ADS)
Davis, Brian Thompson
1998-07-01
An isotropic three-dimensional non-relativistic charged harmonic oscillator immersed in the stochastic zero point field, an applied classical radiation field, and a constant uniform magnetic field is treated. The method followed is that of previous work [1, 2, 3, 4] with no static magnetic field present. Starting from a non-runaway classical stochastic motion equation, an appropriate conjugate momentum is derived. The classical position/conjugate momentum phase space distribution, a product of Dirac delta distributions, is ensemble averaged. The Liouville equation for this ensemble averaged phase space distribution, along with a separate independent equation that the distribution must satisfy, are derived in dipole approximation. The Weyl transformed Liouville, equation is used to derive a stochastic Schroedinger equation valid to first order in the Larmor frequency. The stochastic equation is the same as the quantum one to this order, except for the presence of radiation reaction vector potentials that produce spontaneous emission without quantization of the applied radiation field. The ensemble averaged Weyl transformed phase space distribution is also shown to be separable into a product of Schroedinger eigenfunctions, in general. Electric dipole spectra and transition probabilities for spontaneous emission and resonant absorption are calculated using the stochastic Schroedinger equation and its exact solutions. The results are compared to the corresponding predictions of quantum electrodynamics and found to be in agreement.
Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges
NASA Astrophysics Data System (ADS)
Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, W. M.; Tobias, B. J.; Yan, Z.
2016-07-01
In the quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHOs) play an important role in avoiding transient edge localized mode (ELM) power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n ⩽ 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended magentoohydrodynamics (MHD) code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-Imaging and microwave imaging reflectometer (MIR) diagnostics, as well as the kink/peeling mode properties found by the ideal MHD code ELITE. Numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by rotation and/or rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that EHOs can be destabilized in principle with rotation in either direction. The modeling results are consistent with observations of EHO, support the proposed theory of the EHO as a low-n kink/peeling mode destabilized by edge E × B rotational shear, and improve our understanding and confidence in creating and sustaining QH-mode in present and future devices.
Rotational Shear Effects on Edge Harmonic Oscillations in DIII-D Quiescent H-mode Discharges
NASA Astrophysics Data System (ADS)
Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, Wm.; Tobias, B. J.; Yan, Z.
2015-11-01
In quiescent H-mode (QH) regime, the edge harmonic oscillations (EHO) play an important role in avoiding the transient ELM power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n <= 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended MHD code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-I and MIR diagnostics, as well as the kink/peeling mode properties of the ideal MHD code ELITE. The numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by the toroidal rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that the low-n EHO can be destabilized in principle with rotation in both directions. These modeling results are consistent with experimental observations of the EHO and support the proposed theory of the EHO as a rotational shear driven kink/peeling mode.
Paul, N; Corsi, A; Obertelli, A; Doornenbal, P; Authelet, G; Baba, H; Bally, B; Bender, M; Calvet, D; Château, F; Chen, S; Delaroche, J-P; Delbart, A; Gheller, J-M; Giganon, A; Gillibert, A; Girod, M; Heenen, P-H; Lapoux, V; Libert, J; Motobayashi, T; Niikura, M; Otsuka, T; Rodríguez, T R; Roussé, J-Y; Sakurai, H; Santamaria, C; Shimizu, N; Steppenbeck, D; Taniuchi, R; Togashi, T; Tsunoda, Y; Uesaka, T; Ando, T; Arici, T; Blazhev, A; Browne, F; Bruce, A M; Carroll, R; Chung, L X; Cortés, M L; Dewald, M; Ding, B; Flavigny, F; Franchoo, S; Górska, M; Gottardo, A; Jungclaus, A; Lee, J; Lettmann, M; Linh, B D; Liu, J; Liu, Z; Lizarazo, C; Momiyama, S; Moschner, K; Nagamine, S; Nakatsuka, N; Nita, C; Nobs, C R; Olivier, L; Patel, Z; Podolyák, Zs; Rudigier, M; Saito, T; Shand, C; Söderström, P-A; Stefan, I; Orlandi, R; Vaquero, V; Werner, V; Wimmer, K; Xu, Z
2017-01-20
The first measurement of the low-lying states of the neutron-rich ^{110}Zr and ^{112}Mo was performed via in-beam γ-ray spectroscopy after one proton removal on hydrogen at ∼200 MeV/nucleon. The 2_{1}^{+} excitation energies were found at 185(11) keV in ^{110}Zr, and 235(7) keV in ^{112}Mo, while the R_{42}=E(4_{1}^{+})/E(2_{1}^{+}) ratios are 3.1(2), close to the rigid rotor value, and 2.7(1), respectively. These results are compared to modern energy density functional based configuration mixing models using Gogny and Skyrme effective interactions. We conclude that first levels of ^{110}Zr exhibit a rotational behavior, in agreement with previous observations of lighter zirconium isotopes as well as with the most advanced Monte Carlo shell model predictions. The data, therefore, do not support a harmonic oscillator shell stabilization scenario at Z=40 and N=70. The present data also invalidate predictions for a tetrahedral ground state symmetry in ^{110}Zr.
Coupled predator-prey oscillations in a chaotic food web.
Benincà, Elisa; Jöhnk, Klaus D; Heerkloss, Reinhard; Huisman, Jef
2009-12-01
Coupling of several predator-prey oscillations can generate intriguing patterns of synchronization and chaos. Theory predicts that prey species will fluctuate in phase if predator-prey cycles are coupled through generalist predators, whereas they will fluctuate in anti-phase if predator-prey cycles are coupled through competition between prey species. Here, we investigate predator-prey oscillations in a long-term experiment with a marine plankton community. Wavelet analysis of the species fluctuations reveals two predator-prey cycles that fluctuate largely in anti-phase. The phase angles point at strong competition between the phytoplankton species, but relatively little prey overlap among the zooplankton species. This food web architecture is consistent with the size structure of the plankton community, and generates highly dynamic food webs. Continued alternations in species dominance enable coexistence of the prey species through a non-equilibrium 'killing-the-winner' mechanism, as the system shifts back and forth between the two predator-prey cycles in a chaotic fashion.
Xu, L; Chan, H-Y; Alam, S-U; Richardson, D J; Shepherd, D P
2015-07-15
We demonstrate the generation of high-energy, mid-IR, picosecond pulses in a high-harmonic-cavity optical parametric oscillator (OPO) that has a relatively compact cavity with a length that is a small fraction of that required to match the pump repetition rate. The OPO, based on an MgO-doped periodically poled LiNbO3 crystal, is pumped by a fiber master-oscillator-power-amplifier system employing direct amplification and delivering 11-μJ, 150-ps pulses at 1035 nm. For a 1.554-m-long OPO cavity, resonating near-infrared signal pulses with a repetition rate that is the 193rd harmonic of the 1-MHz pump are demonstrated. The mid-infrared idler output pulses, tunable from 2300 nm to 3500 nm, are generated at a 1-MHz repetition rate and have energies as high as 1.5 μJ.
NASA Astrophysics Data System (ADS)
Chen, Y. F.; Tung, J. C.; Tuan, P. H.; Yu, Y. T.; Liang, H. C.; Huang, K. F.
2017-01-01
A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.
Chen, Y F; Tung, J C; Tuan, P H; Yu, Y T; Liang, H C; Huang, K F
2017-01-01
A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.
NASA Astrophysics Data System (ADS)
Lo, C. F.
2014-02-01
Recently Zhang (2013 J. Phys. A: Math. Theor. 46 455302) proposed an analytical approach to solve the time-independent Schrödinger equation for the single-mode and two-mode squeezed harmonic oscillators in the Bargmann space of entire functions. In this comment we show that the eigenfunctions of these two systems exist in closed form and are expressed in terms of the Hermite polynomials. Moreover, since both oscillators exhibit the SU(1,1) dynamical symmetry, the eigenvalue problem can be tackled in a unified manner. In the Hilbert space of analytic functions of a complex variable in the unit disc, the energy eigenvalue equations involve first-order ordinary differential equations only, so we can easily solve these equations to obtain simple closed-form solutions.
Testing the global flow reconstruction method on coupled chaotic oscillators
NASA Astrophysics Data System (ADS)
Plachy, Emese; Kolláth, Zoltán
2010-03-01
Irregular behaviour of pulsating variable stars may occur due to low dimensional chaos. To determine the quantitative properties of the dynamics in such systems, we apply a suitable time series analysis, the global flow reconstruction method. The robustness of the reconstruction can be tested through the resultant quantities, like Lyapunov dimension and Fourier frequencies. The latter is specially important as it is directly derivable from the observed light curves. We have performed tests using coupled Rossler oscillators to investigate the possible connection between those quantities. In this paper we present our test results.
Transient chaos in two coupled, dissipatively perturbed Hamiltonian Duffing oscillators
NASA Astrophysics Data System (ADS)
Sabarathinam, S.; Thamilmaran, K.; Borkowski, L.; Perlikowski, P.; Brzeski, P.; Stefanski, A.; Kapitaniak, T.
2013-11-01
The dynamics of two coupled, dissipatively perturbed, near-integrable Hamiltonian, double-well Duffing oscillators has been studied. We give numerical and experimental (circuit implementation) evidence that in the case of small positive or negative damping there exist two different types of transient chaos. After the decay of the transient chaos in the neighborhood of chaotic saddle we observe the transient chaos in the neighborhood of unstable tori. We argue that our results are robust and they exist in the wide range of system parameters.
Gupta, Shamik; Bandyopadhyay, Malay
2011-10-01
We obtain the quantum Langevin equation (QLE) of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a quantum heat bath through momentum variables. The bath is modeled as a collection of independent quantum harmonic oscillators. The QLE involves a random force which does not depend on the magnetic field, and a quantum-generalized classical Lorentz force. These features are also present in the QLE for the case of particle-bath coupling through coordinate variables. However, significant differences are also observed. For example, the mean force in the QLE is characterized by a memory function that depends explicitly on the magnetic field. The random force has a modified form with correlation and commutator different from those in the case of coordinate-coordinate coupling. Moreover, the coupling constants, in addition to appearing in the random force and in the mean force, also renormalize the inertial term and the harmonic potential term in the QLE.
Analytical Insights on Theta-Gamma Coupled Neural Oscillators
2013-01-01
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. PMID:23945442
NASA Astrophysics Data System (ADS)
Albeverio, Sergio; Fassari, Silvestro; Rinaldi, Fabio
2013-09-01
We rigorously define the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive δ‧-interaction, of strength β, centred at 0 (the bottom of the confining parabolic potential), by explicitly providing its resolvent. Our approach is based on a ‘coupling constant renormalization’, related to a technique originated in quantum field theory and implemented in the rigorous mathematical construction of the self-adjoint operator representing the negative Laplacian perturbed by the δ-interaction in two and three dimensions. The way the δ‧-interaction enters in our Hamiltonian corresponds to the one originally discussed for the free Hamiltonian (instead of the harmonic oscillator one) by P Sěba. It should not be confused with the δ‧-potential perturbation of the harmonic oscillator discussed, e.g., in a recent paper by Gadella, Glasser and Nieto (also introduced by P Sěba as a perturbation of the one-dimensional free Laplacian and recently investigated in that context by Golovaty, Hryniv and Zolotaryuk). We investigate in detail the spectrum of our perturbed harmonic oscillator. The spectral structure differs from that of the one-dimensional harmonic oscillator perturbed by an attractive δ-interaction centred at the origin: the even eigenvalues are not modified at all by the δ‧-interaction. Moreover, all the odd eigenvalues, regarded as functions of β, exhibit the rather remarkable phenomenon called ‘level crossing’ after first producing the double degeneracy of all the even eigenvalues for the value \\beta = \\beta _0 = \\frac{{2\\sqrt \\pi }}{{B\\left( {\\frac{3}{4},\\frac{1}{2}} \\right)}} \\cong 1.47934(B( ·, ·) being the beta function). Dedicated to Professor Gianfausto Dell'Antonio on the occasion of his 80th birthday.
NASA Astrophysics Data System (ADS)
Kohira, Masahiro I.; Kitahata, Hiroyuki; Magome, Nobuyuki; Yoshikawa, Kenichi
2012-02-01
An oscillatory system called a plastic bottle oscillator is studied, in which the downflow of water and upflow of air alternate periodically in an upside-down plastic bottle containing water. It is demonstrated that a coupled two-bottle system exhibits in- and antiphase synchronization according to the nature of coupling. A simple ordinary differential equation is deduced to interpret the characteristics of a single oscillator. This model is also extended to coupled oscillators, and the model reproduces the essential features of the experimental observations.
EDFA-based coupled opto-electronic oscillator and its phase noise
NASA Technical Reports Server (NTRS)
Salik, Ertan; Yu, Nan; Tu, Meirong; Maleki, Lute
2004-01-01
EDFA-based coupled opto-electronic oscillator (COEO), an integrated optical and microwave oscillator that can generate picosecond optical pulses, is presented. the phase noise measurements of COEO show better performance than synthesizer-driven mode-locked laser.
Walsh, Gary F; Dal Negro, Luca
2013-07-10
In this communication, we systematically investigate the effects of Fano-type coupling between long-range photonic resonances and localized surface plasmons on the second harmonic generation from periodic arrays of Au nanoparticles arranged in monomer and dimer geometries. Specifically, by scanning the wavelength of an ultrafast tunable pump laser over a large range, we measure the second harmonic excitation spectra of these arrays and demonstrate their tunability with particle size and separation. Moreover, through a comparison with linear optical transmission spectra, which feature asymmetric Fano-type lineshapes, we demonstrate that the second harmonic generation is enhanced when coupled photonic-plasmonic resonances of the arrays are excited at the fundamental pump wavelength, thus boosting the intensity of the electromagnetic near-fields. Our experimental results, which are supported by numerical simulations of linear optical transmission and near-field enhancement spectra based on the Finite Difference Time Domain method, demonstrate a direct correlation between the onset of Fano-type coupling and the enhancement of second harmonic generation in arrays of Au nanoparticles. Our findings enable the engineering of the nonlinear optical response of Fano-type coupled nanoparticle arrays that are relevant to a number of device applications in nonlinear nano-optics and plasmonics, such as on-chip frequency generators, modulators, switchers, and sensors.
NASA Astrophysics Data System (ADS)
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.
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.
NASA Astrophysics Data System (ADS)
Fukuyama, T.; Okugawa, M.
2017-03-01
We have experimentally investigated the dynamic behavior of coupled nonlinear oscillators, including chaos caused by the instability of ionization waves in a glow discharge plasma. We studied the phase synchronization process of coupled asymmetric oscillators with increasing coupling strength. Coherence resonance and phase synchronization were observed in the coupled systems. The phase synchronization process revealed scaling laws with a tendency of Type-I intermittency in the relationships between the coupling strength and the average duration of successive laminar states interrupted by a phase slip. Coupled periodic oscillators changed from a periodic state to chaos caused by the interaction of nonlinear periodic waves at increasing coupling strength.
On the effect of acoustic coupling on random and harmonic plate vibrations
NASA Technical Reports Server (NTRS)
Frendi, A.; Robinson, J. H.
1993-01-01
The effect of acoustic coupling on random and harmonic plate vibrations is studied using two numerical models. In the coupled model, the plate response is obtained by integration of the nonlinear plate equation coupled with the nonlinear Euler equations for the surrounding acoustic fluid. In the uncoupled model, the nonlinear plate equation with an equivalent linear viscous damping term is integrated to obtain the response of the plate subject to the same excitation field. For a low-level, narrow-band excitation, the two models predict the same plate response spectra. As the excitation level is increased, the response power spectrum predicted by the uncoupled model becomes broader and more shifted towards the high frequencies than that obtained by the coupled model. In addition, the difference in response between the coupled and uncoupled models at high frequencies becomes larger. When a high intensity harmonic excitation is used, causing a nonlinear plate response, both models predict the same frequency content of the response. However, the level of the harmonics and subharmonics are higher for the uncoupled model. Comparisons to earlier experimental and numerical results show that acoustic coupling has a significant effect on the plate response at high excitation levels. Its absence in previous models may explain the discrepancy between predicted and measured responses.
Harmonically trapped attractive and repulsive spin–orbit and Rabi coupled Bose–Einstein condensates
NASA Astrophysics Data System (ADS)
Chiquillo, Emerson
2017-03-01
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.
Scaling of Harmonic Oscillator Eigenfunctions and Their Nodal Sets Around the Caustic
NASA Astrophysics Data System (ADS)
Hanin, Boris; Zelditch, Steve; Zhou, Peng
2017-03-01
We study the scaling asymptotics of the eigenspace projection kernels Π_{hbar, E}(x,y) of the isotropic Harmonic Oscillator {hat{H}_{hbar} = - hbar^2 Δ +|x|^2} of eigenvalue {E = hbar(N + d/2)} in the semi-classical limit {hbar to 0} . The principal result is an explicit formula for the scaling asymptotics of Π_{hbar, E}(x,y) for x, y in a {hbar^{2/3}} neighborhood of the caustic C_E as {hbar → 0.} The scaling asymptotics are applied to the distribution of nodal sets of Gaussian random eigenfunctions around the caustic as {hbar to 0} . In previous work we proved that the density of zeros of Gaussian random eigenfunctions of {hat{H}_{hbar}} have different orders in the Planck constant {hbar} in the allowed and forbidden regions: In the allowed region the density is of order {hbar^{-1}} while it is {hbar^{-1/2}} in the forbidden region. Our main result on nodal sets is that the density of zeros is of order {hbar^{-2/3}} in an {hbar^{2/3}} -tube around the caustic. This tube radius is the `critical radius'. For annuli of larger inner and outer radii {hbar^{α}} with {0 < α < 2/3} we obtain density results that interpolate between this critical radius result and our prior ones in the allowed and forbidden region. We also show that the Hausdorff ( d-2)-dimensional measure of the intersection of the nodal set with the caustic is of order {hbar^{- 2/3}}.
NASA Astrophysics Data System (ADS)
Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.
1995-08-01
The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.
Collective dynamics of identical phase oscillators with high-order coupling
Xu, Can; Xiang, Hairong; Gao, Jian; Zheng, Zhigang
2016-01-01
In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various regions of parameter space are analyzed. Furthermore, a detailed linear stability analysis proves that the stationary symmetric distribution is only neutrally stable in the marginal regime which stems from the generalized time-reversal symmetry. Moreover, the critical parameters of the transition among various regimes are determined analytically by both the Ott-Antonsen method and linear stability analysis, the transient dynamics are further revealed in terms of the characteristic curves method. Finally, for the more general initial condition the symmetric dynamics could be reduced to a rigorous three-dimensional manifold which shows that the neutrally stable chaos could also occur in this model for particular parameters. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the dynamical properties in general systems with higher-order harmonics couplings. PMID:27491401
Collective dynamics of identical phase oscillators with high-order coupling
NASA Astrophysics Data System (ADS)
Xu, Can; Xiang, Hairong; Gao, Jian; Zheng, Zhigang
2016-08-01
In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various regions of parameter space are analyzed. Furthermore, a detailed linear stability analysis proves that the stationary symmetric distribution is only neutrally stable in the marginal regime which stems from the generalized time-reversal symmetry. Moreover, the critical parameters of the transition among various regimes are determined analytically by both the Ott-Antonsen method and linear stability analysis, the transient dynamics are further revealed in terms of the characteristic curves method. Finally, for the more general initial condition the symmetric dynamics could be reduced to a rigorous three-dimensional manifold which shows that the neutrally stable chaos could also occur in this model for particular parameters. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the dynamical properties in general systems with higher-order harmonics couplings.
Intermediate vibrational coordinate localization with harmonic coupling constraints
NASA Astrophysics Data System (ADS)
Hanson-Heine, Magnus W. D.
2016-05-01
Optimized normal coordinates can significantly improve the speed and accuracy of vibrational frequency calculations. However, over-localization can occur when using unconstrained spatial localization techniques. The unintuitive mixtures of stretching and bending coordinates that result can make interpreting spectra more difficult and also cause artificial increases in mode-coupling during anharmonic calculations. Combining spatial localization with a constraint on the coupling between modes can be used to generate coordinates with properties in-between the normal and fully localized schemes. These modes preserve the diagonal nature of the mass-weighted Hessian matrix to within a specified tolerance and are found to prevent contamination between the stretching and bending vibrations of the molecules studied without a priori classification of the different types of vibration present. Relaxing the constraint can also be used to identify which normal modes form specific groups of localized modes. The new coordinates are found to center on more spatially delocalized functional groups than their fully localized counterparts and can be used to tune the degree of vibrational correlation energy during anharmonic calculations.
Oscillation quenching in third order phase locked loop coupled by mean field diffusive coupling
NASA Astrophysics Data System (ADS)
Chakraborty, S.; Dandapathak, M.; Sarkar, B. C.
2016-11-01
We explored analytically the oscillation quenching phenomena (amplitude death and parameter dependent inhomogeneous steady state) in a coupled third order phase locked loop (PLL) both in periodic and chaotic mode. The phase locked loops were coupled through mean field diffusive coupling. The lower and upper limits of the quenched state were identified in the parameter space of the coupled PLL using the Routh-Hurwitz technique. We further observed that the ability of convergence to the quenched state of coupled PLLs depends on the design parameters. For identical systems, both the systems converge to the homogeneous steady state, whereas for non-identical parameter values they converge to an inhomogeneous steady state. It was also observed that for identical systems, the quenched state is wider than the non-identical case. When the system parameters are so chosen that each isolated loop is chaotic in nature, we observe narrowing down of the quenched state. All these phenomena were also demonstrated through numerical simulations.
Oscillation quenching in third order phase locked loop coupled by mean field diffusive coupling.
Chakraborty, S; Dandapathak, M; Sarkar, B C
2016-11-01
We explored analytically the oscillation quenching phenomena (amplitude death and parameter dependent inhomogeneous steady state) in a coupled third order phase locked loop (PLL) both in periodic and chaotic mode. The phase locked loops were coupled through mean field diffusive coupling. The lower and upper limits of the quenched state were identified in the parameter space of the coupled PLL using the Routh-Hurwitz technique. We further observed that the ability of convergence to the quenched state of coupled PLLs depends on the design parameters. For identical systems, both the systems converge to the homogeneous steady state, whereas for non-identical parameter values they converge to an inhomogeneous steady state. It was also observed that for identical systems, the quenched state is wider than the non-identical case. When the system parameters are so chosen that each isolated loop is chaotic in nature, we observe narrowing down of the quenched state. All these phenomena were also demonstrated through numerical simulations.
NASA Astrophysics Data System (ADS)
Zheng, Zhigang; Wang, Xingang; Cross, Michael C.
2002-05-01
Generalized synchronization in an array of mutually (bidirectionally) coupled nonidentical chaotic oscillators is studied. Coupled Lorenz oscillators and coupled Lorenz-Rossler oscillators are adopted as our working models. With increasing the coupling strengths, the system experiences a cascade of transitions from the partial to the global generalized synchronizations, i.e., different oscillators are gradually entrained through a clustering process. This scenario of transitions reveals an intrinsic self-organized order in groups of interacting units, which generalizes the idea of generalized synchronizations in drive-response systems.
Coupled rotor-flexible fuselage vibration reduction using open loop higher harmonic control
NASA Technical Reports Server (NTRS)
Papavassiliou, I.; Friedmann, P. P.; Venkatesan, C.
1991-01-01
A fundamental study of vibration prediction and vibration reduction in helicopters using active controls was performed. The nonlinear equations of motion for a coupled rotor/flexible fuselage system have been derived using computer algebra on a special purpose symbolic computer facility. The trim state and vibratory response of the helicopter are obtained in a single pass by applying the harmonic balance technique and simultaneously satisfying the trim and the vibratory response of the helicopter for all rotor and fuselage degrees of freedom. The influence of the fuselage flexibility on the vibratory response is studied. It is shown that the conventional single frequency higher harmonic control is capable of reducing either the hub loads or only the fuselage vibrations but not both simultaneously. It is demonstrated that for simultaneous reduction of hub shears and fuselae vibrations a new scheme called multiple higher harmonic control is required.
Properties of Coupled Oscillator Model for Bidirectional Associative Memory
NASA Astrophysics Data System (ADS)
Kawaguchi, Satoshi
2016-08-01
In this study, we consider the stationary state and dynamical properties of a coupled oscillator model for bidirectional associative memory. For the stationary state, we apply the replica method to obtain self-consistent order parameter equations. The theoretical results for the storage capacity and overlap agree well with the numerical simulation. For the retrieval process, we apply statistical neurodynamics to include temporal noise correlations. For the successful retrieval process, the theoretical result obtained with the fourth-order approximation qualitatively agrees with the numerical simulation. However, for the unsuccessful retrieval process, higher-order noise correlations suppress severely; therefore, the maximum value of the overlap and the relaxation time are smaller than those of the numerical simulation. The reasons for the discrepancies between the theoretical result and numerical simulation, and the validity of our analysis are discussed.
Elementary modes of coupled oscillators as whispering-gallery microresonators
NASA Astrophysics Data System (ADS)
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.
Dynamically Coupled Oscillators: Cooperative Behavior via Dynamical Interaction
NASA Astrophysics Data System (ADS)
Aonishi, Toru; Okada, Masato
2003-06-01
We propose a theoretical framework for studying the cooperative behavior of dynamically coupled oscillators (DCOs) that possess dynamical interactions. Then, to clarify synchronization phenomena in networks of interneurons which possess inhibitory interactions, we propose a DCO model with dynamics of interactions that tend to cause 180^\\circ phase lags. Employing the approach developed here, we demonstrate that although our model displays synchronization at high frequencies, it does not exhibit synchronization at low frequencies because this dynamical interaction does not cause a phase lag sufficiently large to cancel the effect of the inhibition. We interpret the disappearance of synchronization in our model with decreasing frequency as describing the breakdown of synchronization in the interneuron network of the CA1 area below the critical frequency of 20 Hz.
On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator
ERIC Educational Resources Information Center
Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru
2009-01-01
The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.
Interplay of coupling and common noise at the transition to synchrony in oscillator populations
Pimenova, Anastasiya V.; Goldobin, Denis S.; Rosenblum, Michael; Pikovsky, Arkady
2016-01-01
There are two ways to synchronize oscillators: by coupling and by common forcing, which can be pure noise. By virtue of the Ott-Antonsen ansatz for sine-coupled phase oscillators, we obtain analytically tractable equations for the case where both coupling and common noise are present. While noise always tends to synchronize the phase oscillators, the repulsive coupling can act against synchrony, and we focus on this nontrivial situation. For identical oscillators, the fully synchronous state remains stable for small repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion (instead of usual convergence) of the oscillators frequencies at synchrony; the latter effect disappears if noise vanishes. PMID:27922105
Interplay of coupling and common noise at the transition to synchrony in oscillator populations
NASA Astrophysics Data System (ADS)
Pimenova, Anastasiya V.; Goldobin, Denis S.; Rosenblum, Michael; Pikovsky, Arkady
2016-12-01
There are two ways to synchronize oscillators: by coupling and by common forcing, which can be pure noise. By virtue of the Ott-Antonsen ansatz for sine-coupled phase oscillators, we obtain analytically tractable equations for the case where both coupling and common noise are present. While noise always tends to synchronize the phase oscillators, the repulsive coupling can act against synchrony, and we focus on this nontrivial situation. For identical oscillators, the fully synchronous state remains stable for small repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion (instead of usual convergence) of the oscillators frequencies at synchrony; the latter effect disappears if noise vanishes.
NASA Astrophysics Data System (ADS)
Krylov, S. N.; Smirnov, D. A.; Osipov, G. V.; Bezruchko, B. P.
2015-06-01
To analyze the coupling between oscillating systems by time series, the Granger causality assessment—an improved prognosis of the autoregression model—is widely used. It is known that wrong conclusions regarding the presence of bidirectional coupling can be obtained in the case of unidirectional coupled systems when the sampling interval is rather wide. However, it remains unclear under what conditions the effect of false coupling is significant, and thus criteria of significance to account for this effect in practice are absent. In this work, such conditions were studied and qualitatively formulated for an etalon system of coupled oscillators. In particular, it is shown that this effect is negligible in the case of insufficient data if a "fast" oscillator (with a smaller oscillation period and relaxation time) is driving a "slow" oscillator, while the effect is strong otherwise. If both periods are considerably larger than the sampling interval, the effect increases with relaxation time of the driving oscillator and decreases with increasing relaxation time of the driven one.
Higher-order harmonics coupling in different free-electron laser codes
NASA Astrophysics Data System (ADS)
Giannessi, L.; Freund, H. P.; Musumeci, P.; Reiche, S.
2008-08-01
The capability for simulation of the dynamics of a free-electron laser including the higher-order harmonics in linear undulators exists in several existing codes as MEDUSA [H.P. Freund, S.G. Biedron, and S.V. Milton, IEEE J. Quantum Electron. 27 (2000) 243; H.P. Freund, Phys. Rev. ST-AB 8 (2005) 110701] and PERSEO [L. Giannessi, Overview of Perseo, a system for simulating FEL dynamics in Mathcad, < http://www.jacow.org>, in: Proceedings of FEL 2006 Conference, BESSY, Berlin, Germany, 2006, p. 91], and has been recently implemented in GENESIS 1.3 [See < http://www.perseo.enea.it>]. MEDUSA and GENESIS also include the dynamics of even harmonics induced by the coupling through the betatron motion. In addition MEDUSA, which is based on a non-wiggler averaged model, is capable of simulating the generation of even harmonics in the transversally cold beam regime, i.e. when the even harmonic coupling arises from non-linear effects associated with longitudinal particle dynamics and not to a finite beam emittance. In this paper a comparison between the predictions of the codes in different conditions is given.
Barnes, George L.; Kellman, Michael E.
2013-12-07
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is “designed” by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of “classicalizing” behavior in the approach to thermal equilibrium are briefly considered.
NASA Astrophysics Data System (ADS)
Barnes, George L.; Kellman, Michael E.
2013-12-01
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of "classicalizing" behavior in the approach to thermal equilibrium are briefly considered.
Barnes, George L; Kellman, Michael E
2013-12-07
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of "classicalizing" behavior in the approach to thermal equilibrium are briefly considered.
Synchronization of phase oscillators with coupling mediated by a diffusing substance
NASA Astrophysics Data System (ADS)
Batista, C. A. S.; Szezech, J. D.; Batista, A. M.; Macau, E. E. N.; Viana, R. L.
2017-03-01
We investigate the transition to phase and frequency synchronization in a one-dimensional chain of phase oscillator "cells" where the coupling is mediated by the local concentration of a chemical which can diffuse in the inter-oscillator medium and it is both secreted and absorbed by the oscillator "cells", influencing their dynamical behavior. This coupling has the advantage of having a tunable parameter which makes it possible to pass continuously from a global (all-to-all) to a local (nearest-neighbor) coupling form. We have verified that synchronous behavior depends on the coupling strength and coupling length.
The q-DEFORMED SCHRÖDINGER Equation of the Harmonic Oscillator on the Quantum Euclidean Space
NASA Astrophysics Data System (ADS)
Carow-Watamura, Ursula; Watamura, Satoshi
We consider the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidean space. The creation and annihilation operators are found, which systematically produce all energy levels and eigenfunctions of the Schrödinger equation. In order to get the q series representation of the eigenfunction, we also give an alternative way to solve the Schrödinger equation which is based on the q analysis. We represent the Schrödinger equation by the q difference equation and solve it by using q polynomials and q exponential functions.
NASA Technical Reports Server (NTRS)
Isar, Aurelian
1995-01-01
The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.
Coupled vibration of driving sections for an electromechanical integrated harmonic piezodrive system
NASA Astrophysics Data System (ADS)
Li, Chong; Xing, Jichun; Xu, Lizhong
2014-03-01
An electromechanical integrated harmonic piezodrive system was developed that elicits fast responses with nanoscale accuracy and large torque density. The operating principle of the drive system is discussed and its dynamic equations are deduced. Coupled with boundary conditions and continuity conditions, these equations provide the natural frequencies and modal functions. The effects of the principal factors affecting the natural frequencies are investigated. These results provide a basis for improving the rotational accuracy of such systems.
NASA Astrophysics Data System (ADS)
Pascoe, D. J.; Anfinogentov, S.; Nisticò, G.; Goddard, C. R.; Nakariakov, V. M.
2017-04-01
Context. The strong damping of kink oscillations of coronal loops can be explained by mode coupling. The damping envelope depends on the transverse density profile of the loop. Observational measurements of the damping envelope have been used to determine the transverse loop structure which is important for understanding other physical processes such as heating. Aims: The general damping envelope describing the mode coupling of kink waves consists of a Gaussian damping regime followed by an exponential damping regime. Recent observational detection of these damping regimes has been employed as a seismological tool. We extend the description of the damping behaviour to account for additional physical effects, namely a time-dependent period of oscillation, the presence of additional longitudinal harmonics, and the decayless regime of standing kink oscillations. Methods: We examine four examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). We use forward modelling of the loop position and investigate the dependence on the model parameters using Bayesian inference and Markov chain Monte Carlo (MCMC) sampling. Results: Our improvements to the physical model combined with the use of Bayesian inference and MCMC produce improved estimates of model parameters and their uncertainties. Calculation of the Bayes factor also allows us to compare the suitability of different physical models. We also use a new method based on spline interpolation of the zeroes of the oscillation to accurately describe the background trend of the oscillating loop. Conclusions: This powerful and robust method allows for accurate seismology of coronal loops, in particular the transverse density profile, and potentially reveals additional physical effects.
Spontaneous mode switching in coupled oscillators competing for constant amounts of resources.
Hirata, Yoshito; Aono, Masashi; Hara, Masahiko; Aihara, Kazuyuki
2010-03-01
We propose a widely applicable scheme of coupling that models competitions among dynamical systems for fixed amounts of resources. Two oscillators coupled in this way synchronize in antiphase. Three oscillators coupled circularly show a number of oscillation modes such as rotation and partially in-phase synchronization. Intriguingly, simple oscillators in the model also produce complex behavior such as spontaneous switching among different modes. The dynamics reproduces well the spatiotemporal oscillatory behavior of a true slime mold Physarum, which is capable of computational optimization.
The effects of dual-channel coupling on the transition from amplitude death to oscillation death
NASA Astrophysics Data System (ADS)
Chen, Jiangnan; Liu, Weiqing; Zhu, Yun; Xiao, Jinghua
2016-07-01
Oscillation quenching including amplitude death (AD) and oscillation death (OD) in addition to the transition processes between them have been hot topics in aspect of chaos control, physical and biological applications. The effects of dual-channel coupling on the AD and OD dynamics regimes, and their transition processes in coupled nonidentical oscillators are explored numerically and theoretically. Our results indicate that an additional repulsive coupling tends to shrink the AD domain while it enlarges the OD domain, however, an additional attractive coupling acts inversely. As a result, the transitions from AD to OD are replaced by transitions from oscillation state (OS) to AD or from OS to OD in the dual-channel coupled oscillators with different frequency mismatches. Our results are helpful to better understand the control of AD and OD and their transition processes.
NASA Astrophysics Data System (ADS)
Chen, Xiaoxiao; Feng, Xiuqin; Tian, Zuolin; Yao, Zhihai
2016-06-01
We present the control and synchronization of spatiotemporal chaos in the photo-refractive ring oscillator systems with coupling technology. First, we realize the synchronization of spatiotemporal chaos in the two photorefractive ring oscillator systems via mutual coupling by choosing a suitable coupling strength. With the mutual coupling strength enlarging, the two mutual coupling photorefractive ring oscillator systems are controlled into periodic state, period number differs on account of the coupling strength and lattice coordinates. By increasing the coupling strength, the photorefractive ring oscillator is converted into period 8, subsequently it is converted into periods 4 and 2, periodic synchronization of the photorefractive ring oscillator systems is achieved at the same time. Calculation results show that period 1 is impossible by mutual coupling technology. Then, we investigate the influence of noise and parameter deviation on chaotic synchronization. We find that mutual coupling chaotic synchronization method can synchronize two chaotic systems with the weak noise and parameter deviation and has very good robustness. Given that the weak noise and parameter deviation have a slight effect on synchronization. Furthermore, we investigate two dimension control and synchronization of spatiotemporal chaos in the photorefractive ring osillator systems with coupling technology and get successful results. Mutual coupling technology is suitable in practical photorefractive ring oscillator systems.
Campione, Salvatore; Benz, Alexander; Brener, Igal; Sinclair, Michael B.; Capolino, Filippo
2014-03-31
We theoretically analyze the second harmonic generation capacity of two-dimensional periodic metamaterials comprising sub-wavelength resonators strongly coupled to intersubband transitions in quantum wells (QWs) at mid-infrared frequencies. The metamaterial is designed to support a fundamental resonance at ∼30 THz and an orthogonally polarized resonance at the second harmonic frequency (∼60 THz), while the asymmetric quantum well structure is designed to provide a large second order susceptibility. Upon continuous wave illumination at the fundamental frequency we observe second harmonic signals in both the forward and backward directions, with the forward efficiency being larger. We calculate the overall second harmonic conversion efficiency of the forward wave to be ∼1.3 × 10{sup −2} W/W{sup 2}—a remarkably large value, given the deep sub-wavelength dimensions of the QW structure (about 1/15th of the free space wavelength of 10 μm). The results shown in this Letter provide a strategy for designing easily fabricated sources across the entire infrared spectrum through proper choice of QW and resonator designs.
Dynamics of three coupled van der Pol oscillators with application to circadian rhythms
NASA Astrophysics Data System (ADS)
Rompala, Kevin; Rand, Richard; Howland, Howard
2007-08-01
In this work we study a system of three van der Pol oscillators. Two of the oscillators are identical, and are not directly coupled to each other, but rather are coupled via the third oscillator. We investigate the existence of the in-phase mode in which the two identical oscillators have the same behavior. To this end we use the two variable expansion perturbation method (also known as multiple scales) to obtain a slow flow, which we then analyze using the computer algebra system MACSYMA and the numerical bifurcation software AUTO. Our motivation for studying this system comes from the presence of circadian rhythms in the chemistry of the eyes. We model the circadian oscillator in each eye as a van der Pol oscillator. Although there is no direct connection between the two eyes, they are both connected to the brain, especially to the pineal gland, which is here represented by a third van der Pol oscillator.
Phase-flip and oscillation-quenching-state transitions through environmental diffusive coupling
NASA Astrophysics Data System (ADS)
Sharma, Amit; Verma, Umesh Kumar; Shrimali, Manish Dev
2016-12-01
We study the dynamics of nonlinear oscillators coupled through environmental diffusive coupling. The interaction between the dynamical systems is maintained through its agents which, in turn, interact globally with each other in the common dynamical environment. We show that this form of coupling scheme can induce an important transition like phase-flip transition as well transitions among oscillation quenching states in identical limit-cycle oscillators. This behavior is analyzed in the parameter plane by analytical and numerical studies of specific cases of the Stuart-Landau oscillator and van der Pol oscillator. Experimental evidences of the phase-flip transition and quenching states are shown using an electronic version of the van der Pol oscillators.
Collective oscillations and coupled modes in confined microfluidic droplet arrays
NASA Astrophysics Data System (ADS)
Schiller, Ulf D.; Fleury, Jean-Baptiste; Seemann, Ralf; Gompper, Gerhard
Microfluidic droplets have a wide range of applications ranging from analytic assays in cellular biology to controlled mixing in chemical engineering. Ensembles of microfluidic droplets are interesting model systems for non-equilibrium many-body phenomena. When flowing in a microchannel, trains of droplets can form microfluidic crystals whose dynamics are governed by long-range hydrodynamic interactions and boundary effects. In this contribution, excitation mechanisms for collective waves in dense and confined microfluidic droplet arrays are investigated by experiments and computer simulations. We demonstrate that distinct modes can be excited by creating specific `defect' patterns in flowing droplet trains. While longitudinal modes exhibit a short-lived cascade of pairs of laterally displacing droplets, transversely excited modes form propagating waves that behave like microfluidic phonons. We show that the confinement induces a coupling between longitudinal and transverse modes. We also investigate the life time of the collective oscillations and discuss possible mechanisms for the onset of instabilities. Our results demonstrate that microfluidic phonons can exhibit effects beyond the linear theory, which can be studied particularly well in dense and confined systems. This work was supported by Deutsche Forschungsgemeinschaft under Grant No. SE 1118/4.
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.
NASA Astrophysics Data System (ADS)
Jia, Ji; Shangguan, Zhichun; Li, Haihong; Wu, Ye; Liu, Weiqing; Xiao, Jinghua; Kurths, Jürgen
2016-11-01
Upside-down bottles containing water which are common in our daily life exhibit rich vibration dynamics. Rich dynamic regimes are observed in bottle oscillators by directly measuring the pressure difference between inside and outside of a bottle with the aid of pressure sensors. We observe experimentally that an asymmetrical oscillation process between the outflow of water and the inflow of air is formed in a single bottle oscillator and, in addition, a kind of 2:1 frequency synchronization occurs in a coupled system of two non-identical bottle oscillators. The peak values of the oscillation of pressure differences between inside and outside of the bottle decease as the height of the liquid surface steps down, while the oscillation period increases gradually. The theoretical model of the oscillator is amended to understand the regimes in the experiment by introducing time-dependent parameters related to the asymmetrical oscillation processes. Our numerical results based on the model fit well with the experimental ones.
Implication of Two-Coupled Differential Van der Pol Duffing Oscillator in Weak Signal Detection
NASA Astrophysics Data System (ADS)
Peng, Hang-hang; Xu, Xue-mei; Yang, Bing-chu; Yin, Lin-zi
2016-04-01
The principle of the Van der Pol Duffing oscillator for state transition and for determining critical value is described, which has been studied to indicate that the application of the Van der Pol Duffing oscillator in weak signal detection is feasible. On the basis of this principle, an improved two-coupled differential Van der Pol Duffing oscillator is proposed which can identify signals under any frequency and ameliorate signal-to-noise ratio (SNR). The analytical methods of the proposed model and the construction of the proposed oscillator are introduced in detail. Numerical experiments on the properties of the proposed oscillator compared with those of the Van der Pol Duffing oscillator are carried out. Our numerical simulations have confirmed the analytical treatment. The results demonstrate that this novel oscillator has better detection performance than the Van der Pol Duffing oscillator.
Decoherence of a quantum harmonic oscillator monitored by a Bose-Einstein condensate
Brouard, S.; Alonso, D.; Sokolovski, D.
2011-07-15
We investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double-well potential. It is demonstrated that the oscillator may experience various degrees of decoherence depending on the variable being measured and the state in which the BEC is prepared. These range from a ''coherent'' regime in which only the variances of the oscillator position and momentum are affected by measurement, to a slow (power-law) or rapid (Gaussian) decoherence of the mean values themselves.
Universal control of an oscillator with dispersive coupling to a qubit
NASA Astrophysics Data System (ADS)
Krastanov, Stefan; Heeres, Reinier; Reinhold, Philip; Albert, Victor V.; Shen, Chao; Zou, Chang-Ling; Vlastakis, Brian; Schoelkopf, Robert; Jiang, Liang
2016-05-01
We investigate quantum control of an oscillator mode that dispersively couples to an ancillary qubit. In the strong dispersive regime, we may drive the qubit conditioned on the selected number states of the oscillator, which enables selective number-dependent arbitrary phase (SNAP) operation and universal control of the oscillator. We provide explicit constructions for arbitrary state preparation and arbitrary unitary operation of the oscillator. Moreover, using optimal control techniques, we develop fast and efficient pulse sequences to achieve high fidelity unitary gates. This universal control scheme of the oscillator can readily be implemented using superconducting circuits. Supported by ARO, AFOSR MURI, Sloan Foundation, and Packard Foundation.
Synchronization and quorum sensing in an ensemble of indirectly coupled chaotic oscillators
NASA Astrophysics Data System (ADS)
Li, Bing-Wei; Fu, Chenbo; Zhang, Hong; Wang, Xingang
2012-10-01
The fact that the elements in some realistic systems are influenced by each other indirectly through a common environment has stimulated a new surge of studies on the collective behavior of coupled oscillators. Most of the previous studies, however, consider only the case of coupled periodic oscillators, and it remains unknown whether and to what extent the findings can be applied to the case of coupled chaotic oscillators. Here, using the population density and coupling strength as the tuning parameters, we explore the synchronization and quorum sensing behaviors in an ensemble of chaotic oscillators coupled through a common medium, in which some interesting phenomena are observed, including the appearance of the phase synchronization in the process of progressive synchronization, the various periodic oscillations close to the quorum sensing transition, and the crossover of the critical population density at the transition. These phenomena, which have not been reported for indirectly coupled periodic oscillators, reveal a corner of the rich dynamics inherent in indirectly coupled chaotic oscillators, and are believed to have important implications to the performance and functionality of some realistic systems.
NASA Astrophysics Data System (ADS)
Ghosh, Debarati; Banerjee, Tanmoy
2014-12-01
We report the transitions among different oscillation quenching states induced by the interplay of diffusive (direct) coupling and environmental (indirect) coupling in coupled identical oscillators. This coupling scheme was introduced by Resmi et al. [Phys. Rev. E 84, 046212 (2011), 10.1103/PhysRevE.84.046212] as a general scheme to induce amplitude death (AD) in nonlinear oscillators. Using a detailed bifurcation analysis we show that, in addition to AD, which actually occurs only in a small region of parameter space, this coupling scheme can induce other oscillation quenching states, namely oscillation death (OD) and a novel nontrvial AD (NAD) state, which is a nonzero bistable homogeneous steady state; more importantly, this coupling scheme mediates a transition from the AD state to the OD state and a new transition from the AD state to the NAD state. We identify diverse routes to the NAD state and map all the transition scenarios in the parameter space for periodic oscillators. Finally, we present the first experimental evidence of oscillation quenching states and their transitions induced by the interplay of direct and indirect coupling.
Lin, J. Y. Y.; Aczel, Adam A; Abernathy, Douglas L; Nagler, Stephen E; Buyers, W. J. L.; Granroth, Garrett E
2014-01-01
Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of- flight chopper spectrometers [A.A. Aczel et al, Nature Communications 3, 1124 (2012)]. These modes are well described by 3D isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for the nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states (PDOS), and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T-dependence of the scattering from these modes is strongly influenced by the uranium lattice.
NASA Astrophysics Data System (ADS)
Lin, J. Y. Y.; Aczel, A. A.; Abernathy, D. L.; Nagler, S. E.; Buyers, W. J. L.; Granroth, G. E.
2014-04-01
Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of-flight chopper spectrometers [A. A. Aczel et al., Nat. Commun. 3, 1124 (2012), 10.1038/ncomms2117]. These modes are well described by three-dimensional isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states, and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature-dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T dependence of the scattering from these modes is strongly influenced by the uranium lattice.
NASA Technical Reports Server (NTRS)
Bgattacharyya, Sudip; Strohmayer, E.
2005-01-01
We report on a study of the evolution of burst oscillation properties during the rising phase of X-ray bursts from 4U 1636-536 observed with the proportional counter array (PCA) on board the Rossi X-Ray Timing Explorer (RXTE) . We present evidence for significant harmonic structure of burst oscillation pulses during the early rising phases of bursts. This is the first such detection in burst rise oscillations, and is very important for constraining neutron star structure parameters and the equation of state models of matter at the core of a neutron star. The detection of harmonic content only during the initial portions of the burst rise is consistent with the theoretical expectation that with time the thermonuclear burning region becomes larger, and hence the fundamental and harmonic amplitudes both diminish. We also find, for the first time from this source, strong evidence of oscillation frequency increase during the burst rise. The timing behavior of harmonic content, amplitude, and frequency of burst rise oscillations may be important in understanding the spreading of thermonuclear flames under the extreme physical conditions on neutron star surfaces.
Coupling dynamics of Nb/Nb2O5 relaxation oscillators
NASA Astrophysics Data System (ADS)
Li, Shuai; Liu, Xinjun; Nandi, Sanjoy Kumar; Venkatachalam, Dinesh Kumar; Elliman, Robert Glen
2017-03-01
The coupling dynamics of capacitively coupled Nb/Nb2O5 relaxation oscillators are shown to exhibit rich collective behaviour depending on the negative differential resistance response of the individual devices, the operating voltage and the coupling capacitance. These coupled oscillators are shown to exhibit stable frequency and phase locking states at source voltages as low as 2.2 V, with frequency control in the range from 0.85 to 16.2 MHz and frequency tunability of ∼8 MHz V–1. The experimental realisation of such compact, scalable and low power coupled-oscillator systems is of particular significance for the development and implementation of large oscillator networks in non-Boolean computing architectures.
Coupling dynamics of Nb/Nb2O5 relaxation oscillators.
Li, Shuai; Liu, Xinjun; Nandi, Sanjoy Kumar; Venkatachalam, Dinesh Kumar; Elliman, Robert Glen
2017-03-24
The coupling dynamics of capacitively coupled Nb/Nb2O5 relaxation oscillators are shown to exhibit rich collective behaviour depending on the negative differential resistance response of the individual devices, the operating voltage and the coupling capacitance. These coupled oscillators are shown to exhibit stable frequency and phase locking states at source voltages as low as 2.2 V, with frequency control in the range from 0.85 to 16.2 MHz and frequency tunability of ∼8 MHz V(-1). The experimental realisation of such compact, scalable and low power coupled-oscillator systems is of particular significance for the development and implementation of large oscillator networks in non-Boolean computing architectures.
Chaotic weak chimeras and their persistence in coupled populations of phase oscillators
NASA Astrophysics Data System (ADS)
Bick, Christian; Ashwin, Peter
2016-05-01
Nontrivial collective behavior may emerge from the interactive dynamics of many oscillatory units. Chimera states are chaotic patterns of spatially localized coherent and incoherent oscillations. The recently-introduced notion of a weak chimera gives a rigorously testable characterization of chimera states for finite-dimensional phase oscillator networks. In this paper we give some persistence results for dynamically invariant sets under perturbations and apply them to coupled populations of phase oscillators with generalized coupling. In contrast to the weak chimeras with nonpositive maximal Lyapunov exponents constructed so far, we show that weak chimeras that are chaotic can exist in the limit of vanishing coupling between coupled populations of phase oscillators. We present numerical evidence that positive Lyapunov exponents can persist for a positive measure set of this inter-population coupling strength.
Control of individual phase relationship between coupled oscillators using multilinear feedback.
Kano, T; Kinoshita, S
2010-02-01
Due to various technological and medical demands, several methods for controlling the dynamical behavior of coupled oscillators have been developed. In the present study, we develop a method to control the individual phase relationship between coupled oscillators, in which multilinear feedback is used to modify the interaction between the oscillators. By carrying out a simulation, we show that the phase relationship can be well controlled by using the proposed method and the control is particularly robust when the target coupling function is selected properly.
Bubbling effect in the electro-optic delayed feedback oscillator coupled network
NASA Astrophysics Data System (ADS)
Liu, Lingfeng; Lin, Jun; Miao, Suoxia
2017-03-01
Synchronization in the optical systems coupled network always suffers from bubbling events. In this paper, we numerically investigate the statistical properties of the synchronization characteristics and bubbling effects in the electro-optic delayed feedback oscillator coupled network with different coupling strength, delay time and gain coefficient. Furthermore, we compare our results with the synchronization properties of semiconductor laser (SL) coupled network, which indicates that the electro-optic delayed feedback oscillator can be better to suppress the bubbling effects in the synchronization of coupled network under the same conditions.
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.
Finite temperature vibronic spectra of harmonic surfaces: a time-dependent coupled cluster approach
NASA Astrophysics Data System (ADS)
Sridhar Reddy, Ch.; Durga Prasad, M.
2015-10-01
An algorithm to compute vibronic spectra of harmonic surfaces including Dushinsky rotation and Hertzberg-Teller terms is described. The method, inspired by thermo field dynamics, maps the thermal density matrix onto the vacuum state and uses the time-dependent coupled cluster ansatz to propagate it in time. In the Franck-Condon approximation where the dipole matrix elements are taken to be constants, this reduces to the auto correlation function of the new vacuum. In the Hertzberg-Teller approximation, the full time evolution operator is needed. This too is governed by a closed set of equations. The theoretical development is presented along with an application to anthracene.
NASA Astrophysics Data System (ADS)
Chen, Hongtao; Slipchenko, Mikhail N.; Zhu, Jiabin; Buhman, Kimberly K.; Cheng, Ji-Xin
2009-02-01
Multimodal nonlinear optical imaging has opened new opportunities and becomes a powerful tool for imaging complex tissue samples with inherent 3D spatial resolution.. We present a robust and easy-to-operate approach to add the coherent anti-stokes Raman scattering (CARS) imaging modality to a widely used multiphoton microscope. The laser source composed of a Mai Tai femtosecond laser and an optical parametric oscillator (OPO) offers one-beam, two-beam and three-beam modalities. The Mai Tai output at 790 nm is split into two beams, with 80% of the power being used to pump the OPO. The idler output at 2036 nm from OPO is doubled using a periodically poled lithium niobate (PPLN) crystal. This frequency-doubled idler beam at 1018 nm is sent through a delay line and collinearly combined with the other Mai Tai beam for CARS imaging on a laser-scanning microscope. This Mai Tai beam is also used for multiphoton fluorescence and second harmonic generation (SHG) imaging. The signal output at 1290 nm from OPO is used for SHG and third-harmonic generation (THG) imaging. External detectors are installed for both forward and backward detection, whereas two internal lamda-scan detectors are employed for microspectroscopy analysis. This new system allows vibrationally resonant CARS imaging of lipid bodies, SHG imaging of collagen fibers, and multiphoton fluorescence analysis in fresh tissues. As a preliminary application, the effect of diacylglycerol acyltransferase 1 (DGAT1) deficiency on liver lipid metabolism in mice was investigated.
Femtosecond Microbunching of Electron Beam in a 7{sup th} Harmonic Coupled IFEL
Tochitsky, S. Ya.; Williams, O. B.; Musumeci, P.; Sung, C.; Haberberger, D. J.; Cook, A. M.; Rosenzweig, J. B.; Joshi, C.
2009-01-22
We report the results of studying electron beam microbunching in a 7{sup th} order IFEL interaction using coherent transition radiation emitted by the bunched beam as a diagnostic. The resonant wavelength for the undulator with a period of 3.3 cm and K = 1.8 is 74.2 {mu}m, but it was seeded by a CO{sub 2} laser with a seven times shorter wavelength of 10.6 {mu}m. The {approx}12.3 MeV electrons were efficiently bunched longitudinally inside a ten period long undulator producing the first, second, and third harmonics in a CTR spectrum. It is shown that in the case of approximately equal sizes of the electron and the seed radiation beams, the IFEL interaction results in transverse variation of bunching which significantly affects the CTR harmonic content. The measurements were compared to the predictions of IFEL simulations. These experimental results demonstrate for the first time feasibility of using very high order harmonic coupling for efficient IFEL/FEL interactions.
Bright multi-keV harmonic generation from relativistically oscillating plasma surfaces.
Dromey, B; Kar, S; Bellei, C; Carroll, D C; Clarke, R J; Green, J S; Kneip, S; Markey, K; Nagel, S R; Simpson, P T; Willingale, L; McKenna, P; Neely, D; Najmudin, Z; Krushelnick, K; Norreys, P A; Zepf, M
2007-08-24
The first evidence of x-ray harmonic radiation extending to 3.3 A, 3.8 keV (order n>3200) from petawatt class laser-solid interactions is presented, exhibiting relativistic limit efficiency scaling (eta approximately n{-2.5}-n{-3}) at multi-keV energies. This scaling holds up to a maximum order, n{RO} approximately 8{1/2}gamma;{3}, where gamma is the relativistic Lorentz factor, above which the first evidence of an intensity dependent efficiency rollover is observed. The coherent nature of the generated harmonics is demonstrated by the highly directional beamed emission, which for photon energy hnu>1 keV is found to be into a cone angle approximately 4 degrees , significantly less than that of the incident laser cone (20 degrees ).
Transverse mode coupling and supermode establishment in a free-electron laser oscillator
Pinhasi, Y.; Gover, A.
1995-12-31
A three-dimensional study of transverse mode evolution in a free-electron laser (FEL) oscillator is presented. The total electromagnetic field circulating in the resonator is represented as a superposition of transverse modes of the cavity. Coupled-mode theory is employed to derive a generalized 3-D steady-state oscillation criterion, from which the oscillator supermode is found analytically. The oscillator supermode keeps its transverse features after each round-trip, and it is the eigenmode solution of the oscillator at steady-state. Relations between the oscillator supermode and the amplifier supermode are discussed. It is shown that they are identical only when the feedback process is entirely non-disperssive and non-discriminating. We employ a 3-D, non-linear simulation code to demonstrate the evolvement of transverse modes in the oscillator towards formation of a supermode. The simulation shows that the resulted supermode is identical to that predicted by the analytical approach.
Coupling mechanism in the gate and oscillator model of the SCN
NASA Astrophysics Data System (ADS)
Li, Ying; Liu, Zengrong
2016-09-01
In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus is considered as the master circadian pacemaker. The SCN is divided into two subgroups of gate and oscillator cells: the ventrolateral (VL) neurons, which receive the periodic light-dark (LD) signal, and the dorsomedial (DM) neurons, which are coupled to the VL cells. The fundamental question is how the individual cellular oscillators, expressing a wide range of periods, interact and assemble to create an integrated pacemaker that can govern behavioral and physiological rhythmicity and be reset by environmental light. The key is that the heterogeneous network formed by the cellular clocks within the SCN must synchronize to maintain timekeeping activity. Based on the structural and functional heterogeneity of the SCN, the authors bring forward a mathematical model including gate cells and oscillator cells with a wide range of periods. The gate neurons offer daily injection to oscillator neurons and the activation of gate is determined by the output of the oscillator neurons. In this model, the authors consider two kinds of coupling: interior coupling among the oscillator cells and exterior coupling from the gate cells to the oscillator cells. The authors mainly analyze the combined effects of these two kinds of coupling on the entrainment of the oscillator cells in the DM part. It is found that the interior coupling is conducive to entrainment, but a stronger coupling is not beneficial to entrainment. The gate mechanism in exterior coupling is more propitious to entrainment than continuous coupling. This study helps to understand collective circadian rhythm in the mammals.
NASA Astrophysics Data System (ADS)
Premalatha, K.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2017-02-01
We show the existence of chimeralike states in two distinct groups of identical populations of globally coupled Stuart-Landau oscillators. The existence of chimeralike states occurs only for a small range of frequency difference between the two populations, and these states disappear for an increase of mismatch between the frequencies. Here the chimeralike states are characterized by the synchronized oscillations in one population and desynchronized oscillations in another population. We also find that such states observed in two distinct groups of identical populations of nonlocally coupled oscillators are different from the above case in which coexisting domains of synchronized and desynchronized oscillations are observed in one population and the second population exhibits synchronized oscillations for spatially prepared initial conditions. Perturbation from such spatially prepared initial condition leads to the existence of imperfectly synchronized states. An imperfectly synchronized state represents the existence of solitary oscillators which escape from the synchronized group in population I and synchronized oscillations in population II. Also the existence of chimera state is independent of the increase of frequency mismatch between the populations. We also find the coexistence of different dynamical states with respect to different initial conditions, which causes multistability in the globally coupled system. In the case of nonlocal coupling, the system does not show multistability except in the cluster state region.
NASA Astrophysics Data System (ADS)
Liu, Q. H.; Zhuo, H.
The Perelomov and the Barut-Girardello SU(1, 1) coherent states for harmonic oscillator in one-dimensional half space are constructed. Results show that the uncertainty products ΔxΔp for these two coherent states are bound from below √ {9/4-6/π } that is the uncertainty for the ground state, and the mean values for position x and momentum p in classical limit go over to their classical quantities respectively. In classical limit, the uncertainty given by Perelomov coherent does not vanish, and the Barut-Girardello coherent state reveals a node structure when positioning closest to the boundary x = 0 which has not been observed in coherent states for other systems.
Effect of spatial distribution on the synchronization in rings of coupled oscillators
NASA Astrophysics Data System (ADS)
Ma, Hongjing; Liu, Weiqing; Wu, Ye; Yang, Yixian; Xiao, Jinghua
2013-10-01
In this paper, the effects of spatial distribution of coupling on the synchronizability are explored in a ring of diffusively coupled oscillators. We find that the inhomogeneity and spatial arrangements of coupling strength have great impacts on the synchronizability. When the inhomogeneous coupling constants are spatially rearranged, the eigenvalues λ2 (the second largest eigenvalue of the coupling matrixes) for all possible spatial arrangements, which may describe the synchronizability of coupled oscillators, obey a log-normal distribution. The spatial arrangement of period 1 achieves the best synchronizability while that of period 2 has the worst one. In addition, the regimes of the effects of spatial distribution on synchronizability are analyzed by a ring of coupled Rossler systems. The spatial rearrangement of coupling has meaningful applications in the manipulation of self- organization for coupled systems.
NASA Astrophysics Data System (ADS)
Scafetta, Nicola
2013-11-01
Power spectra of global surface temperature (GST) records (available since 1850) reveal major periodicities at about 9.1, 10-11, 19-22 and 59-62 years. Equivalent oscillations are found in numerous multisecular paleoclimatic records. The Coupled Model Intercomparison Project 5 (CMIP5) general circulation models (GCMs), to be used in the IPCC Fifth Assessment Report (AR5, 2013), are analyzed and found not able to reconstruct this variability. In particular, from 2000 to 2013.5 a GST plateau is observed while the GCMs predicted a warming rate of about 2 °C/century. In contrast, the hypothesis that the climate is regulated by specific natural oscillations more accurately fits the GST records at multiple time scales. For example, a quasi 60-year natural oscillation simultaneously explains the 1850-1880, 1910-1940 and 1970-2000 warming periods, the 1880-1910 and 1940-1970 cooling periods and the post 2000 GST plateau. This hypothesis implies that about 50% of the ~ 0.5 °C global surface warming observed from 1970 to 2000 was due to natural oscillations of the climate system, not to anthropogenic forcing as modeled by the CMIP3 and CMIP5 GCMs. Consequently, the climate sensitivity to CO2 doubling should be reduced by half, for example from the 2.0-4.5 °C range (as claimed by the IPCC, 2007) to 1.0-2.3 °C with a likely median of ~ 1.5 °C instead of ~ 3.0 °C. Also modern paleoclimatic temperature reconstructions showing a larger preindustrial variability than the hockey-stick shaped temperature reconstructions developed in early 2000 imply a weaker anthropogenic effect and a stronger solar contribution to climatic changes. The observed natural oscillations could be driven by astronomical forcings. The ~ 9.1 year oscillation appears to be a combination of long soli-lunar tidal oscillations, while quasi 10-11, 20 and 60 year oscillations are typically found among major solar and heliospheric oscillations driven mostly by Jupiter and Saturn movements. Solar models based
Breakdown of order preservation in symmetric oscillator networks with pulse-coupling.
Kielblock, Hinrich; Kirst, Christoph; Timme, Marc
2011-06-01
Symmetric networks of coupled dynamical units exhibit invariant subspaces with two or more units synchronized. In time-continuously coupled systems, these invariant sets constitute barriers for the dynamics. For networks of units with local dynamics defined on the real line, this implies that the units' ordering is preserved and that their winding number is identical. Here, we show that in permutation-symmetric networks with pulse-coupling, the order is often no longer preserved. We analytically study a class of pulse-coupled oscillators (characterizing for instance the dynamics of spiking neural networks) and derive quantitative conditions for the breakdown of order preservation. We find that in general pulse-coupling yields additional dimensions to the state space such that units may change their order by avoiding the invariant sets. We identify a system of two symmetrically pulse-coupled identical oscillators where, contrary to intuition, the oscillators' average frequencies and thus their winding numbers are different.
Development of an X-Band Coupled-Oscillator Transmit/Receive Phased Array
NASA Astrophysics Data System (ADS)
Venkatesan, J.; Pogorzelski, R.
2007-08-01
The development of an 8.4 GHz (X-band) coupled-oscillator phased array employing full-duplex transmit and receive capability is described. Attractive features of phased arrays for deep-space communication include enabling high-data-rate communication and providing low-mass electronic beam steering. The coupled-oscillator phased-array concept seeks to reduce the cost and power consumption incurred in a conventional phased array by simplifying the beam-steering mechanism of the array. In this article, the overall system-level architecture of a full-duplex transmit and receive coupled-oscillator array is described, and the progress made in designing various specific components of a linear 1 x 7 coupled-oscillator array is also detailed.
Bloch Oscillations in Optical and Zeeman Lattices in the Presence of Spin-Orbit Coupling
NASA Astrophysics Data System (ADS)
Kartashov, Yaroslav V.; Konotop, Vladimir V.; Zezyulin, Dmitry A.; Torner, Lluis
2016-11-01
We address Bloch oscillations of a spin-orbit coupled atom in periodic potentials of two types: optical and Zeeman lattices. We show that in optical lattices the spin-orbit coupling allows controlling the direction of atomic motion and may lead to complete suppression of the oscillations at specific values of the coupling strength. In Zeeman lattices the energy bands are found to cross each other at the boundaries of the Brillouin zone, resulting in period doubling of the oscillations. In all cases, the oscillations are accompanied by rotation of the pseudospin, with a dynamics that is determined by the strength of the spin-orbit coupling. The predicted effects are discussed also in terms of a Wannier-Stark ladder, which in optical lattices consist of two mutually shifted equidistant subladders.
Quantum noise and squeezing in optical parametric oscillator with arbitrary output coupling
NASA Technical Reports Server (NTRS)
Prasad, Sudhakar
1993-01-01
The redistribution of intrinsic quantum noise in the quadratures of the field generated in a sub-threshold degenerate optical parametric oscillator exhibits interesting dependences on the individual output mirror transmittances, when they are included exactly. We present a physical picture of this problem, based on mirror boundary conditions, which is valid for arbitrary transmittances. Hence, our picture applies uniformly to all values of the cavity Q factor representing, in the opposite extremes, both perfect oscillator and amplifier configurations. Beginning with a classical second-harmonic pump, we shall generalize our analysis to the finite amplitude and phase fluctuations of the pump.
Stable integrated hyper-parametric oscillator based on coupled optical microcavities.
Armaroli, Andrea; Feron, Patrice; Dumeige, Yannick
2015-12-01
We propose a flexible scheme based on three coupled optical microcavities that permits us to achieve stable oscillations in the microwave range, the frequency of which depends only on the cavity coupling rates. We find that the different dynamical regimes (soft and hard excitation) affect the oscillation intensity, but not their periods. This configuration may permit us to implement compact hyper-parametric sources on an integrated optical circuit with interesting applications in communications, sensing, and metrology.
NASA Astrophysics Data System (ADS)
Walsh, Gary F.; Trevino, Jacob T.; Pecora, Emanuele Francesco; Dal Negro, Luca
2015-09-01
Scattering by plasmon resonances of metallic nanoparticles can be tailored by particle material, size, shape, and local as well as long-range order. In this presentation we discuss a series of experiments in which long-range Fano-type coupling between grating resonances and localized surface palsmon (LSP) resonances were studied using second harmonic excitation (SH-E) spectroscopy. By tuning the excitation wavelength of a femtosecond laser and measuring the relative second harmonic (SH) signal we demonstrated that when long-range grating resonances spectrally overlap with those of the LSPs, electromagnetic field enhancement occurs on the surface of the nanoparticles leading to an increase in nonlinear scattering. This effect has been demonstrated for periodic arrays of monomers and dimers, bi-periodic antenna arrays for multi-spectral focusing to a single point, and chirped nanoparticle structures for broadband field enhancement. Results are supported by finite difference time domain simulations showing that electromagnetic fields are enhanced close on the surface of the nanoparticles when long-range structural resonances are excited. These studies have revealed design principles for engineering the interplay of photonic and plasmonic coupling for future linear and nonlinear plasmonic devices.
Geometrical and Anderson transitions in harmonic chains with constrained long-range couplings.
Morais, P A; Andrade, J S; Nascimento, E M; Lyra, M L
2011-10-01
Low-dimensional systems with long-range couplings usually present phase transitions which are absent in the short-ranged counterpart model. In this work, we show that a harmonic chain with long-range couplings restricted by a cost function proportional to the chain length N exhibits two distinct phase transitions. In the present model, two sites at a distance r>1 are connected by a spring with probability 1/r(α) with the constraint that the total length of the non-nearest-neighbor couplings is limited to λN, where λ is a cost parameter. A geometrical phase transition is found at α=1.5 between a phase with a finite number of long-range couplings and a phase on which the number of long-range couplings is proportional to the system size. Further, the normal vibrational modes of this chain display a phase transition from delocalized to localized modes at a smaller value of α. Maximum effective disorder is reached at α=2 for which the frequency of the lowest vibrational mode exhibits a pronounced peak.
Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode.
Verhagen, E; Deléglise, S; Weis, S; Schliesser, A; Kippenberg, T J
2012-02-01
Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions, molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities. If the optomechanical coupling is 'quantum coherent'--that is, if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate--quantum states are transferred from the optical field to the mechanical oscillator and vice versa. This transfer allows control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far, however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at millikelvin temperatures. Optical experiments have not attained this regime owing to the large mechanical decoherence rates and the difficulty of overcoming optical dissipation. Here we achieve quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of 1.7 ± 0.1 motional quanta. Excitation with weak classical light pulses reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibres. Our results offer a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links.
Self-feedback electrically coupled spin-Hall oscillator array for pattern-matching operation
NASA Astrophysics Data System (ADS)
Kudo, Kiwamu; Morie, Takashi
2017-04-01
An oscillator array has been proposed for associative memory, in which the synchronization of multiple oscillators is utilized for pattern-matching operations. An input pattern is represented by a set of frequency shifts of the oscillators and the matching result is attributed to the degree of synchronization. Here, we propose an electrically coupled spin-Hall oscillator (SHO) array in which multiple SHOs exhibit synchronization by interacting with each other through self-feedback spin torques. We numerically demonstrate the pattern matching functionality of the proposed SHO array.
NASA Astrophysics Data System (ADS)
Pecora, Louis
2001-03-01
We show here that it is possible to solve, once and for all, the stability problem of synchronizing any array of identical oscillators , whether chaotic or limit cycle. The scheme gives a master stability function. We apply this to a system of 8 coupled Rossler-like circuits. We further show that this approach allows an experimental probe of the stability of any array of any number of identical oscillators using only three oscillators. Finally, the synchronization of oscillators in smallworld systems is understandable using a master stability approach.
NASA Astrophysics Data System (ADS)
De Rosis, Alessandro
2014-12-01
In this paper, a rigid thickless lamina is immersed in a quiescent viscous fluid and it undergoes transverse finite amplitude harmonic oscillations near a solid surface. The surrounding flow physics is computed through the lattice Boltzmann method. In order to account for the presence of the lamina in the lattice fluid background, the Immersed Boundary method is adopted. Several scenarios are investigated by varying the distance between the initial position of the lamina and the solid wall. For a given lamina-solid surface distance, the effect of the Reynolds number is investigated, together with the influence of the Keulegan-Carpenter number. Findings in terms of drag coefficient show that the force exerted by the encompassing fluid upon the lamina is remarkably influenced by the distance from the solid surface, especially for low values of the Reynolds number. Moreover, such results are confirmed by the computation of the hydrodynamic function. In fact, it highlights that the added mass effect and the non-linear damping experienced by the oscillating lamina grow as the above mentioned distance and the Reynolds number reduce.
Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling.
Komarov, Maxim; Pikovsky, Arkady
2015-08-01
We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent approach and direct numerical simulations, we argue that a transition to synchrony occurs only for finite-size ensembles and disappears in the thermodynamic limit. For all considered setups, which include purely deterministic oscillators with or without heterogeneity in natural oscillatory frequencies, and an ensemble of noise-driven identical oscillators, we establish scaling relations describing the order parameter as a function of the coupling constant and the system size.
Experimental Observation of Multifrequency Patterns in Arrays of Coupled Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
in, Visarath; Kho, Andy; Neff, Joseph D.; Palacios, Antonio; Longhini, Patrick; Meadows, Brian K.
2003-12-01
Frequency-related oscillations in coupled oscillator systems, in which one or more oscillators oscillate at different frequencies than the other oscillators, have been studied using group theoretical methods by Armbruster and Chossat [
1988-08-15
could. The criterion for the validity of semiclassical calculation is that, for given initial oscillator and incident energies, the ;% possible...This is an expression of the correspondence principle. As is well known, suitable semiclassical calculations may give rather accurate results even when...follows: I "> - Ikot> + Co +’ VKT >, (6) where ;o,> is the normalized eigen function of Ho and Go is the Green s function, defined by ’,.4 G lim (7) -oE-Ho
Limits to detection of generalized synchronization in delay-coupled chaotic oscillators.
Kato, Hideyuki; Soriano, Miguel C; Pereda, Ernesto; Fischer, Ingo; Mirasso, Claudio R
2013-12-01
We study how reliably generalized synchronization can be detected and characterized from time-series analysis. To that end, we analyze synchronization in a generalized sense of delay-coupled chaotic oscillators in unidirectional ring configurations. The generalized synchronization condition can be verified via the auxiliary system approach; however, in practice, this might not always be possible. Therefore, in this study, widely used indicators to directly quantify generalized and phase synchronization from noise-free time series of two oscillators are employed complementarily to the auxiliary system approach. In our analysis, none of the indices provide the consistent results of the auxiliary system approach. Our findings indicate that it is a major challenge to directly detect synchronization in a generalized sense between two oscillators that are connected via a chain of other oscillators, even if the oscillators are identical. This has major consequences for the interpretation of the dynamics of coupled systems and applications thereof.
Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators
Locatelli, Nicolas; Hamadeh, Abbass; Abreu Araujo, Flavio; Belanovsky, Anatoly D.; Skirdkov, Petr N.; Lebrun, Romain; Naletov, Vladimir V.; Zvezdin, Konstantin A.; Muñoz, Manuel; Grollier, Julie; Klein, Olivier; Cros, Vincent; de Loubens, Grégoire
2015-01-01
Due to their nonlinear properties, spin transfer nano-oscillators can easily adapt their frequency to external stimuli. This makes them interesting model systems to study the effects of synchronization and brings some opportunities to improve their microwave characteristics in view of their applications in information and communication technologies and/or to design innovative computing architectures. So far, mutual synchronization of spin transfer nano-oscillators through propagating spinwaves and exchange coupling in a common magnetic layer has been demonstrated. Here we show that the dipolar interaction is also an efficient mechanism to synchronize neighbouring oscillators. We experimentally study a pair of vortex-based spin transfer nano-oscillators, in which mutual synchronization can be achieved despite a significant frequency mismatch between oscillators. Importantly, the coupling efficiency is controlled by the magnetic configuration of the vortices, as confirmed by an analytical model and micromagnetic simulations highlighting the physics at play in the synchronization process. PMID:26608230
Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators
NASA Astrophysics Data System (ADS)
Locatelli, Nicolas; Hamadeh, Abbass; Abreu Araujo, Flavio; Belanovsky, Anatoly D.; Skirdkov, Petr N.; Lebrun, Romain; Naletov, Vladimir V.; Zvezdin, Konstantin A.; Muñoz, Manuel; Grollier, Julie; Klein, Olivier; Cros, Vincent; de Loubens, Grégoire
2015-11-01
Due to their nonlinear properties, spin transfer nano-oscillators can easily adapt their frequency to external stimuli. This makes them interesting model systems to study the effects of synchronization and brings some opportunities to improve their microwave characteristics in view of their applications in information and communication technologies and/or to design innovative computing architectures. So far, mutual synchronization of spin transfer nano-oscillators through propagating spinwaves and exchange coupling in a common magnetic layer has been demonstrated. Here we show that the dipolar interaction is also an efficient mechanism to synchronize neighbouring oscillators. We experimentally study a pair of vortex-based spin transfer nano-oscillators, in which mutual synchronization can be achieved despite a significant frequency mismatch between oscillators. Importantly, the coupling efficiency is controlled by the magnetic configuration of the vortices, as confirmed by an analytical model and micromagnetic simulations highlighting the physics at play in the synchronization process.
NASA Astrophysics Data System (ADS)
Wan, Yu; Jin, Kai; Ahmad, Talha J.; Black, Michael J.; Xu, Zhiping
2017-03-01
Fluidic environment is encountered for mechanical components in many circumstances, which not only damps the oscillation but also modulates their dynamical behaviors through hydrodynamic interactions. In this study, we examine energy transfer and motion synchronization between two mechanical micro-oscillators by performing thermal lattice-Boltzmann simulations. The coefficient of inter-oscillator energy transfer is measured to quantify the strength of microhydrodynamic coupling, which depends on their distance and fluid properties such as density and viscosity. Synchronized motion of the oscillators is observed in the simulations for typical parameter sets in relevant applications, with the formation and loss of stable anti-phase synchronization controlled by the oscillating frequency, amplitude, and hydrodynamic coupling strength. The critical ranges of key parameters to assure efficient energy transfer or highly synchronized motion are predicted. These findings could be used to advise mechanical design of passive and active devices that operate in fluid.
An analytical and numerical study of the bifurcations in a system of linearly-coupled oscillators
NASA Astrophysics Data System (ADS)
Aronson, D. G.; Doedel, E. J.; Othmer, H. G.
1987-03-01
We study a two-parameter family of ordinary differential equations in R 4 that governs the dynamics of two coupled planar oscillators. Each oscillator has a unique periodic solution that is attracting and the uncoupled product system has a unique invariant torus that is attracting. The torus persists for weak coupling and contains two periodic solutions when the coupling is linear and conservative. One of these, in which the oscillators are synchronized, persists and is stable for all coupling strengths. The other, in which the oscillators are π radiant out of phase, disappears either in a Hopf bifurcation or when fixed points appear on the orbit at a critical ratio of the coupling strength to the frequency. The out-of-phase oscillation is unstable except on an open set in the frequency-coupling-strength plane which contains moderate values of both parameters. Furthermore, there are tori bifurcating from the out-of-phase solution, which means, according to the Arnol'd theory for Hopf bifurcations in maps, that there may be periodic solutions of arbitrarily large period and chaotic solutions as well. Numerous other bifurcations occur, and there are a number of higher codimension singularities. In a large region of the frequency-coupling parameter plane stable steady states coexist with stable periodic solutions.
The bistability phenomenon in single and coupled oscillators based on VO2 switches
NASA Astrophysics Data System (ADS)
Belyaev, M. A.; Putrolaynen, V. V.; Velichko, A. A.
2017-01-01
New operation regimes of single and coupled oscillators in circuits based on planar VO2 switches have been studied. The phenomenon of bistability is discovered, which consists in controlled switching of self-sustained oscillations by external pulses, which is a promising basis for the creation of oscillatory memory cells and implementation of pulse coupling regimes in artificial neural networks (ANNs). The duration of switch-on and switch-off pulses is no less that 20 μs and 30 ms, respectively. It is established that the region of threshold voltages for bistable switching in coupled oscillators is much wider than in a single oscillator and the hysteresis width in the former case can reach 2 V. A regime of initiation of switching packets has been observed that models the ANN packet activity.
Amplitude and phase effects on the synchronization of delay-coupled oscillators
D'Huys, O.; Vicente, R.; Danckaert, J.; Fischer, I.
2010-12-15
We consider the behavior of Stuart-Landau oscillators as generic limit-cycle oscillators when they are interacting with delay. We investigate the role of amplitude and phase instabilities in producing symmetry-breaking/restoring transitions. Using analytical and numerical methods we compare the dynamics of one oscillator with delayed feedback, two oscillators mutually coupled with delay, and two delay-coupled elements with self-feedback. Taking only the phase dynamics into account, no chaotic dynamics is observed, and the stability of the identical synchronization solution is the same in each of the three studied networks of delay-coupled elements. When allowing for a variable oscillation amplitude, the delay can induce amplitude instabilities. We provide analytical proof that, in case of two mutually coupled elements, the onset of an amplitude instability always results in antiphase oscillations, leading to a leader-laggard behavior in the chaotic regime. Adding self-feedback with the same strength and delay as the coupling stabilizes the system in the transverse direction and, thus, promotes the onset of identically synchronized behavior.
Aouani, Heykel; Rahmani, Mohsen; Navarro-Cía, Miguel; Maier, Stefan A
2014-04-01
The ability to convert low-energy quanta into a quantum of higher energy is of great interest for a variety of applications, including bioimaging, drug delivery and photovoltaics. Although high conversion efficiencies can be achieved using macroscopic nonlinear crystals, upconverting light at the nanometre scale remains challenging because the subwavelength scale of materials prevents the exploitation of phase-matching processes. Light-plasmon interactions that occur in nanostructured noble metals have offered alternative opportunities for nonlinear upconversion of infrared light, but conversion efficiency rates remain extremely low due to the weak penetration of the exciting fields into the metal. Here, we show that third-harmonic generation from an individual semiconductor indium tin oxide nanoparticle is significantly enhanced when coupled within a plasmonic gold dimer. The plasmonic dimer acts as a receiving optical antenna, confining the incident far-field radiation into a near field localized at its gap; the indium tin oxide nanoparticle located at the plasmonic dimer gap acts as a localized nonlinear transmitter upconverting three incident photons at frequency ω into a photon at frequency 3ω. This hybrid nanodevice provides third-harmonic-generation enhancements of up to 10(6)-fold compared with an isolated indium tin oxide nanoparticle, with an effective third-order susceptibility up to 3.5 × 10(3) nm V(-2) and conversion efficiency of 0.0007%. We also show that the upconverted third-harmonic emission can be exploited to probe the near-field intensity at the plasmonic dimer gap.
NASA Astrophysics Data System (ADS)
Ishifuji, Miki; Mitsuishi, Masaya; Miyashita, Tokuji
2006-07-01
Effective utilization of coupled surface plasmon resonance from gold nanoparticles was demonstrated experimentally for optoelectronic applications based on second-order nonlinear optics. Hybrid polymer nanoassemblies were constructed by manipulating gold nanoparticle arrays with nonlinear optical active polymer nanosheets to investigate the second harmonic generation. The gold nanoparticle arrays were assembled on heterodeposited polymer nanosheets. The second harmonic light intensity was enhanced by a factor of 8. The observed enhancement was attributed to coupling of surface plasmons between two adjacent gold nanoparticles, thereby enhancing the surface electromagnetic field around the nanoparticles at the fundamental light wavelength (1064nm).
Nonlinear coupled rotor-fuselage helicopter vibration studies with higher harmonic control
NASA Technical Reports Server (NTRS)
Friedmann, P. P.; Venkatesan, C.; Papavassiliou, I.
1990-01-01
This paper addresses the problem of vibration prediction and vibration reduction in helicopters by means of active control methodologies. The nonlinear equations of a coupled rotor/flexible-fuselage system have been derived using computer algebra, thus relegating this tedious task to the computer. In the solution procedure the trim state and vibratory response of the helicopter are obtained in a single pass by using a harmonic balance technique and simultaneously satisfying the trim and the vibratory response of the helicopter in all the rotor and fuselage degrees of freedom. Using this solution procedure, the influence of the fuselage flexibility on the vibratory response is studied. In addition, it is shown that the conventional single frequency HHC is capable of reducing either the hub loads or only the fuselage vibrations but not both simultaneously. A new scheme called MHHC, having multiple higher harmonic pitch inputs, was used to accomplish this task of simultaneously reducing both the vibratory hub loads and fuselage vibratory response. In addition, the uniqueness of this MHHC scheme is explained in detail.
Two pulse-coupled non-identical, frequency-different BZ oscillators with time delay.
Lavrova, Anastasia I; Vanag, Vladimir K
2014-04-14
Two non-identical, frequency-different pulse-coupled oscillators with time delay have been systematically studied using four-variable model of the Belousov-Zhabotinsky (BZ) reaction at mutual inhibitory, mutual excitatory, and mixed excitatory-inhibitory types of coupling. Different resonances like 1 : 2, 2 : 3, 1 : 3, etc., as well as complex rhythms and abrupt changes between them occur depending on the coupling strengths, time delay, and frequency ratio. Analogously to in-phase and anti-phase oscillations for 1 : 1 resonance, a similar phase locking exists for 1 : 2 resonance in the case of inhibitory coupling. For excitatory coupling, a bursting regime is found. The number of spikes in a single burst can be tuned by both the frequency ratio and time delay. For excitatory-inhibitory coupling, a region where one oscillator is suppressed (OS zone) has been found. Boundary of the OS zone depends on the frequency ratio. For weakly coupled oscillators, Farey sequence has been found for excitatory-inhibitory and mutual excitatory coupling.
Synchronization of coupled noisy oscillators: Coarse graining from continuous to discrete phases
NASA Astrophysics Data System (ADS)
Escaff, Daniel; Rosas, Alexandre; Toral, Raúl; Lindenberg, Katja
2016-11-01
The theoretical description of synchronization phenomena often relies on coupled units of continuous time noisy Markov chains with a small number of states in each unit. It is frequently assumed, either explicitly or implicitly, that coupled discrete-state noisy Markov units can be used to model mathematically more complex coupled noisy continuous phase oscillators. In this work we explore conditions that justify this assumption by coarse graining continuous phase units. In particular, we determine the minimum number of states necessary to justify this correspondence for Kuramoto-like oscillators.
Synchronization of coupled noisy oscillators: Coarse graining from continuous to discrete phases.
Escaff, Daniel; Rosas, Alexandre; Toral, Raúl; Lindenberg, Katja
2016-11-01
The theoretical description of synchronization phenomena often relies on coupled units of continuous time noisy Markov chains with a small number of states in each unit. It is frequently assumed, either explicitly or implicitly, that coupled discrete-state noisy Markov units can be used to model mathematically more complex coupled noisy continuous phase oscillators. In this work we explore conditions that justify this assumption by coarse graining continuous phase units. In particular, we determine the minimum number of states necessary to justify this correspondence for Kuramoto-like oscillators.
Snyder, Gregory R; Chowdhury, Azhad U; Simpson, Garth J
2014-06-19
A simple model is presented for interpreting the presence of substantial second harmonic generation (SHG) activity from assemblies of centrosymmetric molecular building blocks. Using butadiene as a computationally tractable centrosymmetric model system, time-dependent Hartree-Fock calculations of the nonlinear polarizability of butadiene dimer were well-described through exciton coupling arguments based on the electronic structure of the monomer and the relative orientation between the monomers within the dimer. Experimental studies of the centrosymmetric molecule 2,6-di-tert-butylanthraquinone suggest the formation of a combination of SHG-active and SHG-inactive crystal forms. The structure for the centrosymmetric form is known, serving as a negative control for the model, while the presence of an additional SHG-active metastable form is consistent with predictions of the model for alternative molecular packing configurations.
Anomalous quantum heat transport in a one-dimensional harmonic chain with random couplings.
Yan, Yonghong; Zhao, Hui
2012-07-11
We investigate quantum heat transport in a one-dimensional harmonic system with random couplings. In the presence of randomness, phonon modes may normally be classified as ballistic, diffusive or localized. We show that these modes can roughly be characterized by the local nearest-neighbor level spacing distribution, similarly to their electronic counterparts. We also show that the thermal conductance G(th) through the system decays rapidly with the system size (G(th) ∼ L(-α)). The exponent α strongly depends on the system size and can change from α < 1 to α > 1 with increasing system size, indicating that the system undergoes a transition from a heat conductor to a heat insulator. This result could be useful in thermal control of low-dimensional systems.
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Lepri, Stefano; Pikovsky, Arkady
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.
Apical oscillations in amnioserosa cells: basolateral coupling and mechanical autonomy.
Jayasinghe, Aroshan K; Crews, Sarah M; Mashburn, David N; Hutson, M Shane
2013-07-02
Holographic laser microsurgery is used to isolate single amnioserosa cells in vivo during early dorsal closure. During this stage of Drosophila embryogenesis, amnioserosa cells undergo oscillations in apical surface area. The postisolation behavior of individual cells depends on their preisolation phase in these contraction/expansion cycles: cells that were contracting tend to collapse quickly after isolation; cells that were expanding do not immediately collapse, but instead pause or even continue to expand for ∼40 s. In either case, the postisolation apical collapse can be prevented by prior anesthetization of the embryos with CO2. These results suggest that although the amnioserosa is under tension, its cells are subjected to only small elastic strains. Furthermore, their postisolation apical collapse is not a passive elastic relaxation, and both the contraction and expansion phases of their oscillations are driven by intracellular forces. All of the above require significant changes to existing computational models.
Apical Oscillations in Amnioserosa Cells: Basolateral Coupling and Mechanical Autonomy
Jayasinghe, Aroshan K.; Crews, Sarah M.; Mashburn, David N.; Hutson, M. Shane
2013-01-01
Holographic laser microsurgery is used to isolate single amnioserosa cells in vivo during early dorsal closure. During this stage of Drosophila embryogenesis, amnioserosa cells undergo oscillations in apical surface area. The postisolation behavior of individual cells depends on their preisolation phase in these contraction/expansion cycles: cells that were contracting tend to collapse quickly after isolation; cells that were expanding do not immediately collapse, but instead pause or even continue to expand for ∼40 s. In either case, the postisolation apical collapse can be prevented by prior anesthetization of the embryos with CO2. These results suggest that although the amnioserosa is under tension, its cells are subjected to only small elastic strains. Furthermore, their postisolation apical collapse is not a passive elastic relaxation, and both the contraction and expansion phases of their oscillations are driven by intracellular forces. All of the above require significant changes to existing computational models. PMID:23823245
How to induce multiple delays in coupled chaotic oscillators?
Bhowmick, Sourav K.; Ghosh, Dibakar; Roy, Prodyot K.; Kurths, Jürgen; Dana, Syamal K.
2013-12-15
Lag synchronization is a basic phenomenon in mismatched coupled systems, delay coupled systems, and time-delayed systems. It is characterized by a lag configuration that identifies a unique time shift between all pairs of similar state variables of the coupled systems. In this report, an attempt is made how to induce multiple lag configurations in coupled systems when different pairs of state variables attain different time shift. A design of coupling is presented to realize this multiple lag synchronization. Numerical illustration is given using examples of the Rössler system and the slow-fast Hindmarsh-Rose neuron model. The multiple lag scenario is physically realized in an electronic circuit of two Sprott systems.
Phase chaos in the dynamics of an ensemble of oscillators with time-modulated global coupling
NASA Astrophysics Data System (ADS)
Kuznetsov, S. P.; Sedova, Yu. V.
2013-01-01
The object of consideration is an ensemble of globally coupled self-sustained oscillating elements with a finite-width frequency distribution. The ensemble interacts with the field of a resonator, which is a linear oscillator with a frequency doubly exceeding the mean frequency of the oscillators in the ensemble. The global coupling is switched on and off alternately, so that the ensemble alternatively passes from synchrony to asynchrony (Kuramoto transition). At each stage of activity (synchronization), the field of the resonator causes the mean field of the ensemble to oscillate so that the phase doubles compared with the previous stage of excitation. Therefore, the mean field dynamics is chaotic and, as follows from numerical simulation data, can be associated with the Smale-Williams attractor. Systems of this type can be applied in electronics, specifically, in secure communication systems, noise location, etc.
Thoke, Henrik Seir; Tobiesen, Asger; Brewer, Jonathan; Hansen, Per Lyngs; Stock, Roberto P.; Olsen, Lars F.; Bagatolli, Luis A.
2015-01-01
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 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 D2O 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. PMID:25705902
Quantum synchronization of chaotic oscillator behaviors among coupled BEC-optomechanical systems
NASA Astrophysics Data System (ADS)
Li, Wenlin; Li, Chong; Song, Heshan
2017-03-01
We consider and theoretically analyze a Bose-Einstein condensate (BEC) trapped inside an optomechanical system consisting of single-mode optical cavity with a moving end mirror. The BEC is formally analogous to a mirror driven by radiation pressure with strong nonlinear coupling. Such a nonlinear enhancement can make the oscillator display chaotic behavior. By establishing proper oscillator couplings, we find that this chaotic motion can be synchronized with other oscillators, even an oscillator network. We also discuss the scheme feasibility by analyzing recent experiment parameters. Our results provide a promising platform for the quantum signal transmission and quantum logic control, and they are of potential applications in quantum information processing and quantum networks.
Correlated dynamics of a Rabi oscillation and a quantum tunneling in coupled quantum dots
NASA Astrophysics Data System (ADS)
Xie, Weidong; Chu, Bingxin; Duan, Suqing; Xie, Yan; Chu, Weidong; Yang, Ning; Zhao, Xian-Geng
2015-08-01
We couple the Rabi oscillation in a double quantum dot (DQD) with the quantum tunneling in another DQD by Coulomb interaction between the neighboring dots. Such a coupling leads to correlation of the Rabi oscillating electron and the quantum tunneling one, and gives a tendency of synchronizing them under appropriate Rabi frequency ΩR and tunneling rate Tc. The correlated oscillation is shown clearly in the tunneling current. As ΩR =Tc, the Rabi oscillation and the quantum tunneling reach their strongest correlation and the two electrons finish their complete transitions simultaneously. And then, a single optical signal accomplishes a gang control of two electrons. This result encourages superior design of two-qubit quantum gates based on correlated DQDs.
Zhu, Yenan; Hsieh, Yee-Hsee; Dhingra, Rishi R.; Dick, Thomas E.; Jacono, Frank J.; Galán, Roberto F.
2013-01-01
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. E 65, 041909 (2002); M. G. Rosenblum and A. S. Pikovsky, Phys. Rev. E 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. PMID:23496550
NASA Astrophysics Data System (ADS)
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.
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.
NASA Astrophysics Data System (ADS)
Nkomo, Simbarashe; Tinsley, Mark R.; Showalter, Kenneth
2016-09-01
Chimera and chimera-like states are characterized in populations of photochemically coupled Belousov-Zhabotinsky (BZ) oscillators. Simple chimeras and chimera states with multiple and traveling phase clusters, phase-slip behavior, and chimera-like states with phase waves are described. Simulations with a realistic model of the discrete BZ system of populations of homogeneous and heterogeneous oscillators are compared with each other and with experimental behavior.
Linear stability and the Braess paradox in coupled-oscillator networks and electric power grids.
Coletta, Tommaso; Jacquod, Philippe
2016-03-01
We investigate the influence that adding a new coupling has on the linear stability of the synchronous state in coupled-oscillator networks. Using a simple model, we show that, depending on its location, the new coupling can lead to enhanced or reduced stability. We extend these results to electric power grids where a new line can lead to four different scenarios corresponding to enhanced or reduced grid stability as well as increased or decreased power flows. Our analysis shows that the Braess paradox may occur in any complex coupled system, where the synchronous state may be weakened and sometimes even destroyed by additional couplings.
Signatures of the A2 term in ultrastrongly coupled oscillators
NASA Astrophysics Data System (ADS)
Tufarelli, Tommaso; McEnery, K. R.; Maier, S. A.; Kim, M. S.
2015-06-01
We study a bosonic matter excitation coupled to a single-mode cavity field via electric dipole. Counter-rotating and A2 terms are included in the interaction model, A being the vector potential of the cavity field. In the ultrastrong coupling regime the vacuum of the bare modes is no longer the ground state of the Hamiltonian and contains a nonzero population of polaritons, the true normal modes of the system. If the parameters of the model satisfy the Thomas-Reiche-Kuhn sum rule, we find that the two polaritons are always equally populated. We show how this prediction could be tested in a quenching experiment, by rapidly switching on the coupling and analyzing the radiation emitted by the cavity. A refinement of the model based on a microscopic minimal coupling Hamiltonian is also provided, and its consequences on our results are characterized analytically.
Average dynamics of a finite set of coupled phase oscillators
Dima, Germán C. Mindlin, Gabriel B.
2014-06-15
We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate.
Low-noise sub-harmonic injection locked multiloop ring oscillator
NASA Astrophysics Data System (ADS)
Weilin, Xu; Di, Wu; Xueming, Wei; Baolin, Wei; Jihai, Duan; Fadi, Gui
2016-09-01
A three-stage differential voltage-controlled ring oscillator is presented for wide-tuning and low-phase noise requirement of clock and data recovery circuit in ultra wideband (UWB) wireless body area network. To improve the performance of phase noise of delay cell with coarse and fine frequency tuning, injection locked technology together with pseudo differential architecture are adopted. In addition, a multiloop is employed for frequency boosting. Two RVCOs, the standard RVCO without the IL block and the proposed IL RVCO, were fabricated in SMIC 0.18 μm 1P6M Salicide CMOS process. The proposed IL RVCO exhibits a measured phase noise of -112.37 dBc/Hz at 1 MHz offset from the center frequency of 1 GHz, while dissipating a current of 8 mA excluding the buffer from a 1.8-V supply voltage. It shows a 16.07 dB phase noise improvement at 1 MHz offset compared to the standard topology. Project supported by the National Natural Science Foundation of China (No. 61264001), the Guangxi Natural Science Foundation (Nos. 2013GXNSFAA019333, 2015GXNSFAA139301, 2014GXNSFAA118386), the Graduate Education Innovation Program of GUET (No. GDYCSZ201457), the Project of Guangxi Education Department (No. LD14066B) and the High-Level-Innovation Team and Outstanding Scholar Project of Guangxi Higher Education Institutes.
Yashin, Victor V.; Levitan, Steven P.; Balazs, Anna C.
2015-01-01
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”. PMID:26105979
Gasulla, Ivana; Sancho, Juan; Capmany, José; Lloret, Juan; Sales, Salvador
2010-12-06
We theoretically and experimentally evaluate the propagation, generation and amplification of signal, harmonic and intermodulation distortion terms inside a Semiconductor Optical Amplifier (SOA) under Coherent Population Oscillation (CPO) regime. For that purpose, we present a general optical field model, valid for any arbitrarily-spaced radiofrequency tones, which is necessary to correctly describe the operation of CPO based slow light Microwave Photonic phase shifters which comprise an electrooptic modulator and a SOA followed by an optical filter and supplements another recently published for true time delay operation based on the propagation of optical intensities. The phase shifter performance has been evaluated in terms of the nonlinear distortion up to 3rd order, for a modulating signal constituted of two tones, in function of the electrooptic modulator input RF power and the SOA input optical power, obtaining a very good agreement between theoretical and experimental results. A complete theoretical spectral analysis is also presented which shows that under small signal operation conditions, the 3rd order intermodulation products at 2Ω1 + Ω2 and 2Ω2 + Ω1 experience a power dip/phase transition characteristic of the fundamental tones phase shifting operation.
Jakas, M. M.; Perez de la Rosa, F. J.; Custidiano, E. R.
2003-09-01
The accuracy of Bohr's and more recent analytical calculations of the electronic stopping of heavy charges by a classical harmonic oscillator is analyzed. According to results in this paper, for |{xi}|{>=}100 ({xi} being the Bohr stopping parameter) the present simulations agree with previous theoretical calculations, whereas for smaller |{xi}| values, discrepancies are evident. In fact, for |{xi}|<100 the stopping cross section seems to be sensitive to the sign of the ion charge. The so-called Barkas effect is unambiguously observed and positively charged projectiles appear to have a larger stopping compared to that of negative ones at the same {xi}. Bohr's calculations, however, seem to reproduce the stopping of negative charges relatively well, but those of positive ions are consequently underestimated. By giving the electron an initial velocity, the so-called inner-shell effect on the stopping can be readily studied. The present simulations show that previous analytical predictions of this effect do not account for the present results.
NASA Astrophysics Data System (ADS)
Ivanovich Aptekarev, Alexander; Nikolaevich Tulyakov, Dmitry; Valero Toranzo, Irene; Sanchez Dehesa, Jesús
2016-03-01
The Rényi entropies Rp [ ρ ], p> 0, ≠ 1 of the highly-excited quantum states of the D-dimensional isotropic harmonic oscillator are analytically determined by use of the strong asymptotics of the orthogonal polynomials which control the wavefunctions of these states, the Laguerre polynomials. This Rydberg energetic region is where the transition from classical to quantum correspondence takes place. We first realize that these entropies are closely connected to the entropic moments of the quantum-mechanical probability ρn(r) density of the Rydberg wavefunctions Ψn,l, { μ }(r); so, to the ℒp-norms of the associated Laguerre polynomials. Then, we determine the asymptotics n → ∞ of these norms by use of modern techniques of approximation theory based on the strong Laguerre asymptotics. Finally, we determine the dominant term of the Rényi entropies of the Rydberg states explicitly in terms of the hyperquantum numbers (n,l), the parameter order p and the universe dimensionality D for all possible cases D ≥ 1. We find that (a) the Rényi entropy power decreases monotonically as the order p is increasing and (b) the disequilibrium (closely related to the second order Rényi entropy), which quantifies the separation of the electron distribution from equiprobability, has a quasi-Gaussian behavior in terms of D.
NASA Astrophysics Data System (ADS)
Aptekarev, Alexander Ivanovich; Tulyakov, Dmitry Nikolaevich; Toranzo, Irene Valero; Dehesa, Jesús Sanchez
2016-03-01
The Rényi entropies R p [ ρ ], p> 0, ≠ 1 of the highly-excited quantum states of the D-dimensional isotropic harmonic oscillator are analytically determined by use of the strong asymptotics of the orthogonal polynomials which control the wavefunctions of these states, the Laguerre polynomials. This Rydberg energetic region is where the transition from classical to quantum correspondence takes place. We first realize that these entropies are closely connected to the entropic moments of the quantum-mechanical probability ρ n (r) density of the Rydberg wavefunctions Ψ n,l, { μ }(r); so, to the ℒ p -norms of the associated Laguerre polynomials. Then, we determine the asymptotics n → ∞ of these norms by use of modern techniques of approximation theory based on the strong Laguerre asymptotics. Finally, we determine the dominant term of the Rényi entropies of the Rydberg states explicitly in terms of the hyperquantum numbers (n,l), the parameter order p and the universe dimensionality D for all possible cases D ≥ 1. We find that (a) the Rényi entropy power decreases monotonically as the order p is increasing and (b) the disequilibrium (closely related to the second order Rényi entropy), which quantifies the separation of the electron distribution from equiprobability, has a quasi-Gaussian behavior in terms of D.
NASA Astrophysics Data System (ADS)
Liu, Yongfang; Zhao, Yu; Chen, Guanrong
2016-11-01
This paper studies the distributed consensus and containment problems for a group of harmonic oscillators with a directed communication topology. First, for consensus without a leader, a class of distributed consensus protocols is designed by using motion planning and Pontryagin's principle. The proposed protocol only requires relative information measurements at the sampling instants, without requiring information exchange over the sampled interval. By using stability theory and the properties of stochastic matrices, it is proved that the distributed consensus problem can be solved in the motion planning framework. Second, for the case with multiple leaders, a class of distributed containment protocols is developed for followers such that their positions and velocities can ultimately converge to the convex hull formed by those of the leaders. Compared with the existing consensus algorithms, a remarkable advantage of the proposed sampled-data-based protocols is that the sampling periods, communication topologies and control gains are all decoupled and can be separately designed, which relaxes many restrictions in controllers design. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.
Liu, Yongfang; Zhao, Yu; Chen, Guanrong
2016-11-01
This paper studies the distributed consensus and containment problems for a group of harmonic oscillators with a directed communication topology. First, for consensus without a leader, a class of distributed consensus protocols is designed by using motion planning and Pontryagin's principle. The proposed protocol only requires relative information measurements at the sampling instants, without requiring information exchange over the sampled interval. By using stability theory and the properties of stochastic matrices, it is proved that the distributed consensus problem can be solved in the motion planning framework. Second, for the case with multiple leaders, a class of distributed containment protocols is developed for followers such that their positions and velocities can ultimately converge to the convex hull formed by those of the leaders. Compared with the existing consensus algorithms, a remarkable advantage of the proposed sampled-data-based protocols is that the sampling periods, communication topologies and control gains are all decoupled and can be separately designed, which relaxes many restrictions in controllers design. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.
NASA Technical Reports Server (NTRS)
Weatherill, W. H.; Ehlers, F. E.; Yip, E.; Sebastian, J. D.
1980-01-01
Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.
Analysis and design of coupled-oscillator arrays for microwave systems
NASA Astrophysics Data System (ADS)
Moussounda, Renaud
The concept of synchronized nonlinear coupled oscillators is applied to microwave and antenna engineering for the analysis and design of wireless communication and sensing systems operating at the microwave and/or millimeter (mm)-wave frequencies. The significance of such approach is justified from the potential gain in efficiency, weight, cost and functionality although technical challenges stand in the way. Unlike typical phased array systems, which are currently used to construct such systems, coupled-oscillator systems present additional challenges that mainly arise from maintaining stability and synchronization as the the coupled nonlinear system is operated. Linear systems do not present such stability issues and are consequently faster since they do not rely on any gradual synchronization mechanism in order to function. However, at significantly higher frequencies in the quasi-optical domain, coupled-oscillator systems can make up for the speed difference and present significant efficiency advantages over typical phased array architectures. In addition, coupled nonlinear systems possess inherent analog properties that can be used for a multitude of functions. This dissertation advances the topic of coupled-oscillator arrays by 1) developing an alternative set of techniques for designing the oscillating unit cells called active integrated antennas (AIAs) at microwave or mm-wave frequencies, 2) developing a more accurate description of the dynamics of the array, 3) developing and implementing a new topology for a coupling network that is able to extend stability, 4) implementing a fully non-reciprocally coupled array able to produce large scan angle without loss of stability, 5) proposing an architecture based on a single phase-locked loop (PLL) and containing a self-calibration mechanism, and finally 6) implementing a phase-boosting mechanism using simple circuits to amplify the phase difference between adjacent radiating antennas in order to increase
Effect of parameter mismatch on the dynamics of strongly coupled self sustained oscillators
NASA Astrophysics Data System (ADS)
Chakrabarty, Nilaj; Jain, Aditya; Lal, Nijil; Das Gupta, Kantimay; Parmananda, Punit
2017-01-01
In this paper, we present an experimental setup and an associated mathematical model to study the synchronization of two self-sustained, strongly coupled, mechanical oscillators (metronomes). The effects of a small detuning in the internal parameters, namely, damping and frequency, have been studied. Our experimental system is a pair of spring wound mechanical metronomes; coupled by placing them on a common base, free to move along a horizontal direction. We designed a photodiode array based non-contact, non-magnetic position detection system driven by a microcontroller to record the instantaneous angular displacement of each oscillator and the small linear displacement of the base, coupling the two. In our system, the mass of the oscillating pendula forms a significant fraction of the total mass of the system, leading to strong coupling of the oscillators. We modified the internal mechanism of the spring-wound "clockwork" slightly, such that the natural frequency and the internal damping could be independently tuned. Stable synchronized and anti-synchronized states were observed as the difference in the parameters was varied in the experiments. The simulation results showed a rapid increase in the phase difference between the two oscillators beyond a certain threshold of parameter mismatch. Our simple model of the escapement mechanism did not reproduce a complete 180° out of phase state. However, the numerical simulations show that increased mismatch in parameters leads to a synchronized state with a large phase difference.
Noguera, Norman; Rózga, Krzysztof
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.
NASA Astrophysics Data System (ADS)
Graham Hoover, William; Clinton Sprott, Julien; Griswold Hoover, Carol
2016-10-01
We describe the application of adaptive (variable time step) integrators to stiff differential equations encountered in many applications. Linear harmonic oscillators subject to nonlinear thermal constraints can exhibit either stiff or smooth dynamics. Two closely related examples, Nosé's dynamics and Nosé-Hoover dynamics, are both based on Hamiltonian mechanics and generate microstates consistent with Gibbs' canonical ensemble. Nosé's dynamics is stiff and can present severe numerical difficulties. Nosé-Hoover dynamics, although it follows exactly the same trajectory, is smooth and relatively trouble-free. We emphasize the power of adaptive integrators to resolve stiff problems such as the Nosé dynamics for the harmonic oscillator. The solutions also illustrate the power of computer graphics to enrich numerical solutions.
Baykusheva, Denitsa; Kraus, Peter M; Zhang, Song Bin; Rohringer, Nina; Wörner, Hans Jakob
2014-01-01
The sensitivities of high-harmonic generation (HHG) and strong-field ionization (SFI) to coupled electronic and nuclear dynamics are studied, using the nitric oxide (NO) molecule as an example. A coherent superposition of electronic and rotational states of NO is prepared by impulsive stimulated Raman scattering and probed by simultaneous detection of HHG and SFI yields. We observe a fourfold higher sensitivity of high-harmonic generation to electronic dynamics and attribute it to the presence of inelastic quantum paths connecting coherently related electronic states [Kraus et al., Phys. Rev. Lett.111, 243005 (2013)]. Whereas different harmonic orders display very different sensitivities to rotational or electronic dynamics, strong-field ionization is found to be most sensitive to electronic motion. We introduce a general theoretical formalism for high-harmonic generation from coupled nuclear-electronic wave packets. We show that the unequal sensitivities of different harmonic orders to electronic or rotational dynamics result from the angle dependence of the photorecombination matrix elements which encode several autoionizing and shape resonances in the photoionization continuum of NO. We further study the dependence of rotational and electronic coherences on the intensity of the excitation pulse and support the observations with calculations.
Chaotic dynamics of coupled transverse-longitudinal plasma oscillations in magnetized plasmas.
Teychenné, D; Bésuelle, E; Oloumi, A; Salomaa, R R
2000-12-25
The propagation of intense electromagnetic waves in cold magnetized plasma is tackled through a relativistic hydrodynamic approach. The analysis of coupled transverse-longitudinal plasma oscillations is performed for traveling plane waves. When these waves propagate perpendicularly to a static magnetic field, the model is describable in terms of a nonlinear dynamical system with 2 degrees of freedom. A constant of motion is obtained and the powerful classical mechanics methods can be used. A new class of solutions, i.e., the chaotic solutions, is discovered by the Poincaré surface of sections. As a result, coupled transverse-longitudinal plasma oscillations become aperiodically modulated.
Probabilistic convergence guarantees for type-II pulse-coupled oscillators
NASA Astrophysics Data System (ADS)
Nishimura, Joel; Friedman, Eric J.
2012-08-01
We show that a large class of pulse-coupled oscillators converge with high probability from random initial conditions on a large class of graphs with time delays. Our analysis combines previous local convergence results, probabilistic network analysis, and a classification scheme for type-II phase response curves to produce rigorous lower bounds for convergence probabilities based on network density. These results suggest methods for the analysis of pulse-coupled oscillators, and provide insights into the balance of excitation and inhibition in the operation of biological type-II phase response curves and also the design of decentralized and minimal clock synchronization schemes in sensor nets.
Frequency adjustment and synchrony in networks of delayed pulse-coupled oscillators
NASA Astrophysics Data System (ADS)
Nishimura, Joel
2015-01-01
We introduce a system of pulse-coupled oscillators that can change both their phases and frequencies and prove that when there is a separation of time scales between phase and frequency adjustment the system converges to exact synchrony on strongly connected graphs with time delays. The analysis involves decomposing the network into a forest of tree-like structures that capture causality. These results provide a robust method of sensor net synchronization as well as demonstrate a new avenue of possible pulse-coupled oscillator research.
NASA Astrophysics Data System (ADS)
Timms, L.; English, L. Q.
2014-03-01
We explore both analytically and numerically an ensemble of coupled phase oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time delay (due to finite signal-propagation speeds) and network plasticity (via dynamic coupling constants) inspired by the Hebbian learning rule in neuroscience. When time delay and learning effects combine, interesting synchronization phenomena are observed. We investigate the formation of spatiotemporal patterns in both one- and two-dimensional oscillator lattices with periodic boundary conditions and comment on the role of dimensionality.
Zanotto, Simone; Tredicucci, Alessandro
2016-01-01
In this article we discuss a model describing key features concerning the lineshapes and the coherent absorption conditions in Fano-resonant dissipative coupled oscillators. The model treats on the same footing the weak and strong coupling regimes, and includes the critical coupling concept, which is of great relevance in numerous applications; in addition, the role of asymmetry is thoroughly analyzed. Due to the wide generality of the model, which can be adapted to various frameworks like nanophotonics, plasmonics, and optomechanics, we envisage that the analytical formulas presented here will be crucial to effectively design devices and to interpret experimental results. PMID:27091489
NASA Astrophysics Data System (ADS)
Zanotto, Simone; Tredicucci, Alessandro
2016-04-01
In this article we discuss a model describing key features concerning the lineshapes and the coherent absorption conditions in Fano-resonant dissipative coupled oscillators. The model treats on the same footing the weak and strong coupling regimes, and includes the critical coupling concept, which is of great relevance in numerous applications; in addition, the role of asymmetry is thoroughly analyzed. Due to the wide generality of the model, which can be adapted to various frameworks like nanophotonics, plasmonics, and optomechanics, we envisage that the analytical formulas presented here will be crucial to effectively design devices and to interpret experimental results.
Entrainment of a Synthetic Oscillator through Queueing Coupling
NASA Astrophysics Data System (ADS)
Hochendoner, Philip; Mather, William; Butzin, Nicholas; Ogle, Curtis
2014-03-01
Many biological systems naturally exhibit (often noisy) oscillatory patterns that are capable of being entrained by external stimuli, though the mechanism of entrainment is typically obscured by the complexity of native networks. A synthetic biology approach, where genetic programs are wired ``by hand,'' has proven useful in this regard. In the present study, we use a synthetic oscillator in Escherichia coli to demonstrate a novel and potentially widespread mechanism for biological entrainment: competition of proteins for degradation by common pathway, i.e. a entrainment by a bottleneck. To faithfully represent the discrete and stochastic nature of this bottleneck, we leverage results from a recent biological queueing theory, where in particular, the queueing theoretic concept of workload is discovered to simplify the analysis. NSF Award 1330180.