Rabi oscillation between states of a coupled harmonic oscillator
International Nuclear Information System (INIS)
Park, Tae Jun
2003-01-01
Rabi oscillation between bound states of a single potential is well known. However the corresponding formula between the states of two different potentials has not been obtained yet. In this work, we derive Rabi formula between the states of a coupled harmonic oscillator which may be used as a simple model for the electron transfer. The expression is similar to typical Rabi formula for a single potential. This result may be used to describe transitions between coupled diabatic potential curves
Coupled harmonic oscillators and their quantum entanglement
Makarov, Dmitry N.
2018-04-01
A system of two coupled quantum harmonic oscillators with the Hamiltonian H ̂=1/2 (1/m1p̂1 2+1/m2p̂2 2+A x12+B x22+C x1x2) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H ̂Ψ =i ℏ ∂/Ψ ∂ t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.
One dimension harmonic oscillator
International Nuclear Information System (INIS)
Cohen-Tannoudji, Claude; Diu, Bernard; Laloe, Franck.
1977-01-01
The importance of harmonic oscillator in classical and quantum physics, eigenvalues and eigenstates of hamiltonian operator are discussed. In complement are presented: study of some physical examples of harmonic oscillators; study of stationnary states in the /x> representation; Hermite polynomials; resolution of eigenvalue equation of harmonic oscillator by polynomial method; isotope harmonic oscillator with three dimensions; charged harmonic oscillator in uniform electric field; quasi classical coherent states of harmonic oscillator; eigenmodes of vibration of two coupled harmonic oscillators; vibration modus of a continuous physical system (application to radiation: photons); vibration modus of indefinite linear chain of coupled harmonic oscillators (phonons); one-dimensional harmonic oscillator in thermodynamic equilibrium at temperature T [fr
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearity...
Controllability in tunable chains of coupled harmonic oscillators
Buchmann, L. F.; Mølmer, K.; Petrosyan, D.
2018-04-01
We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N -1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach any desired Gaussian state requires at most 3 N (N -1 )/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides.
Controllability in tunable chains of coupled harmonic oscillators
DEFF Research Database (Denmark)
Buchmann, Lukas Filip; Mølmer, Klaus; Petrosyan, David
2018-01-01
We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N −1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach...... any desired Gaussian state requires at most 3 N ( N −1)/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can...... be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides....
Controllability in tunable chains of coupled harmonic oscillators
DEFF Research Database (Denmark)
Buchmann, Lukas Filip; Mølmer, Klaus; Petrosyan, David
2018-01-01
any desired Gaussian state requires at most 3 N ( N −1)/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can......We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N −1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach...... be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides....
Time-dependent coupled harmonic oscillators: classical and quantum solutions
International Nuclear Information System (INIS)
Macedo, D.X.; Guedes, I.
2014-01-01
In this work we present the classical and quantum solutions for an arbitrary system of time-dependent coupled harmonic oscillators, where the masses (m), frequencies (ω) and coupling parameter (k) are functions of time. To obtain the classical solutions, we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld (LR) invariant method. The exact wave functions are obtained by solving the respective Milne–Pinney (MP) equation for each system. We obtain the solutions for the system with m 1 = m 2 = m 0 e γt , ω 1 = ω 01 e -γt/2 , ω 2 = ω 02 e -γt/2 and k = k 0 . (author)
Spontaneous decoherence of coupled harmonic oscillators confined in a ring
Gong, ZhiRui; Zhang, ZhenWei; Xu, DaZhi; Zhao, Nan; Sun, ChangPu
2018-04-01
We study the spontaneous decoherence of coupled harmonic oscillators confined in a ring container, where the nearest-neighbor harmonic potentials are taken into consideration. Without any external symmetry-breaking field or surrounding environment, the quantum superposition state prepared in the relative degrees of freedom gradually loses its quantum coherence spontaneously. This spontaneous decoherence is interpreted by the gauge couplings between the center-of-mass and the relative degrees of freedoms, which actually originate from the symmetries of the ring geometry and the corresponding nontrivial boundary conditions. In particular, such spontaneous decoherence does not occur at all at the thermodynamic limit because the nontrivial boundary conditions become the trivial Born-von Karman boundary conditions when the perimeter of the ring container tends to infinity. Our investigation shows that a thermal macroscopic object with certain symmetries has a chance for its quantum properties to degrade even without applying an external symmetry-breaking field or surrounding environment.
Infinite-time and finite-time synchronization of coupled harmonic oscillators
International Nuclear Information System (INIS)
Cheng, S; Ji, J C; Zhou, J
2011-01-01
This paper studies the infinite-time and finite-time synchronization of coupled harmonic oscillators with distributed protocol in the scenarios with and without a leader. In the absence of a leader, the convergence conditions and the final trajectories that each harmonic oscillator follows are developed. In the presence of a leader, it is shown that all harmonic oscillators can achieve the trajectory of the leader in finite time. Numerical simulations of six coupled harmonic oscillators are given to show the effects of the interaction function parameter, algebraic connectivity and initial conditions on the convergence time.
International Nuclear Information System (INIS)
Woafo, P.
1999-12-01
This paper deals with the dynamics of a model describing systems consisting of the classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. Both the forced and autonomous cases are considered. Harmonic response is investigated along with its stability boundaries. Condition for quenching phenomena in the autonomous case is derived. Neimark bifurcation is observed and it is found that our model shows period doubling and period-m sudden transitions to chaos. Synchronization of two and more systems in their chaotic regime is presented. (author)
Quantum entanglement in coupled harmonic oscillator systems: from micro to macro
International Nuclear Information System (INIS)
Kao, Jhih-Yuan; Chou, Chung-Hsien
2016-01-01
We investigate the entanglement dynamics of several models of coupled harmonic oscillators, whereby a number of properties concerning entanglement have been scrutinized, such as how the environment affects entanglement of a system, and death and revival of entanglement. Among them, there are two models for which we are able to vary their particle numbers easily by assuming identicalness, thereby examining how the particle number affects entanglement. We have found that the upper bound of entanglement between identical oscillators is approximately inversely proportional to the particle number. (paper)
Park, DaeKil
2018-06-01
The dynamics of entanglement and uncertainty relation is explored by solving the time-dependent Schrödinger equation for coupled harmonic oscillator system analytically when the angular frequencies and coupling constant are arbitrarily time dependent. We derive the spectral and Schmidt decompositions for vacuum solution. Using the decompositions, we derive the analytical expressions for von Neumann and Rényi entropies. Making use of Wigner distribution function defined in phase space, we derive the time dependence of position-momentum uncertainty relations. To show the dynamics of entanglement and uncertainty relation graphically, we introduce two toy models and one realistic quenched model. While the dynamics can be conjectured by simple consideration in the toy models, the dynamics in the realistic quenched model is somewhat different from that in the toy models. In particular, the dynamics of entanglement exhibits similar pattern to dynamics of uncertainty parameter in the realistic quenched model.
Entanglement entropy in the quantum networks of a coupled quantum harmonic oscillator
International Nuclear Information System (INIS)
Jafarizadeh, M A; Nami, S; Eghbalifam, F
2015-01-01
We investigate the entanglement of the ground state in the quantum networks that their nodes are considered as quantum harmonic oscillators. To this aim, the Schmidt numbers and entanglement entropy between two arbitrary partitions of a network are calculated.In partitioning an arbitrary graph into two parts there are some nodes in each part which are not connected to the nodes of the other part. So, these nodes of each part can be in distinct subsets. Therefore, the graph is separated into four subsets. The nodes of the first and last subsets are those which are not connected to the nodes of the other part. In theorem 1, by using the generalized Schur complement method in these four subsets, we prove that all the graphs whose connections between the two alternative subsets are complete, have the same entropy. A large number of graphs satisfy this theorem. Then the entanglement entropy in the limit of the large coupling and large size of the system is investigated in these graphs. Also, the asymptotic behaviors of the Schmidt numbers and entanglement entropy in the limit of infinite coupling are shown.One important quantity about partitioning is the conductance of the graph. The conductance of the graph is considered in various graphs. In these graphs we compare the conductance of the graph and the entanglement entropy. (paper)
Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Ghesquière, Anne, E-mail: Anne.Ghesquiere@nithep.ac.za; Sinayskiy, Ilya, E-mail: sinayskiy@ukzn.ac.za; Petruccione, Francesco, E-mail: petruccione@ukzn.ac.za
2013-10-15
A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal entanglement is found in the high-temperature limit. In the weak coupling limit the system converges to an entangled non-equilibrium steady state. A critical temperature for the appearance of quantum correlations is found.
AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2006-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...
On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress
International Nuclear Information System (INIS)
Bocko, M.F.; Onofrio, R.
1996-01-01
Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them, have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves et al., 1980, Rev. Mod. Phys. 52, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review. copyright 1996 The American Physical Society
'quantumness' measures in the decohering harmonic oscillator
Indian Academy of Sciences (India)
We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of ...
Non-singular spiked harmonic oscillator
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Guardiola, R.
1990-01-01
A perturbative study of a class of non-singular spiked harmonic oscillators defined by the hamiltonian H = d sup(2)/dr sup(2) + r sup(2) + λ/r sup(α) in the domain [0,∞] is carried out, in the two extremes of a weak coupling and a strong coupling regimes. A path has been found to connect both expansions for α near 2. (author)
Harmonic oscillator in Snyder space
Indian Academy of Sciences (India)
The harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. An effective cut-off to high frequencies is found. The quantum version is developed and an equivalent usual ...
The relativistic harmonic oscillator reconsidered
International Nuclear Information System (INIS)
Hofsaess, T.
1978-01-01
The bound states of scalar quarks interacting through a scalar harmonic oscillator are investigated. In the presence of this interaction the dressed quark propagator differs substantially from the free one. This leads to a Bethe Salpeter equation which does not allow for any stable bound states of positive mass. (orig.) [de
Demonstration of Double EIT Using Coupled Harmonic Oscillators and RLC Circuits
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…
Generating transverse response explicitly from harmonic oscillators
Yao, Yuan; Tang, Ying; Ao, Ping
2017-10-01
We obtain stochastic dynamics from a system-plus-bath mechanism as an extension of the Caldeira-Leggett (CL) model in the classical regime. An effective magnetic field and response functions with both longitudinal and transverse parts are exactly generated from the bath of harmonic oscillators. The effective magnetic field and transverse response are antisymmetric matrices: the former is explicitly time-independent corresponding to the geometric magnetism, while the latter can have memory. The present model can be reduced to previous representative examples of stochastic dynamics describing nonequilibrium processes. Our results demonstrate that a system coupled with a bath of harmonic oscillators is a general approach to studying stochastic dynamics, and provides a method to experimentally implement an effective magnetic field from coupling to the environment.
Introduction to Classical and Quantum Harmonic Oscillators
International Nuclear Information System (INIS)
Latal, H
1997-01-01
As the title aptly states, this book deals with harmonic oscillators of various kinds, from classical mechanical and electrical oscillations up to quantum oscillations. It is written in a lively language, and occasional interspersed anecdotes make the reading of an otherwise mathematically oriented text quite a pleasure. Although the author claims to have written an 'elementary introduction', it is certainly necessary to have a good deal of previous knowledge in physics (mechanics, electrodynamics, quantum theory), electrical engineering and, of course, mathematics in order to follow the general line of his arguments. The book begins with a thorough treatment of classical oscillators (free, damped, forced) that is followed by an elaboration on Fourier analysis. Lagrange and Hamilton formalisms are then introduced before the problem of coupled oscillations is attacked. A chapter on statistical perspectives leads over to the final discussion of quantum oscillations. With the book comes a diskette containing a number of worksheets (Microsoft Excel) that can be used by the reader for instant visualization to get a better qualitative and quantitative understanding of the material. To the reviewer it seems difficult to pinpoint exactly the range of prospective readership of the book. It can certainly not be intended as a textbook for students, but rather as a reference book for teachers of physics or researchers, who want to look up one or other aspect of harmonic oscillations, for which purpose the diskette represents a very valuable tool. (book review)
Harmonic oscillator on a lattice
International Nuclear Information System (INIS)
Ader, J.P.; Bonnier, B.; Hontebeyrie, M.; Meyers, C.
1983-01-01
The continuum limit of the ground state energy for the harmonic oscillator with discrete time is derived for all possible choices of the lattice derivative. The occurrence of unphysical values is shown to arise whenever the lattice laplacian is not strictly positive on its Brillouin zone. These undesirable limits can either be finite and arbitrary (multiple spectrum) or infinite (overlapping sublattices with multiple spectrum). (orig.)
Introduction to classical and quantum harmonic oscillators
Bloch, Sylvan C
2013-01-01
From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating con
Harmonic synchronization in resistively coupled Josephson junctions
International Nuclear Information System (INIS)
Blackburn, J.A.; Gronbech-Jensen, N.; Smith, H.J.T.
1994-01-01
The oscillations of two resistively coupled Josephson junctions biased only by a single dc current source are shown to lock harmonically in a 1:2 mode over a significant range of bias current, even when the junctions are identical. The dependence of this locking on both junction and coupling parameters is examined, and it is found that, for this particular two-junction configuration, 1:1 locking can never occur, and also that a minimum coupling coefficient is needed to support harmonic locking. Some issues related to subharmonic locking are also discussed
Interbasis expansions for isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Dong, Shi-Hai, E-mail: dongsh2@yahoo.com [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, Mexico D.F. 07738 (Mexico)
2012-03-12
The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n. -- Highlights: ► Exact solutions of harmonic oscillator are reviewed in three coordinates. ► Interbasis expansions of the eigenfunctions is solved completely. ► This is occurred only for those degenerated states for given quantum number n.
Quantization of the damped harmonic oscillator revisited
Energy Technology Data Exchange (ETDEWEB)
Baldiotti, M.C., E-mail: baldiott@fma.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Fresneda, R., E-mail: fresneda@gmail.co [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Gitman, D.M., E-mail: gitman@dfn.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil)
2011-04-11
We return to the description of the damped harmonic oscillator with an assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model proposed by one of the authors. We argue the latter has better high energy behavior and is connected to existing open-systems approaches. - Highlights: We prove the local equivalence of two damped harmonic oscillator models. We find different high energy behaviors between the two models. Based on the local equivalence, we make a simple construction of the coherent states.
Quantization of the damped harmonic oscillator revisited
International Nuclear Information System (INIS)
Baldiotti, M.C.; Fresneda, R.; Gitman, D.M.
2011-01-01
We return to the description of the damped harmonic oscillator with an assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model proposed by one of the authors. We argue the latter has better high energy behavior and is connected to existing open-systems approaches. - Highlights: → We prove the local equivalence of two damped harmonic oscillator models. → We find different high energy behaviors between the two models. → Based on the local equivalence, we make a simple construction of the coherent states.
Sticky orbits of a kicked harmonic oscillator
International Nuclear Information System (INIS)
Lowenstein, J H
2005-01-01
We study a Hamiltonian dynamical system consisting of a one-dimensional harmonic oscillator kicked impulsively in 4:1 resonance with its natural frequency, with the amplitude of the kick proportional to a sawtooth function of position. For special values of the coupling parameter, the dynamical map W relating the phase-space coordinates just prior to each kick acts locally as a piecewise affine map K on a square with rational rotation number p/q. For λ = 2cos2πp/q a quadratic irrational, a recursive return-map structure allows us to completely characterize the orbits of the map K. The aperiodic orbits of this system are sticky in the sense that they spend all of their time wandering pseudo-chaotically (with strictly zero Lyapunov exponent) in the vicinity of self-similar archipelagos of periodic islands. The same recursive structure used locally for K gives us the asymptotic scaling features of long orbits of W on the infinite plane. For some coupling parameters the orbits remain bounded, but for others the distance from the origin increases as a logarithm or power of the time. In the latter case, we find examples of sub-diffusive, diffusive, super-diffusive, and ballistic power-law behavior
Sobolev Spaces Associated to the Harmonic Oscillator
Indian Academy of Sciences (India)
We define the Hermite-Sobolev spaces naturally associated to the harmonic oscillator H = − + | x | 2 . Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrödinger equation are also considered.
Information cloning of harmonic oscillator coherent states
Indian Academy of Sciences (India)
We show that in the case of unknown harmonic oscillator coherent statesit is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state. By making use ...
Laguerre polynomials by a harmonic oscillator
Baykal, Melek; Baykal, Ahmet
2014-09-01
The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators.
Laguerre polynomials by a harmonic oscillator
International Nuclear Information System (INIS)
Baykal, Melek; Baykal, Ahmet
2014-01-01
The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators. (paper)
Symmetries of the quantum damped harmonic oscillator
International Nuclear Information System (INIS)
Guerrero, J; López-Ruiz, F F; Aldaya, V; Cossío, F
2012-01-01
For the non-conservative Caldirola–Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg–Weyl algebra can be found. The inclusion of the standard time evolution generator (which is not a symmetry) as a symmetry in this algebra, in a unitary manner, requires a non-trivial extension of this basic algebra and hence of the physical system itself. Surprisingly, this extension leads directly to the so-called Bateman dual system, which now includes a new particle acting as an energy reservoir. In addition, the Caldirola–Kanai dissipative system can be retrieved by imposing constraints. The algebra of symmetries of the dual system is presented, as well as a quantization that implies, in particular, a first-order Schrödinger equation. As opposed to other approaches, where it is claimed that the spectrum of the Bateman Hamiltonian is complex and discrete, we obtain that it is real and continuous, with infinite degeneracy in all regimes. (paper)
Propagator for a spin-Bose system with the Bose field coupled to a reservoir of harmonic oscillators
Banerjee, S
2003-01-01
We consider the general problem of a single two-level atom interacting with a multimode radiation field (without the rotating-wave approximation), and additionally take the field to be coupled to a thermal reservoir. Using the method of bosonization of the spin operators in the Hamiltonian, and working in the Bargmann representation for all the boson operators, we obtain the propagator for the composite system using the techniques of functional integration, under a reasonable approximation scheme. The propagator is explicitly evaluated for a simplified version of the system with one spin and a dynamically coupled single-mode field. The results are also checked on the known problem of quantum Brownian motion.
The macroscopic harmonic oscillator and quantum measurements
International Nuclear Information System (INIS)
Hayward, R.W.
1982-01-01
A quantum mechanical description of a one-dimensional macroscopic harmonic oscillator interacting with its environment is given. Quasi-coherent states are introduced to serve as convenient basis states for application of a density matrix formalism to characterize the system. Attention is given to the pertinent quantum limits to the precision of measurement of physical observables that may provide some information on the nature of a weak classical force interacting with the oscillator. A number of ''quantum nondemolition'' schemes proposed by various authors are discussed. (Auth.)
Hyperchaotic circuit with damped harmonic oscillators
DEFF Research Database (Denmark)
Lindberg, Erik; Murali, K.; Tamasevicius, A.
2001-01-01
A simple fourth-order hyperchaotic circuit with damped harmonic oscillators is described. ANP3 and PSpice simulations including an eigenvalue study of the linearized Jacobian are presented together with a hardware implementation. The circuit contains two inductors with series resistance, two ideal...... capacitors and one nonlinear active conductor. The Lyapunov exponents are presented to confirm the hyperchaotic nature of the oscillations of the circuit. The nonlinear conductor is realized with a diode. A negative impedance converter and a linear resistor. The performance of the circuit is investigated...... by means of numerical integration of the appropriate differential equations....
Variational and perturbative schemes for a spiked harmonic oscillator
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Estevez, G.A.; Guardiola, R.
1989-01-01
A variational analysis of the spiked harmonic-oscillator Hamiltonian operator -d 2 /dx 2 + x 2 + l(l+1)/x 2 + λ |x| -α , where α is a real positive parameter, is reported in this work. The formalism makes use of the functional space spanned by the solutions of the Schroedinger equation for the linear harmonic-oscillator Hamiltonian supplemented by a Dirichlet boundary condition, and a standard procedure for diagonalizing symmetric matrices. The eigenvalues obtained by increasing the dimension of the basis set provides accurate approximations for the ground-state energy of the model system, valid for positive and relatively large values of the coupling parameter λ. Additionally, a large-coupling pertubative-expansion is carried out and the contributions up to fourth order to the ground-state energy are explicitly evaluated. Numerical results are compared for the special case α=5/2. (author) [pt
Energy Technology Data Exchange (ETDEWEB)
Chandra, J; Scott, A C
1983-01-01
Topics discussed include transitions in weakly coupled nonlinear oscillators, singularly perturbed delay-differential equations, and chaos in simple laser systems. Papers are presented on truncated Navier-Stokes equations in a two-dimensional torus, on frequency locking in Josephson point contacts, and on soliton excitations in Josephson tunnel junctions. Attention is also given to the nonlinear coupling of radiation pulses to absorbing anharmonic molecular media, to aspects of interrupted coarse-graining in stimulated excitation, and to a statistical analysis of long-term dynamic irregularity in an exactly soluble quantum mechanical model.
A quantum harmonic oscillator and strong chaos
International Nuclear Information System (INIS)
Oprocha, Piotr
2006-01-01
It is known that many physical systems which do not exhibit deterministic chaos when treated classically may exhibit such behaviour if treated from the quantum mechanics point of view. In this paper, we will show that an annihilation operator of the unforced quantum harmonic oscillator exhibits distributional chaos as introduced in B Schweizer and J SmItal (1994 Trans. Am. Math. Soc. 344 737-54). Our approach strengthens previous results on chaos in this model and provides a very powerful tool to measure chaos in other (quantum or classical) models
Spectral inverse problem for q-deformed harmonic oscillator
Indian Academy of Sciences (India)
The supersymmetric quantization condition is used to study the wave functions of SWKB equivalent -deformed harmonic oscillator which are obtained by using only the knowledge of bound-state spectra of -deformed harmonic oscillator. We have also studied the nonuniqueness of the obtained interactions by this ...
A Look at Damped Harmonic Oscillators through the Phase Plane
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…
Chaos in generically coupled phase oscillator networks with nonpairwise interactions.
Bick, Christian; Ashwin, Peter; Rodrigues, Ana
2016-09-01
The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling-including three and four-way interactions of the oscillator phases-that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.
Harmonic and Anharmonic Behaviour of a Simple Oscillator
O'Shea, Michael J.
2009-01-01
We consider a simple oscillator that exhibits harmonic and anharmonic regimes and analyse its behaviour over the complete range of possible amplitudes. The oscillator consists of a mass "m" fixed at the midpoint of a horizontal rope. For zero initial rope tension and small amplitude the period of oscillation, tau, varies as tau is approximately…
Hyperchaos in coupled Colpitts oscillators
DEFF Research Database (Denmark)
Cenys, Antanas; Tamasevicius, Arunas; Baziliauskas, Antanas
2003-01-01
The paper suggests a simple solution of building a hyperchaotic oscillator. Two chaotic Colpitts oscillators, either identical or non-identical ones are coupled by means of two linear resistors R-k. The hyperchaotic output signal v(t) is a linear combination, specifically the mean of the individual...
Chaos in generically coupled phase oscillator networks with nonpairwise interactions
Energy Technology Data Exchange (ETDEWEB)
Bick, Christian; Ashwin, Peter; Rodrigues, Ana [Centre for Systems, Dynamics and Control and Department of Mathematics, University of Exeter, Exeter EX4 4QF (United Kingdom)
2016-09-15
The Kuramoto–Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling—including three and four-way interactions of the oscillator phases—that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.
A harmonic oscillator having “volleyball damping”
Mickens, R. E.; Oyedeji, K.; Rucker, S. A.
2006-05-01
Volleyball damping corresponds to linear damping up to a certain critical velocity, with zero damping above this value. The dynamics of a linear harmonic oscillator is investigated with this damping mechanism.
Two-dimensional generalized harmonic oscillators and their Darboux partners
International Nuclear Information System (INIS)
Schulze-Halberg, Axel
2011-01-01
We construct two-dimensional Darboux partners of the shifted harmonic oscillator potential and of an isotonic oscillator potential belonging to the Smorodinsky–Winternitz class of superintegrable systems. The transformed solutions, their potentials and the corresponding discrete energy spectra are computed in explicit form. (paper)
A new analytical approximation to the Duffing-harmonic oscillator
International Nuclear Information System (INIS)
Fesanghary, M.; Pirbodaghi, T.; Asghari, M.; Sojoudi, H.
2009-01-01
In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations.
On quantum harmonic oscillator being subjected to absolute
Indian Academy of Sciences (India)
In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. In this paper, assuming a boundary condition that the product of momentum and position, or the product of energy density and position remains constant in the QHO, it is established that a particle subjected to increasing ...
Chimera states in nonlocally coupled phase oscillators with biharmonic interaction
Cheng, Hongyan; Dai, Qionglin; Wu, Nianping; Feng, Yuee; Li, Haihong; Yang, Junzhong
2018-03-01
Chimera states, which consist of coexisting domains of coherent and incoherent parts, have been observed in a variety of systems. Most of previous works on chimera states have taken into account specific form of interaction between oscillators, for example, sinusoidal coupling or diffusive coupling. Here, we investigate chimera dynamics in nonlocally coupled phase oscillators with biharmonic interaction. We find novel chimera states with features such as that oscillators in the same coherent cluster may split into two groups with a phase difference around π/2 and that oscillators in adjacent coherent clusters may have a phase difference close to π/2. The different impacts of the coupling ranges in the first and the second harmonic interactions on chimera dynamics are investigated based on the synchronous dynamics in globally coupled phase oscillators. Our study suggests a new direction in the field of chimera dynamics.
On the moment of inertia of a quantum harmonic oscillator
International Nuclear Information System (INIS)
Khamzin, A. A.; Sitdikov, A. S.; Nikitin, A. S.; Roganov, D. A.
2013-01-01
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.
Magnetically Coupled Magnet-Spring Oscillators
Donoso, G.; Ladera, C. L.; Martin, P.
2010-01-01
A system of two magnets hung from two vertical springs and oscillating in the hollows of a pair of coils connected in series is a new, interesting and useful example of coupled oscillators. The electromagnetically coupled oscillations of these oscillators are experimentally and theoretically studied. Its coupling is electromagnetic instead of…
Time-dependent Hartree approximation and time-dependent harmonic oscillator model
International Nuclear Information System (INIS)
Blaizot, J.P.
1982-01-01
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 Schroedinger 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. (orig.)
Fundamental and Harmonic Oscillations in Neighboring Coronal Loops
Li, Hongbo; Liu, Yu; Vai Tam, Kuan
2017-06-01
We present observations of multimode (fundamental and harmonic) oscillations in a loop system, which appear to be simultaneously excited by a GOES C-class flare. Analysis of the periodic oscillations reveals that (1) the primary loop with a period of P a ≈ 4 minutes and a secondary loop with two periods of P a ≈ 4 minutes and P b ≈ 2 minutes are detected simultaneously in closely spaced loop strands; (2) both oscillation components have their peak amplitudes near the loop apex, while in the second loop the low-frequency component P a dominates in a loop segment that is two times larger than the high-frequency component P b ; (3) the harmonic mode P b shows the largest deviation from a sinusoidal loop shape at the loop apex. We conclude that multiple harmonic modes with different displacement profiles can be excited simultaneously even in closely spaced strands, similar to the overtones of a violin string.
International Nuclear Information System (INIS)
Oishi, Tetsutarou; Yoshinuma, Mikirou; Ida, Katsumi; Akiyama, Tsuyoshi; Minami, Takashi; Nagaoka, Kenichi; Shimizu, Akihiro; Okamura, Shoichi; Kado, Shinichiro
2008-01-01
The coherent MHD oscillation, which consists of the fundamental frequency of several kilohertz and its higher harmonics, (harmonic oscillation: HO) has been observed in Compact Helical System. HO consists of two pairs of harmonic series. One is located in the core region near the ι=0.5 rational surface (denoted as 'HO (core)'), the other is located in the edge region near the ι=1.0 rational surface (denoted as 'HO (edge)'). In the present study, bispectral analysis is applied to the fluctuation data, for which HO is measured by beam emission spectroscopy (BES) and using magnetic probes. The analysis has revealed that fundamental mode of HO in both the magnetic and core density fluctuations have phase correlation with the harmonics including fundamental oscillation, while HO in edge density fluctuation does not have such phase correlation. Mode numbers of HOs are identical for harmonic components having different frequencies, i.e., m/n=-2/1 for HO (core) and m/n=-1/1 for HO (edge). It suggests that the generation of harmonics cannot be interpreted simply as mode coupling because the summation rule for the wavenumber is not satisfied, even though the bicoherence value is significant. The bicoherence value and relative amplitude of higher harmonics correlate with each other, which suggests that bicoherence indicates the degree of distortion of the signals. (author)
Coupled oscillators and Feynman's three papers
International Nuclear Information System (INIS)
Kim, Y S
2007-01-01
According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the 'rest of the universe' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators
Predicting charmonium and bottomonium spectra with a quark harmonic oscillator
Norbury, J. W.; Badavi, F. F.; Townsend, L. W.
1986-01-01
The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.
Parametric Resonance in a Time-Dependent Harmonic Oscillator
Directory of Open Access Journals (Sweden)
P. N. Nesterov
2013-01-01
Full Text Available In this paper, we study the phenomenon of appearance of new resonances in a timedependent harmonic oscillator under an oscillatory decreasing force. The studied equation belongs to the class of adiabatic oscillators and arises in connection with the spectral problem for the one-dimensional Schr¨odinger equation with Wigner–von Neumann type potential. We use a specially developed method for asymptotic integration of linear systems of differential equations with oscillatory decreasing coefficients. This method uses the ideas of the averaging method to simplify the initial system. Then we apply Levinson’s fundamental theorem to get the asymptotics for its solutions. Finally, we analyze the features of a parametric resonance phenomenon. The resonant frequencies of perturbation are found and the pointwise type of the parametric resonance phenomenon is established. In conclusion, we construct an example of a time-dependent harmonic oscillator (adiabatic oscillator in which the parametric resonances, mentioned in the paper, may occur.
Damped driven coupled oscillators: entanglement, decoherence and the classical limit
Energy Technology Data Exchange (ETDEWEB)
Mancilla, R D Guerrero; Rey-Gonzalez, R R; Fonseca-Romero, K M [Grupo de Optica e Informacion Cuantica, Departamento de Fisica, Universidad Nacional de Colombia, Bogota (Colombia)], E-mail: rdguerrerom@unal.edu.co, E-mail: rrreyg@unal.edu.co, E-mail: kmfonsecar@unal.edu.co
2009-03-13
We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, comprising a first subsystem (a harmonic oscillator) coupled to a driven and damped second subsystem (another harmonic oscillator). We choose initial states whose dynamics is confined to a couple of two-level systems, and show that the maximum value of entanglement between the two subsystems, as measured by concurrence, depends on the dissipation rate to the coupling-constant ratio and the initial state. While in a related model the entropy of the first subsystem (a two-level system) never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model.
Damped driven coupled oscillators: entanglement, decoherence and the classical limit
International Nuclear Information System (INIS)
Mancilla, R D Guerrero; Rey-Gonzalez, R R; Fonseca-Romero, K M
2009-01-01
We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, comprising a first subsystem (a harmonic oscillator) coupled to a driven and damped second subsystem (another harmonic oscillator). We choose initial states whose dynamics is confined to a couple of two-level systems, and show that the maximum value of entanglement between the two subsystems, as measured by concurrence, depends on the dissipation rate to the coupling-constant ratio and the initial state. While in a related model the entropy of the first subsystem (a two-level system) never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model
Quenching oscillating behaviors in fractional coupled Stuart-Landau oscillators
Sun, Zhongkui; Xiao, Rui; Yang, Xiaoli; Xu, Wei
2018-03-01
Oscillation quenching has been widely studied during the past several decades in fields ranging from natural sciences to engineering, but investigations have so far been restricted to oscillators with an integer-order derivative. Here, we report the first study of amplitude death (AD) in fractional coupled Stuart-Landau oscillators with partial and/or complete conjugate couplings to explore oscillation quenching patterns and dynamics. It has been found that the fractional-order derivative impacts the AD state crucially. The area of the AD state increases along with the decrease of the fractional-order derivative. Furthermore, by introducing and adjusting a limiting feedback factor in coupling links, the AD state can be well tamed in fractional coupled oscillators. Hence, it provides one an effective approach to analyze and control the oscillating behaviors in fractional coupled oscillators.
QUANTUM THEORY OF DAMPED HARMONIC OSCILLATOR
African Journals Online (AJOL)
DJFLEX
However, the problem of quantum oscillator with time-varying frequency had been solved (Um et al,. 1987). The Hamiltonian of this model is usually quadratic in co-ordinates and momentum operators (Ikot et al, 2008). The quantum calculation is applied because it will give the information about the particle at intermediate ...
The forced harmonic oscillator with damping and thermal effects
International Nuclear Information System (INIS)
Menezes Franca, H. de; Thomaz, M.T.
1984-01-01
Nonperturbative quantum mechanical solutions of the forced harmonic oscillator with radiation reaction damping are obtained from previous analysis based on Stochastic Electrodynamics. The transition to excited states is shown to be to coherent states which follow the classical trajectory. The quantum Wigner distribution in phase space is constructed. All the results are extended to finite temperatures. (Author) [pt
Maximal Regularity of the Discrete Harmonic Oscillator Equation
Directory of Open Access Journals (Sweden)
Airton Castro
2009-01-01
Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the ...
Thermal state of the general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. The uncertainty relation of the system is always larger than ħ=2 not only in number but also in the thermal state as expected. We used the diagonal elements of density operator ...
A simple mechanical model for the isotropic harmonic oscillator
International Nuclear Information System (INIS)
Nita, Gelu M
2010-01-01
A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels.
Quantum theory of damped harmonic oscillator | Antia | Global ...
African Journals Online (AJOL)
The exact solutions of the Schrödinger equation for damped harmonic oscillator with pulsating mass and modified Caldirola-Kanai Hamiltonian are evaluated. We also investigated the case of under-damped for the two models constructed and the results obtained in both cases do not violate Heisenberg uncertainty principle ...
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
symmetries are expressed in the form of generators. We have studied the ..... For λ = 0, Iβ=1 represents the total energy of the harmonic oscillator with Uβ=1 as the time .... Ind. J. Pure Appl. Phys. 43, 479 (2005); Classical and quantum me-.
Statistical mechanics of quantum one-dimensional damped harmonic oscillator
International Nuclear Information System (INIS)
Borges, E.N.M.; Borges, O.N.; Ribeiro, L.A.A.
1985-01-01
We calculate the thermal correlation functions of the one-dimensional damped harmonic oscillator in contact with a reservoir, in an exact form by applying Green's function method. In this way the thermal fluctuations are incorporated in the Caldirola-Kanai Hamiltonian
The resonating group method in an harmonic oscillator basis
International Nuclear Information System (INIS)
Silvestre-Brac, B.; Gignoux, C.; Ayant, Y.
1987-05-01
The scattering states for a general many body system is formulated within the resonating group method. The resulting Lippman-Schwinger equation is solved in an harmonic oscillator basis for which a number of advantages are emphasized. The analytical formula giving the free propagator in that basis is fully derived
Revisiting the quantum harmonic oscillator via unilateral Fourier transforms
International Nuclear Information System (INIS)
Nogueira, Pedro H F; Castro, Antonio S de
2016-01-01
The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions. (paper)
Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps
Pendrill, Ann-Marie; Eager, David
2015-01-01
Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…
New construction of coherent states for generalized harmonic oscillators
International Nuclear Information System (INIS)
El Baz, M.; Hassouni, Y.; Madouri, F.
2001-08-01
A dynamical algebra A q , englobing many of the deformed harmonic oscillator algebras is introduced. One of its special cases is extensively developed. A general method for constructing coherent states related to any algebra of the type A q is discussed. The construction following this method is carried out for the special case. (author)
On quantum harmonic oscillator being subjected to absolute ...
Indian Academy of Sciences (India)
On quantum harmonic oscillator being subjected to absolute potential state. SWAMI NITYAYOGANANDA. Ramakrishna Mission Ashrama, R.K. Beach, Visakhapatnam 530 003, India. E-mail: nityayogananda@gmail.com. MS received 1 May 2015; accepted 6 May 2016; published online 3 December 2016. Abstract.
Coherent states of general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
Abstract. By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator. The coherent states, both in x- and p-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger than Η/2 and is equal to the minimum of the ...
International Nuclear Information System (INIS)
Caetano Neto, E.S.
1976-01-01
A stationary Green function is calculated for the Schroedinger Hamiltonian of the multidimensional isotropic harmonic oscillator and for physical systems, which may, somehow, have their Hamiltonian reduced to one in the form of a harmonic oscillator, for any dimension [pt
Modeling of Coupled Chaotic Oscillators
International Nuclear Information System (INIS)
Lai, Y.; Grebogi, C.
1999-01-01
Chaotic dynamics may impose severe limits to deterministic modeling by dynamical equations of natural systems. We give theoretical argument that severe modeling difficulties may occur for high-dimensional chaotic systems in the sense that no model is able to produce reasonably long solutions that are realized by nature. We make these ideas concrete by investigating systems of coupled chaotic oscillators. They arise in many situations of physical and biological interests, and they also arise from discretization of nonlinear partial differential equations. copyright 1999 The American Physical Society
Effective harmonic oscillator description of anharmonic molecular ...
Indian Academy of Sciences (India)
Administrator
are carried out in HO basis, this study ought to pro- vide an insight into ... coupling are presented in Section 2 and the con- truction of VOHB is ..... quantum numbers of the target state. After initializing .... Computational facilities pro- vided by the ...
Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator
International Nuclear Information System (INIS)
Belendez, Augusto; Pascual, Carolina
2007-01-01
The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A
Energy Technology Data Exchange (ETDEWEB)
Rosu, H.C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosi, S.L.P. (Mexico); Khmelnytskaya, K.V. [Universidad Autonoma de Queretaro, Centro Universitario, Cerro de las Campanas s/n, C.P. 76010 Santiago de Queretaro, Qro. (Mexico)
2011-09-19
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned. -- Highlights: → A particular Riccati solution of the classical harmonic oscillator is shifted by a constant. → Such a solution is used in the factorization brackets to get different equations of motion. → The properties of the parametric oscillators obtained in this way are examined.
Predicting chaos in memristive oscillator via harmonic balance method.
Wang, Xin; Li, Chuandong; Huang, Tingwen; Duan, Shukai
2012-12-01
This paper studies the possible chaotic behaviors in a memristive oscillator with cubic nonlinearities via harmonic balance method which is also called the method of describing function. This method was proposed to detect chaos in classical Chua's circuit. We first transform the considered memristive oscillator system into Lur'e model and present the prediction of the existence of chaotic behaviors. To ensure the prediction result is correct, the distortion index is also measured. Numerical simulations are presented to show the effectiveness of theoretical results.
Synchronization of indirectly coupled Lorenz oscillators
Indian Academy of Sciences (India)
Synchronization of indirectly coupled Lorenz oscillators: An experimental study. Amit Sharma Manish Dev Shrimali. Synchronization, Coupled Systems and Networks Volume 77 Issue 5 November 2011 pp 881-889 ... The in-phase and anti-phase synchronization of indirectly coupled chaotic oscillators reported in Phys. Rev ...
Coupled oscillators with parity-time symmetry
Energy Technology Data Exchange (ETDEWEB)
Tsoy, Eduard N., E-mail: etsoy@uzsci.net
2017-02-05
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. - Highlights: • A generalization of a Hamiltonian system of linear coupled oscillators with the parity-time (PT) symmetry is suggested. • It is found that an increase of the gain-loss parameter can stabilize the system. • A family of Hamiltonian functions for two coupled nonlinear oscillators with PT-symmetry is obtained.
First, Second Quantization and Q-Deformed Harmonic Oscillator
International Nuclear Information System (INIS)
Van Ngu, Man; Vinh, Ngo Gia; Lan, Nguyen Tri; Viet, Nguyen Ai; Thanh, Luu Thi Kim
2015-01-01
Relations between the first, the second quantized representations and deform algebra are investigated. In the case of harmonic oscillator, the axiom of first quantization (the commutation relation between coordinate and momentum operators) and the axiom of second quantization (the commutation relation between creation and annihilation operators) are equivalent. We shown that in the case of q-deformed harmonic oscillator, a violence of the axiom of second quantization leads to a violence of the axiom of first quantization, and inverse. Using the coordinate representation, we study fine structures of the vacuum state wave function depend in the deformation parameter q. A comparison with fine structures of Cooper pair of superconductivity in the coordinate representation is also performed. (paper)
Harmonic response of coupled and uncoupled granular YBCO
International Nuclear Information System (INIS)
Torralba, Maria Veronica S; Sarmago, Roland V
2004-01-01
The harmonic responses of granular YBCO were obtained via mutual inductance measurements. Two samples, one with and another without intergranular coupling, were investigated in terms of the harmonic components of magnetization at various field amplitudes and frequencies. By comparing the behaviour of the features in the harmonics to that of the peaks in the fundamental response, we explicitly identified which features in the harmonics originate from intragranular harmonic generation and which arise due to a contribution of intergranular coupling. Harmonic responses were obtained despite the absence of vortices and even harmonics were detected in a purely AC magnetic field
An analogue of the Berry phase for simple harmonic oscillators
Suslov, S. K.
2013-03-01
We evaluate a variant of Berry's phase for a ‘missing’ family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables (in a natural way). Instead, it is obtained by the action of the maximal kinematical invariance group on the standard solutions. A simple closed formula for the phase (in terms of elementary functions) is found here by integration with the help of a computer algebra system.
Pisot q-coherent states quantization of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Gazeau, J.P., E-mail: gazeau@apc.univ-paris7.fr [Laboratoire APC, Univ. Paris Diderot, Sorbonne Paris Cite, 75205 Paris (France); Olmo, M.A. del, E-mail: olmo@fta.uva.es [Departamento de Fisica Teorica and IMEVA, Universidad de Valladolid, E-47005, Valladolid (Spain)
2013-03-15
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories. - Highlights: Black-Right-Pointing-Pointer Quantized version of the harmonic oscillator (HO) through a q-family of coherent states. Black-Right-Pointing-Pointer For q,0
oscillator.
Nonlocal synchronization in nearest neighbour coupled oscillators
International Nuclear Information System (INIS)
El-Nashar, H.F.; Elgazzar, A.S.; Cerdeira, H.A.
2002-02-01
We investigate a system of nearest neighbour coupled oscillators. We show that the nonlocal frequency synchronization, that might appear in such a system, occurs as a consequence of the nearest neighbour coupling. The power spectra of nonadjacent oscillators shows that there is no complete coincidence between all frequency peaks of the oscillators in the nonlocal cluster, while the peaks for neighbouring oscillators approximately coincide even if they are not yet in a cluster. It is shown that nonadjacent oscillators closer in frequencies, share slow modes with their adjacent oscillators which are neighbours in space. It is also shown that when a direct coupling between non-neighbours oscillators is introduced explicitly, the peaks of the spectra of the frequencies of those non-neighbours coincide. (author)
The Harmonically Coupled 2-Beam FEL
McNeil, Brian W J
2004-01-01
A 1-D model of a 2-beam Free Electron Laser amplifier is presented. The two co-propagating electron beams have different energies, chosen so that the fundamental resonant FEL interaction of the higher energy beam is at an harmonic of the lower energy beam. In this way, a coupling between the FEL interactions of the two beams occurs via the harmonic components of the electron bunching and radiation emission of the lower energy interaction. Such resonantly coupled FEL interactions may offer potential benefits over existing single beam FEL schemes. A simple example is presented where the lower energy FEL interaction only is seeded with radiation at its fundamental resonant wavelength. It is predicted that the coherence properties of this seed field are transfered via the resonantly coupled FEL interaction to the un-seeded higher energy FEL interaction, thereby improving its coherence properties over that of a SASE interaction alone. This method may offer an alternative seeding scheme for FELs operating in the XU...
Balaji, Nidish Narayanaa; Krishna, I. R. Praveen; Padmanabhan, C.
2018-05-01
The Harmonic Balance Method (HBM) is a frequency-domain based approximation approach used for obtaining the steady state periodic behavior of forced dynamical systems. Intrinsically these systems are non-autonomous and the method offers many computational advantages over time-domain methods when the fundamental period of oscillation is known (generally fixed as the forcing period itself or a corresponding sub-harmonic if such behavior is expected). In the current study, a modified approach, based on He's Energy Balance Method (EBM), is applied to obtain the periodic solutions of conservative systems. It is shown that by this approach, periodic solutions of conservative systems on iso-energy manifolds in the phase space can be obtained very efficiently. The energy level provides the additional constraint on the HBM formulation, which enables the determination of the period of the solutions. The method is applied to the linear harmonic oscillator, a couple of nonlinear oscillators, the elastic pendulum and the Henon-Heiles system. The approach is used to trace the bifurcations of the periodic solutions of the last two, being 2 degree-of-freedom systems demonstrating very rich dynamical behavior. In the process, the advantages offered by the current formulation of the energy balance is brought out. A harmonic perturbation approach is used to evaluate the stability of the solutions for the bifurcation diagram.
Compensation of oscillation coupling induced by solenoids
International Nuclear Information System (INIS)
Zelinskij, A.Yu.; Karnaukhov, I.M.; Shcherbakov, A.A.
1988-01-01
Methods for construction of various schemes of oscillation coupling compensation, induced by solenoids in charged particle storage rings, are described. Peculiarities of magnetic structure, enabling to localize oscillation coupling in wide energy range are discussed. Results of calculation of compensation schemes for design of NR-2000 storage ring spin rotation are presented
Harmonic-oscillator pattern arising from an algebraic approach to chiral symmetry
Buccella, F; Savoy, C A
1972-01-01
The Weinberg equation for the (mass)/sup 2/ operator (Q/sub 5//sup +/, (Q/sub 5//sup +/, m/sup 2/))=0, between meson states, is saturated in a perturbative approach. The generator Z of the mixing operators is completely established as Z=(W*M)/sub z/, where W is the W-spin operator and M is the co-ordinate of the three-dimensional harmonic oscillator. In a perturbative expansion of the (mass)/sup 2/ operator, the lowest term consists of two parts, the harmonic-oscillator energy and a spin-orbit coupling of the form (-1)/sup L+1/(L.S+/sup 1///sub 2 /). The resulting (mass)/sup 2/ consists of families of equispaced linearly rising trajectories. (11 refs).
Kraus representation of a damped harmonic oscillator and its application
International Nuclear Information System (INIS)
Liu Yuxi; Oezdemir, Sahin K.; Miranowicz, Adam; Imoto, Nobuyuki
2004-01-01
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
Optimal control of a harmonic oscillator: Economic interpretations
Janová, Jitka; Hampel, David
2013-10-01
Optimal control is a popular technique for modelling and solving the dynamic decision problems in economics. A standard interpretation of the criteria function and Lagrange multipliers in the profit maximization problem is well known. On a particular example, we aim to a deeper understanding of the possible economic interpretations of further mathematical and solution features of the optimal control problem: we focus on the solution of the optimal control problem for harmonic oscillator serving as a model for Phillips business cycle. We discuss the economic interpretations of arising mathematical objects with respect to well known reasoning for these in other problems.
A Generalized Time-Dependent Harmonic Oscillator at Finite Temperature
International Nuclear Information System (INIS)
Majima, H.; Suzuki, A.
2006-01-01
We show how a generalized time-dependent harmonic oscillator (GTHO) is extended to a finite temperature case by using thermo field dynamics (TFD). We derive the general time-dependent annihilation and creation operators for the system, and obtain the time-dependent quasiparticle annihilation and creation operators for the GTHO by using the temperature-dependent Bogoliubov transformation of TFD. We also obtain the thermal state as a two-mode squeezed vacuum state in the time-dependent case as well as in the time-independent case. The general formula is derived to calculate the thermal expectation value of operators
Complex-potential description of the damped harmonic oscillator
International Nuclear Information System (INIS)
Exner, P.
1981-01-01
Multidimensional damped harmonic oscillator is treated by means of a non-selfadjoint Hamiltonian with complex potential. The latter is chosen as V(x)=xx(A-iW)x with positive matrices A, W, By a perturbation-theory argument, the corresponding Hamiltonian H=-1/2Δ+V with the natural domain is shown to be closed and such that Vsub(t)=exp(-iHt) is a continuous contractive semigroup. Explicit integral-operator form of Vsub(t) is found by use of Lie-Trotter formula [ru
Elementary derivation of the quantum propagator for the harmonic oscillator
Shao, Jiushu
2016-10-01
Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.
A method of solving simple harmonic oscillator Schroedinger equation
Maury, Juan Carlos F.
1995-01-01
A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.
Free harmonic oscillators, Jack polynomials, and Calogero-Sutherland systems
International Nuclear Information System (INIS)
Gurappa, N.; Panigrahi, Prasanta K.
2000-01-01
The algebraic structure and the relationships between the eigenspaces of the Calogero-Sutherland model (CSM) and the Sutherland model (SM) on a circle are investigated through the Cherednik operators. We find an exact connection between the simultaneous nonsymmetric eigenfunctions of the A N-1 Cherednik operators, from which the eigenfunctions of the CSM and SM are constructed, and the monomials. This construction allows us to simultaneously diagonalize both CSM and SM (after gauging away the Hamiltonians by suitable measures) and also enables us to write down a harmonic oscillator algebra involving the Cherednik operators, which yields the raising and lowering operators for both of these models. The connections of the CSM with free oscillators and the SM with free particles on a circle are established in a novel way. We also point out the subtle differences between the excitations of the CSM and the SM
The Aerodynamic Behavior of a Harmonically Oscillating Finite Sweptback Wing in Supersonic Flow
National Research Council Canada - National Science Library
Chang, Chieh-Chien
1951-01-01
By an extension of Evvard's "diaphragm" concept outside the wing tip, the present paper presents two approximate methods for calculating the aerodynamic behavior of harmonically oscillating, sweptback...
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
International Nuclear Information System (INIS)
Chou, Chia-Chun
2016-01-01
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.
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw
2016-10-15
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Non-unique monopole oscillations of harmonically confined Yukawa systems
Ducatman, Samuel; Henning, Christian; Kaehlert, Hanno; Bonitz, Michael
2008-11-01
Recently it was shown that the Breathing Mode (BM), the mode of uniform radial expansion and contraction, which is well known from harmonically confined Coulomb systems [1], does not exist in general for other systems [2]. As a consequence the monopole oscillation (MO), the radial collective excitation, is not unique, but there are several MO with different frequencies. Within this work we show simulation results of those monopole oscillations of 2-dimensional harmonically confined Yukawa systems, which are known from, e.g., dusty plasma crystals [3,4]. We present the corresponding spectrum of the particle motion, including analysis of the frequencies found, and compare with theoretical investigations.[1] D.H.E. Dubin and J.P. Schiffer, Phys. Rev. E 53, 5249 (1996)[2] C. Henning at al., accepted for publication in Phys. Rev. Lett. (2008)[3] A. Melzer et al., Phys. Rev. Lett. 87, 115002 (2001)[4] M. Bonitz et al., Phys. Rev. Lett. 96, 075001 (2006)
International Nuclear Information System (INIS)
Blasone, Massimo; Jizba, Petr
2004-01-01
By using the Feynman-Hibbs prescription for the evolution amplitude, we quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. The time-dependent quantum states of such a system are constructed and discussed entirely in the framework of the classical theory. The corresponding geometric (Pancharatnam) phase is calculated and found to be directly related to the ground-state energy of the 1D linear harmonic oscillator to which the 2D system reduces under appropriate constraint
International Nuclear Information System (INIS)
Fox, Ronald F.; Vela-Arevalo, Luz V.
2002-01-01
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
International Nuclear Information System (INIS)
Yeh, Y.S.; Chang, T.H.; Wu, T.S.
2004-01-01
A comparative analysis between the fundamental and second cyclotron harmonics of gyrotron backward-wave oscillators (gyro-BWOs) is presented. The simulation results reveal that nonlinear field contraction is a common feature for both harmonic interactions. Besides, the electron transit angle, used to characterize the axial modes of the fundamental harmonic TE 11 mode at the start-oscillation conditions, is found to be applicable even for the second harmonic TE 21 mode. Each axial mode of either the fundamental harmonic TE 11 or the second harmonic TE 21 modes is maintained at a constant value of the electron transit angle while changing the operating parameters, such as magnetic field and beam voltage. Extensive numerical calculations are conducted for the start-oscillation currents and tuning properties. Moreover, single-mode operating regimes are suggested where the second harmonic TE 21 gyro-BWO could generate a considerable output power, comparing with the fundamental harmonic TE 11 gyro-BWO
Quantization of a free particle interacting linearly with a harmonic oscillator
International Nuclear Information System (INIS)
Mainiero, Thomas; Porter, Mason A.
2007-01-01
We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the quantization of mixed systems. We identify key signatures of the classically chaotic and regular portions in the quantum system by constructing Husimi distributions and investigating avoided level crossings of eigenvalues as functions of the strength and range of the interaction between the system's two components. We show, in particular, that the Husimi structure becomes mixed and delocalized as the classical dynamics becomes more chaotic
High spin rotations of nuclei with the harmonic oscillator potential
International Nuclear Information System (INIS)
Cerkaski, M.; Szymanski, Z.
1978-01-01
Calculations of the nuclear properties at high angular momentum have been performed recently. They are based on the liquid drop model of a nucleus and/or on the assumption of the single particle shell structure of the nucleonic motion. The calculations are usually complicated and involve long computer codes. In this article we shall discuss general trends in fast rotating nuclei in the approximation of the harmonic oscillator potential. We shall see that using the Bohr Mottelson simplified version of the rigorous solution of Valatin one can perform a rather simple analysis of the rotational bands, structure of the yrast line, moments of inertia etc. in the rotating nucleus. While the precision fit to experimental data in actual nuclei is not the purpose of this paper, one can still hope to reach some general understanding within the model of the simple relations resulting in nuclei at high spin. (author)
Quantization with maximally degenerate Poisson brackets: the harmonic oscillator!
International Nuclear Information System (INIS)
Nutku, Yavuz
2003-01-01
Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these degenerate Poisson brackets are brought to the form of Heisenberg's equations. We propose a definition for constructing quantum operators for classical functions, which enables us to turn the maximally degenerate Poisson brackets into operators. They pose a set of eigenvalue problems for a new state vector. The requirement of the single-valuedness of this eigenfunction leads to quantization. The example of the harmonic oscillator is used to illustrate this general procedure for quantizing a class of maximally super-integrable systems
Refined Weyl Law for Homogeneous Perturbations of the Harmonic Oscillator
Doll, Moritz; Gannot, Oran; Wunsch, Jared
2018-02-01
Let H denote the harmonic oscillator Hamiltonian on R}^d,} perturbed by an isotropic pseudodifferential operator of order 1. We consider the Schrödinger propagator {U(t)=e^{-itH},} and find that while sing-supp Tr U(t) \\subset 2 π Z as in the unperturbed case, there exists a large class of perturbations in dimensions {d ≥ 2 for which the singularities of {Tr U(t)} at nonzero multiples of {2 π} are weaker than the singularity at t = 0. The remainder term in the Weyl law is of order {o(λ^{d-1})} , improving in these cases the {o(λ^{d-1})} remainder previously established by Helffer-Robert.
Modeling stock return distributions with a quantum harmonic oscillator
Ahn, K.; Choi, M. Y.; Dai, B.; Sohn, S.; Yang, B.
2017-11-01
We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.
Shapes of nuclear configurations in a cranked harmonic oscillator model
International Nuclear Information System (INIS)
Troudet, T.; Arvieu, R.
1980-05-01
The shapes of nuclear configurations are calculated using Slater determinants built with cranked harmonic oscillator single particle states. The nuclear forces role is played by a volume conservation condition (of the potential or of the density) in a first part. In a second part, we have used the finite range, density dependent interaction of Cogny. A very simple classification of configurations emerges in the first part, the relevant parameter being the equatorial eccentricity of the nuclear density. A critical equatorial eccentricity is obtained which governs the accession to the case for which the nucleus is oblate and symmetric around its axis of rotation. Nuclear configurations calculated in the second part observe remarkably well these behaviors
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
Lee, Keeyung
2009-01-01
The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…
Exact solution of a quantum forced time-dependent harmonic oscillator
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
1992-01-01
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
Excitation of high numbers harmonics by flows of oscillators in a periodic potential
International Nuclear Information System (INIS)
Buts, V.A.; Marekha, V.I.; Tolstoluzhsky, A.P.
2005-01-01
It is shown that the maximum of radiation spectrum of nonrelativistic oscillators, which move into a periodically inhomogeneous potential, can be in the region of high numbers harmonics. Spectrum of such oscillators radiation becomes similar to the radiation spectrum of relativistic oscillators. The equations, describing the non-linear self-consistent theory of excitations, of high numbers harmonics by ensemble of oscillators are formulated and its numerical analysis is conducted. The numerical analysis has confirmed the capability of radiation of high numbers of harmonics. Such peculiarity of radiation allows t expect of creation of nonrelativistic FEL
Symmetries of cyclic work distributions for an isolated harmonic oscillator
International Nuclear Information System (INIS)
Ford, Ian J; Minor, David S; Binnie, Simon J
2012-01-01
We have calculated the distribution of work W done on a 1D harmonic oscillator that is initially in canonical equilibrium at temperature T, then thermally isolated and driven by an arbitrary time-dependent cyclic spring constant κ(t), and demonstrated that it satisfies P(W) = exp (βW)P( − W), where β = 1/k B T, in both classical and quantum dynamics. This differs from the celebrated Crooks relation of nonequilibrium thermodynamics, since the latter relates distributions for forward and backward protocols of driving. We show that it is a special case of a symmetry that holds for non-cyclic work processes on the isolated oscillator, and that consideration of time reversal invariance shows it to be consistent with the Crooks relation. We have verified that the symmetry holds in both classical and quantum treatments of the dynamics, but that inherent uncertainty in the latter case leads to greater fluctuations in work performed for a given process. (paper)
Adaptive elimination of synchronization in coupled oscillator
Zhou, Shijie; Ji, Peng; Zhou, Qing; Feng, Jianfeng; Kurths, Jürgen; Lin, Wei
2017-08-01
We present here an adaptive control scheme with a feedback delay to achieve elimination of synchronization in a large population of coupled and synchronized oscillators. We validate the feasibility of this scheme not only in the coupled Kuramoto’s oscillators with a unimodal or bimodal distribution of natural frequency, but also in two representative models of neuronal networks, namely, the FitzHugh-Nagumo spiking oscillators and the Hindmarsh-Rose bursting oscillators. More significantly, we analytically illustrate the feasibility of the proposed scheme with a feedback delay and reveal how the exact topological form of the bimodal natural frequency distribution influences the scheme performance. We anticipate that our developed scheme will deepen the understanding and refinement of those controllers, e.g. techniques of deep brain stimulation, which have been implemented in remedying some synchronization-induced mental disorders including Parkinson disease and epilepsy.
Adaptive elimination of synchronization in coupled oscillator
International Nuclear Information System (INIS)
Zhou, Shijie; Lin, Wei; Ji, Peng; Feng, Jianfeng; Zhou, Qing; Kurths, Jürgen
2017-01-01
We present here an adaptive control scheme with a feedback delay to achieve elimination of synchronization in a large population of coupled and synchronized oscillators. We validate the feasibility of this scheme not only in the coupled Kuramoto’s oscillators with a unimodal or bimodal distribution of natural frequency, but also in two representative models of neuronal networks, namely, the FitzHugh–Nagumo spiking oscillators and the Hindmarsh–Rose bursting oscillators. More significantly, we analytically illustrate the feasibility of the proposed scheme with a feedback delay and reveal how the exact topological form of the bimodal natural frequency distribution influences the scheme performance. We anticipate that our developed scheme will deepen the understanding and refinement of those controllers, e.g. techniques of deep brain stimulation, which have been implemented in remedying some synchronization-induced mental disorders including Parkinson disease and epilepsy. (paper)
Verreault, René
2017-08-01
In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes' dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2-3 orders of magnitude is achieved.
Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom
Plenio, M. B.; Hartley, J.; Eisert, J.
2004-03-01
We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest-neighbour interactions. For a one-dimensional chain, we provide compact analytical solutions and approximations to the dynamical evolution of the entanglement between spatially separated oscillators. Key properties such as the speed of entanglement propagation, the maximum amount of transferred entanglement and the efficiency for the entanglement transfer are computed. For harmonic oscillators coupled by springs, corresponding to a phonon model, we observe a non-monotonic transfer efficiency in the initially prepared amount of entanglement, i.e. an intermediate amount of initial entanglement is transferred with the highest efficiency. In contrast, within the framework of the rotating-wave approximation (as appropriate, e.g. in quantum optical settings) one finds a monotonic behaviour. We also study geometrical configurations that are analogous to quantum optical devices (such as beamsplitters and interferometers) and observe characteristic differences when initially thermal or squeezed states are entering these devices. We show that these devices may be switched on and off by changing the properties of an individual oscillator. They may therefore be used as building blocks of large fixed and pre-fabricated but programmable structures in which quantum information is manipulated through propagation. We discuss briefly possible experimental realizations of systems of interacting harmonic oscillators in which these effects may be confirmed experimentally.
Flashing coupled density wave oscillation
International Nuclear Information System (INIS)
Jiang Shengyao; Wu Xinxin; Zhang Youjie
1997-07-01
The experiment was performed on the test loop (HRTL-5), which simulates the geometry and system design of the 5 MW reactor. The phenomenon and mechanism of different kinds of two-phase flow instabilities, namely geyser instability, flashing instability and flashing coupled density wave instability are described. The especially interpreted flashing coupled density wave instability has never been studied well, it is analyzed by using a one-dimensional non-thermo equilibrium two-phase flow drift model computer code. Calculations are in good agreement with the experiment results. (5 refs.,5 figs., 1 tab.)
Mode coupling in spin torque oscillators
International Nuclear Information System (INIS)
Zhang, Steven S.-L.; Zhou, Yan; Li, Dong; Heinonen, Olle
2016-01-01
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. Our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. The acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature. - Highlights: • Deriving equations for coupled modes in spin torque oscillators. • Including Hamiltonian formalism and elimination of three–magnon processes. • Thermal bath of magnons central to mode coupling. • Numerical examples of circular and elliptical devices.
Mode coupling in spin torque oscillators
Energy Technology Data Exchange (ETDEWEB)
Zhang, Steven S.-L., E-mail: ZhangShule@missouri.edu [Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211 (United States); Zhou, Yan, E-mail: yanzhou@hku.hk [Department of Physics, The University of Hong Kong, Hong Kong (China); Center of Theoretical and Computational Physics, University of Hong Kong, Hong Kong (China); Li, Dong, E-mail: geodesic.ld@gmail.com [Department of Physics, Centre for Nonlinear Studies, and Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems, Hong Kong Baptist University, Kowloon Tong, Hong Kong (China); Heinonen, Olle, E-mail: heinonen@anl.gov [Material Science Division, Argonne National Laboratory, Lemont, IL 60439 (United States); Northwestern-Argonne Institute of Science and Technology, 2145 Sheridan Road, Evanston, IL 60208 (United States); Computation Institute, The Unversity of Chicago, 5735 S Ellis Avenue, Chicago, IL 60637 (United States)
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. Our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. The acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature. - Highlights: • Deriving equations for coupled modes in spin torque oscillators. • Including Hamiltonian formalism and elimination of three–magnon processes. • Thermal bath of magnons central to mode coupling. • Numerical examples of circular and elliptical devices.
Synchronization in Coupled Oscillators with Two Coexisting Attractors
International Nuclear Information System (INIS)
Han-Han, Zhu; Jun-Zhong, Yang
2008-01-01
Dynamics in coupled Duffing oscillators with two coexisting symmetrical attractors is investigated. For a pair of Duffing oscillators coupled linearly, the transition to the synchronization generally consists of two steps: Firstly, the two oscillators have to jump onto a same attractor, then they reach synchronization similarly to coupled monostable oscillators. The transition scenarios to the synchronization observed are strongly dependent on initial conditions. (general)
Isotropic harmonic oscillator plus inverse quadratic potential in N-dimensional spaces
International Nuclear Information System (INIS)
Oyewumi, K.A.; Bangudu, E.A.
2003-01-01
Some aspects of the N-dimensional isotropic harmonic plus inverse quadratic potential were discussed. The hyperradial equation for isotropic harmonic oscillator plus inverse quadratic potential is solved by transformation into the confluent hypergeometric equation to obtain the normalized hyperradial solution. Together with the hyperangular solutions (hyperspherical harmonics), these form the complete energy eigenfunctions of the N-dimensional isotropic harmonic oscillator plus inverse quadratic potential and the energy eigenvalues are also obtained. These are dimensionally dependent. The dependence of radial solution on the dimensions or potential strength and the degeneracy of the energy levels are discussed. (author)
The quantum harmonic oscillator on a circle and a deformed quantum field theory
International Nuclear Information System (INIS)
Rego-Monteiro, M.A.
2001-05-01
We construct a deformed free quantum field theory with an standard Hilbert space based on a deformed Heisenberg algebra. This deformed algebra is a Heisenberg-type algebra describing the first levels of the quantum harmonic oscillator on a circle of large length L. The successive energy levels of this quantum harmonic oscillator on a circle of large length L are interpreted, similarly to the standard quantum one-dimensional harmonic oscillator on an infinite line, as being obtained by the creation of a quantum particle of frequency w at very high energies. (author)
Li, Xiaoli; Li, Duan; Voss, Logan J; Sleigh, Jamie W
2009-11-15
Brain functions are related to neuronal networks of different sizes and distribution, and neuronal networks of different sizes oscillate at different frequencies. Thus the synchronization of neuronal networks is often reflected by cross-frequency interaction. The description of this cross-frequency interaction is therefore a crucial issue in understanding the modulation mechanisms between neuronal populations. A number of different kinds of interaction between frequencies have been reported. In this paper, we develop a general harmonic wavelet transform based bicoherence using a phase randomization method. This allows us to measure the comodulation of oscillations between different frequency bands in neuronal populations. The performance of the method is evaluated by a simulation study. The results show that the improved wavelet bicoherence method can detect a reliable phase coupling value, and also identify zero bicoherence for waves that are not phase-coupled. Spurious bicoherences can be effectively eliminated through the phase randomization method. Finally, this method is applied to electrocorticogram data recorded from rats during transitions between slow-wave sleep, rapid-eye movement sleep and waking. The phase coupling in rapid-eye movement sleep is statistically lower than that during slow-wave sleep, and slightly less than those in the wakeful state. The degree of phase coupling in rapid-eye movement sleep after slow-wave sleep is greater than in rapid-eye movement sleep prior to waking. This method could be applied to investigate the cross-frequency interactions in other physiological signals.
A position-dependent mass harmonic oscillator and deformed space
da Costa, Bruno G.; Borges, Ernesto P.
2018-04-01
We consider canonically conjugated generalized space and linear momentum operators x^ q and p^ q in quantum mechanics, associated with a generalized translation operator which produces infinitesimal deformed displacements controlled by a deformation parameter q. A canonical transformation (x ^ ,p ^ ) →(x^ q,p^ q ) leads the Hamiltonian of a position-dependent mass particle in usual space to another Hamiltonian of a particle with constant mass in a conservative force field of the deformed space. The equation of motion for the classical phase space (x, p) may be expressed in terms of the deformed (dual) q-derivative. We revisit the problem of a q-deformed oscillator in both classical and quantum formalisms. Particularly, this canonical transformation leads a particle with position-dependent mass in a harmonic potential to a particle with constant mass in a Morse potential. The trajectories in phase spaces (x, p) and (xq, pq) are analyzed for different values of the deformation parameter. Finally, we compare the results of the problem in classical and quantum formalisms through the principle of correspondence and the WKB approximation.
West Coast Swing Dancing as a Driven Harmonic Oscillator Model
Ferrara, Davon; Holzer, Marie; Kyere, Shirley
The study of physics in sports not only provides valuable insight for improved athletic performance and injury prevention, but offers undergraduate students an opportunity to engage in both short- and long-term research efforts. In this project, conducted by two non-physics majors, we hypothesized that a driven harmonic oscillator model can be used to better understand the interaction between two west coast swing dancers since the stiffness of the physical connection between dance partners is a known factor in the dynamics of the dance. The hypothesis was tested by video analysis of two dancers performing a west coast swing basic, the sugar push, while changing the stiffness of the physical connection. The difference in stiffness of the connection from the ideal was estimated by the leader; the position with time data from the video was used to measure changes in the amplitude and phase difference between the leader and follower. While several aspects of our results agree with the proposed model, some key characteristics do not, possibly due to the follower relying on visual leads. Corresponding author and principal investigator.
Classical and quantum mechanics of the damped harmonic oscillator
International Nuclear Information System (INIS)
Dekker, H.
1981-01-01
The relations between various treatments of the classical linearly damped harmonic oscillator and its quantization are investigated. In the course of a historical survey typical features of the problem are discussed on the basis of Havas' classical Hamiltonian and the quantum mechanical Suessmann-Hasse-Albrecht models as coined by the Muenchen/Garching nuclear physics group. It is then shown how by imposing a restriction on the classical trajectories in order to connect the Hamiltonian with the energy, the time-independent Bateman-Morse-Feshbach-Bopp Hamiltonian leads to the time-dependent Caldirola-Kanai Hamiltonian. Canonical quantization of either formulation entails a violation of Heisenberg's principle. By means of a unified treatment of both the electrical and mechanical semi-infinite transmission line, this defect is related to the disregard of additional quantum fluctuations that are intrinsically connected with the dissipation. The difficulties of these models are discussed. Then it is proved that the Bateman dual Hamiltonian is connected to a recently developed complex symplectic formulation by a simple canonical transformation. (orig.)
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Ley Koo, E.
The exact solution of the Schrodinger equation for the systems and the boundary condition stated in the title is constructed. The familiar cases of the ordinary harmonic oscillator and the half oscillator are immediately identified. The connection with the double oscillator is also established and is helpful to understand the energy spectrum of the latter. Similar connections can be used to study other partial oscillators. (Author) [pt
Dynamics of microbubble oscillators with delay coupling
Heckman, C. R.; Sah, S. M.; Rand, R. H.
2010-10-01
We investigate the stability of the in-phase mode in a system of two delay-coupled bubble oscillators. The bubble oscillator model is based on a 1956 paper by Keller and Kolodner. Delay coupling is due to the time it takes for a signal to travel from one bubble to another through the liquid medium that surrounds them. Using techniques from the theory of differential-delay equations as well as perturbation theory, we show that the equilibrium of the in-phase mode can be made unstable if the delay is long enough and if the coupling strength is large enough, resulting in a Hopf bifurcation. We then employ Lindstedt's method to compute the amplitude of the limit cycle as a function of the time delay. This work is motivated by medical applications involving noninvasive localized drug delivery via microbubbles.
Study of the phase delay in the amplitude-modulated harmonic oscillator
International Nuclear Information System (INIS)
Krupska, Aldona; Krupski, Marcin
2003-01-01
The delayed response of a damped harmonic oscillator (RLC circuit) to a slow periodic disturbance is presented. This communication is supplementary to the paper published recently (Krupska et al 2001 Eur. J. Phys. 22 133-8)
International Nuclear Information System (INIS)
Wang Jisuo; Sun Changyong; He Jinyu
1996-01-01
The eigenstates of the higher power of the annihilation operator a qs k (k≥3) of the two-parameter deformed harmonic oscillator are constructed. Their completeness is demonstrated in terms of the qs-integration
Schwinger's formula and the partition function for the bosonic and fermionic harmonic oscillators
International Nuclear Information System (INIS)
Albuquerque, L.C. de; Farina, C.; Rabello, S.J.
1994-01-01
We use Schwinger's formula, introduced by himself in the early fifties to compute effective actions for Qed, and recently applied to the Casimir effect, to obtain the partition functions for both the bosonic and fermionic harmonic oscillators. (author)
Energy spectrum inverse problem of q -deformed harmonic oscillator and WBK approximation
International Nuclear Information System (INIS)
Sang, Nguyen Anh; Thuy, Do Thi Thu; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai
2016-01-01
Using the connection between q-deformed harmonic oscillator and Morse-like anharmonic potential we investigate the energy spectrum inverse problem. Consider some energy levels of energy spectrum of q -deformed harmonic oscillator are known, we construct the corresponding Morse-like potential then find out the deform parameter q . The application possibility of using the WKB approximation in the energy spectrum inverse problem was discussed for the cases of parabolic potential (harmonic oscillator), Morse-like potential ( q -deformed harmonic oscillator). so we consider our deformed-three-levels simple model, where the set-parameters of Morse potential and the corresponding set-parameters of level deformations are easily and explicitly defined. For practical problems, we propose the deformed- three-levels simple model, where the set-parameters of Morse potential and the corresponding set-parameters of level deformations are easily and explicitly defined. (paper)
Supersymmetry and the constants of motion of the two-dimensional isotropic harmonic oscillator
International Nuclear Information System (INIS)
Torres del Castillo, G.F.; Tepper G, T.
2002-01-01
It is shown that the constants of motion of the two-dimensional isotropic harmonic oscillator not related to the rotational invariance of the Hamiltonian can be derived using the ideas of supersymmetric quantum mechanics. (Author)
Exact diagonalization of the D-dimensional spatially confined quantum harmonic oscillator
Directory of Open Access Journals (Sweden)
Kunle Adegoke
2016-01-01
Full Text Available In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.
Ge, Li; Zhao, Nan
2018-04-01
We study the coherence dynamics of a qubit coupled to a harmonic oscillator with both linear and quadratic interactions. As long as the linear coupling strength is much smaller than the oscillator frequency, the long time behavior of the coherence is dominated by the quadratic coupling strength g 2. The coherence decays and revives at a period , with the width of coherence peak decreasing as the temperature increases, hence providing a way to measure g 2 precisely without cooling. Unlike the case of linear coupling, here the coherence dynamics never reduces to the classical limit in which the oscillator is classical. Finally, the validity of linear coupling approximation is discussed and the coherence under Hahn-echo is evaluated.
Virtanen, J.E.; Maten, ter E.J.W.; Beelen, T.G.J.; Honkala, M.; Hulkkonen, M.
2011-01-01
Poor initial conditions for Harmonic Balance (HB) analysis of freerunning oscillators may lead to divergence of the direct Newton-Raphson method or may prevent to find the solution within an optimization approach. We exploit time integration to obtain estimates for the oscillation frequency and for
Virtanen, J.E.; Maten, ter E.J.W.; Honkala, M.; Hulkkonen, M.; Günther, M.; Bartel, A.; Brunk, M.; Schoeps, S.; Striebel, M.
2012-01-01
Poor initial conditions for Harmonic Balance (HB) analysis of free-running oscillators may lead to divergence of the direct Newton-Raphson method or may prevent to find the solution within an optimization approach. We exploit time integration to obtain estimates for the oscillation frequency and for
Momentum diffusion for coupled atom-cavity oscillators
International Nuclear Information System (INIS)
Murr, K.; Maunz, P.; Pinkse, P. W. H.; Puppe, T.; Schuster, I.; Rempe, G.; Vitali, D.
2006-01-01
It is shown that the momentum diffusion of free-space laser cooling has a natural correspondence in optical cavities when the internal state of the atom is treated as a harmonic oscillator. We derive a general expression for the momentum diffusion, which is valid for most configurations of interest: The atom or the cavity or both can be probed by lasers, with or without the presence of traps inducing local atomic frequency shifts. It is shown that, albeit the (possibly strong) coupling between atom and cavity, it is sufficient for deriving the momentum diffusion to consider that the atom couples to a mean cavity field, which gives a first contribution, and that the cavity mode couples to a mean atomic dipole, giving a second contribution. Both contributions have an intuitive form and present a clear symmetry. The total diffusion is the sum of these two contributions plus the diffusion originating from the fluctuations of the forces due to the coupling to the vacuum modes other than the cavity mode (the so-called spontaneous emission term). Examples are given that help to evaluate the heating rates induced by an optical cavity for experiments operating at low atomic saturation. We also point out intriguing situations where the atom is heated although it cannot scatter light
Third harmonic generation by Bloch-oscillating electrons in a quasioptical array
International Nuclear Information System (INIS)
Ghosh, A.W.; Wanke, M.C.; Allen, S.J.; Wilkins, J.W.
1999-01-01
We compute the third harmonic field generated by Bloch-oscillating electrons in a quasioptical array of superlattices under THz irradiation. The third harmonic power transmitted oscillates with the internal electric field, with nodes associated with Bessel functions in eEd/ℎω. The nonlinear response of the array causes the output power to be a multivalued function of the incident laser power. The output can be optimized by adjusting the frequency of the incident pulse to match one of the Fabry-Pacute erot resonances in the substrate. Within the transmission-line model of the array, the maximum conversion efficiency is 0.1%. copyright 1999 American Institute of Physics
On the effects of a screw dislocation and a linear potential on the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Bueno, M.J.; Furtado, C., E-mail: furtado@fisica.ufpb.br; Bakke, K., E-mail: kbakke@fisica.ufpb.br
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.
SOLUTION OF HARMONIC OSCILLATOR OF NONLINEAR MASTER SCHRÃ–DINGER
Directory of Open Access Journals (Sweden)
T B Prayitno
2012-02-01
Full Text Available We have computed the solution of a nonrelativistic particle motion in a harmonic oscillator potential of the nonlinear master SchrÃ¶dinger equation. The equation itself is based on two classical conservation laws, the Hamilton-Jacobi and the continuity equations. Those two equations give each contribution for the definition of quantum particle. We also prove that the solution canâ€™t be normalized. Â Keywords : harmonic oscillator, nonlinear SchrÃ¶dinger.
On the connection between the hydrogen atom and the harmonic oscillator: the continuum case
International Nuclear Information System (INIS)
Kibler, M.; Negadi, T.
1983-05-01
The connection between a three-dimensional nonrelativistic hydrogen atom with positive energy and a four-dimensional isotropic harmonic oscillator with repulsive potential is established by applying Jordan-Schwinger boson calculus to the algebra of the Laplace-Runge-Lenz-Pauli vector. The spectrum generating group SO(4,2) both for the bound and free states of the three-dimensional hydrogen atom arises as a quotient of the group Sp(8,R) associated to a four-dimensional isotropic harmonic oscillator with constraint
Information measures of a deformed harmonic oscillator in a static electric field
Nascimento, J. P. G.; Ferreira, F. A. P.; Aguiar, V.; Guedes, I.; Costa Filho, Raimundo N.
2018-06-01
The Shannon entropy and the Fischer information are calculated for an harmonic oscillator in the presence of an applied electric field (ε) in a space with metrics given by gxx-1/2 = 1 + γx. For that metric the harmonic oscillator can be mapped into a Morse potential in an Euclidean space. For ε = 0, the ground state energy decreases when γ increases. However, for certain values of ε the energy decrease can be canceled out. The dependence of the uncertainties, the entropy, and the information on the parameters γ and ε are shown.
On the Quantum Potential and Pulsating Wave Packet in the Harmonic Oscillator
International Nuclear Information System (INIS)
Dubois, Daniel M.
2008-01-01
A fundamental mathematical formalism related to the Quantum Potential factor, Q, is presented in this paper. The Schroedinger equation can be transformed to two equations depending on a group velocity and a density of presence of the particle. A factor, in these equations, was called ''Quantum Potential'' by D. Bohm and B. Hiley. In 1999, I demonstrated that this Quantum Potential, Q, can be split in two Quantum Potentials, Q 1 , and Q 2 , for which the relation, Q=Q 1 +Q 2 , holds. These two Quantum Potentials depend on a fundamental new variable, what I called a phase velocity, u, directly related to the probability density of presence of the wave-particle, given by the modulus of the wave function. This paper gives some further developments for explaining the Quantum Potential for oscillating and pulsating Gaussian wave packets in the Harmonic Oscillator. It is shown that the two Quantum Potentials play a central role in the interpretation of quantum mechanics. A breakthrough in the formalism of the Quantum Mechanics could be provoked by the physical properties of these Quantum Potentials. The probability density of presence of the oscillating and pulsating Gaussian wave packets in the Harmonic Oscillator is directly depending on the ratio Q 2 /Q 1 of the two Quantum Potentials. In the general case, the energy of these Gaussian wave packets is not constant, but is oscillating. The energy is given by the sum of the kinetic energy, T, the potential energy, V, and the two Quantum Potentials: E=T+V+Q 1 +Q 2 . For some conditions, given in the paper, the energy can be a constant. The first remarkable result is the fact that the first Quantum Potential, Q 1 , is related to the ground state energy, E 0 , of the Quantum Harmonic Oscillator: Q 1 =h-bar ω/2=E 0 . The second result is related to the property of the second Quantum Potential, Q 2 , which plays the role of an anti-potential, Q 2 =-V(x), where V is the harmonic oscillator potential. This Quantum Potential
International Nuclear Information System (INIS)
Tian Youwei; Yu Wei; Lu Peixiang; Senecha, Vinod K; Han, Xu; Deng Degang; Li Ruxin; Xu Zhizhan
2006-01-01
The characteristics of backward harmonic radiation due to electron oscillations driven by a linearly polarized fs laser pulse are analysed considering a single electron model. The spectral distributions of the electron's backward harmonic radiation are investigated in detail for different parameters of the driver laser pulse. Higher order harmonic radiations are possible for a sufficiently intense driving laser pulse. We have shown that for a realistic pulsed photon beam, the spectrum of the radiation is red shifted as well as broadened because of changes in the longitudinal velocity of the electrons during the laser pulse. These effects are more pronounced at higher laser intensities giving rise to higher order harmonics that eventually leads to a continuous spectrum. Numerical simulations have further shown that by increasing the laser pulse width the broadening of the high harmonic radiations can be controlled
International Nuclear Information System (INIS)
Martinez, D; Flores-Urbina, J C; Mota, R D; Granados, V D
2010-01-01
We apply the Schroedinger factorization to construct the ladder operators for the hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the dynamical algebra for these problems is the su(1, 1) Lie algebra.
Nonlinear coupling of flow harmonics: Hexagonal flow and beyond
Giacalone, Giuliano; Yan, Li; Ollitrault, Jean-Yves
2018-05-01
Higher Fourier harmonics of anisotropic flow (v4 and beyond) get large contributions induced by elliptic and triangular flow through nonlinear response. We present a general framework of nonlinear hydrodynamic response which encompasses the existing one and allows us to take into account the mutual correlation between the nonlinear couplings affecting Fourier harmonics of any order. Using Large Hadron Collider data on Pb+Pb collisions at s =2.76 TeV, we perform an application of our formalism to hexagonal flow, v6, a coefficient affected by several nonlinear contributions which are of the same order of magnitude. We obtain the first experimental measure of the coefficient χ624, which couples v6 to v2 and v4. This is achieved by putting together the information from several analyses: event-plane correlations, symmetric cumulants, and higher order moments recently analyzed by the ALICE Collaboration. The value of χ624 extracted from data is in fair agreement with hydrodynamic calculations, although with large error bars, which would be dramatically reduced by a dedicated analysis. We argue that within our formalism the nonlinear structure of a given higher order harmonic can be determined more accurately than the harmonic itself, and we emphasize potential applications to future measurements of v7 and v8.
Chemical event chain model of coupled genetic oscillators.
Jörg, David J; Morelli, Luis G; Jülicher, Frank
2018-03-01
We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.
Chemical event chain model of coupled genetic oscillators
Jörg, David J.; Morelli, Luis G.; Jülicher, Frank
2018-03-01
We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.
Behavior of orbits of two coupled oscillators
International Nuclear Information System (INIS)
Greene, J.M.
1984-06-01
There has been very considerable progress in the past few years on the theory of two conservative, coupled, nonlinear oscillators. This is a very general theory, and applies to many equivalent systems. A typical problem of this class has a solution that is so complicated that it is impossible to find an expression for the state of the system that is valid for all time. However, recent results are making it possible to determine the next most useful type of information. This is the asymptotic behavior of individual orbits in the limit of very long times. It is just the information that is desired in many situations. For example, it determines the stability of the motion. The key to our present understanding is renormalization. The present state of the art has been described in Robert MacKay's thesis, for which this is an advertisement
Classical and quantum position-dependent mass harmonic oscillators
International Nuclear Information System (INIS)
Cruz y Cruz, S.; Negro, J.; Nieto, L.M.
2007-01-01
The position-dependent mass oscillator is studied from both, classical and quantum mechanical points of view, in order to discuss the ambiguity on the operator ordering of the kinetic term in the quantum framework. The results are illustrated by some examples of specific mass functions
International Nuclear Information System (INIS)
Morales, J.; Ovando, G.; Pena, J. J.
2010-01-01
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.
The study of entanglement and teleportation of the harmonic oscillator bipartite coherent states
Directory of Open Access Journals (Sweden)
A Rabeie and
2015-01-01
Full Text Available In this paper, we reproduce the harmonic oscillator bipartite coherent states with imperfect cloning of coherent states. We show that if these entangled coherent states are embedded in a vacuum environment, their entanglement is degraded but not totally lost . Also, the optimal fidelity of these states is worked out for investigating their teleportation
About the functions of the Wigner distribution for the q-deformed harmonic oscillator model
International Nuclear Information System (INIS)
Atakishiev, N.M.; Nagiev, S.M.; Djafarov, E.I.; Imanov, R.M.
2005-01-01
Full text : A q-deformed model of the linear harmonic oscillator in the Wigner phase-space is studied. It was derived an explicit expression for the Wigner probability distribution function, as well as the Wigner distribution function of a thermodynamic equilibrium for this model
Coherent states for the time dependent harmonic oscillator: the step function
International Nuclear Information System (INIS)
Moya-Cessa, Hector; Fernandez Guasti, Manuel
2003-01-01
We study the time evolution for the quantum harmonic oscillator subjected to a sudden change of frequency. It is based on an approximate analytic solution to the time dependent Ermakov equation for a step function. This approach allows for a continuous treatment that differs from former studies that involve the matching of two time independent solutions at the time when the step occurs
On the Pseudospectrum of the Harmonic Oscillator with Imaginary Cubic Potential
Czech Academy of Sciences Publication Activity Database
Novák, Radek
2015-01-01
Roč. 54, č. 11 (2015), s. 4142-4153 ISSN 0020-7748 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : pseudospectrum * harmonic oscillator * imaginary qubic potential * PT-symmetry * semiclassical method Subject RIV: BE - Theoretical Physics Impact factor: 1.041, year: 2015
Is there a lower bound energy in the harmonic oscillator interacting with a heat bath?
International Nuclear Information System (INIS)
Arevalo Aguilar, L.M.; Almeida, N.G. de; Villas-Boas, C.J.
2003-01-01
In this Letter we investigate the lower bound energy of the usual Hamiltonian employed in Quantum Optics to model the interaction between a harmonic oscillator and a reservoir without the rotating wave approximation. We show that this model has serious inconsistencies and then we discuss the origin of these inconsistencies
Attainable conditions and exact invariant for the time-dependent harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)
2006-09-22
The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.
Attainable conditions and exact invariant for the time-dependent harmonic oscillator
International Nuclear Information System (INIS)
Guasti, Manuel Fernandez
2006-01-01
The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system
Dynamics of nonlinear oscillators with time-varying conjugate coupling
Indian Academy of Sciences (India)
oscillators. We analyze the behavior of coupled systems with respect to the coupling switching frequency using ..... are of potential utility in appropriate design strategies and/or understanding of complex systems with dynamic interaction ...
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
2017-02-22
Feb 22, 2017 ... i.e., ρ(θ,q ,p |q,p,t) is a measure of the interference effects associated ... an oscillating electric field, when the initial state is cho- sen as a .... The conclusive effect is that. A±(q,p,t) ...... wave functions ±(q,p,t) stem from the time depen- dence of ..... define a two-dimensional cell in phase space, which is centred ...
Microbubble generator excited by fluidic oscillator's third harmonic frequency
Czech Academy of Sciences Publication Activity Database
Tesař, Václav
2014-01-01
Roč. 92, č. 9 (2014), s. 1603-1615 ISSN 0263-8762 R&D Projects: GA ČR GA13-23046S Institutional support: RVO:61388998 Keywords : fluidic oscillator * microbubble generation * fluidic feedback loop Subject RIV: BK - Fluid Dynamics Impact factor: 2.348, year: 2014 http://dx.doi.org/10.1016/j.cherd.2013.12.004
Phase patterns of coupled oscillators with application to wireless communication
Energy Technology Data Exchange (ETDEWEB)
Arenas, A.
2008-01-02
Here we study the plausibility of a phase oscillators dynamical model for TDMA in wireless communication networks. We show that emerging patterns of phase locking states between oscillators can eventually oscillate in a round-robin schedule, in a similar way to models of pulse coupled oscillators designed to this end. The results open the door for new communication protocols in a continuous interacting networks of wireless communication devices.
poincare surface analysis of two coupled quintic oscillators in a ...
African Journals Online (AJOL)
DJFLEX
We have investigated the chaotic dynamics of two coupled quintic oscillators in a single well potential as the energy of the oscillator increases, keeping the coupling strength constant. The degree of chaoticity does not increase monotonously with the energy as regular regions reappear within chaotic seas as the energy ...
Poincare surface analysis of two coupled quintic oscillators in a ...
African Journals Online (AJOL)
We have investigated the chaotic dynamics of two coupled quintic oscillators in a single well potential as the energy of the oscillator increases, keeping the coupling strength constant. The degree of chaoticity does not increase monotonously with the energy as regular regions reappear within chaotic seas as the energy ...
Surprises of the Transformer as a Coupled Oscillator System
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…
Surprises of the transformer as a coupled oscillator system
International Nuclear Information System (INIS)
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 oscillators differ; (iv) for certain choices of parameters, there is only one resonant frequency, instead of the two expected
Surprises of the transformer as a coupled oscillator system
Energy Technology Data Exchange (ETDEWEB)
Silva, J P; Silvestre, A J [Instituto Superior de Engenharia de Lisboa, Rua Conselheiro EmIdio Navarro, 1950-062 Lisboa (Portugal)], E-mail: jpsilva@deea.isel.ipl.pt, E-mail: asilvestre@deq.isel.ipl.pt
2008-05-15
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 oscillators differ; (iv) for certain choices of parameters, there is only one resonant frequency, instead of the two expected.
Rigorous quantum limits on monitoring free masses and harmonic oscillators
Roy, S. M.
2018-03-01
There are heuristic arguments proposing that the accuracy of monitoring position of a free mass m is limited by the standard quantum limit (SQL): σ2( X (t ) ) ≥σ2( X (0 ) ) +(t2/m2) σ2( P (0 ) ) ≥ℏ t /m , where σ2( X (t ) ) and σ2( P (t ) ) denote variances of the Heisenberg representation position and momentum operators. Yuen [Phys. Rev. Lett. 51, 719 (1983), 10.1103/PhysRevLett.51.719] discovered that there are contractive states for which this result is incorrect. Here I prove universally valid rigorous quantum limits (RQL), viz. rigorous upper and lower bounds on σ2( X (t ) ) in terms of σ2( X (0 ) ) and σ2( P (0 ) ) , given by Eq. (12) for a free mass and by Eq. (36) for an oscillator. I also obtain the maximally contractive and maximally expanding states which saturate the RQL, and use the contractive states to set up an Ozawa-type measurement theory with accuracies respecting the RQL but beating the standard quantum limit. The contractive states for oscillators improve on the Schrödinger coherent states of constant variance and may be useful for gravitational wave detection and optical communication.
Chaotic Motion of Nonlinearly Coupled Quintic Oscillators | Adeloye ...
African Journals Online (AJOL)
With a fixed energy, we investigate the motion of two nonlinearly coupled quintic oscillators for various values of the coupling strength with the aid of the Poincare surface of section. It is observed that chaotic motion sets in for coupling strength as low as 0.001. The degree of chaoticity generally increases as the coupling ...
Behavior of orbits of two coupled oscillators
International Nuclear Information System (INIS)
Greene, J.M.
1985-01-01
There has been very considerable progress in the past few years on the theory of two conservative, coupled, nonlinear oscillators. This work also applies to many equivalent systems, so it has applications to particle containment and heating, for example, and wherever else in plasma physics that the validity of adiabatic invariants is a matter of concern. A general problem of this class has a solution that is so complicated that it is impossible to find an expression for the state of the system that is valid for all time. However, recent results are making it possible to determine the next most useful type of information. This is the asymptotic behavior of individual orbits in the limit of very long times. This is just the information that is desired in many situations. For example, it determines the stability of the motion. The key to our present understanding is renormalization. The present state of the art has been described in Robert Mackay's thesis, for which this is an advertisement
Basin stability measure of different steady states in coupled oscillators
Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-04-01
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.
An easy trick to a periodic solution of relativistic harmonic oscillator
Directory of Open Access Journals (Sweden)
Jafar Biazar
2014-04-01
Full Text Available In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is investigated by Homotopy perturbation method. Selection of a linear operator, which is a part of the main operator, is one of the main steps in HPM. If the aim is to obtain a periodic solution, this choice does not work here. To overcome this lack, a linear operator is imposed, and Fourier series of sines will be used in solving the linear equations arise in the HPM. Comparison of the results, with those of resulted by Differential Transformation and Harmonic Balance Method, shows an excellent agreement.
International Nuclear Information System (INIS)
Macias-Diaz, J.E.; Puri, A.
2007-01-01
In the present Letter, we simulate the propagation of binary signals in semi-infinite, mechanical chains of coupled oscillators harmonically driven at the end, by making use of the recently discovered process of nonlinear supratransmission. Our numerical results-which are based on a brand-new computational technique with energy-invariant properties-show an efficient and reliable transmission of information
International Nuclear Information System (INIS)
Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2009-01-01
In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden-type nonlinear oscillator equation with linear forcing, xe+αxx+βx 3 +γx=0, which preserves the form of the time independent integral, conservative Hamiltonian, and the equation of motion. Generalizing this transformation we prove the existence of nonstandard conservative Hamiltonian structure for a general class of damped nonlinear oscillators including Lienard-type systems. Further, using the above Hamiltonian structure for a specific example, namely, the generalized modified Emden equation xe+αx q x+βx 2q+1 =0, where α, β, and q are arbitrary parameters, the general solution is obtained through appropriate canonical transformations. We also present the conservative Hamiltonian structure of the damped Mathews-Lakshmanan oscillator equation. The associated Lagrangian description for all the above systems is also briefly discussed.
Laser cooling of a harmonic oscillator's bath with optomechanics
Xu, Xunnong; Taylor, Jacob
Thermal noise reduction in mechanical systems is a topic both of fundamental interest for studying quantum physics at the macroscopic level and for application of interest, such as building high sensitivity mechanics based sensors. Similar to laser cooling of neutral atoms and trapped ions, the cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce additional damping channel to mechanical motion, while keeping its thermal noise at the same level, and as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of temperature to quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an efficient scheme for reducing the thermal load on a mechanical resonator while improving its quality factor. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme. Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA.
López-Ruiz, F. F.; Guerrero, J.; Aldaya, V.; Cossío, F.
2012-08-01
Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.
International Nuclear Information System (INIS)
López-Ruiz, F F; Guerrero, J; Aldaya, V; Cossío, F
2012-01-01
Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.
Forced harmonic oscillations of the Euler-Bernoulli beam with resistance forces
Directory of Open Access Journals (Sweden)
Yuriy S. Krutiy
2015-12-01
Full Text Available The important issue in the oscillation theory is the study of resistance impact on oscillatory processes. Unlike the calculations of free oscillations, that reside in determination of natural frequencies and waveshapes and unlike the calculations of forced oscillations far away from resonance, that are performing without reference to friction, the oscillations researches in vicinity of resonance need accounting of friction forces. Special attention is paid to forced transverse fluctuations in beams as an important technical problem for engineering and building. Aim: The aim of the work is constructing of analytical solution of the problem of forced transverse vibrations of a straight rod with constant cross-section, which is under the influence of the harmonic load taking into account external and internal resistances. Materials and Methods: The internal resistance is taken into account using the corrected hypothesis of Kelvin-Voigt which reflects the empirically proven fact about the frequency-independent internal friction in the material. The external friction is also considered as frequency-independent. Results: An analytical solution is built for the differential equation of forced transverse oscillations of a straight rod with constant cross-section which is under the influence of the harmonic load taking into account external and internal resistances. As a result, analytically derived formulae are presented which describe the forced dynamic oscillations and the dynamic internal forces due to the harmonic load applied to the rod thus reducing the problem with any possible fixed ends to the search of unknown integration constants represented in a form of initial parameters.
Phase Multistability in Coupled Oscillator Systems
DEFF Research Database (Denmark)
Mosekilde, Erik; Postnov, D.E.; Sosnovtseva, Olga
2003-01-01
along the orbit of the individual oscillator. Focusing on the mechanisms underlying the appearance of phase multistability, the paper examines a variety of phase-locked patterns. In particular we demonstrate the nested structure of synchronization regions for oscillations with multicrest wave forms...
International Nuclear Information System (INIS)
Wang Qing; Hou Yu-Long; Jing Jian; Long Zheng-Wen
2014-01-01
In this paper, we study symmetrical properties of two-dimensional (2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude (SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly, the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed. (general)
Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method
Directory of Open Access Journals (Sweden)
A. M. El-Naggar
2015-11-01
Full Text Available Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.
Nonlinear transient waves in coupled phase oscillators with inertia.
Jörg, David J
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
Transformations of the perturbed two-body problem to unperturbed harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Szebehely, V; Bond, V
1983-05-01
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. 11 references.
Action-angle variables for the harmonic oscillator : ambiguity spin x duplication spin
International Nuclear Information System (INIS)
Oliveira, C.R. de; Malta, C.P.
1983-08-01
The difficulties of obtaining for the harmonic oscillator a well defined unitary transformation to action-angle variables were overcome by M. Moshinsky and T.H. Seligman through the introduction of a spinlike variable (ambiguity spin) from a classical point of view. The difficulty of defining a unitary phase operator for the harmonic oscillator was overcome by Roger G. Newton also through the introduction of a spinlike variable (named duplication spin by us) but within a quantum framework. The relation between the ambiguity spin and the duplication spin by introducing these two types of spins in the canonical transformation to action-angle variables is investigated. Doing this it is possible to obtain both well defined unitary transformation and phase operator. (Author) [pt
Zeta functions for the spectrum of the non-commutative harmonic oscillators
Ichinose, T
2004-01-01
This paper investigates the spectral zeta function of the non-commutative harmonic oscillator studied in \\cite{PW1, 2}. It is shown, as one of the basic analytic properties, that the spectral zeta function is extended to a meromorphic function in the whole complex plane with a simple pole at $s=1$, and further that it has a zero at all non-positive even integers, i.e. at $s=0$ and at those negative even integers where the Riemann zeta function has the so-called trivial zeros. As a by-product of the study, both the upper and the lower bounds are also given for the first eigenvalue of the non-commutative harmonic oscillator.
Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Midya, Bikashkali; Dube, P P; Roychoudhury, Rajkumar, E-mail: bikash.midya@gmail.com, E-mail: ppdube1@gmail.com, E-mail: raj@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)
2011-02-11
The generalized Swanson Hamiltonian H{sub GS}=w(a-tilde a-tilde{sup {dagger}}+1/2)+{alpha}{alpha}-tilde{sup 2}+{beta}a-tilde{sup {dagger}}{sup 2} with a-tilde = A(x) d/dx + B(x) can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as [a-ilde,a-tilde{sup {dagger}}]=constant. However, the main objective of this communication is to show that though the commutator of a-tilde and a-tilde{sup {dagger}} is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. The reason for this anomaly is discussed in the framework of position-dependent mass models by choosing A(x) as the inverse square root of the mass function. (fast track communication)
On the connection between the hydrogen atom and the harmonic oscillator: the zero-energy case
International Nuclear Information System (INIS)
Kibler, M.; Negali, T.
1983-09-01
The connection between the three-dimensional hydrogen atom and a four-dimensional harmonic oscillator obtained in previous works, from an hybridization of the infinitesimal Pauli approach to the hydrogen system with the Schwinger approach to spherical and hyperbolical angular momenta, is worked out in the case of the zero-energy point of the hydrogen atom. This leads to the equivalence of the three-dimensional hydrogen problem with a four-dimensional free-particle problem involving a constraint condition. For completeness, the latter results is also derived by using the Kustaanheimo-Stiefel transformation introduced in celestial mechanics. Finally, it is shown how the Lie algebra of SO(4,2) quite naturally arises for the whole spectrum (discrete + continuum + zero-energy point) of the three-dimensional hydrogen atom from the introduction of the constraint condition into the Lie algebra of Sp(8,R) associated to the four-dimensional harmonic oscillator
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
DEFF Research Database (Denmark)
Jensen, Arne; Yajima, Kenji
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials, which grow at spatial infinity slower than quadratic, but faster than linear functions, and whose Hessian matrices have a fixed sign. We prove that the fundamental...... solution at resonant times grows indefinitely at spatial infinity with the algebraic growth rate, which increases indefinitely, when the growth rate of perturbations at infinity decrease from the near quadratic to the near linear ones....
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
DEFF Research Database (Denmark)
Jensen, Arne; Yajima, Kenji
2010-01-01
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials which grow at spatial infinity slower than quadratic but faster than linear functions and whose Hessian matrices have a fixed sign. We prove that the fundamental...... solution at resonant times grows indefinitely at spatial infinity with an algebraic growth rate, which increases indefinitely when the growth rate of perturbations at infinity decreases from the near quadratic to the near linear ones....
A non-orthogonal harmonic-oscillator basis for three-body problems
International Nuclear Information System (INIS)
Agrello, D.A.; Aguilera-Navarro, V.C.; Chacon, E.
1979-01-01
A set of harmonic-oscillator states suitable for the representation of the wave function of the bound states of a system of three identical particles, is presented. As an illustration of the possibilities of the states defined in this paper, they are applied in a variational determination of the lowest symmetric S state of 12 C, in the model of three structureless α particles interacting through the Coulomb force plus a phenomenological two-body force. (author) [pt
Weakly Coupled Oscillators in a Slowly Varying World
Park, Youngmin; Ermentrout, Bard
2016-01-01
We extend the theory of weakly coupled oscillators to incorporate slowly varying inputs and parameters. We employ a combination of regular perturbation and an adiabatic approximation to derive equations for the phase-difference between a pair of oscillators. We apply this to the simple Hopf oscillator and then to a biophysical model. The latter represents the behavior of a neuron that is subject to slow modulation of a muscarinic current such as would occur during transient attention through ...
Chaotic synchronization of three coupled oscillators with ring connection
International Nuclear Information System (INIS)
Kyprianidis, I.M.; Stouboulos, I.N.
2003-01-01
We study the evolution of three identical, resistively coupled with ring connection, nonlinear and nonautonomous electric circuits from nonsynchronized oscillations to synchronized ones, when they exhibit chaotic behavior. Phase-locked states are also observed, as the coupling parameter is varied. The system's dynamics depends on the way of coupling (unidirectional or bidirectional)
Chaotic synchronization of three coupled oscillators with ring connection
Kyprianidis, I M
2003-01-01
We study the evolution of three identical, resistively coupled with ring connection, nonlinear and nonautonomous electric circuits from nonsynchronized oscillations to synchronized ones, when they exhibit chaotic behavior. Phase-locked states are also observed, as the coupling parameter is varied. The system's dynamics depends on the way of coupling (unidirectional or bidirectional).
Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams
Steely, Sidney L.
1993-01-01
The similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite-Gaussian laser beams is illustrated. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite-Gaussian laser beams. The classical limits of a corresponding two-dimensional harmonic oscillator provide a definition of the spot size of Hermite-Gaussian laser beams. The classical limits of the harmonic oscillator provide integration limits for the photon probability densities of the laser beam modes to determine the fraction of photons detected therein. Mathematica is used to integrate the probability densities for large-order beam modes and to illustrate the functional similarities. The probabilities of detecting photons within the classical limits of Hermite-Gaussian laser beams asymptotically approach unity in the limit of large-order modes, in agreement with the Correspondence Principle. The classical limits for large-order modes include all of the nodes for Hermite Gaussian laser beams; Sturm's theorem provides a direct proof.
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.
Detecting phase synchronization between coupled non-phase-coherent oscillators
International Nuclear Information System (INIS)
Follmann, Rosangela; Macau, Elbert E.N.; Rosa, Epaminondas
2009-01-01
We compare two methods for detecting phase synchronization in coupled non-phase-coherent oscillators. One method is based on the locking of self-sustained oscillators with an irregular signal. The other uses trajectory recurrences in phase space. We identify the pros and cons of both methods and propose guidelines to detect phase synchronization in data series.
Emergent organization of oscillator clusters in coupled self ...
Indian Academy of Sciences (India)
Additionally, the maps are coupled sequentially and unidirectionally, to their nearest neighbor, through the difference of their parametric variations. Interestingly we find that this model asymptotically yields clusters of superstable oscillators with different periods. We observe that the sizes of these oscillator clusters have a ...
Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Senthilkumar, D. V., E-mail: skumarusnld@gmail.com [School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695016 (India); Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401 (India); Suresh, K. [Department of Physics, Anjalai Ammal-Engineering College, Kovilvenni 614 403, Tamilnadu (India); Centre for Nonlinear Dynamics, Bharathidasan University, Trichy 620024, Tamilnadu (India); Chandrasekar, V. K. [Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401 (India); Zou, Wei [School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074 (China); Centre for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074 (China); Dana, Syamal K. [CSIR-Indian Institute of Chemical Biology, Kolkata 700032 (India); Kathamuthu, Thamilmaran [Centre for Nonlinear Dynamics, Bharathidasan University, Trichy 620024, Tamilnadu (India); Kurths, Jürgen [Potsdam Institute for Climate Impact Research, Telegrafenberg, Potsdam D-14415 (Germany); Institute of Physics, Humboldt University Berlin, Berlin D-12489 (Germany); Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3FX (United Kingdom); Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod (Russian Federation)
2016-04-15
We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results.
Cluster synchronization modes in an ensemble of coupled chaotic oscillators
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Belykh, Igor V.; Mosekilde, Erik
2001-01-01
Considering systems of diffusively coupled identical chaotic oscillators, an effective method to determine the possible states of cluster synchronization and ensure their stability is presented. The method, which may find applications in communication engineering and other fields of science...
Stochastic Resonance in a System of Coupled Chaotic Oscillators
International Nuclear Information System (INIS)
Krawiecki, A.
1999-01-01
Noise-free stochastic resonance is investigated numerically in a system of two coupled chaotic Roessler oscillators. Periodic signal is applied either additively or multiplicatively to the coupling term. When the coupling constant is varied the oscillators lose synchronization via attractor bubbling or on-off intermittency. Properly chosen signals are analyzed which reflect the sequence of synchronized (laminar) phases and non-synchronized bursts in the time evolution of the oscillators. Maximum of the signal-to-noise ratio as a function of the coupling constant is observed. Dependence of the signal-to-noise ratio on the frequency of the periodic signal and parameter mismatch between the oscillators is investigated. Possible applications of stochastic resonance in the recovery of signals in secure communication systems based on chaotic synchronization are briefly discussed. (author)
Quantifying the dynamics of coupled networks of switches and oscillators.
Directory of Open Access Journals (Sweden)
Matthew R Francis
Full Text Available Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's evolution. We, therefore, introduce a new modeling framework that describes the dynamics of networks composed of both oscillators and switches. Both oscillator synchronization and switch stability are preserved in these heterogeneous, coupled networks. Furthermore, this model recapitulates the qualitative dynamics for the yeast cell cycle consistent with the hypothesized dynamics resulting from decomposition of the regulatory network into dynamic motifs. Introducing feedback into the cell-cycle network induces qualitative dynamics analogous to limitless replicative potential that is a hallmark of cancer. As a result, the proposed model of switch and oscillator coupling provides the ability to incorporate mechanisms that underlie the synchronized stimulus response ubiquitous in biochemical systems.
Monlinear fish-scale metamaterial via coupled duffing oscillators
Kochetov, Bogdan; Tuz, Vladimir; Mladyonov, Pavel; Prosvirnin, Sergey; Kochetova, Lyudmila
2012-01-01
The dynamic system of two coupled Duffing oscillators is considered in order to predict the optical response of the nonlinear planar fish-scale metamaterial. The direct numerical calculation of meta material response confirms the correctness of the proposed model
A quantitative analysis of coupled oscillations using mobile accelerometer sensors
International Nuclear Information System (INIS)
Castro-Palacio, Juan Carlos; Velázquez-Abad, Luisberis; Giménez, Fernando; Monsoriu, Juan A
2013-01-01
In this paper, smartphone acceleration sensors were used to perform a quantitative analysis of mechanical coupled oscillations. Symmetric and asymmetric normal modes were studied separately in the first two experiments. In the third, a coupled oscillation was studied as a combination of the normal modes. Results indicate that acceleration sensors of smartphones, which are very familiar to students, represent valuable measurement instruments for introductory and first-year physics courses. (paper)
A quantitative analysis of coupled oscillations using mobile accelerometer sensors
Castro-Palacio, Juan Carlos; Velázquez-Abad, Luisberis; Giménez, Fernando; Monsoriu, Juan A.
2013-05-01
In this paper, smartphone acceleration sensors were used to perform a quantitative analysis of mechanical coupled oscillations. Symmetric and asymmetric normal modes were studied separately in the first two experiments. In the third, a coupled oscillation was studied as a combination of the normal modes. Results indicate that acceleration sensors of smartphones, which are very familiar to students, represent valuable measurement instruments for introductory and first-year physics courses.
Persistent chimera states in nonlocally coupled phase oscillators
Suda, Yusuke; Okuda, Koji
2015-01-01
Chimera states in the systems of nonlocally coupled phase oscillators are considered stable in the continuous limit of spatially distributed oscillators. However, it is reported that in the numerical simulations without taking such limit, chimera states are chaotic transient and finally collapse into the completely synchronous solution. In this Rapid Communication, we numerically study chimera states by using the coupling function different from the previous studies and obtain the result that...
International Nuclear Information System (INIS)
Belendez, A.; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A.
2008-01-01
An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities
Crypto-harmonic oscillator in higher dimensions: classical and quantum aspects
International Nuclear Information System (INIS)
Ghosh, Subir; Majhi, Bibhas Ranjan
2008-01-01
We study complexified harmonic oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga (2007 Preprint 0706.4064 (J. Phys. A: Math. Theor. at press)) who initiated the study of these Crypto-gauge invariant models that can be related to PT-symmetric models. We show that rotational symmetry in higher spatial dimensions naturally introduces more constraints (in contrast to Smilga (2007 Preprint 0706.4064 (J. Phys. A: Math. Theor. at press)) where one deals with a single constraint) with a much richer constraint structure. Some common as well as distinct features in the study of the same Crypto-oscillator in different dimensions are revealed. We also quantize the two dimensional Crypto-oscillator
On the quantization of a nonlinear oscillator with quasi-harmonic behaviour
International Nuclear Information System (INIS)
Ranada, M.F.; Carinena, J.F.; Satander, M.
2006-01-01
Full text: (author)The quantum version of a non-linear oscillator, depending of a parameter λ, is studied. This λ-dependent system can be considered deformation of the harmonic oscillator in the sense that for λ→0 all the characteristics of the linear oscillator are recovered. This is a problem of quantization of a system with position-dependent mass and with a λ-dependent nonpolynominal rational potential. The quantization problem is solved using existence of a Killing vector, the λ-dependent Schroedinger equation is exactly solved and λ-dependent eigenenergies and eigenfunctions are obtained. The λ-dependent wave functions appear as related with a family of orthogonal polynomials that can be considered as deformations of the standard Hermite polynomials. In the second part, it is proved the superintegrability of the two-dimensional system
The vertical oscillations of coupled magnets
International Nuclear Information System (INIS)
Li Kewei; Lin Jiahuang; Kang Zi Yang; Liang, Samuel Yee Wei; Juan, Jeremias Wong Say
2011-01-01
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.
Suppression and revival of oscillation in indirectly coupled limit cycle oscillators
International Nuclear Information System (INIS)
Sharma, P.R.; Kamal, N.K.; Verma, U.K.; Suresh, K.; Thamilmaran, K.; Shrimali, M.D.
2016-01-01
Highlights: • The phenomena of suppression and revival of oscillations are studied in indirectly coupled nonlinear oscillators. • The decay parameter and a feedback factor play a crucial role in emergent dynamical behavior of oscillators. • The critical curves for different dynamical regions are obtained analytically using linear stability analysis. • Electronic circuit experiments demonstrate these emergent dynamical states. - Abstract: We study the phenomena of suppression and revival of oscillations in a system of limit cycle oscillators coupled indirectly via a dynamic local environment. The dynamics of the environment is assumed to decay exponentially with time. We show that for appropriate coupling strength, the decay parameter of the environment plays a crucial role in the emergent dynamics such as amplitude death (AD) and oscillation death (OD). We also show that introducing a feedback factor in the diffusion term revives the oscillations in this system. The critical curves for the regions of different emergent states as a function of coupling strength, decay parameter of the environment and feedback factor in the coupling are obtained analytically using linear stability analysis. These results are found to be consistent with the numerics and are also observed experimentally.
Seizure Dynamics of Coupled Oscillators with Epileptor Field Model
Zhang, Honghui; Xiao, Pengcheng
The focus of this paper is to investigate the dynamics of seizure activities by using the Epileptor coupled model. Based on the coexistence of seizure-like event (SLE), refractory status epilepticus (RSE), depolarization block (DB), and normal state, we first study the dynamical behaviors of two coupled oscillators in different activity states with Epileptor model by linking them with slow permittivity coupling. Our research has found that when one oscillator in normal states is coupled with any oscillator in SLE, RSE or DB states, these two oscillators can both evolve into SLE states under appropriate coupling strength. And then these two SLE oscillators can perform epileptiform synchronization or epileptiform anti-synchronization. Meanwhile, SLE can be depressed when considering the fast electrical or chemical coupling in Epileptor model. Additionally, a two-dimensional reduced model is also given to show the effect of coupling number on seizures. Those results can help to understand the dynamical mechanism of the initiation, maintenance, propagation and termination of seizures in focal epilepsy.
Synchronization of three electrochemical oscillators: From local to global coupling
Liu, Yifan; Sebek, Michael; Mori, Fumito; Kiss, István Z.
2018-04-01
We investigate the formation of synchronization patterns in an oscillatory nickel electrodissolution system in a network obtained by superimposing local and global coupling with three electrodes. We explored the behavior through numerical simulations using kinetic ordinary differential equations, Kuramoto type phase models, and experiments, in which the local to global coupling could be tuned by cross resistances between the three nickel wires. At intermediate coupling strength with predominant global coupling, two of the three oscillators, whose natural frequencies are closer, can synchronize. By adding even a relatively small amount of local coupling (about 9%-25%), a spatially organized partially synchronized state can occur where one of the two synchronized elements is in the center. A formula was derived for predicting the critical coupling strength at which full synchronization will occur independent of the permutation of the natural frequencies of the oscillators over the network. The formula correctly predicts the variation of the critical coupling strength as a function of the global coupling fraction, e.g., with local coupling the critical coupling strength is about twice than that required with global coupling. The results show the importance of the topology of the network on the synchronization properties in a simple three-oscillator setup and could provide guidelines for decrypting coupling topology from identification of synchronization patterns.
PT -symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
We provide a systematic analysis of a prototypical nonlinear oscillator ... recently, a number of nonlinear variants have been explored, like split-ring resonator chain .... Note that these solutions are valid for any value of ǫ (and hence δ) including ǫ ..... [16] M Abramowitz and I A Stegun, Handbook of mathematical functions ...
Statistical properties of spectra in harmonically trapped spin-orbit coupled systems
DEFF Research Database (Denmark)
V. Marchukov, O.; G. Volosniev, A.; V. Fedorov, D.
2014-01-01
We compute single-particle energy spectra for a one-body Hamiltonian consisting of a two-dimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin......-orbit and Zeeman strengths we examine the distributions of the nearest neighbor spacings. We find that the shapes of these distributions depend strongly on the three potential parameters. We show that the obtained shapes in some cases can be well approximated with the standard Poisson, Brody and Wigner...... distributions. The Brody and Wigner distributions characterize irregular motion and help identify quantum chaotic systems. We present a special choices of deformation and spin-orbit strengths without the Zeeman term which provide a fair reproduction of the fourth-power repelling Wigner distribution. By adding...
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing
2010-12-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing; Arcak, Murat; Salama, Khaled N.
2010-01-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
Synchronization of hyperchaotic oscillators via single unidirectional chaotic-coupling
International Nuclear Information System (INIS)
Zou Yanli; Zhu Jie; Chen Guanrong; Luo Xiaoshu
2005-01-01
In this paper, synchronization of two hyperchaotic oscillators via a single variable's unidirectional coupling is studied. First, the synchronizability of the coupled hyperchaotic oscillators is proved mathematically. Then, the convergence speed of this synchronization scheme is analyzed. In order to speed up the response with a relatively large coupling strength, two kinds of chaotic coupling synchronization schemes are proposed. In terms of numerical simulations and the numerical calculation of the largest conditional Lyapunov exponent, it is shown that in a given range of coupling strengths, chaotic-coupling synchronization is quicker than the typical continuous-coupling synchronization. Furthermore, A circuit realization based on the chaotic synchronization scheme is designed and Pspice circuit simulation validates the simulated hyperchaos synchronization mechanism
Llewellyn-Jones, D. T.; Knight, R. J.; Gebbie, H. A.
1980-07-01
A new technique of measuring absolute power exploiting an untuned cavity and Fourier spectroscopy has been used to examine the power spectrum of the harmonics and other overtones produced by a 95 GHz IMPATT oscillator. The conditions which favor the production of a rich harmonic spectrum are not those which maximize the fundamental power. Under some conditions of mismatch at the fundamental frequency it is possible to produce over 200 microW of harmonic power in the 100-200 GHz region comparable with the fundamental power from the oscillator.
Dynamics of chaotic oscillations in mutually coupled microchip lasers
Uchida, A; Kinugawa, S; Yoshimori, S
2003-01-01
We have numerically and experimentally investigated the dynamics of mutually coupled microchip lasers. Chaotic oscillations are observed in the vicinity of the boundary of the injection-locking range when the coupling strength and the difference of the optical frequencies are varied. Synchronization of chaos is always achieved under the condition to generate chaos.
Directory of Open Access Journals (Sweden)
William E Wood
Full Text Available Complex motor skills are more difficult to perform at certain points in the day (for example, shortly after waking, but the daily trajectory of motor-skill error is more difficult to predict. By undertaking a quantitative analysis of the fundamental frequency (FF and amplitude of hundreds of zebra finch syllables per animal per day, we find that zebra finch song follows a previously undescribed daily oscillation. The FF and amplitude of harmonic syllables rises across the morning, reaching a peak near mid-day, and then falls again in the late afternoon until sleep. This oscillation, although somewhat variable, is consistent across days and across animals and does not require serotonin, as animals with serotonergic lesions maintained daily oscillations. We hypothesize that this oscillation is driven by underlying physiological factors which could be shared with other taxa. Song production in zebra finches is a model system for studying complex learned behavior because of the ease of gathering comprehensive behavioral data and the tractability of the underlying neural circuitry. The daily oscillation that we describe promises to reveal new insights into how time of day affects the ability to accomplish a variety of complex learned motor skills.
Thermal coupling and effect of subharmonic synchronization in a system of two VO2 based oscillators
Velichko, Andrey; Belyaev, Maksim; Putrolaynen, Vadim; Perminov, Valentin; Pergament, Alexander
2018-03-01
We explore a prototype of an oscillatory neural network (ONN) based on vanadium dioxide switching devices. The model system under study represents two oscillators based on thermally coupled VO2 switches. Numerical simulation shows that the effective action radius RTC of coupling depends both on the total energy released during switching and on the average power. It is experimentally and numerically proved that the temperature change ΔT commences almost synchronously with the released power peak and T-coupling reveals itself up to a frequency of about 10 kHz. For the studied switching structure configuration, the RTC value varies over a wide range from 4 to 45 μm, depending on the external circuit capacitance C and resistance Ri, but the variation of Ri is more promising from the practical viewpoint. In the case of a "weak" coupling, synchronization is accompanied by attraction effect and decrease of the main spectra harmonics width. In the case of a "strong" coupling, the number of effects increases, synchronization can occur on subharmonics resulting in multilevel stable synchronization of two oscillators. An advanced algorithm for synchronization efficiency and subharmonic ratio calculation is proposed. It is shown that of the two oscillators the leading one is that with a higher main frequency, and, in addition, the frequency stabilization effect is observed. Also, in the case of a strong thermal coupling, the limit of the supply current parameters, for which the oscillations exist, expands by ∼10%. The obtained results have a universal character and open up a new kind of coupling in ONNs, namely, T-coupling, which allows for easy transition from 2D to 3D integration. The effect of subharmonic synchronization hold promise for application in classification and pattern recognition.
Harmonic Coupling Analysis of a Multi-Drive System with Slim DC-link Drive
DEFF Research Database (Denmark)
Yang, Feng; Kwon, Jun Bum; Blaabjerg, Frede
2017-01-01
One of the problems with slim dc-link adjustable speed drive is the difficulties to analyze the harmonic coupling when it is integrated into a multi-drive system. The traditional methods analyze this harmonic issue by neglecting the harmonic coupling, and base on the linear time-invariant methods....... Its disadvantages include the time consumption and large computer memory. This paper proposes to do harmonic analysis by using the harmonic state-space modeling method by using the linear time-periodic theory. By using the proposed model, the harmonic couplings, between dc-link and point of common...... coupling in different drives, are all analyzed in the multi-drive system. In the meantime, the effects of the small film dc-link capacitance and the nonlinear characteristic of the diode rectifier are considered. The detailed modeling procedure, the simulations and the lab experiment on a two-drive system...
Hong, Hyunsuk; Strogatz, Steven H
2011-02-04
We consider a generalization of the Kuramoto model in which the oscillators are coupled to the mean field with random signs. Oscillators with positive coupling are "conformists"; they are attracted to the mean field and tend to synchronize with it. Oscillators with negative coupling are "contrarians"; they are repelled by the mean field and prefer a phase diametrically opposed to it. The model is simple and exactly solvable, yet some of its behavior is surprising. Along with the stationary states one might have expected (a desynchronized state, and a partially-synchronized state, with conformists and contrarians locked in antiphase), it also displays a traveling wave, in which the mean field oscillates at a frequency different from the population's mean natural frequency.
International Nuclear Information System (INIS)
Santos, Marcelo Franca
2005-01-01
We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an auxiliary three-level system and a classical external driving source, and enables any unitary operations on Fock states, two by two. One circuit is equivalent to a single qubit unitary logical gate on Fock states qubits. Sequences of similar protocols allow for complete, deterministic, and state-independent manipulation of the harmonic oscillator quantum state
Synchronization of diffusively coupled oscillators near the homoclinic bifurcation
International Nuclear Information System (INIS)
Postnov, D.; Han, Seung Kee; Kook, Hyungtae
1998-09-01
It has been known that a diffusive coupling between two limit cycle oscillations typically leads to the inphase synchronization and also that it is the only stable state in the weak coupling limit. Recently, however, it has been shown that the coupling of the same nature can result in the distinctive dephased synchronization when the limit cycles are close to the homoclinic bifurcation, which often occurs especially for the neuronal oscillators. In this paper we propose a simple physical model using the modified van der Pol equation, which unfolds the generic synchronization behaviors of the latter kind and in which one may readily observe changes in the synchronization behaviors between the distinctive regimes as well. The dephasing mechanism is analyzed both qualitatively and quantitatively in the weak coupling limit. A general form of coupling is introduced and the synchronization behaviors over a wide range of the coupling parameters are explored to construct the phase diagram using the bifurcation analysis. (author)
International Nuclear Information System (INIS)
Lo, C.F.
2009-01-01
By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schroedinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well. (general)
Dynamics of multi-frequency oscillator ensembles with resonant coupling
Lück, S.; Pikovsky, A.
2011-07-01
We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two interacting subpopulations are in relation 2:1. Depending on the parameter of coupling, ensembles can demonstrate fully synchronous clusters, partial synchrony (only one subpopulation synchronizes), or asynchrony in both subpopulations. Theoretical description of the dynamics based on the Watanabe-Strogatz approach is developed.
Coupled oscillators as models of phantom and scalar field cosmologies
International Nuclear Information System (INIS)
Faraoni, Valerio
2004-01-01
We study a toy model for phantom cosmology recently introduced in the literature and consisting of two oscillators, one of which carries negative kinetic energy. The results are compared with the exact phase space picture obtained for similar dynamical systems describing, respectively, a massive canonical scalar field conformally coupled to the spacetime curvature and a conformally coupled massive phantom. Finally, the dynamical system describing exactly a minimally coupled phantom is studied and compared with the toy model
Relativistic corrections to one-particle neutron levels in the harmonic oscillator well
International Nuclear Information System (INIS)
Yanavichyus, A.I.
1983-01-01
Relativistic corrections to mass and potential energy for one-particle levels in the harmonic oscillator well are calculated in the first approximation of the perturbation theory. These corrections are, mainly negliqible, but they sharply increase with growth of the head and orbital quantum numbers. For the state 1s the relativistic correction is of the order of 0.01 MeV, and for 3p it is equal to 0.4 MeV. Thus, the relativistic correction for certain states approaches the energy of spin-orbital interactions and it should be taken into account in calculating the energy of one-particle levels
DEFF Research Database (Denmark)
Dahl, Jens Peder; Schleich, W. P.
2009-01-01
For a closed quantum system the state operator must be a function of the Hamiltonian. When the state is degenerate, additional constants of the motion enter the play. But although it is the Weyl transform of the state operator, the Wigner function is not necessarily a function of the Weyl...... transforms of the constants of the motion. We derive conditions for which this is actually the case. The Wigner functions of the energy eigenstates of a two-dimensional isotropic harmonic oscillator serve as an important illustration....
Entanglement of a class of non-Gaussian states in disordered harmonic oscillator systems
Abdul-Rahman, Houssam
2018-03-01
For disordered harmonic oscillator systems over the d-dimensional lattice, we consider the problem of finding the bipartite entanglement of the uniform ensemble of the energy eigenstates associated with a particular number of modes. Such an ensemble defines a class of mixed, non-Gaussian entangled states that are labeled, by the energy of the system, in an increasing order. We develop a novel approach to find the exact logarithmic negativity of this class of states. We also prove entanglement bounds and demonstrate that the low energy states follow an area law.
International Nuclear Information System (INIS)
Mota, R D; Granados, V D; Queijeiro, A; Garcia, J; Guzman, L
2003-01-01
We show that the supersymmetric radial ladder operators of the three-dimensional isotropic harmonic oscillator are contained in the spherical components of the creation and annihilation operators of the system. Also, we show that the constants of motion of the problem, written in terms of these spherical components, lead us to second-order radial operators. Further, we show that these operators change the orbital angular momentum quantum number by two units and are equal to those obtained by the Infeld-Hull factorization method
(1 + 1) Newton-Hooke group for the simple and damped harmonic oscillator
Brzykcy, Przemysław
2018-03-01
It is demonstrated that, in the framework of the orbit method, a simple and damped harmonic oscillator is indistinguishable at the level of an abstract Lie algebra. This opens a possibility for treating the dissipative systems within the orbit method. An in-depth analysis of the coadjoint orbits of the (1 + 1) dimensional Newton-Hooke group is presented. Furthermore, it is argued that the physical interpretation is carried by a specific realisation of the Lie algebra of smooth functions on a phase space rather than by an abstract Lie algebra.
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
International Nuclear Information System (INIS)
Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung
2009-01-01
We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung [Department of Physics, HCMC University of Pedagogy, 280 An Duong Vuong, Ward 10, Dist. 5, Ho Chi Minh City (Viet Nam)
2009-05-01
We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./.
Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2014-09-02
A complete equation of state (EOS) for a molecular solid is derived utilizing a Helmholtz free energy. Assuming that the solid is nonconducting, phonon excitations dominate the specific heat. Phonons are approximated as independent quasi-harmonic oscillators with vibrational frequencies depending on the specific volume. The model is suitable for calibrating an EOS based on isothermal compression data and infrared/Raman spectroscopy data from high pressure measurements utilizing a diamond anvil cell. In contrast to a Mie-Gruneisen EOS developed for an atomic solid, the specific heat and Gruneisen coefficient depend on both density and temperature.
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.
Synchronization as Aggregation: Cluster Kinetics of Pulse-Coupled Oscillators.
O'Keeffe, Kevin P; Krapivsky, P L; Strogatz, Steven H
2015-08-07
We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators progressively coalesce into larger ones. Using tools from the study of aggregation phenomena, we obtain exact results for the time-dependent distribution of cluster sizes as the system evolves from disorder to synchrony.
Solvable model for chimera states of coupled oscillators.
Abrams, Daniel M; Mirollo, Rennie; Strogatz, Steven H; Wiley, Daniel A
2008-08-22
Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.
Oscillations in magnetoresistance and interlayer coupling in magnetic sandwich structures
International Nuclear Information System (INIS)
Barnas, J.; Bulka, B.
1997-01-01
Kubo formalism is used to calculate the magnetoresistance due to magnetization rotation in a structure consisting two magnetic films separated by nonmagnetic layer. In the approximation of an uniform relaxation time of each layer, the oscillatory term in magnetoresistance corresponds to the oscillation period which depends on the potential barriers at the interfaces. This period is longer than the oscillation period observed in the coupling parameter. (author)
Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback
Directory of Open Access Journals (Sweden)
A.F. EL-Bassiouny
2006-01-01
Full Text Available Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. We investigate the fundamental resonance and subharmonic resonance of order one-half of a harmonically oscillation under state feedback control with a time delay. By using the multiple scale perturbation technique, the first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the external excitation-response and frequency-response curves. We analyze the effect of time delay and the other different parameters on these oscillations.
Synchronization of indirectly coupled Lorenz oscillators: An ...
Indian Academy of Sciences (India)
[7], the magnetoencephalographic activity of Parkinsonian patients [8], electrosensitive cells of paddlefish [9] ... with coherent electromagnetic field [16]. ... can also be explained with a model of two excitatory synaptically coupled neurons in the.
Limit cycle analysis of nuclear coupled density wave oscillations
International Nuclear Information System (INIS)
Ward, M.E.
1985-01-01
An investigation of limit cycle behavior for the nuclear-coupled density wave oscillation (NCDWO) in a boiling water reactor (BWR) was performed. A simplified nonlinear model of BWR core behavior was developed using a two-region flow channel representation, coupled with a form of the point-kinetics equation. This model has been used to investigate the behavior of large amplitude NCDWO's through conventional time-integration solutions and through application of a direct relaxation-oscillation limit cycle solution in phase space. The numerical solutions demonstrate the potential for severe global power and flow oscillations in a BWR core at off-normal conditions, such as might occur during Anticipated Transients without Scram. Because of the many simplifying assumptions used, it is felt that the results should not be interpreted as an absolute prediction of core behavior, but as an indication of the potential for large oscillations and a demonstration of the corresponding limit cycle mechanisms. The oscillations in channel density drive the core power variations, and are reinforced by heat flux variations due to the changing fuel temperature. A global temperature increase occurs as energy is accumulated in the fuel, and limits the magnitude of the oscillations because as the average channel density decreases, the amplitude and duration of positive void reactivity at a given oscillation amplitude is lessened
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.
Control of coupled oscillator networks with application to microgrid technologies
Arenas, Alex
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions-a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable syn- chronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.
International Nuclear Information System (INIS)
Chaudhury, Srabanti; Chatterjee, Debarati; Cherayil, Binny J
2008-01-01
A harmonic oscillator that evolves under the action of both a systematic time-dependent force and a random time-correlated force can do work w. This work is a random quantity, and Mai and Dhar have recently shown, using the generalized Langevin equation (GLE) for the oscillator's position x, that it satisfies a fluctuation theorem. In principle, the same result could have been derived from the Fokker–Planck equation (FPE) for the probability density function, P(x,w,t), for the oscillator being at x at time t, having done work w. Although the FPE equivalent to the above GLE is easily constructed and solved, one finds, unexpectedly, that its predictions for the mean and variance of w do not agree with the fluctuation theorem. We show that to resolve this contradiction, it is necessary to construct an FPE that includes the velocity of the oscillator, v, as an additional variable. The FPE for P(x,v,w,t) does indeed yield expressions for the mean and variance of w that agree with the fluctuation theorem
International Nuclear Information System (INIS)
Mshelia, E.D.
1994-07-01
The method of normal coordinates of the theory of vibrations is used in decoupling the motion of n oscillators (1 ≤ n ≤4) representing intrinsic degrees of freedom coupled to collective motion in a quantum mechanical model that allows the determination of the probability for energy transfer from collective to intrinsic excitations in a dissipative system. (author). 21 refs
International Nuclear Information System (INIS)
Belendez, A; Pascual, C; Fernandez, E; Neipp, C; Belendez, T
2008-01-01
A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient
The dynamics of two linearly coupled Goodwin oscillators
Antonova, A. O.; Reznik, S. N.; Todorov, M. D.
2017-10-01
In this paper the Puu model of the interaction of Goodwin's business cycles for two regions is reconsidered. We investigated the effect of the accelerator coefficients and the Hicksian 'ceiling' and 'floor' parameters on the time dynamics of incomes for different values of marginal propensity to import. The cases when the periods of isolated Goodwin's cycles are close, and when they differ approximately twice are considered. By perturbation theory we obtained the formulas for slowly varying amplitudes and phase difference of weakly nonlinear coupled Goodwin oscillations. The coupled oscillations of two Goodwin's cycles with piecewise linear accelerators with only 'floor' are considered.
Bonkobara, Yasuhiro; Mori, Hiroki; Kondou, Takahiro; Ayabe, Takashi
Self-synchronized phenomena generated in rotor-type oscillators mounted on a straight-line spring-mass system are investigated experimentally and analytically. In the present study, we examine the occurrence region and pattern of self-synchronization in two types of coupled oscillators: rigidly coupled oscillators and elastically coupled oscillators. It is clarified that the existence regions of stable solutions are governed mainly by the linear natural frequency of each spring-mass system. The results of numerical analysis confirm that the self-synchronized solutions of the elastically coupled oscillators correspond to those of the rigidly coupled oscillators. In addition, the results obtained in the present study are compared with the previously reported results for a metronome system and a moving apparatus and the different properties of the phenomena generated in the rotor-type oscillators and the pendulum-type oscillators are shown in terms of the construction of branches of self-synchronized solution and the stability.
The two-capacitor problem revisited: a mechanical harmonic oscillator model approach
International Nuclear Information System (INIS)
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 force is dissipated irrespective of the form of dissipation mechanism when the system comes to a new equilibrium after a constant force is abruptly applied. This model is then applied to the energy loss mechanism in the capacitor charging problem or the two-capacitor problem. This approach allows a simple explanation of the energy dissipation mechanism in these problems and shows that the dissipated energy should always be exactly half the supplied energy whether that is caused by the Joule heat or by the radiation. This paper, which provides a simple treatment of the energy dissipation mechanism in the two-capacitor problem, is suitable for all undergraduate levels
ABC of ladder operators for rationally extended quantum harmonic oscillator systems
Cariñena, José F.; Plyushchay, Mikhail S.
2017-07-01
The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler transformations by which such systems can be generated from the quantum harmonic oscillator. Any REQHO system is characterized by the number of separated states in its spectrum, the number of ‘valence bands’ in which the separated states are organized, and by the total number of the missing energy levels and their position. All these peculiarities of a REQHO system are shown to be detected and reflected by a trinity (A^+/- , B^+/- , C^+/-) of the basic (primary) lowering and raising ladder operators related between themselves by certain algebraic identities with coefficients polynomially-dependent on the Hamiltonian. We show that all the secondary, higher-order ladder operators are obtainable by a composition of the basic ladder operators of the trinity which form the set of the spectrum-generating operators. Each trinity, in turn, can be constructed from the intertwining operators of the two complementary minimal schemes of the Darboux-Crum-Krein-Adler transformations.
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.
Phase dynamics of oscillating magnetizations coupled via spin pumping
Taniguchi, Tomohiro
2018-05-01
A theoretical formalism is developed to simultaneously solve equation of motion of the magnetizations in two ferromagnets and the spin-pumping induced spin transport equation. Based on the formalism, a coupled motion of the magnetizations in a self-oscillation state is studied. The spin pumping is found to induce an in-phase synchronization of the magnetizations for the oscillation around the easy axis. For an out-of-plane self-oscillation around the hard axis, on the other hand, the spin pumping leads to an in-phase synchronization in a small current region, whereas an antiphase synchronization is excited in a large current region. An analytical theory based on the phase equation reveals that the phase difference between the magnetizations in a steady state depends on the oscillation direction, clockwise or counterclockwise, of the magnetizations.
Heterogeneity of time delays determines synchronization of coupled oscillators.
Petkoski, Spase; Spiegler, Andreas; Proix, Timothée; Aram, Parham; Temprado, Jean-Jacques; Jirsa, Viktor K
2016-07-01
Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyze delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations.
Synchronization of coupled stochastic oscillators: The effect of ...
Indian Academy of Sciences (India)
as an approximate means of accounting for a separation of time-scales between ... phase relationships between coupled oscillator systems as well as to effect a variety ... ations are often termed as internal noise since their origin is in the very ..... design and control of synthetic biological networks where synchronous ...
Scaling Features of Multimode Motions in Coupled Chaotic Oscillators
DEFF Research Database (Denmark)
Pavlov, A.N.; Sosnovtseva, Olga; Mosekilde, Erik
2003-01-01
Two different methods (the WTMM- and DFA-approaches) are applied to investigate the scaling properties in the return-time sequences generated by a system of two coupled chaotic oscillators. Transitions from twomode asynchronous dynamics (torus or torus-Chaos) to different states of chaotic phase ...
Directory of Open Access Journals (Sweden)
Cornelia A. Bulucea
2012-03-01
Full Text Available Over the last several decades, it has become increasingly accepted that the term xenobiotic relates to environmental impact, since environmental xenobiotics are understood to be substances foreign to a biological system, which did not exist in nature before their synthesis by humans. In this context, xenobiotics are persistent pollutants such as dioxins and polychlorinated biphenyls, as well as plastics and pesticides. Dangerous and unstable situations can result from the presence of environmental xenobiotics since their harmful effects on humans and ecosystems are often unpredictable. For instance, the immune system is extremely vulnerable and sensitive to modulation by environmental xenobitics. Various experimental assays could be performed to ascertain the immunotoxic potential of environmental xenobiotics, taking into account genetic factors, the route of xenobiotic penetration, and the amount and duration of exposure, as well as the wave shape of the xenobiotic. In this paper, we propose an approach for the analysis of xenobiotic metabolism using mathematical models and corresponding methods. This study focuses on a pattern depicting mathematically modeled processes of resonant absorption of a xenobiotic harmonic oscillation by an organism modulated as an absorbing oscillator structure. We represent the xenobiotic concentration degree through a spatial concentration vector, and we model and simulate the oscillating regime of environmental xenobiotic absorption. It is anticipated that the results could be used to facilitate the assessment of the processes of environmental xenobiotic absorption, distribution, biotransformation and removal within the framework of compartmental analysis, by establishing appropriate mathematical models and simulations.
International Nuclear Information System (INIS)
Xu Hao; Shi Tianjun
2011-01-01
In this article,the qualities of Wigner function and the corresponding stationary perturbation theory are introduced and applied to one-dimensional infinite potential well and one-dimensional harmonic oscillator, and then the particular Wigner function of one-dimensional infinite potential well is specified and a special constriction effect in its pure state Wigner function is discovered, to which,simultaneously, a detailed and reasonable explanation is elaborated from the perspective of uncertainty principle. Ultimately, the amendment of Wigner function and energy of one-dimensional infinite potential well and one-dimensional harmonic oscillator under perturbation are calculated according to stationary phase space perturbation theory. (authors)
International Nuclear Information System (INIS)
Arcos-Olalla, Rafael; Reyes, Marco A.; Rosu, Haret C.
2012-01-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
International Nuclear Information System (INIS)
Belendez, A.; Fernandez, E.; Rodes, J.J.; Fuentes, R.; Pascual, I.
2009-01-01
The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed
Energy Technology Data Exchange (ETDEWEB)
Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)
2012-10-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
Coupling-induced oscillations in nonhomogeneous, overdamped, bistable systems
International Nuclear Information System (INIS)
Hernandez, Mayra; In, Visarath; Longhini, Patrick; Palacios, Antonio; Bulsara, Adi; Kho, Andy
2008-01-01
Coupling-induced oscillations in a homogeneous network of overdamped bistable systems have been previously studied both theoretically and experimentally for a system of N (odd) elements, unidirectionally coupled in a ring topology. In this work, we extend the analysis of this system to include a network of nonhomogeneous elements with respect to the parameter that controls the topology of the potential function and the bistability of each element. In particular, we quantify the effects of the nonhomogeneity on the onset of oscillations and the response of the network to external (assumed to be constant and very small) perturbations, using our (recently developed) coupled core fluxgate magnetometer as a representative system. The potential applications of this work include signal detection and characterization for a large class of sensor systems
Coupling-induced oscillations in nonhomogeneous, overdamped, bistable systems
Energy Technology Data Exchange (ETDEWEB)
Hernandez, Mayra [Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182 (United States)], E-mail: mayra.alina@yahoo.com; In, Visarath [Space and Naval Warfare Systems Center, Code 71730, 53560 Hull Street, San Diego, CA 92152-5001 (United States)], E-mail: visarath.in@navy.mil; Longhini, Patrick [Space and Naval Warfare Systems Center, Code 71730, 53560 Hull Street, San Diego, CA 92152-5001 (United States)], E-mail: longhini@navy.mil; Palacios, Antonio [Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182 (United States)], E-mail: palacios@euler.sdsu.edu; Bulsara, Adi [Space and Naval Warfare Systems Center, Code 71730, 53560 Hull Street, San Diego, CA 92152-5001 (United States)], E-mail: bulsara@spawar.navy.mil; Kho, Andy [Space and Naval Warfare Systems Center, Code 71730, 53560 Hull Street, San Diego, CA 92152-5001 (United States)], E-mail: kho@spawar.navy.mil
2008-06-09
Coupling-induced oscillations in a homogeneous network of overdamped bistable systems have been previously studied both theoretically and experimentally for a system of N (odd) elements, unidirectionally coupled in a ring topology. In this work, we extend the analysis of this system to include a network of nonhomogeneous elements with respect to the parameter that controls the topology of the potential function and the bistability of each element. In particular, we quantify the effects of the nonhomogeneity on the onset of oscillations and the response of the network to external (assumed to be constant and very small) perturbations, using our (recently developed) coupled core fluxgate magnetometer as a representative system. The potential applications of this work include signal detection and characterization for a large class of sensor systems.
Dynamics of multi-frequency oscillator ensembles with resonant coupling
International Nuclear Information System (INIS)
Lueck, S.; Pikovsky, A.
2011-01-01
We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two interacting subpopulations are in relation 2:1. Depending on the parameter of coupling, ensembles can demonstrate fully synchronous clusters, partial synchrony (only one subpopulation synchronizes), or asynchrony in both subpopulations. Theoretical description of the dynamics based on the Watanabe-Strogatz approach is developed. -- Highlights: → Kuramoto model is generalized on the case of resonantly interacting oscillators having frequency ratio 2:1. → Regimes of full and partial synchrony, as well as non-synchronous ones are reported. → Analytical description is developed on the basis of the Watanabe-Strogatz approach.
Dynamics of multi-frequency oscillator ensembles with resonant coupling
Energy Technology Data Exchange (ETDEWEB)
Lueck, S. [Department of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Str. 24-25, 14476 Potsdam (Germany); Pikovsky, A., E-mail: pikovsky@stat.physik.uni-potsdam.de [Department of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Str. 24-25, 14476 Potsdam (Germany)
2011-07-11
We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two interacting subpopulations are in relation 2:1. Depending on the parameter of coupling, ensembles can demonstrate fully synchronous clusters, partial synchrony (only one subpopulation synchronizes), or asynchrony in both subpopulations. Theoretical description of the dynamics based on the Watanabe-Strogatz approach is developed. -- Highlights: → Kuramoto model is generalized on the case of resonantly interacting oscillators having frequency ratio 2:1. → Regimes of full and partial synchrony, as well as non-synchronous ones are reported. → Analytical description is developed on the basis of the Watanabe-Strogatz approach.
Directory of Open Access Journals (Sweden)
Diego Lozano-Soldevilla
2016-08-01
Full Text Available Neuronal oscillations support cognitive processing. Modern views suggest that neuronal oscillations do not only reflect coordinated activity in spatially distributed networks, but also that there is interaction between the oscillations at different frequencies. For example, invasive recordings in animals and humans have found that the amplitude of fast oscillations (> 40 Hz occur non-uniformly within the phase of slower oscillations, forming the so-called cross-frequency coupling (CFC. However, the CFC patterns be influenced by features in the signal that do not relate to underlying physiological interactions. For example, CFC estimates may be sensitive to spectral correlations due to non-sinusoidal properties of the alpha band wave morphology. To investigate this issue, we performed CFC analysis using experimental and synthetic data. The former consisted in a double-blind magnetoencephalography pharmacological study in which participants received either placebo, 0.5 mg or 1.5 mg of lorazepam (LZP; GABAergic enhancer in different experimental sessions. By recording oscillatory brain activity with during rest and working memory (WM, we were able to demonstrate that posterior alpha (8 – 12 Hz phase was coupled to beta-low gamma band (20 – 45 Hz amplitude envelope during all sessions. Importantly, bicoherence values around the harmonics of the alpha frequency were similar both in magnitude and topographic distribution to the cross-frequency coherence (CFCoh values observed in the alpha-phase to beta-low gamma coupling. In addition, despite the large CFCoh we found no significant cross-frequency directionality (CFD. Critically, simulations demonstrated that a sizable part of our empirical CFCoh between alpha and beta-low gamma coupling and the lack of CFD could be explained by two-three harmonics aligned in zero phase-lag produced by the physiologically characteristic alpha asymmetry in the amplitude of the peaks relative to the troughs
Breathing multichimera states in nonlocally coupled phase oscillators
Suda, Yusuke; Okuda, Koji
2018-04-01
Chimera states for the one-dimensional array of nonlocally coupled phase oscillators in the continuum limit are assumed to be stationary states in most studies, but a few studies report the existence of breathing chimera states. We focus on multichimera states with two coherent and incoherent regions and numerically demonstrate that breathing multichimera states, whose global order parameter oscillates temporally, can appear. Moreover, we show that the system exhibits a Hopf bifurcation from a stationary multichimera to a breathing one by the linear stability analysis for the stationary multichimera.
Harmonic oscillator states with integer and non-integer orbital angular momentum
International Nuclear Information System (INIS)
Land, Martin
2011-01-01
We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as basis states for representing their respective symmetry groups — O(2), O(1,1), O(3), and O(2,1). The goal of this study is to establish a correspondence between Hilbert space descriptions found by solving the Schrodinger equation in polar coordinates, and Fock space descriptions constructed by expressing the symmetry operators in terms of creation/annihilation operators. We obtain wavefunctions characterized by a principal quantum number, the group Casimir eigenvalue, and one group generator whose eigenvalue is m + s, for integer m and real constant parameter s. For the three groups that contain O(2), the solutions split into two inequivalent representations, one associated with s = 0, from which we recover the familiar description of the oscillator as a product of one-dimensional solutions, and the other with s > 0 (in three dimensions, solutions are found for s = 0 and s = 1/2) whose solutions are non-separable in Cartesian coordinates, and are hence overlooked by the standard Fock space approach. The O(1,1) solutions are singlet states, restricted to zero eigenvalue of the symmetry operator, which represents the boost, not angular momentum. For O(2), a single set of creation and annihilation operators forms a ladder representation for the allowed oscillator states for any s, and the degeneracy of energy states is always finite. However, in three dimensions, the integer and half-integer eigenstates are qualitatively different: the former can be expressed as finite dimensional irreducible tensors under O(3) or O(2,1) while the latter exhibit infinite degeneracy. Creation operators that produce the allowed integer states by acting on the non-degenerate ground state are constructed as irreducible tensor products of the fundamental vector representation. However, the half-integer eigenstates are infinite-dimensional, as expected for the non
Coupled Langmuir oscillations in 2-dimensional quantum plasmas
International Nuclear Information System (INIS)
Akbari-Moghanjoughi, M.
2014-01-01
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
Pulse-coupled Belousov-Zhabotinsky oscillators with frequency modulation
Horvath, Viktor; Epstein, Irving R.
2018-04-01
Inhibitory perturbations to the ferroin-catalyzed Belousov-Zhabotinsky (BZ) chemical oscillator operated in a continuously fed stirred tank reactor cause long term changes to the limit cycle: the lengths of the cycles subsequent to the perturbation are longer than that of the unperturbed cycle, and the unperturbed limit cycle is recovered only after several cycles. The frequency of the BZ reaction strongly depends on the acid concentration of the medium. By adding strong acid or base to the perturbing solutions, the magnitude and the direction of the frequency changes concomitant to excitatory or inhibitory perturbations can be controlled independently of the coupling strength. The dynamics of two BZ oscillators coupled through perturbations carrying a coupling agent (activator or inhibitor) and a frequency modulator (strong acid or base) was explored using a numerical model of the system. Here, we report new complex temporal patterns: higher order, partially synchronized modes that develop when inhibitory coupling is combined with positive frequency modulation (FM), and complex bursting patterns when excitatory coupling is combined with negative FM. The role of time delay between the peak and perturbation (the analog of synaptic delays in networks of neurons) has also been studied. The complex patterns found under inhibitory coupling and positive FM vanish when the delay is significant, whereas a sufficiently long time delay is required for the complex temporal dynamics to occur when coupling is excitatory and FM is negative.
The Tucson-Melbourne Three-Body Force in a Translationally-Invariant Harmonic Oscillator Basis
Marsden, David; Navratil, Petr; Barrett, Bruce
2000-09-01
A translationally-invariant three-body basis set has been employed in shell model calculations on ^3H and ^3He including the Tucson-Melbourne form of the real nuclear three-body force. The basis consists of harmonic oscillators in Jacobi coordinates, explicitly avoiding the centre of mass drift problem in the calculations. The derivation of the three-body matrix elements and the results of large basis effective interaction shell model calculations will be presented. J. L. Friar, B. F. Gibson, G. L. Payne and S. A. Coon; Few Body Systems 5, 13 (1988) P. Navratil, G.P. Kamuntavicius and B.R. Barrett; Phys. Rev. C. 61, 044001 (2000)
From the harmonic oscillator to the A-D-E classification of conformal models
International Nuclear Information System (INIS)
Itzykson, C.
1988-01-01
Arithmetical aspects of the solution of systems involving dimensional statistical models and conformal field theory. From this perspective, the analysis of the harmonic oscillator, the free particle in a box, the rational billards is effectuated. Moreover, the description of the classification of minimal conformal models and Weiss-Lumino-Witten models, based on the simplest affine algebra is also given. Attempts to interpret and justify the appearance of A-D-E classification of algebra in W-Z-W model are made. Extensions of W-Z-W model, based on SU(N) level one, and the ways to deal with rank two Lie groups, using the arithmetics of quadratic intergers, are described
Sang, Nguyen Anh; Thu Thuy, Do Thi; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai
2017-06-01
Using the simple deformed three-level model (D3L model) proposed in our early work, we study the entanglement problem of composite bosons. Consider three first energy levels are known, we can get two energy separations, and can define the level deformation parameter δ. Using connection between q-deformed harmonic oscillator and Morse-like anharmonic potential, the deform parameter q also can be derived explicitly. Like the Einstein’s theory of special relativity, we introduce the observer e˙ects: out side observer (looking from outside the studying system) and inside observer (looking inside the studying system). Corresponding to those observers, the outside entanglement entropy and inside entanglement entropy will be defined.. Like the case of Foucault pendulum in the problem of Earth rotation, our deformation energy level investigation might be useful in prediction the environment e˙ect outside a confined box.
Directory of Open Access Journals (Sweden)
Rong Haiwu
2014-01-01
Full Text Available The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.
Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
International Nuclear Information System (INIS)
Alvarez, Pedro D.; Gomis, Joaquim; Kamimura, Kiyoshi; Plyushchay, Mikhail S.
2008-01-01
We investigate the planar anisotropic harmonic oscillator with explicit rotational symmetry as a particle model with non-commutative coordinates. It includes the exotic Newton-Hooke particle and the non-commutative Landau problem as special, isotropic and maximally anisotropic, cases. The system is described by the same (2+1)-dimensional exotic Newton-Hooke symmetry as in the isotropic case, and develops three different phases depending on the values of the two central charges. The special cases of the exotic Newton-Hooke particle and non-commutative Landau problem are shown to be characterized by additional, so(3) or so(2,1) Lie symmetry, which reflects their peculiar spectral properties
International Nuclear Information System (INIS)
Yu, Rong Mei; Zan, Li Rong; Jiao, Li Guang; Ho, Yew Kam
2017-01-01
Spatially confined atoms have been extensively investigated to model atomic systems in extreme pressures. For the simplest hydrogen-like atoms and isotropic harmonic oscillators, numerous physical quantities have been established with very high accuracy. However, the expectation value of which is of practical importance in many applications has significant discrepancies among calculations by different methods. In this work we employed the basis expansion method with cut-off Slater-type orbitals to investigate these two confined systems. Accurate values for several low-lying bound states were obtained by carefully examining the convergence with respect to the size of basis. A scaling law for was derived and it is used to verify the accuracy of numerical results. Comparison with other calculations show that the present results establish benchmark values for this quantity, which may be useful in future studies. (author)
High efficiency fourth-harmonic generation from nanosecond fiber master oscillator power amplifier
Mu, Xiaodong; Steinvurzel, Paul; Rose, Todd S.; Lotshaw, William T.; Beck, Steven M.; Clemmons, James H.
2016-03-01
We demonstrate high power, deep ultraviolet (DUV) conversion to 266 nm through frequency quadrupling of a nanosecond pulse width 1064 nm fiber master oscillator power amplifier (MOPA). The MOPA system uses an Yb-doped double-clad polarization-maintaining large mode area tapered fiber as the final gain stage to generate 0.5-mJ, 10 W, 1.7- ns single mode pulses at a repetition rate of 20 kHz with measured spectral bandwidth of 10.6 GHz (40 pm), and beam qualities of Mx 2=1.07 and My 2=1.03, respectively. Using LBO and BBO crystals for the second-harmonic generation (SHG) and fourth-harmonic generation (FHG), we have achieved 375 μJ (7.5 W) and 92.5 μJ (1.85 W) at wavelengths of 532 nm and 266 nm, respectively. To the best of our knowledge these are the highest narrowband infrared, green and UV pulse energies obtained to date from a fully spliced fiber amplifier. We also demonstrate high efficiency SHG and FHG with walk-off compensated (WOC) crystal pairs and tightly focused pump beam. An SHG efficiency of 75%, FHG efficiency of 47%, and an overall efficiency of 35% from 1064 nm to 266 nm are obtained.
The optimal performance of a quantum refrigeration cycle working with harmonic oscillators
International Nuclear Information System (INIS)
Lin Bihong; Chen Jincan; Hua Ben
2003-01-01
The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here are compared with those of an Ericsson or Stirling refrigeration cycle using an ideal gas as the working substance. Finally, the optimal performance of a harmonic quantum Carnot refrigeration cycle at high temperatures is derived easily
Stochastic and superharmonic stochastic resonances of a confined overdamped harmonic oscillator
Zhang, Lu; Lai, Li; Peng, Hao; Tu, Zhe; Zhong, Suchuan
2018-01-01
The dynamics of many soft condensed matter and biological systems is affected by space limitations, which produce some peculiar effects on the systems' stochastic resonance (SR) behavior. In this study, we propose a model where SR can be observed: a confined overdamped harmonic oscillator that is subjected to a sinusoidal driving force and is under the influence of a multiplicative white noise. The output response of the system is a periodic signal with harmonic frequencies that are odd multiples of the driving frequency. We verify the amplitude resonances at the driving frequencies and superharmonic frequencies that are equal to three, five, and seven times the driving frequency, using a numerical method based on the stochastic Taylor expansion. The synergistic effect of the multiplicative white noise, constant boundaries, and periodic driving force that can induce a SR in the output amplitude at the driving and superharmonic frequencies is found. The SR phenomenon found in this paper is sensitive to the driving amplitude and frequency, inherent potential parameter, and boundary width, thus leading to various resonance conditions. Therefore, the mechanism found could be beneficial for the characterization of these confined systems and could constitute an important tool for controlling their basic properties.
DEFF Research Database (Denmark)
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-01-01
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...
Energy Technology Data Exchange (ETDEWEB)
Cari, C., E-mail: carinln@yahoo.com; Suparmi, A., E-mail: carinln@yahoo.com [Physics Department, Sebelas Maret University, Jl. Ir. Sutami no 36A Kentingan Surakarta 57126 (Indonesia)
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.
Improved time-dependent harmonic oscillator method for vibrationally inelastic collisions
International Nuclear Information System (INIS)
DePristo, A.E.
1985-01-01
A quantal solution to vibrationally inelastic collisions is presented based upon a linear expansion of the interaction potential around the time-dependent classical positions of all translational and vibrational degrees of freedom. The full time-dependent wave function is a product of a Gaussian translational wave packet and a multidimensional harmonic oscillator wave function, both centered around the appropriate classical position variables. The computational requirements are small since the initial vibrational coordinates are the equilibrium values in the classical trajectory (i.e., phase space sampling does not occur). Different choices of the initial width of the translational wave packet and the initial classical translational momenta are possible, and two combinations are investigated. The first involves setting the initial classical momenta equal to the quantal expectation value, and varying the width to satisfy normalization of the transition probability matrix. The second involves adjusting the initial classical momenta to ensure detailed balancing for each set of transitions, i→f and f→i, and varying the width to satisfy normalization. This choice illustrates the origin of the empirical correction of using the arithmetic average momenta as the initial classical momenta in the forced oscillator approximation. Both methods are tested for the collinear collision systems CO 2 --(He, Ne), and are found to be accurate except for near-resonant vibration--vibration exchange at low initial kinetic energies
Partially coherent twisted states in arrays of coupled phase oscillators
Energy Technology Data Exchange (ETDEWEB)
Omel' chenko, Oleh E.; Wolfrum, Matthias [Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin (Germany); Laing, Carlo R. [INMS, Massey University, Private Bag 102-904 NSMC, Auckland (New Zealand)
2014-06-15
We consider a one-dimensional array of phase oscillators with non-local coupling and a Lorentzian distribution of natural frequencies. The primary objects of interest are partially coherent states that are uniformly “twisted” in space. To analyze these, we take the continuum limit, perform an Ott/Antonsen reduction, integrate over the natural frequencies, and study the resulting spatio-temporal system on an unbounded domain. We show that these twisted states and their stability can be calculated explicitly. We find that stable twisted states with different wave numbers appear for increasing coupling strength in the well-known Eckhaus scenario. Simulations of finite arrays of oscillators show good agreement with results of the analysis of the infinite system.
Partially coherent twisted states in arrays of coupled phase oscillators
International Nuclear Information System (INIS)
Omel'chenko, Oleh E.; Wolfrum, Matthias; Laing, Carlo R.
2014-01-01
We consider a one-dimensional array of phase oscillators with non-local coupling and a Lorentzian distribution of natural frequencies. The primary objects of interest are partially coherent states that are uniformly “twisted” in space. To analyze these, we take the continuum limit, perform an Ott/Antonsen reduction, integrate over the natural frequencies, and study the resulting spatio-temporal system on an unbounded domain. We show that these twisted states and their stability can be calculated explicitly. We find that stable twisted states with different wave numbers appear for increasing coupling strength in the well-known Eckhaus scenario. Simulations of finite arrays of oscillators show good agreement with results of the analysis of the infinite system
Oscillation thresholds for "striking outwards" reeds coupled to a resonator
Silva , Fabrice; Kergomard , Jean; Vergez , Christophe
2007-01-01
International audience; This paper considers a "striking outwards" reed coupled to a resonator. This expression, due to Helmholtz, is not discussed here : it corresponds to the most common model of a lip-type valve, when the valve is assumed to be a one degree of freedom oscillator. The presented work is an extension of the works done by Wilson and Beavers (1974), Tarnopolsky (2000). The range of the playing frequencies is investigated. The first results are analytical : when no losses are pr...
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
International Nuclear Information System (INIS)
Belendez, A.; Mendez, D.I.; Fernandez, E.; Marini, S.; Pascual, I.
2009-01-01
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
Ponomarenko, V I; Kulminskiy, D D; Prokhorov, M D
2017-08-01
We study the collective dynamics of oscillators in a network of identical bistable time-delayed feedback systems globally coupled via the mean field. The influence of delay and inertial properties of the mean field on the collective behavior of globally coupled oscillators is investigated. A variety of oscillation regimes in the network results from the presence of bistable states with substantially different frequencies in coupled oscillators. In the physical experiment and numerical simulation we demonstrate the existence of chimeralike states, in which some of the oscillators in the network exhibit synchronous oscillations, while all other oscillators remain asynchronous.
Eigenmode analysis of coupled magnetohydrodynamic oscillations in the magnetosphere
International Nuclear Information System (INIS)
Fujita, S.; Patel, V.L.
1992-01-01
The authors have performed an eigenmode analysis of the coupled magnetohydrodynamic oscillations in the magnetosphere with a dipole magnetic field. To understand the behavior of the spatial structure of the field perturbations with a great accuracy, they use the finite element method. The azimuthal and radial electric field perturbations are assumed to vanish at the ionosphere, and the azimuthal electric field is assumed to be zero on the outer boundary. The global structures of the electromagnetic field perturbations associated with the coupled magnetohydrodynamic oscillations are presented. In addition, the three-dimensional current system associated with the coupled oscillations is numerically calculated and the following characteristics are found: (1) A strong field-aligned current flows along a resonant field line. The current is particularly strong near the ionosphere. (2) The radial current changes its direction on the opposite sides of the resonant L shell. Unlike the field-aligned current, the radial currents exist in the entire magnetosphere. (3) Although the azimuthal and radial currents are intense on the resonant field line, these currents do not form a loop in the plane perpendicular to the ambient magnetic field. Therefore the field-aligned component of the perturbed magnetic field does not have a maximum at the resonant L shell
Coupled Person Orientation Estimation and Appearance Modeling using Spherical Harmonics
Liem, M.C.; Gavrila, D.M.
2014-01-01
We present a novel approach for the estimation of a person's overall body orientation, 3D shape and texture, from overlapping cameras. A distinguishing aspect of our approach is the use of spherical harmonics for 3D shape- and texture-representation; it offers a compact, low-dimensional
International Nuclear Information System (INIS)
Sarkar, P.; Bhattacharyya, S.P.
1995-01-01
The effects of quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent force constant (K) or harmonic frequency (ω) are studied both perturbatively and numerically by the time-dependent Fourier grid Hamiltonian method. In the absence of anharmonicity, the ground-state population decreases and the population of an accessible excited state (k = 2.4, 6 ... ) increases with time. However, when anharmonicity is introduced, both the ground- and excited-state populations show typical oscillations. For weak coupling, the population of an accessible excited state at a certain instant of time (short) turns out to be a parabolic function of the anharmonic coupling constant (λ), when all other parameters of the system are kept fixed. This parabolic nature of the excited-state population vs. the λ profile is independent of the specific form of the time dependence of the force constant, K t . However, it depends upon the rate at which K t relaxes. For small anharmonic coupling strength and short time scales, the numerical results corroborate expectations based on the first-order time-dependent perturbative analysis, using a suitably repartitioned Hamiltonian that makes H 0 time-independent. Some of the possible experimental implications of our observations are analyzed, especially in relation to intensity oscillations observed in some charge-transfer spectra in systems in which the dephasing rates are comparable with the time scale of the electron transfer. 21 refs., 7 figs., 1 tab
Chimera and phase-cluster states in populations of coupled chemical oscillators
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.
Vasil'ev, M. G.
2017-02-01
A technique for measuring the crystal cross-sectional area with a weight sensor based on the difference between its readings at the extreme rod positions in the stepwise and continuous modes of modulation of the pulling rate is proposed for the low-thermal gradient Czochralski method. A change in the crystallization rate at harmonic oscillations of the pulling rate is estimated with the aim of conserving the quality of the growing crystal for this measurement method.
Quantization and instability of the damped harmonic oscillator subject to a time-dependent force
International Nuclear Information System (INIS)
Majima, H.; Suzuki, A.
2011-01-01
We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity (-γx) 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)+(γ)/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) 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.
Mixed synchronization in chaotic oscillators using scalar coupling
Energy Technology Data Exchange (ETDEWEB)
Bhowmick, Sourav K.; Hens, Chittaranjan [CSIR – Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India); Ghosh, Dibakar, E-mail: drghosh_math@yahoo.co.in [Department of Mathematics, University of Kalyani, West Bengal 741235 (India); Dana, Syamal K. [CSIR – Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India)
2012-07-23
We report experimental evidence of mixed synchronization in two unidirectionally coupled chaotic oscillators using a scalar coupling. In this synchronization regime, some of the state variables may be in complete synchronization while others may be in anti-synchronization state. We extended the theory by using an adaptive controller with an updating law based on Lyapunov function stability to include parameter fluctuation. Using the scheme, we implemented a cryptographic encoding for digital signal through parameter modulation. -- Highlights: ► We provided experimental evidence of the mixed synchronization scheme while other methods are mostly theoretical nature. ► We numerically studied adaptive mixed synchronization when the parameters are not completely known using scalar coupling. ► We proposed a secure communication system where three digital messages are transmitted using parameter modulation.
Two dimensional (4,0) supergravity in harmonic superspace. The action and the matter couplings
International Nuclear Information System (INIS)
Lhallabi, T.; Saidi, E.H.
1988-08-01
The superfield formulation of the two dimensional (4,0) supergravity is developed using the harmonic superspace techniques. The different sets of constraints are given and their solutions are expressed in terms of a SU(2) self dual torsion superfield and harmonic prepotentials. The pure auxiliary (4,0) Einstein action generalizing the (2,0) one is written down and the most general (4,0) matter couplings are given. (author). 24 refs
Harmonic emission due to the nonlinear coupling of a Gaussian laser and a plasma wave
Energy Technology Data Exchange (ETDEWEB)
Pathak, R; Jain, R K [Department of Mathematics, SSL Jain College, Vidisha, MP, 464001 (India); Parashar, J [Department of Physics, Samrat Ashok Technological Institute, Vidisha, MP, 464001 (India)
2010-04-15
A high-power Gaussian laser propagating through a plasma couples with a large-amplitude plasma wave and undergoes scattering to produce harmonics. The process is sensitive to the phase matching angle between the laser and plasma wave numbers and the plasma wave frequency. For larger harmonics, the phase matching angle is high. The efficiency of the process is comparatively high at higher plasma wave frequencies.
Awakened Oscillations in Coupled Consumer-Resource Pairs
Directory of Open Access Journals (Sweden)
Almaz Mustafin
2014-01-01
Full Text Available The paper concerns two interacting consumer-resource pairs based on chemostat-like equations under the assumption that the dynamics of the resource is considerably slower than that of the consumer. The presence of two different time scales enables to carry out a fairly complete analysis of the problem. This is done by treating consumers and resources in the coupled system as fast-scale and slow-scale variables, respectively, and subsequently considering developments in phase planes of these variables, fast and slow, as if they are independent. When uncoupled, each pair has unique asymptotically stable steady state and no self-sustained oscillatory behavior (although damped oscillations about the equilibrium are admitted. When the consumer-resource pairs are weakly coupled through direct reciprocal inhibition of consumers, the whole system exhibits self-sustained relaxation oscillations with a period that can be significantly longer than intrinsic relaxation time of either pair. It is shown that the model equations adequately describe locally linked consumer-resource systems of quite different nature: living populations under interspecific interference competition and lasers coupled via their cavity losses.
International Nuclear Information System (INIS)
Zeng Bei; Zeng Jinyan
2002-01-01
It is shown that for any central potential V(r) there exist a series of conserved aphelion and perihelion vectors R-tilde=pxL-g(r)r, g(r)=rV ' (r). However, if and only if V(r) is a pure or screened Coulomb potential, R-tilde and L constitute an SO 4 algebra in the subspace spanned by the degenerate states with a given energy eigenvalue E ' . While dR/dt=0 always holds, dR ' /dt=0 holds only at the aphelia and perihelia. Moreover, the space spanning the SO 4 algebra for a screened Coulomb potential is smaller than that for a pure Coulomb potential. The relation of closed orbits for a screened Coulomb potential with that for a pure Coulomb potential is clarified. The ratio of the radial frequency ω r and angular frequency ω φ , ω r /ω φ =κ=1 for a pure Coulomb potential irrespective of the angular momentum L and energy E(<0). For a screened Coulomb potential κ is determined by the angular momentum L, and when κ is any rational number (κ<1), the orbit is closed. The situation for a pure or screened isotropic harmonic oscillator is similar
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
A new look at the quantum mechanics of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Kastrup, H.A.
2006-12-15
At first sight it is probably hard to believe that something new can be said about the harmonic oscillator (HO). But that is so indeed: Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables {phi} element of R mod 2{pi} and I>0. However, the transformation q= {radical}(2I)cos {phi}, p=-{radical}(2I)sin {phi} is only locally symplectic and singular for (q,p)=(0,0). Globally the phase space {l_brace}(q,p){r_brace} has the topological structure of the plane R{sup 2}, whereas the phase space {l_brace}({phi},I){r_brace} corresponds globally to the punctured plane R{sup 2}-(0,0) or to a simple cone S{sup 1} x R{sup +} with the tip deleted. This makes a qualitative difference as to the quantum theory of the two phase spaces: The quantizing canonical group for the plane R{sup 2} consists of the (centrally extended) translations generated by the Poisson Lie algebra basis {l_brace}q,p,1{r_brace}, whereas the corresponding canonical group of the phase space {l_brace}({phi},I){r_brace} is the group SO{up_arrow}(1,2)=Sp(2,R)/Z{sub 2}, where Sp(2,R) is the sympletic group of the plane, with the generating Poisson Lie algebra basis {l_brace}h{sub 0}=I,h{sub 1}=Icos{phi},h{sub 2}=-Isin{phi}{r_brace} which provides also the basic ''observables'' on {l_brace}({phi}, I){r_brace}. In the quantum mechanics of the ({phi},I)-model of the HO the three h{sub j} correspond to self-adjoint generators K{sub j}, j=0,1,2, of irreducible unitary representations from the positive discrete series of the group SO{up_arrow}(1,2) or one of its infinitely many covering groups, the representations parametrized by the Bargmann index k>0. This index k determines the ground state energy E{sub k,n=0}={Dirac_h}{omega}k of the ({phi},I)-Hamiltonian H(anti K)={Dirac_h}{omega}K{sub 0}. For an m-fold covering the lowest possible value for k is k=1/m, which can be made arbitrarily small by choosing m accordingly. This is not in contraction to
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.
Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems
DEFF Research Database (Denmark)
Bayat, M.; Shahidi, M.; Barari, Amin
2011-01-01
approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...
Coupled-oscillator based active-array antennas
Pogorzelski, Ronald J
2012-01-01
Describing an innovative approach to phased-array control in antenna design This book explores in detail phased-array antennas that use coupled-oscillator arrays, an arrangement featuring a remarkably simple beam steering control system and a major reduction in complexity compared with traditional methods of phased-array control. It brings together in one convenient, self-contained volume the many salient research results obtained over the past ten to fifteen years in laboratories around the world, including the California Institute of Technology's Jet Propulsion Laboratory.
International Nuclear Information System (INIS)
Fueloep, L.
1987-10-01
The forceless mechanics of Hertz is a reformulation of the classical mechanics in a curved configuration space. The relationship between the forceless mechanics and the general relativity theory which uses curved Riemann spaces as well is investigated on the simple example of the harmonic oscillator. The mathematical similarities and differences and the different interpretations of similar formulas are discussed. Some formal constants of the Hertz mechanics have got concrete physical meanings in the general relativity. (D.Gy.)
Coupled oscillations of flow along a perforated plate
International Nuclear Information System (INIS)
Celik, E.; Rockwell, D.
2004-01-01
Turbulent shear flow past a perforated plate bounded by a closed cavity can give rise to highly coherent oscillations, which have a wavelength of the order of the plate length. The present investigation focuses on the coupling between unsteady events on either side of the plate when the oscillations are self-sustaining. A cinema technique of high-image-density particle image velocimetry, which provides a space-time representation of the unsteadiness at a large number of locations over entire planes, is employed to characterize the distinctively different patterns of flow structure on the back (low-speed) side of the plate relative to those on the front (high-speed) side. Global cross-spectral analysis leads to patterns of spectral peaks and phase variations, along and across the plate. This approach, along with complementary types of image evaluation, delineates the physics of the oscillations, which include downstream propagating disturbances along either side of the plate and a coherent region of unsteadiness at its trailing-edge. On the backside of the plate, a sequence of upstream-oriented, pulsatile jets are formed, and the time-averaged flow pattern is a counterflow wall jet
International Nuclear Information System (INIS)
Mota, R D; Xicotencatl, M A; Granados, V D
2004-01-01
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse
Mota, R. D.; Xicoténcatl, M. A.; Granados, V. D.
2004-02-01
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.
Energy Technology Data Exchange (ETDEWEB)
Mota, R D [Unidad Profesional Interdisciplinaria de IngenierIa y TecnologIas Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, 07340 Mexico DF (Mexico); Xicotencatl, M A [Departamento de Matematicas del Centro de Investigacion y Estudios Avanzados del IPN, Mexico DF, 07000 (Mexico); Granados, V D [Escuela Superior de FIsica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)
2004-02-20
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.
On the (Frequency) Modulation of Coupled Oscillator Arrays in Phased Array Beam Control
Pogorzelski, R.; Acorn, J.; Zawadzki, M.
2000-01-01
It has been shown that arrays of voltage controlled oscillators coupled to nearest neighbors can be used to produce useful aperture phase distributions for phased array antennas. However, placing information of the transmitted signal requires that the oscillations be modulated.
Non-linear phenomena in electronic systems consisting of coupled single-electron oscillators
International Nuclear Information System (INIS)
Kikombo, Andrew Kilinga; Hirose, Tetsuya; Asai, Tetsuya; Amemiya, Yoshihito
2008-01-01
This paper describes non-linear dynamics of electronic systems consisting of single-electron oscillators. A single-electron oscillator is a circuit made up of a tunneling junction and a resistor, and produces simple relaxation oscillation. Coupled with another, single electron oscillators exhibit complex behavior described by a combination of continuous differential equations and discrete difference equations. Computer simulation shows that a double-oscillator system consisting of two coupled oscillators produces multi-periodic oscillation with a single attractor, and that a quadruple-oscillator system consisting of four oscillators also produces multi-periodic oscillation but has a number of possible attractors and takes one of them determined by initial conditions
Hybrid Systems: Cold Atoms Coupled to Micro Mechanical Oscillators =
Montoya Monge, Cris A.
Micro mechanical oscillators can serve as probes in precision measurements, as transducers to mediate photon-phonon interactions, and when functionalized with magnetic material, as tools to manipulate spins in quantum systems. This dissertation includes two projects where the interactions between cold atoms and mechanical oscillators are studied. In one of the experiments, we have manipulated the Zeeman state of magnetically trapped Rubidium atoms with a magnetic micro cantilever. The results show a spatially localized effect produced by the cantilever that agrees with Landau-Zener theory. In the future, such a scalable system with highly localized interactions and the potential for single-spin sensitivity could be useful for applications in quantum information science or quantum simulation. In a second experiment, work is in progress to couple a sample of optically trapped Rubidium atoms to a levitated nanosphere via an optical lattice. This coupling enables the cooling of the center-of-mass motion of the nanosphere by laser cooling the atoms. In this system, the atoms are trapped in the optical lattice while the sphere is levitated in a separate vacuum chamber by a single-beam optical tweezer. Theoretical analysis of such a system has determined that cooling the center-of-mass motion of the sphere to its quantum ground state is possible, even when starting at room temperature, due to the excellent environmental decoupling achievable in this setup. Nanospheres cooled to the quantum regime can provide new tests of quantum behavior at mesoscopic scales and have novel applications in precision sensing.
Fluid-structure coupling for an oscillating hydrofoil
Münch, C.; Ausoni, P.; Braun, O.; Farhat, M.; Avellan, F.
2010-08-01
Fluid-structure investigations in hydraulic machines using coupled simulations are particularly time-consuming. In this study, an alternative method is presented that linearizes the hydrodynamic load of a rigid, oscillating hydrofoil. The hydrofoil, which is surrounded by incompressible, turbulent flow, is modeled with forced and free pitching motions, where the mean incidence angle is 0° with a maximum angle amplitude of 2°. Unsteady simulations of the flow, performed with ANSYS CFX, are presented and validated with experiments which were carried out in the EPFL High-Speed Cavitation Tunnel. First, forced motion is investigated for reduced frequencies ranging from 0.02 to 100. The hydrodynamic load is modeled as a simple combination of inertia, damping and stiffness effects. As expected, the potential flow analysis showed the added moment of inertia is constant, while the fluid damping and the fluid stiffness coefficients depend on the reduced frequency of the oscillation motion. Behavioral patterns were observed and two cases were identified depending on if vortices did or did not develop in the hydrofoil wake. Using the coefficients identified in the forced motion case, the time history of the profile incidence is then predicted analytically for the free motion case and excellent agreement is found for the results from coupled fluid-structure simulations. The model is validated and may be extended to more complex cases, such as blade grids in hydraulic machinery.
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.
Laas, Katrin; Mankin, Romi; Rekker, Astrid
2009-05-01
The influences of noise flatness and friction coefficient on the long-time behavior of the first two moments and the correlation function for the output signal of a harmonic oscillator with fluctuating frequency subjected to an external periodic force are considered. The colored fluctuations of the oscillator frequency are modeled as a trichotomous noise. The study is a follow up of the previous investigation of a stochastic oscillator [Phys. Rev. E 78, 031120 (2008)], where the connection between the occurrence of energetic instability and stochastic multiresonance is established. Here we report some unexpected results not considered in the previous work. Notably, we have found a nonmonotonic dependence of several stochastic resonance characteristics such as spectral amplification, variance of the output signal, and signal-to-noise ratio on the friction coefficient and on the noise flatness. In particular, in certain parameter regions spectral amplification exhibits a resonancelike enhancement at intermediate values of the friction coefficient.
Direction of coupling from phases of interacting oscillators: An information-theoretic approach
Paluš, Milan; Stefanovska, Aneta
2003-05-01
A directionality index based on conditional mutual information is proposed for application to the instantaneous phases of weakly coupled oscillators. Its abilities to distinguish unidirectional from bidirectional coupling, as well as to reveal and quantify asymmetry in bidirectional coupling, are demonstrated using numerical examples of quasiperiodic, chaotic, and noisy oscillators, as well as real human cardiorespiratory data.
CSIR Research Space (South Africa)
Grobler, TL
2012-06-01
Full Text Available . The Fourier transform and maximum-likelihood parameter estimation are used to estimate the harmonic and noise parameters of the colored simple harmonic oscillator. Two case studies in South Africa show that reliable class differentiation can be obtained...
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.
International Nuclear Information System (INIS)
Stan, Cristina; Cristescu, C.P.; Agop, M.
2007-01-01
In this work, we present a novel evidence of the importance of the golden mean criticality of a system of oscillators in agreement with El Naschie's E-infinity theory. We focus on chaos inhibition in a system of two coupled modified van der Pol oscillators. Depending on the coupling between the two oscillators, the system shows chaotic behavior for different ranges of the coupling parameter. Chaos suppression, as a transition from irregular behavior to a periodical one, is induced by perturbing the system with a harmonic signal with amplitude considerably lower than the value which causes entrainment. The frequency of the perturbation is related to the main frequencies in the spectrum of the freely running system (without perturbation) by the golden mean. We demonstrate that this effect is also obtained for a perturbation with frequency such that the ratio of half the frequency of the first main component in the freely running chaotic spectrum over the frequency of the perturbation is very close (five digits coincidence) to the golden mean. This result is shown to hold for arbitrary values of the coupling parameter in the various ranges of chaotic dynamics of the free running system
Pintér, Balázs; Erdélyi, R.
2018-01-01
Solar fundamental (f) acoustic mode oscillations are investigated analytically in a magnetohydrodynamic (MHD) model. The model consists of three layers in planar geometry, representing the solar interior, the magnetic atmosphere, and a transitional layer sandwiched between them. Since we focus on the fundamental mode here, we assume the plasma is incompressible. A horizontal, canopy-like, magnetic field is introduced to the atmosphere, in which degenerated slow MHD waves can exist. The global (f-mode) oscillations can couple to local atmospheric Alfvén waves, resulting, e.g., in a frequency shift of the oscillations. The dispersion relation of the global oscillation mode is derived, and is solved analytically for the thin-transitional layer approximation and for the weak-field approximation. Analytical formulae are also provided for the frequency shifts due to the presence of a thin transitional layer and a weak atmospheric magnetic field. The analytical results generally indicate that, compared to the fundamental value (ω =√{ gk }), the mode frequency is reduced by the presence of an atmosphere by a few per cent. A thin transitional layer reduces the eigen-frequencies further by about an additional hundred microhertz. Finally, a weak atmospheric magnetic field can slightly, by a few percent, increase the frequency of the eigen-mode. Stronger magnetic fields, however, can increase the f-mode frequency by even up to ten per cent, which cannot be seen in observed data. The presence of a magnetic atmosphere in the three-layer model also introduces non-permitted propagation windows in the frequency spectrum; here, f-mode oscillations cannot exist with certain values of the harmonic degree. The eigen-frequencies can be sensitive to the background physical parameters, such as an atmospheric density scale-height or the rate of the plasma density drop at the photosphere. Such information, if ever observed with high-resolution instrumentation and inverted, could help to
International Nuclear Information System (INIS)
Megam Ngouonkadi, E B; Fotsin, H B; Louodop Fotso, P
2014-01-01
This paper investigates the dynamics of a memristor-based Van der Pol oscillator coupled to a linear circuit (VDPCL). This chaotic oscillator is a modification of the classical Van der Pol coupled to a linear circuit, and is obtained by replacing the classical cubic nonlinearity by the memristive one. The memristive VDPCL oscillator, in addition to having a very special stability property, exhibits interesting spectral characteristics, which makes it suitable for chaos-based secure communication applications. The memristor is realized by using off-the-shelf components. The basic properties of the circuit are analyzed by means of bifurcation analysis. Chaotic attractors from numerical and experimental analysis are presented, followed by a comparison of results obtained from the modified VDPCL oscillator and those from the classical VDPCL oscillator. An application to synchronization and chaos secure communication is also presented. (paper)
Harmonically trapped attractive and repulsive spin–orbit and Rabi coupled Bose–Einstein condensates
International Nuclear Information System (INIS)
Chiquillo, Emerson
2017-01-01
Numerically we investigate the ground state of effective one-dimensional spin–orbit (SO) and Rabi coupled two pseudo-spinor Bose–Einstein condensates (BECs) under the effect of harmonic traps. For both signs of the interaction, density profiles of SO and Rabi coupled BECs in harmonic potentials, which simulate a real experimental situation are obtained. The harmonic trap causes a strong reduction of the multi-peak nature of the condensate and it increases its density. For repulsive interactions, the increase of SO coupling results in an uncompressed less dense condensate and with increased multi-peak nature of the density. The increase of Rabi coupling leads to a density increase with an almost constant number of multi-peaks. For both signs of the interaction and negative values of Rabi coupling, the condensate develops a notch in the central point and it seems to a dark-in-bright soliton. In the case of the attractive nonlinearity, an interesting result is the increase of the collapse threshold under the action of the SO and Rabi couplings. (paper)
Elementary modes of coupled oscillators as whispering-gallery microresonators
Banerjee, Rabin; Mukherjee, Pradip
2015-10-01
We obtain the elementary modes of a system of parity-time reversal (PT)-symmetric coupled oscillators with balanced loss and gain. These modes are used to give a physical picture of the phase transition recently reported [C. M. Bender, M. Gianfreda, B. Peng, S. K. Özdemir and L. Yang, Phys. Rev. A 88, 062111 (2013); L. Yang, S. K. Özdemir and B. Peng, 12th Int. Workshop and Conf. Pseudo-Hermitian Hamiltonians in Quantum Physics, Istanbul, Turkey, July 2013; B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender and L. Yang, Nat. Phys. 10, 394 (2014)] in experiments with whispering-gallery microresonators.
Higher dimensional models of cross-coupled oscillators and application to design
Elwakil, Ahmed S.; Salama, Khaled N.
2010-01-01
We present four-dimensional and five-dimensional models for classical cross-coupled LC oscillators. Using these models, sinusoidal oscillation condition, frequency and amplitude can be found. Further, undesired behaviors such as relaxation-mode oscillations and latchup can be explained and detected. A simple graphical design procedure is also described. © 2010 World Scientific Publishing Company.
Higher dimensional models of cross-coupled oscillators and application to design
Elwakil, Ahmed S.
2010-06-01
We present four-dimensional and five-dimensional models for classical cross-coupled LC oscillators. Using these models, sinusoidal oscillation condition, frequency and amplitude can be found. Further, undesired behaviors such as relaxation-mode oscillations and latchup can be explained and detected. A simple graphical design procedure is also described. © 2010 World Scientific Publishing Company.
Effect of electromagnetic waves and higher harmonics in capacitively coupled plasma phenomena
International Nuclear Information System (INIS)
Upadhyay, R R; Sawada, I; Ventzek, P L G; Raja, L L
2013-01-01
High-resolution self-consistent numerical simulation of electromagnetic wave phenomena in an axisymmetric capacitively coupled plasma reactor is reported. A prominent centre-peaked plasma density profile is observed for driving frequencies of 60 MHz and is consistent with observations in the literature and accompanying experimental studies. A power spectrum of the simulated wave electric field reveals the presence of well-resolved high frequency harmonic content up to the 20th harmonic of the excitation frequency; an observation that has also been reported in experiments. Importantly, the simulation results reveal that the occurrence of higher harmonics is strongly correlated with the occurrence of a centre-peaked plasma density profile. (fast track communication)
Chimera states in two-dimensional networks of locally coupled oscillators
Kundu, Srilena; Majhi, Soumen; Bera, Bidesh K.; Ghosh, Dibakar; Lakshmanan, M.
2018-02-01
Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and existence of chimera states by considering locally coupled two-dimensional networks of identical oscillators where each node is interacting through nonlinear coupling function. This is in contrast with the existence of chimera states in two-dimensional nonlocally coupled oscillators with rectangular kernel in the coupling function. We find that the presence of nonlinearity in the coupling function plays a key role to produce chimera states in two-dimensional locally coupled oscillators. We analytically verify explicitly in the case of a network of coupled Stuart-Landau oscillators in two dimensions that the obtained results using Ott-Antonsen approach and our analytical finding very well matches with the numerical results. Next, we consider another type of important nonlinear coupling function which exists in neuronal systems, namely chemical synaptic function, through which the nearest-neighbor (locally coupled) neurons interact with each other. It is shown that such synaptic interacting function promotes the emergence of chimera states in two-dimensional lattices of locally coupled neuronal oscillators. In numerical simulations, we consider two paradigmatic neuronal oscillators, namely Hindmarsh-Rose neuron model and Rulkov map for each node which exhibit bursting dynamics. By associating various spatiotemporal behaviors and snapshots at particular times, we study the chimera
Nakao, Hiroya; Yasui, Sho; Ota, Masashi; Arai, Kensuke; Kawamura, Yoji
2018-04-01
A general phase reduction method for a network of coupled dynamical elements exhibiting collective oscillations, which is applicable to arbitrary networks of heterogeneous dynamical elements, is developed. A set of coupled adjoint equations for phase sensitivity functions, which characterize the phase response of the collective oscillation to small perturbations applied to individual elements, is derived. Using the phase sensitivity functions, collective oscillation of the network under weak perturbation can be described approximately by a one-dimensional phase equation. As an example, mutual synchronization between a pair of collectively oscillating networks of excitable and oscillatory FitzHugh-Nagumo elements with random coupling is studied.
Isar, Aurelian
1995-01-01
The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.
International Nuclear Information System (INIS)
Demiralp, Metin
2010-01-01
This work focuses on the dynamics of a system of quantum multi harmonic oscillators whose Hamiltonian is conic in positions and momenta with time variant coefficients. While it is simple, this system is useful for modeling the dynamics of a number of systems in contemporary sciences where the equations governing spatial or temporal changes are described by sets of ODEs. The dynamical causal models used readily in neuroscience can be indirectly described by these systems. In this work, we want to show that it is possible to describe these systems using quantum wave function type entities and expectations if the dynamic of the system is related to a set of ODEs.
A model of the two-dimensional quantum harmonic oscillator in an AdS{sub 3} background
Energy Technology Data Exchange (ETDEWEB)
Frick, R. [Universitaet zu Koeln, Institut fuer Theoretische Physik, Cologne (Germany)
2016-10-15
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a three-dimensional anti-de Sitter background. We use a generalized Schroedinger picture in which the analogs of the Schroedinger operators of the particle are independent of both the time and the space coordinates in different representations. The spacetime independent operators of the particle induce the Lie algebra of Killing vector fields of the AdS{sub 3} spacetime. In this picture, we have a metamorphosis of the Heisenberg uncertainty relations. (orig.)
The Madden-Julian Oscillation in NCEP Coupled Model Simulation
Directory of Open Access Journals (Sweden)
Wanqiu Wang Kyong-Hwan Seo
2009-01-01
Full Text Available This study documents a detailed analysis on the Madden-Julian Oscillation (MJO simulated by the National Centers for Environmental Prediction (NCEP using the Global Forecast System (GFS model version 2003 coupled with the Climate Forecast System model (CFS consisting of the 2003 version of GFS and the Geophysical Fluid Dynamics Laboratory (GFDL Modular Ocean Model V.3 (MOM3. The analyses are based upon a 21-year simulation of AMIP-type with GFS and CMIP-type with CFS. It is found that air-sea coupling in CFS is shown to improve the coherence between convection and large-scale circulation associated with the MJO. The too fast propagation of convection from the Indian Ocean to the maritime continents and the western Pacific in GFS is improved (slowed down in CFS. Both GFS and CFS produce too strong intraseasonal convective heating and circulation anomalies in the central-eastern Pacific; further, the air-sea coupling in CFS enhances this unrealistic feature. The simulated mean slow phase speed of east ward propagating low-wavenumber components shown in the wavenumber-frequency spectra is due to the slow propagation in the central-eastern Pacific in both GFS and CFS. Errors in model climatology may have some effect upon the simulated MJO and two possible influences are: (i CFS fails to simulate the westerlies over maritime continents and western Pacific areas, resulting in an unrealistic representation of surface latent heat flux associated with the MJO; and (ii vertical easterly wind shear from the Indian Ocean to the western Pacific in CFS is much weaker than that in the observation and in GFS, which may adversely affect the eastward propagation of the simulated MJO.
Negative Resistance Circuit for Damping an Array of Coupled FitzHugh-Nagumo Oscillators
DEFF Research Database (Denmark)
Tamaševičius, Arūnas; Adomaitienė, Elena; Bumelienė, Skaidra
2015-01-01
An analog circuit, based on a negative impedance converter and a capacitor, for damping oscillations in an array of mean-field coupled neuronal FitzHugh–Nagumo (FHN) type oscillators is described. The circuit is essentially a two-terminal feedback controller. When coupled to an array of the FHN...
Amplitude death and spatiotemporal bifurcations in nonlocally delay-coupled oscillators
International Nuclear Information System (INIS)
Guo, Yuxiao; Niu, Ben
2015-01-01
Amplitude death and spatiotemporal oscillations are remarkable patterns in coupled systems. We consider a ring of n identical oscillators with distance-dependent couplings and time delay. The amplitude death region is the intersection of three stable regions. Employing the method of multiple scales and normal form theory, the stability and criticality of spatiotemporal oscillations are determined. Around the amplitude death boundary there exist one branch of synchronized oscillations, n − 3 branches of co-existing phase-locked oscillations, n branches of mirror-reflecting oscillations, n branches of standing-wave oscillations, one branch of quasiperiodic oscillations and two branches of co-existing synchronized oscillations. It is proved that amplitude death is robust to small inhomogeneity of couplings, and the stability of synchronized or phase-locked oscillations inherits that of the individual decoupled oscillator. For the arbitrary form of coupling functions, some general results are also obtained for the thermodynamic limit. Finally, two examples are given to support the main results. (paper)
Stable amplitude chimera states in a network of locally coupled Stuart-Landau oscillators
Premalatha, K.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2018-03-01
We investigate the occurrence of collective dynamical states such as transient amplitude chimera, stable amplitude chimera, and imperfect breathing chimera states in a locally coupled network of Stuart-Landau oscillators. In an imperfect breathing chimera state, the synchronized group of oscillators exhibits oscillations with large amplitudes, while the desynchronized group of oscillators oscillates with small amplitudes, and this behavior of coexistence of synchronized and desynchronized oscillations fluctuates with time. Then, we analyze the stability of the amplitude chimera states under various circumstances, including variations in system parameters and coupling strength, and perturbations in the initial states of the oscillators. For an increase in the value of the system parameter, namely, the nonisochronicity parameter, the transient chimera state becomes a stable chimera state for a sufficiently large value of coupling strength. In addition, we also analyze the stability of these states by perturbing the initial states of the oscillators. We find that while a small perturbation allows one to perturb a large number of oscillators resulting in a stable amplitude chimera state, a large perturbation allows one to perturb a small number of oscillators to get a stable amplitude chimera state. We also find the stability of the transient and stable amplitude chimera states and traveling wave states for an appropriate number of oscillators using Floquet theory. In addition, we also find the stability of the incoherent oscillation death states.
International Nuclear Information System (INIS)
Yahiaoui, Sid-Ahmed; Bentaiba, Mustapha
2014-01-01
A new SU(1,1) position-dependent effective mass coherent states (PDEM CS) related to the shifted harmonic oscillator (SHO) are deduced. This is accomplished by applying a similarity transformation to the generally deformed oscillator algebra (GDOA) generators for PDEM systems and a new set of operators that close the su(1,1) Lie algebra are constructed, being the PDEM CS of the basis for its unitary irreducible representation. From the Lie algebra generators, we evaluate the uncertainty relationship for a position and momentum-like operators in the PDEM CS and show that it is minimized in the sense of Barut–Girardello CS. We prove that the deduced PDEM CS preserve the same analytical form than those of Glauber states. As an illustration of our procedure, we depicted the 2D-probability density in the PDEM CS for SHO with the explicit form of the mass distribution with no singularities. (paper)
International Nuclear Information System (INIS)
Belendez, A.; Fernandez, E.; Rodes, J.J.; Fuentes, R.; Pascual, I.
2009-01-01
In a previous short communication [A. Belendez, E. Fernandez, J.J. Rodes, R. Fuentes, I. Pascual, Phys. Lett. A 373 (2009) 735] the nonlinear oscillations of a punctual charge in the electric field of a charged ring were analyzed. Approximate frequency-amplitude relations and periodic solutions were obtained using the harmonic balance method. Now we clarify an important aspect about of this oscillation charge. Taking into account Earnshaw's theorem, this punctual charge cannot be a free charge and so it must be confined, for example, on a finite conducting wire placed along the axis of the ring. Then, the oscillatory system may consist of a punctual charge on a conducting wire placed along the axis of the uniformly charged ring.
Higher-order harmonics coupling in different free-electron laser codes
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, , in: Proceedings of FEL 2006 Conference, BESSY, Berlin, Germany, 2006, p. 91], and has been recently implemented in GENESIS 1.3 [See ]. 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.
International Nuclear Information System (INIS)
Chung, N. N.; Chew, L. Y.
2007-01-01
We have generalized the two-step approach to the solution of systems of N coupled quantum anharmonic oscillators. By using the squeezed vacuum state of each individual oscillator, we construct the tensor product state, and obtain the optimal squeezed vacuum product state through energy minimization. We then employ this optimal state and its associated bosonic operators to define a basis set to construct the Heisenberg matrix. The diagonalization of the matrix enables us to obtain the energy eigenvalues of the coupled oscillators. In particular, we have applied our formalism to determine the eigenenergies of systems of two coupled quantum anharmonic oscillators perturbed by a general polynomial potential, as well as three and four coupled systems. Furthermore, by performing a first-order perturbation analysis about the optimal squeezed vacuum product state, we have also examined into the squeezing properties of two coupled oscillator systems
An Application of the Harmonic Oscillator Model to Verify Dunning’s Theory of the Economic Growth
Directory of Open Access Journals (Sweden)
Marcin Salamaga
2013-09-01
Full Text Available Analogies with mechanisms ruling the natural world have oft en been sought in the course of economic phenomena.Th is paper is also an attempt to combine the physical phenomenon of a harmonious oscillator withthe theory of economic growth by J. H. Dunning (1981. In his theory, Dunning distinguished stages of economicgrowth of countries that imply the dependency between the investment position of countries and theirGDP per capita, while the graph presenting this dependency reminds a trajectory of oscillating motion of adamped harmonic oscillator. Th is analogy has given inspiration to reinterpret the theory of economy on thegrounds of the mechanism of a physical model. In this paper, the harmonious oscillator motion equation wasadapted to the description of dependencies shown in the theory of economic growth by J. H. Dunning. Th emathematical solution of this equation is properly parameterised and parameters are estimated with the useof the Gauss-Newton algorithm. Th e main objective of this paper is to allocate a specifi c stage in the economicgrowth to each country on the basis of the values of parameter estimations of the proposed cyclical models ofchanges in the net investment indicator.
Principal component analysis of the nonlinear coupling of harmonic modes in heavy-ion collisions
BoŻek, Piotr
2018-03-01
The principal component analysis of flow correlations in heavy-ion collisions is studied. The correlation matrix of harmonic flow is generalized to correlations involving several different flow vectors. The method can be applied to study the nonlinear coupling between different harmonic modes in a double differential way in transverse momentum or pseudorapidity. The procedure is illustrated with results from the hydrodynamic model applied to Pb + Pb collisions at √{sN N}=2760 GeV. Three examples of generalized correlations matrices in transverse momentum are constructed corresponding to the coupling of v22 and v4, of v2v3 and v5, or of v23,v33 , and v6. The principal component decomposition is applied to the correlation matrices and the dominant modes are calculated.
Isogeometric analysis and harmonic stator-rotor coupling for simulating electric machines
Bontinck, Zeger; Corno, Jacopo; Schöps, Sebastian; De Gersem, Herbert
2018-06-01
This work proposes Isogeometric Analysis as an alternative to classical finite elements for simulating electric machines. Through the spline-based Isogeometric discretization it is possible to parametrize the circular arcs exactly, thereby avoiding any geometrical error in the representation of the air gap where a high accuracy is mandatory. To increase the generality of the method, and to allow rotation, the rotor and the stator computational domains are constructed independently as multipatch entities. The two subdomains are then coupled using harmonic basis functions at the interface which gives rise to a saddle-point problem. The properties of Isogeometric Analysis combined with harmonic stator-rotor coupling are presented. The results and performance of the new approach are compared to the ones for a classical finite element method using a permanent magnet synchronous machine as an example.
International Nuclear Information System (INIS)
Raghavan, S.; Smerzi, A.; Fantoni, S.; Shenoy, S.R.
2001-03-01
We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The boson Josephson junction (BJJ) dynamics is described by the two-mode nonlinear Gross-Pitaevskii equation that is solved analytically in terms of elliptic functions. The BJJ, being a neutral, isolated system, allows the investigations of dynamical regimes for the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ's). These include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to π (π-phase oscillations); (ii) the average population imbalance is nonzero, in states with macroscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJJ ac and plasma oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single universal curve for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of 3 He-B and the internal Josephson effect in 3 He-A are also discussed. (author)
A new look at the harmonic oscillator problem in a finite-dimensional Hilbert space
International Nuclear Information System (INIS)
Bagchi, B.
1995-01-01
In this Letter some basic properties of a truncated oscillator are studied. By using finite-dimensional representation matrices of the truncated oscillator we construct new parasupersymmetric schemes and remark on their relevance to the transition operators of the non-interacting N-level system endowed with bosonic modes. ((orig.))
Collective motions of globally coupled oscillators and some probability distributions on circle
Energy Technology Data Exchange (ETDEWEB)
Jaćimović, Vladimir [Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put, bb., 81000 Podgorica (Montenegro); Crnkić, Aladin, E-mail: aladin.crnkic@hotmail.com [Faculty of Technical Engineering, University of Bihać, Ljubijankićeva, bb., 77000 Bihać, Bosnia and Herzegovina (Bosnia and Herzegovina)
2017-06-28
In 2010 Kato and Jones described a new family of probability distributions on circle, obtained as Möbius transformation of von Mises distribution. We present the model demonstrating that these distributions appear naturally in study of populations of coupled oscillators. We use this opportunity to point out certain relations between Directional Statistics and collective motion of coupled oscillators. - Highlights: • We specify probability distributions on circle that arise in Kuramoto model. • We study how the mean-field coupling affects the shape of distribution of phases. • We discuss potential applications in some experiments on cell cycle. • We apply Directional Statistics to study collective dynamics of coupled oscillators.
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we ...
Collective oscillations and coupled modes in confined microfluidic droplet arrays
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.
Transient chaos in a globally coupled system of nearly conservative Hamiltonian Duffing oscillators
International Nuclear Information System (INIS)
Sabarathinam, S.; Thamilmaran, K.
2015-01-01
Highlights: •We have examined transient chaos in globally coupled oscillators. •We analyze transient chaos using new techniques. •We give experimental confirmation of transient chaos. -- Abstract: In this work, transient chaos in a ring and globally coupled system of nearly conservative Hamiltonian Duffing oscillators is reported. The networks are formed by coupling of three, four and six Duffing oscillators. The nearly conservative Hamiltonian nature of the coupled system is proved by stability analysis. The transient phenomenon is confirmed through various numerical investigations such as recurrence analysis, 0–1 test and Finite Time Lyapunov Exponents. Further, the effect of damping and the average transient lifetime of three, four and six coupled schemes for randomly generated initial conditions have been analyzed. The experimental confirmation of transient chaos in an illustrative system of three ringly coupled Duffing oscillators is also presented
More efficient second harmonic generation of whispering gallery modes by selective out-coupling
Trainor, Luke S.; Sedlmeir, Florian; Peuntinger, Christian; Schwefel, Harald G. L.
2017-01-01
We demonstrate second harmonic generation (SHG) in an $x$-cut congruent lithium niobate (LN) whispering gallery mode resonator. We first show theoretically that independent control of the coupling of the pump and signal modes is optimal for high conversion rates. A scheme based on our earlier work in Ref. [1] is then implemented experimentally to verify this. Thereby we are able to improve on the efficiency of SHG by more than an order of magnitude by selectively out-coupling using a LN prism...
Implication of two-coupled differential Van der Pol Duffing oscillator in weak signal detection
International Nuclear Information System (INIS)
Peng Hanghang; Xu Xuemei; Yang Bingchu; Yin Linzi
2016-01-01
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. (author)
Implication of Two-Coupled Differential Van der Pol Duffing Oscillator in Weak Signal Detection
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.
International Nuclear Information System (INIS)
Wang, C M; Lei, X L
2014-01-01
We study dc-current effects on the magnetoresistance oscillation in a two-dimensional electron gas with Rashba spin-orbit coupling, using the balance-equation approach to nonlinear magnetotransport. In the weak current limit the magnetoresistance exhibits periodical Shubnikov-de Haas oscillation with changing Rashba coupling strength for a fixed magnetic field. At finite dc bias, the period of the oscillation halves when the interbranch contribution to resistivity dominates. With further increasing current density, the oscillatory resistivity exhibits phase inversion, i.e., magnetoresistivity minima (maxima) invert to maxima (minima) at certain values of the dc bias, which is due to the current-induced magnetoresistance oscillation. (paper)
Energy Technology Data Exchange (ETDEWEB)
Kado, S. [High Temperature Plasma Center, University of Tokyo, Kashiwanoha, Kashiwa, Chiba 277-8568 (Japan)]. E-mail: kado@q.t.u-tokyo.ac.jp; Oishi, T. [School of Engineering, University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); Yoshinuma, M. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Ida, K. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Takeuchi, M. [Department of Energy Engineering and Science, Nagoya University, Nagoya 464-8603 (Japan); Toi, K. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Akiyama, T. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Minami, T. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Nagaoka, K. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Shimizu, A. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Okamura, S. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Tanaka, S. [School of Engineering, University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan)
2007-06-15
Edge harmonic oscillations (EHO) offer the potential to relax the H-mode pedestal in a tokamak, thus avoiding edge localised modes (ELM). The mode structure of the EHO in CHS was investigated using a poloidal array of beam emission spectroscopy (BES) and a magnetic probe array. The EHO exhibited a peculiar characteristic in which the first, second and third harmonics show the same wavenumber, suggesting that the propagation velocities are different. Change in the phase of higher harmonics at the time when that of the first harmonic is zero can be described as a variation along the (m, n) = (-2, 1) mode structure, though the EHO lies on the {iota} = 1 surface. This behavior leads to an oscillation that exhibits periodic dependence of shape on spatial position.
International Nuclear Information System (INIS)
Cari, C; Suparmi, A
2013-01-01
The energy eigenvalues and eigenfunctions of Schrodinger equation for three dimensional harmonic oscillator potential plus Rosen-Morse non-central potential are investigated using NU method and Romanovski polynomial. The bound state energy eigenvalues are given in a closed form and corresponding radial wave functions are expressed in associated Laguerre polynomials while angular eigen functions are given in terms of Romanovski polynomials. The Rosen-Morse potential is considered to be a perturbation factor to the three dimensional harmonic oscillator potential that causes the increase of radial wave function amplitude and decrease of angular momentum length. Keywords: Schrodinger Equation, Three dimensional Harmonic Oscillator potential, Rosen-morse non-central potential, NU method, Romanovski Polynomials
Application of He’s Energy Balance Method to Duffing-Harmonic Oscillators
DEFF Research Database (Denmark)
Momeni, M.; Jamshidi, j.; Barari, Amin
2011-01-01
In this article, He's energy balance method is applied for calculating angular frequencies of nonlinear Duffing oscillators. This method offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. We illustrate that the energy balance is very effective and convenient...... and does not require linearization or small perturbation. Contrary to the conventional methods, in energy balance, only one iteration leads to high accuracy of the solutions. It is predicted that the energy balance method finds wide applications in engineering problems....
Harmonic oscillations of a circular cylinder moving with constant velocity in a quiescent fluid
Jan Novaes Recica; Luiz Antonio Alcântara Pereira; Miguel Hiroo Hirata
2008-01-01
The flow around an oscillating circular cylinder which moves with constant velocity in a quiescent Newtonian fluid with constant properties is analyzed. The influences of the frequency and amplitude oscillation on the aerodynamic loads and on the Strouhal number are presented. For the numerical simulation, a cloud of discrete Lamb vortices are utilized. For each time step of the simulation, a number of discrete vortices are placed close to the body surface; the intensity of theirs is determin...
Lai, Yi Ming
2013-07-09
We study ensembles of globally coupled, nonidentical phase oscillators subject to correlated noise, and we identify several important factors that cause noise and coupling to synchronize or desynchronize a system. By introducing noise in various ways, we find an estimate for the onset of synchrony of a system in terms of the coupling strength, noise strength, and width of the frequency distribution of its natural oscillations. We also demonstrate that noise alone can be sufficient to synchronize nonidentical oscillators. However, this synchrony depends on the first Fourier mode of a phase-sensitivity function, through which we introduce common noise into the system. We show that higher Fourier modes can cause desynchronization due to clustering effects, and that this can reinforce clustering caused by different forms of coupling. Finally, we discuss the effects of noise on an ensemble in which antiferromagnetic coupling causes oscillators to form two clusters in the absence of noise. © 2013 American Physical Society.
Chaotic weak chimeras and their persistence in coupled populations of phase oscillators
International Nuclear Information System (INIS)
Bick, Christian; Ashwin, Peter
2016-01-01
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. (paper)
Aging transition in systems of oscillators with global distributed-delay coupling.
Rahman, B; Blyuss, K B; Kyrychko, Y N
2017-09-01
We consider a globally coupled network of active (oscillatory) and inactive (nonoscillatory) oscillators with distributed-delay coupling. Conditions for aging transition, associated with suppression of oscillations, are derived for uniform and gamma delay distributions in terms of coupling parameters and the proportion of inactive oscillators. The results suggest that for the uniform distribution increasing the width of distribution for the same mean delay allows aging transition to happen for a smaller coupling strength and a smaller proportion of inactive elements. For gamma distribution with sufficiently large mean time delay, it may be possible to achieve aging transition for an arbitrary proportion of inactive oscillators, as long as the coupling strength lies in a certain range.
On the dynamics of traveling phase-oscillators with positive and negative couplings
International Nuclear Information System (INIS)
Choi, Jungzae; Choi, Mooyoung; Yoon, Byunggook
2014-01-01
We investigate numerically the dynamics of traveling clusters in systems of phase oscillators, some of which possess positive couplings and others negative couplings. The phase distribution, speed of traveling, and average separation between clusters, as well as the order parameters for positive and negative oscillators, are computed as the ratio of the two coupling constants and the fraction of positive oscillators are varied. The dependence of the traveling speed on these parameters is obtained and is observed to fit well with the numerical data of the systems. With the help of this, we describe the conditions for the traveling state to appear in the systems with and without a periodic driving field.
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.
Wang, Yang; Song, Hai-Ying; Liu, H. Y.; Liu, Shi-Bing
2017-07-01
We theoretically study high-order harmonic generation (HHG) from relativistically driven overdense plasma targets with rectangularly grating-structured surfaces by femtosecond laser pulses. Our particle-in-cell (PIC) simulations show that, under the conditions of low laser intensity and plasma density, the harmonics emit principally along small angles deviating from the target surface. Further investigation of the surface electron dynamics reveals that the electron bunches are formed by the interaction between the laser field and the target surface, giving rise to the oscillation of equivalent electric-dipole (OEED), which enhances specific harmonic orders. Our work helps understand the mechanism of harmonic emissions from grating targets and the distinction from the planar harmonic scheme.
Energy Technology Data Exchange (ETDEWEB)
Wang, Yang; Song, Hai-Ying; Liu, H.Y.; Liu, Shi-Bing, E-mail: sbliu@bjut.edu.cn
2017-07-12
Highlights: • Proposed a valid mechanism of high harmonic generation by laser grating target interaction: oscillation of equivalent electric dipole (OEED). • Found that there also exist harmonic emission at large emission angle but not just near-surface direction as the former researches had pointed out. • Show the process of the formation and motion of electron bunches at the grating-target surface irradiating with femtosecond laser pulse. - Abstract: We theoretically study high-order harmonic generation (HHG) from relativistically driven overdense plasma targets with rectangularly grating-structured surfaces by femtosecond laser pulses. Our particle-in-cell (PIC) simulations show that, under the conditions of low laser intensity and plasma density, the harmonics emit principally along small angles deviating from the target surface. Further investigation of the surface electron dynamics reveals that the electron bunches are formed by the interaction between the laser field and the target surface, giving rise to the oscillation of equivalent electric-dipole (OEED), which enhances specific harmonic orders. Our work helps understand the mechanism of harmonic emissions from grating targets and the distinction from the planar harmonic scheme.
Induction of Hopf bifurcation and oscillation death by delays in coupled networks
International Nuclear Information System (INIS)
Cheng, C.-Y.
2009-01-01
This work explores a system of two coupled networks that each has four nodes. Delayed effects of short-cuts in each network and the coupling between the two groups are considered. When the short-cut delay is fixed, the arising and death of oscillations are caused by the variational coupling delay.
Harmonic oscillations of a circular cylinder moving with constant velocity in a quiescent fluid
Directory of Open Access Journals (Sweden)
Jan Novaes Recica
2008-01-01
Full Text Available The flow around an oscillating circular cylinder which moves with constant velocity in a quiescent Newtonian fluid with constant properties is analyzed. The influences of the frequency and amplitude oscillation on the aerodynamic loads and on the Strouhal number are presented. For the numerical simulation, a cloud of discrete Lamb vortices are utilized. For each time step of the simulation, a number of discrete vortices are placed close to the body surface; the intensity of theirs is determined such as to satisfy the no-slip boundary condition.
Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators?
Wit, Hero P.; van Dijk, Pim
Spontaneous otoacoustic emissions (SOAEs) are generated by self-sustained cochlear oscillators. Properties of a computational model for a linear array of active oscillators with nearest neighbor coupling are investigated. The model can produce many experimentally well-established properties of
Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators?
Wit, Hero P; van Dijk, Pim
2012-08-01
Spontaneous otoacoustic emissions (SOAEs) are generated by self-sustained cochlear oscillators. Properties of a computational model for a linear array of active oscillators with nearest neighbor coupling are investigated. The model can produce many experimentally well-established properties of SOAEs.
Coordination of the Walking Stick Insect Using a System of Nonlinear Coupled Oscillators
National Research Council Canada - National Science Library
Marvin, Daryl J
1992-01-01
The area of walking machines is investigated. A design for a central pattern generator composed of nonlinear coupled oscillators which generates the characteristic gaits of the walking stick insect is presented...
Ichinose, T
2004-01-01
We study the special values at $s=2$ and $3$ of the spectral zeta function $\\zeta_Q(s)$ of the non-commutative harmonic oscillator $Q(x,D_x)$ introduced in \\cite{PW1, 2}. It is shown that the series defining $\\zeta_Q(s)$ converges absolutely for Re $s>1$ and further the respective values $\\zeta_Q(2)$ and $\\zeta_Q(3)$ are represented essentially by contour integrals of the solutions, respectively, of a singly confluent Heun's ordinary differential equation and of exactly the same but an inhomogeneous equation. As a by-product of these results, we obtain integral representations of the solutions of these equations by rational functions. \\par\
International Nuclear Information System (INIS)
Kobe, D.H.
1989-01-01
The Berry phase is derived in a manifestly gauge-invariant way, without adiabatic or cyclic requirements. It is invariant under unitary transformations, contrary to recent assertions. A time-dependent generalized harmonic oscillator is taken as an example. The energy of the system is not in general the Hamiltonian. An energy, the time derivative of which is the power, is obtained from the equation of motion. When the system is quantized, the Berry phase is zero, and is invariant under unitary transformations. If the energy is chosen incorrectly to be the Hamiltonian, a nonzero Berry phase is obtained. In this case the total phase, the sun of the dynamical and Berry phases, is equal to the correct total phase through first order in perturbation theory. (author)
Maxfield, Lynn; Palaparthi, Anil; Titze, Ingo
2017-03-01
The traditional source-filter theory of voice production describes a linear relationship between the source (glottal flow pulse) and the filter (vocal tract). Such a linear relationship does not allow for nor explain how changes in the filter may impact the stability and regularity of the source. The objective of this experiment was to examine what effect unpredictable changes to vocal tract dimensions could have on fo stability and individual harmonic intensities in situations in which low frequency harmonics cross formants in a fundamental frequency glide. To determine these effects, eight human subjects (five male, three female) were recorded producing fo glides while their vocal tracts were artificially lengthened by a section of vinyl tubing inserted into the mouth. It was hypothesized that if the source and filter operated as a purely linear system, harmonic intensities would increase and decrease at nearly the same rates as they passed through a formant bandwidth, resulting in a relatively symmetric peak on an intensity-time contour. Additionally, fo stability should not be predictably perturbed by formant/harmonic crossings in a linear system. Acoustic analysis of these recordings, however, revealed that harmonic intensity peaks were asymmetric in 76% of cases, and that 85% of fo instabilities aligned with a crossing of one of the first four harmonics with the first three formants. These results provide further evidence that nonlinear dynamics in the source-filter relationship can impact fo stability as well as harmonic intensities as harmonics cross through formant bandwidths. Copyright © 2017 The Voice Foundation. Published by Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Jiang Yu; Lozada-Cassou, M.; Vinet, A.
2003-01-01
The spatiotemporal dynamics of networks based on a ring of coupled oscillators with regular shortcuts beyond the nearest-neighbor couplings is studied by using master stability equations and numerical simulations. The generic criterion for dynamic synchronization has been extended to arbitrary network topologies with zero row-sum. The symmetry-breaking oscillation patterns that resulted from the Hopf bifurcation from synchronous states are analyzed by the symmetry group theory
Stability of The Synchronization Manifold in An All-To-All Time LAG- Diffusively Coupled Oscillators
Directory of Open Access Journals (Sweden)
Adu A.M. Wasike
2009-06-01
Full Text Available we consider a lattice system of identical oscillators that are all coupled to one another with a diffusive coupling that has a time lag. We use the natural splitting of the system into synchronized manifold and transversal manifold to estimate the value of the time lag for which the stability of the system follows from that without a time lag. Each oscillator has a unique periodic solution that is attracting.
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.
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.
Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling.
Ryu, Jung-Wan; Kim, Jong-Ho; Son, Woo-Sik; Hwang, Dong-Uk
2017-08-01
We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.
Synchronization and desynchronization in a network of locally coupled Wilson-Cowan oscillators.
Campbell, S; Wang, D
1996-01-01
A network of Wilson-Cowan (WC) oscillators is constructed, and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis. The network is a 2D matrix, where each oscillator is coupled only to its neighbors. We show analytically that a chain of locally coupled oscillators (the piecewise linear approximation to the WC oscillator) synchronizes, and we present a technique to rapidly entrain finite numbers of oscillators. The coupling strengths change on a fast time scale based on a Hebbian rule. A global separator is introduced which receives input from and sends feedback to each oscillator in the matrix. The global separator is used to desynchronize different oscillator groups. Unlike many other models, the properties of this network emerge from local connections that preserve spatial relationships among components and are critical for encoding Gestalt principles of feature grouping. The ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure/ground segregation based on oscillatory correlation.
He, Yong
2017-06-23
We utilize the surface plasmon field of a metal nanoparticle (MNP) to show strain-mediated coupling in a quantum dot-mechanical resonator hybrid system including a quantum dot (QD) embedded within a conical nanowire (NW) and a MNP in the presence of an external field. Based on the numerical solutions of the master equation, we find that a slow oscillation, originating from the strain-mediated coupling between the QD and the NW, appears in the time evolution of the plasmon field enhancement. The results show that the period (about [Formula: see text]) of the slow oscillation is equal to that of the mechanical resonator of NW, which suggests that the time-resolved measurement of the plasmon field enhancement can be easily achieved based on the current experimental conditions. Its amplitude increases with the increasing strain-mediated coupling strength, and under certain conditions there is a linear relationship between them. The slow oscillation of the plasmon field enhancement provides valuable tools for measurements of the mechanical frequency and the strain-mediated coupling strength.
Phase correlation and clustering of a nearest neighbour coupled oscillators system
International Nuclear Information System (INIS)
EI-Nashar, Hassan F.
2002-09-01
We investigated the phases in a system of nearest neighbour coupled oscillators before complete synchronization in frequency occurs. We found that when oscillators under the influence of coupling form a cluster of the same time-average frequency, their phases start to correlate. An order parameter, which measures this correlation, starts to grow at this stage until it reaches maximum. This means that a time-average phase locked state is reached between the oscillators inside the cluster of the same time- average frequency. At this strength the cluster attracts individual oscillators or a cluster to join in. We also observe that clustering in averaged frequencies orders the phases of the oscillators. This behavior is found at all the transition points studied. (author)
Phase correlation and clustering of a nearest neighbour coupled oscillators system
Ei-Nashar, H F
2002-01-01
We investigated the phases in a system of nearest neighbour coupled oscillators before complete synchronization in frequency occurs. We found that when oscillators under the influence of coupling form a cluster of the same time-average frequency, their phases start to correlate. An order parameter, which measures this correlation, starts to grow at this stage until it reaches maximum. This means that a time-average phase locked state is reached between the oscillators inside the cluster of the same time- average frequency. At this strength the cluster attracts individual oscillators or a cluster to join in. We also observe that clustering in averaged frequencies orders the phases of the oscillators. This behavior is found at all the transition points studied.
Institute of Scientific and Technical Information of China (English)
Liu Li; Zhang Liang-Ying; Cao Li
2009-01-01
The diffusion in a harmonic oscillator driven by coloured noises ζ(t) and η(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time τ_3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient λ of the two Orustein-Uhlenbeck (O-U) noises. 2) Changing the value of τ3, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3)Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.
International Nuclear Information System (INIS)
Li, Liu; Li, Cao; Liang-Ying, Zhang
2009-01-01
The diffusion in a harmonic oscillator driven by coloured noises ζ(t) and η(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time τ 3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient λ of the two Ornstein–Uhlenbeck (O-U) noises. 2) Changing the value of τ 3 , the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3) Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model. (general)
Quantum effects in amplitude death of coupled anharmonic self-oscillators
Amitai, Ehud; Koppenhöfer, Martin; Lörch, Niels; Bruder, Christoph
2018-05-01
Coupling two or more self-oscillating systems may stabilize their zero-amplitude rest state, therefore quenching their oscillation. This phenomenon is termed "amplitude death." Well known and studied in classical self-oscillators, amplitude death was only recently investigated in quantum self-oscillators [Ishibashi and Kanamoto, Phys. Rev. E 96, 052210 (2017), 10.1103/PhysRevE.96.052210]. Quantitative differences between the classical and quantum descriptions were found. Here, we demonstrate that for quantum self-oscillators with anharmonicity in their energy spectrum, multiple resonances in the mean phonon number can be observed. This is a result of the discrete energy spectrum of these oscillators, and is not present in the corresponding classical model. Experiments can be realized with current technology and would demonstrate these genuine quantum effects in the amplitude death phenomenon.
The variational spiked oscillator
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Ullah, N.
1992-08-01
A variational analysis of the spiked harmonic oscillator Hamiltonian -d 2 / d x 2 + x 2 + δ/ x 5/2 , δ > 0, is reported in this work. A trial function satisfying Dirichlet boundary conditions is suggested. The results are excellent for a large range of values of the coupling parameter. (author)
Rectification of harmonically oscillating magnetic fields in quarter circular Josephson junctions
International Nuclear Information System (INIS)
Shaju, P.D.; Kuriakose, V.C.
2003-01-01
A novel method for rectifying harmonically varying magnetic fields is demonstrated using fluxons in quarter circular Josephson junctions (JJs). A JJ with a quarter circular geometry terminated with a load resistor at one end is found to be capable of rectifying alternating fields when biased with a constant dc current. An external magnetic field applied parallel to the dielectric barrier of the junction interacts with the edges of the junction and make asymmetric boundary conditions. These asymmetric boundary conditions facilitate fluxon penetration under a dc bias from one end of the junction in alternate half cycles of the applied field. Thus effective rectification of the field can be achieved using quarter circular JJs. This unique phenomenon is specific to this geometry and can be exploited for making superconducting magnetic field rectifiers. This proposed device is expected to have important applications in millimeter and sub-millimeter radio wave astronomy
Correlations in a chain of three oscillators with nearest neighbour coupling
Idrus, B.; Konstadopoulou, A.; Spiller, T.; Vourdas, A.
2010-04-01
A chain of three oscillators A, B, C with nearest neighbour coupling, is considered. It is shown that the correlations between A, C (which are not coupled directly) can be stronger than the correlations between A, B. Also in some cases various witnesses of entanglement show that A, C are entangled but they cannot lead to any conclusion about A, B.
Interaction of chimera states in a multilayered network of nonlocally coupled oscillators
Goremyko, M. V.; Maksimenko, V. A.; Makarov, V. V.; Ghosh, D.; Bera, B.; Dana, S. K.; Hramov, A. E.
2017-08-01
The processes of formation and evolution of chimera states in the model of a multilayered network of nonlinear elements with complex coupling topology are studied. A two-layered network of nonlocally intralayer-coupled Kuramoto-Sakaguchi phase oscillators is taken as the object of investigation. Different modes implemented in this system upon variation of the degree of interlayer interaction are demonstrated.
Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle
C. Feillet (Céline); C.A. Krusche; F. Tamanini (Filippo); R. Janssens (Roel); R.A. Downey (Roger); P. Martin (Patrick); J.L. Teboul (Jean Louis); S. Saito (Seiji); F.A. Lévi (Francis); T. Bretschneider (Till); G.T.J. van der Horst (Gijsbertus); F. Delaunay (Franck); D.A. Rand (David)
2014-01-01
textabstractDaily synchronous rhythms of cell division at the tissue or organism level are observed in many species and suggest that the circadian clock and cell cycle oscillators are coupled. For mammals, despite known mechanistic interactions, the effect of such coupling on clock and cell cycle
Li, Bing-Wei; Cao, Xiao-Zhi; Fu, Chenbo
2017-12-01
Many biological and chemical systems could be modeled by a population of oscillators coupled indirectly via a dynamical environment. Essentially, the environment by which the individual element communicates with each other is heterogeneous. Nevertheless, most of previous works considered the homogeneous case only. Here we investigated the dynamical behaviors in a population of spatially distributed chaotic oscillators immersed in a heterogeneous environment. Various dynamical synchronization states (such as oscillation death, phase synchronization, and complete synchronized oscillation) as well as their transitions were explored. In particular, we uncovered a non-traditional quorum sensing transition: increasing the population density leaded to a transition from oscillation death to synchronized oscillation at first, but further increasing the density resulted in degeneration from complete synchronization to phase synchronization or even from phase synchronization to desynchronization. The underlying mechanism of this finding was attributed to the dual roles played by the population density. What's more, by treating the environment as another component of the oscillator, the full system was then effectively equivalent to a locally coupled system. This fact allowed us to utilize the master stability functions approach to predict the occurrence of complete synchronization oscillation, which agreed with that from the direct numerical integration of the system. The potential candidates for the experimental realization of our model were also discussed.
DEFF Research Database (Denmark)
Granados, Albert
2017-01-01
Energy harvesting systems based on oscillators aim to capture energy from mechanical oscillations and convert it into electrical energy. Widely extended are those based on piezoelectric materials, whose dynamics are Hamiltonian submitted to different sources of dissipation: damping and coupling...... in Hamiltonian systems and hence could be very useful in energy harvesting applications. This article is a first step towards this goal. We consider two piezoelectric beams submitted to a small forcing and coupled through an electric circuit. By considering the coupling, damping and forcing as perturbations, we...
Synchronisation in coupled quantum Hamiltonian superconducting oscillator via a control potential
International Nuclear Information System (INIS)
Al-Khawaja, Sameer
2009-01-01
This paper presents chaos synchronisation in a SQUID device mutually coupled to a resonant LC classical circuit. Via the Hamiltonian of the coupled quantum-classical system and by means of a 'control potential' in the form of a double-well, measure synchronisation has been found to exist. A transition from quasi-periodic to chaotically synchronised orbits in the phase space has been observed, as the strength of coupling is increased between both oscillators. The system reaches a non-synchronised state if the choice of the control potential were to render both oscillators non-identical.
Controlled perturbation-induced switching in pulse-coupled oscillator networks
International Nuclear Information System (INIS)
Schittler Neves, Fabio; Timme, Marc
2009-01-01
Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may in principle support switching processes in these networks and enable novel kinds of neural computations. For small networks of coupled oscillators, we here investigate under which conditions and how system symmetry enforces or forbids certain switching transitions that may be induced by perturbations. For networks of five oscillators, we derive explicit transition rules that for two cluster symmetries deviate from those known from oscillators coupled continuously in time. A third symmetry yields heteroclinic networks that consist of sets of all unstable attractors with that symmetry and the connections between them. Our results indicate that pulse-coupled systems can reliably generate well-defined sets of complex spatiotemporal patterns that conform to specific transition rules. We briefly discuss possible implications for computation with spiking neural systems.
Controlled perturbation-induced switching in pulse-coupled oscillator networks
Energy Technology Data Exchange (ETDEWEB)
Schittler Neves, Fabio; Timme, Marc [Network Dynamics Group, Max Planck Institute for Dynamics and Self-Organization, Goettingen, D-37073 (Germany); Bernstein Center for Computational Neuroscience (BCCN), Goettingen (Germany)], E-mail: neves@nld.ds.mpg.de, E-mail: timme@nld.ds.mpg.de
2009-08-28
Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may in principle support switching processes in these networks and enable novel kinds of neural computations. For small networks of coupled oscillators, we here investigate under which conditions and how system symmetry enforces or forbids certain switching transitions that may be induced by perturbations. For networks of five oscillators, we derive explicit transition rules that for two cluster symmetries deviate from those known from oscillators coupled continuously in time. A third symmetry yields heteroclinic networks that consist of sets of all unstable attractors with that symmetry and the connections between them. Our results indicate that pulse-coupled systems can reliably generate well-defined sets of complex spatiotemporal patterns that conform to specific transition rules. We briefly discuss possible implications for computation with spiking neural systems.
Beam splitter coupled CdSe optical parametric oscillator
International Nuclear Information System (INIS)
Levinos, N.J.; Arnold, G.P.
1980-01-01
An optical parametric oscillator is disclosed in which the resonant radiation is separated from the pump and output radiation so that it can be manipulated without interfering with them. Thus, for example, very narrow band output may readily be achieved by passing the resonant radiation through a line narrowing device which does not in itself interfere with either the pump radiation or the output radiation
Resumption of dynamism in damaged networks of coupled oscillators
Kundu, Srilena; Majhi, Soumen; Ghosh, Dibakar
2018-05-01
Deterioration in dynamical activities may come up naturally or due to environmental influences in a massive portion of biological and physical systems. Such dynamical degradation may have outright effect on the substantive network performance. This requires us to provide some proper prescriptions to overcome undesired circumstances. In this paper, we present a scheme based on external feedback that can efficiently revive dynamism in damaged networks of active and inactive oscillators and thus enhance the network survivability. Both numerical and analytical investigations are performed in order to verify our claim. We also provide a comparative study on the effectiveness of this mechanism for feedbacks to the inactive group or to the active group only. Most importantly, resurrection of dynamical activity is realized even in time-delayed damaged networks, which are considered to be less persistent against deterioration in the form of inactivity in the oscillators. Furthermore, prominence in our approach is substantiated by providing evidence of enhanced network persistence in complex network topologies taking small-world and scale-free architectures, which makes the proposed remedy quite general. Besides the study in the network of Stuart-Landau oscillators, affirmative influence of external feedback has been justified in the network of chaotic Rössler systems as well.
Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts
International Nuclear Information System (INIS)
Luo, Albert C.J.; Chen Lidi
2005-01-01
In this paper, an idealized, piecewise linear system is presented to model the vibration of gear transmission systems. Periodic motions in a generalized, piecewise linear oscillator with perfectly plastic impacts are predicted analytically. The analytical predictions of periodic motion are based on the mapping structures, and the generic mappings based on the discontinuous boundaries are developed. This method for the analytical prediction of the periodic motions in non-smooth dynamic systems can give all possible periodic motions based on the adequate mapping structures. The stability and bifurcation conditions for specified periodic motions are obtained. The periodic motions and grazing motion are demonstrated. This model is applicable to prediction of periodic motion in nonlinear dynamics of gear transmission systems
How to induce multiple delays in coupled chaotic oscillators?
Energy Technology Data Exchange (ETDEWEB)
Bhowmick, Sourav K. [CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India); Department of Electronics, Asutosh College, Kolkata 700026 (India); Ghosh, Dibakar [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India); Roy, Prodyot K. [Department of Physics, Presidency University, Kolkata 700073 (India); Kurths, Jürgen [Potsdam Institute for Climate Impact Research, 14473 Potsdam (Germany); Institute for Physics, Humboldt University, 12489 Berlin (Germany); Dana, Syamal K. [CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India)
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.
Direction of Coupling from Phases of Interacting Oscillators: A Permutation Information Approach
Bahraminasab, A.; Ghasemi, F.; Stefanovska, A.; McClintock, P. V. E.; Kantz, H.
2008-02-01
We introduce a directionality index for a time series based on a comparison of neighboring values. It can distinguish unidirectional from bidirectional coupling, as well as reveal and quantify asymmetry in bidirectional coupling. It is tested on a numerical model of coupled van der Pol oscillators, and applied to cardiorespiratory data from healthy subjects. There is no need for preprocessing and fine-tuning the parameters, which makes the method very simple, computationally fast and robust.
DEFF Research Database (Denmark)
Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth
2015-01-01
As the number of power electronics based systems are increasing, studies about overall stability and harmonic problems are rising. In order to analyze harmonics and stability, most research is using an analysis method, which is based on the Linear Time Invariant (LTI) approach. However, this can...... be difficult in terms of complex multi-parallel connected systems, especially in the case of renewable energy, where possibilities for intermittent operation due to the weather conditions exist. Hence, it can bring many different operating points to the power converter, and the impedance characteristics can...... can demonstrate other phenomenon, which can not be found in the conventional LTI approach. The theoretical modeling and analysis are verified by means of simulations and experiments....
Chimera states in an ensemble of linearly locally coupled bistable oscillators
Shchapin, D. S.; Dmitrichev, A. S.; Nekorkin, V. I.
2017-11-01
Chimera states in a system with linear local connections have been studied. The system is a ring ensemble of analog bistable self-excited oscillators with a resistive coupling. It has been shown that the existence of chimera states is not due to the nonidentity of oscillators and noise, which is always present in real experiments, but is due to the nonlinear dynamics of the system on invariant tori with various dimensions.
Uwate, Y; Nishio, Y; Stoop, R
2009-01-01
We explore the synchronization and switching behavior of a system of two identical van der Pol oscillators coupled by a stochastically timevarying resistor. Triggered by the time-varying resistor, the system of oscillators switches between synchronized and anti-synchronized behavior. We find that the preference of the synchronized/antisynchronized state is determined by the ratio of the probabilities of the two resistor states. The length of the phases of maintained resistor states, however, ...
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.
Sync or anti-sync – dynamical pattern selection in coupled self-sustained oscillator systems
International Nuclear Information System (INIS)
Davidova, Larissa; Újvári, Szeréna; Néda, Zoltán
2014-01-01
The dynamics of similar, self-sustained oscillators coupled by a common platform exhibits fascinating collective behavior. Experiments performed with pendulum clocks and metronomes reported both the absence of synchronization, in-phase synchronization, antiphase synchronization, beat-death phenomenon, or even chaotic dynamics. Here we present a numerical study on two identical self-sustained oscillators placed on a common movable platform. As order parameter for synchronization we use the Pearson correlation coefficient between the oscillators coordinates. As a function of the relevant physical parameters of this system we reproduce all the experimentally reported dynamics. We provide conditions for obtaining stable and emergent in-phase or anti-phase synchronization.
DEFF Research Database (Denmark)
Thoke, Henrik Seir; Tobiesen, Asger; Brewer, Jonathan R.
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 D...
International Nuclear Information System (INIS)
Donko, Z.; Schulze, J.; Czarnetzki, U.; Luggenhoelscher, D.
2009-01-01
At low pressures, nonlinear self-excited plasma series resonance (PSR) oscillations are known to drastically enhance electron heating in geometrically asymmetric capacitively coupled radio frequency discharges by nonlinear electron resonance heating (NERH). Here we demonstrate via particle-in-cell simulations that high-frequency PSR oscillations can also be excited in geometrically symmetric discharges if the driving voltage waveform makes the discharge electrically asymmetric. This can be achieved by a dual-frequency (f+2f) excitation, when PSR oscillations and NERH are turned on and off depending on the electrical discharge asymmetry, controlled by the phase difference of the driving frequencies
Low-noise sub-harmonic injection locked multiloop ring oscillator
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.
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.
Sinusoidal visuomotor tracking: intermittent servo-control or coupled oscillations?
Russell, D M; Sternad, D
2001-12-01
In visuomotor tasks that involve accuracy demands, small directional changes in the trajectories have been taken as evidence of feedback-based error corrections. In the present study variability, or intermittency, in visuomanual tracking of sinusoidal targets was investigated. Two lines of analyses were pursued: First, the hypothesis that humans fundamentally act as intermittent servo-controllers was re-examined, probing the question of whether discontinuities in the movement trajectory directly imply intermittent control. Second, an alternative hypothesis was evaluated: that rhythmic tracking movements are generated by entrainment between the oscillations of the target and the actor, such that intermittency expresses the degree of stability. In 2 experiments, participants (N = 6 in each experiment) swung 1 of 2 different hand-held pendulums, tracking a rhythmic target that oscillated at different frequencies with a constant amplitude. In 1 line of analyses, the authors tested the intermittency hypothesis by using the typical kinematic error measures and spectral analysis. In a 2nd line, they examined relative phase and its variability, following analyses of rhythmic interlimb coordination. The results showed that visually guided corrective processes play a role, especially for slow movements. Intermittency, assessed as frequency and power components of the movement trajectory, was found to change as a function of both target frequency and the manipulandum's inertia. Support for entrainment was found in conditions in which task frequency was identical to or higher than the effector's eigenfrequency. The results suggest that it is the symmetry between task and effector that determines which behavioral regime is dominant.
Chaos and routes to chaos in coupled Duffing oscillators with multiple degrees of freedom
International Nuclear Information System (INIS)
Musielak, D.E.; Musielak, Z.E.; Benner, J.W.
2005-01-01
New results are reported on the routes to chaos in increasingly complex Duffing oscillator systems, which are formed by coupling several oscillators, thereby increasing the number of degrees of freedom. Other forms of increasing system complexity through distributed excitation, different forcing function phasing, different excitation frequency ratios, and higher order coupling are also studied. Changes in the quantitative aspects of the chaotic regions and in the routes to chaos of complex Duffing systems are investigated by performing numerical simulations. It is shown that the number of chaotic regions in these systems is significantly reduced when compared to the original Duffing system, and that crisis replaces period doubling as the dominant route to chaos when the number of degrees of freedom is increased. A new discovered phenomenon is that chaos emerges in the symmetrically and asymmetrically coupled Duffing oscillators only after the quasi-periodic torus breaks down through a 3-periodic and 2-periodic window, respectively
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.
Effect of parameter mismatch on the dynamics of strongly coupled self sustained oscillators.
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.
Entanglement of higher-derivative oscillators in holographic systems
Energy Technology Data Exchange (ETDEWEB)
Dimov, Hristo, E-mail: h_dimov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Mladenov, Stefan, E-mail: smladenov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Rashkov, Radoslav C., E-mail: rash@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstr. 8–10, 1040 Vienna (Austria); Vetsov, Tsvetan, E-mail: vetsov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria)
2017-05-15
We study the quantum entanglement of coupled Pais–Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of N coupled Pais–Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. We also make remarks on the appearance of instabilities of higher-derivative oscillators in the context of AdS/CFT correspondence. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.
International Nuclear Information System (INIS)
Wang Peng-Fei; Xu Zhong-Bin; Ruan Xiao-Dong; Fu Xin
2015-01-01
The Hong–Strogatz (HS) model of globally coupled phase oscillators with attractive and repulsive interactions reflects the fact that each individual (oscillator) has its own attitude (attractive or repulsive) to the same environment (mean field). Previous studies on HS model focused mainly on the stable states on Ott–Antonsen (OA) manifold. In this paper, the eigenvalues of the Jacobi matrix of each fixed point in HS model are explicitly derived, with the aim to understand the local dynamics around each fixed point. Phase transitions are described according to relative population and coupling strength. Besides, the dynamics off OA manifold is studied. (paper)
Generating macroscopic chaos in a network of globally coupled phase oscillators
So, Paul; Barreto, Ernest
2011-01-01
We consider an infinite network of globally coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when the coupling strength varies periodically in time. We identify period-doubling cascades to chaos, attractor crises, and horseshoe dynamics for the macroscopic mean field. Based on recent work that clarified the bifurcation structure of the static bimodal Kuramoto system, we qualitatively describe the mechanism for the generation of such complicated behavior in the time varying case. PMID:21974662
Synchronization scenarios in the Winfree model of coupled oscillators
Gallego, Rafael; Montbrió, Ernest; Pazó, Diego
2017-10-01
Fifty years ago Arthur Winfree proposed a deeply influential mean-field model for the collective synchronization of large populations of phase oscillators. Here we provide a detailed analysis of the model for some special, analytically tractable cases. Adopting the thermodynamic limit, we derive an ordinary differential equation that exactly describes the temporal evolution of the macroscopic variables in the Ott-Antonsen invariant manifold. The low-dimensional model is then thoroughly investigated for a variety of pulse types and sinusoidal phase response curves (PRCs). Two structurally different synchronization scenarios are found, which are linked via the mutation of a Bogdanov-Takens point. From our results, we infer a general rule of thumb relating pulse shape and PRC offset with each scenario. Finally, we compare the exact synchronization threshold with the prediction of the averaging approximation given by the Kuramoto-Sakaguchi model. At the leading order, the discrepancy appears to behave as an odd function of the PRC offset.
Partial synchronization in diffusively time-delay coupled oscillator networks
Steur, E.; Oguchi, T.; Leeuwen, van C.; Nijmeijer, H.
2012-01-01
We study networks of diffusively time-delay coupled oscillatory units and we show that networks with certain symmetries can exhibit a form of incomplete synchronization called partial synchronization. We present conditions for the existence and stability of partial synchronization modes in networks
Synchronization and basin bifurcations in mutually coupled oscillators
Indian Academy of Sciences (India)
its motivation from its role in understanding the basic features of coupled nonlinear systems and in view of potential applications in communication systems, time ..... [21] U E Vincent, A N Njah, O Akinlade and A R T Solarin, Physica A360, 186 (2006). [22] U E Vincent, A N Njah, O Akinlade and A R T Solarin, Chaos 14, 1018 ...
N=4 Super Yang-Mills: the harmonic oscillator of interacting quantum field theories
International Nuclear Information System (INIS)
Minahan, Joseph A.
2012-01-01
Full text: In this talk I discuss progress over the last ten years in solving N=4 Super Yang-Mills in the planar limit, where the number of colors is taken to infinity. The key to the solution is mapping the theory to an integrable one-dimensional spin chain. At the leading perturbative level the spin-chain in question is the Heisenberg chain which was solved by Bethe in 1931. We discuss how the analysis of spin-chains ultimately allows to compute the spectrum of observables in the theory for any value of the coupling constant. I then discuss ongoing work to find the so-called three-point functions, which when combined with the spectrum would completely solve the theory in the planar limit. (author)
International Nuclear Information System (INIS)
Kamath, S.G.
1978-01-01
Arguments are presented to show that the new resonance parameters obtained by Alston-Garnjost et al. in a recent analysis of the K-barN system from 365 to 1320 MeV/c provide a prima facie case for the even-wave harmonic-oscillator theory of baryonic states in the framework of SU(6)/sub W/ x O(3). A new quantum classification of the Λ states belonging to the (70,1 - ) is also proposed
Pulse-coupled mixed-mode oscillators: Cluster states and extreme noise sensitivity
Karamchandani, Avinash J.; Graham, James N.; Riecke, Hermann
2018-04-01
Motivated by rhythms in the olfactory system of the brain, we investigate the synchronization of all-to-all pulse-coupled neuronal oscillators exhibiting various types of mixed-mode oscillations (MMOs) composed of sub-threshold oscillations (STOs) and action potentials ("spikes"). We focus particularly on the impact of the delay in the interaction. In the weak-coupling regime, we reduce the system to a Kuramoto-type equation with non-sinusoidal phase coupling and the associated Fokker-Planck equation. Its linear stability analysis identifies the appearance of various cluster states. Their type depends sensitively on the delay and the width of the pulses. Interestingly, long delays do not imply slow population rhythms, and the number of emerging clusters only loosely depends on the number of STOs. Direct simulations of the oscillator equations reveal that for quantitative agreement of the weak-coupling theory the coupling strength and the noise have to be extremely small. Even moderate noise leads to significant skipping of STO cycles, which can enhance the diffusion coefficient in the Fokker-Planck equation by two orders of magnitude. Introducing an effective diffusion coefficient extends the range of agreement significantly. Numerical simulations of the Fokker-Planck equation reveal bistability and solutions with oscillatory order parameters that result from nonlinear mode interactions. These are confirmed in simulations of the full spiking model.
International Nuclear Information System (INIS)
Chae, Jongchul; Litvinenko, Yuri E.
2017-01-01
The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D 2 and H α lines.
Energy Technology Data Exchange (ETDEWEB)
Chae, Jongchul [Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 08826 (Korea, Republic of); Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand)
2017-08-01
The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D{sub 2} and H α lines.
Synchronization of vortex-based spin torque nano-oscillators by magnetostatic coupling
Energy Technology Data Exchange (ETDEWEB)
Zaspel, C.E., E-mail: craig.zaspel@umwestern.edu
2015-12-15
Synchronization of two nanopillar oscillators driven by spin torque and coupled through the magnetic dipolar interaction. The dominant mode in each oscillator is gyrotropic motion of the vortex core in an elliptical orbit about the free layer disk center. The dynamic properties of this mode is investigated by solution the coupled Thiele equations with both nanopillar oscillators having identical dimensions, but with a current mismatch. It is noticed that there is a range in the current difference where the oscillators will be synchronized where the vortex gyrotropic motion will be frequency-locked with the radii of gyrotropic motion equal for both disks. There is, however, a phase shift between the gyrotropic motion with the smaller current disk lagging the higher current disk by a few degrees. - Highlights: • Vortex-based nanopillar oscillators re synchronized by the dipolar interaction. • There is a range of frequencies where both oscillators will frequency-locked. • There are upper and lower critical currents defining a locking range.
Study of λφ4 theory in the coupled independent double-oscillator approximation
International Nuclear Information System (INIS)
Bray, H.; Stevenson, P.M.
1992-01-01
A scalar field can be viewed as an infinite set of coupled oscillators, one at each lattice point in space, as the lattice spacing goes to zero. Λφ 4 theory considers the case when each oscillator is given a potential of the form V(φ) = 1/2m 2 φ 2 + λφ 4 . The question the authors wish to investigate is whether or not such a potential can cause spontaneous symmetry breaking. They approach this problem by defining an open-quotes effective potentialclose quotes which takes into account the quantum effects of the oscillators. This is useful because a double well effective potential would imply spontaneous symmetry breaking. They consider a variational calculation with a trial wavefunctional that is a product of independent double-oscillator wavefunctions. Each double-oscillator wavefunction is defined to be the sum of two Gaussians with the same widths, centered around φ o . They then define the effective potential at φ o to be the energy density resulting from this variational calculation, where the separation and the width of the Gaussians are the parameters which are allowed to vary. They call this the open-quotes Coupled Independent Double-Oscillator Approximation.close quotes The goal of this research is to compute this effective potential, renormalize the variables, and to gain additional insight into whether or not spontaneous symmetry breaking occurs
Energy Technology Data Exchange (ETDEWEB)
Emenheiser, Jeffrey [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Chapman, Airlie; Mesbahi, Mehran [William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195 (United States); Pósfai, Márton [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Crutchfield, James P. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); D' Souza, Raissa M. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616 (United States)
2016-09-15
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.
International Nuclear Information System (INIS)
Menouar, Salah; Maamache, Mustapha; Choi, Jeong Ryeol
2010-01-01
The quantum states of time-dependent coupled oscillator model for charged particles subjected to variable magnetic field are investigated using the invariant operator methods. To do this, we have taken advantage of an alternative method, so-called unitary transformation approach, available in the framework of quantum mechanics, as well as a generalized canonical transformation method in the classical regime. The transformed quantum Hamiltonian is obtained using suitable unitary operators and is represented in terms of two independent harmonic oscillators which have the same frequencies as that of the classically transformed one. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators. One can easily take a complete description of how the charged particle behaves under the given Hamiltonian by taking advantage of these analytical wave functions.
International Nuclear Information System (INIS)
Menouar, Salah; Maamache, Mustapha; Choi, Jeong Ryeol
2010-01-01
The dynamics of the time-dependent coupled oscillator model for the motion of a charged particle subjected to a time-dependent external magnetic field is investigated. We use the canonical transformation approach for the classical treatment of the system, whereas the unitary transformation approach is used in managing the system in the framework of quantum mechanics. For both approaches, the original system is transformed into a much more simple system that is the sum of two independent harmonic oscillators with time-dependent frequencies. We therefore easily identify the wavefunctions in the transformed system with the help of an invariant operator of the system. The full wavefunctions in the original system are derived from the inverse unitary transformation of the wavefunctions associated with the transformed system.
The Coupling between Gamma and Theta Oscillation and Visuotactile Integration Process
Directory of Open Access Journals (Sweden)
Noriaki Kanayama
2011-10-01
Full Text Available Some researches revealed the relationship between multisensory integration and EEG oscillations. Previous studies revealed that the visuotactile integration process could be explained by gamma and theta band oscillation. In addition, recent studies have showed the possibility that a coupling between oscillations at the different frequency bands plays an important role on the multisensory integration system. This study aimed to investigate whether the gamma and theta oscillations show the coupling during the visuotactile integration. Using congruency effect paradigm only for left hand, we measured scalp EEG during simultaneous presentation of “spatially congruent” or “spatially incongruent” visuotactile stimuli. In Experiment 1, the proportion of the spatially congruent trials (80% vs 20% was changed across the experimental blocks. The results showed that the relationship between gamma power and theta phase at the parietal area was modulated by the proportion. In Experiment 2, the saliency of the vibration stimulus (0dB vs −20dB was changed across trials. The results showed that the relationship between gamma power and theta phase was immune to the saliency. These results suggest that multisensory integration process has a plasticity, which is modulated by the proportion of congruent trial, and the process could be explained by the coupling between gamma/theta oscillations.
Tuning the synchronization of a network of weakly coupled self-oscillating gels via capacitors
Fang, Yan; Yashin, Victor V.; Dickerson, Samuel J.; Balazs, Anna C.
2018-05-01
We consider a network of coupled oscillating units, where each unit comprises a self-oscillating polymer gel undergoing the Belousov-Zhabotinsky (BZ) reaction and an overlaying piezoelectric (PZ) cantilever. Through chemo-mechano-electrical coupling, the oscillations of the networked BZ-PZ units achieve in-phase or anti-phase synchronization, enabling, for example, the storage of information within the system. Herein, we develop numerical and computational models to show that the introduction of capacitors into the BZ-PZ system enhances the dynamical behavior of the oscillating network by yielding additional stable synchronization modes. We specifically show that the capacitors lead to a redistribution of charge in the system and alteration of the force that the PZ cantilevers apply to the underlying gel. Hence, the capacitors modify the strength of the coupling between the oscillators in the network. We utilize a linear stability analysis to determine the phase behavior of BZ-PZ networks encompassing different capacitances, force polarities, and number of units and then verify our findings with numerical simulations. Thus, through analytical calculations and numerical simulations, we determine the impact of the capacitors on the existence of the synchronization modes, their stability, and the rate of synchronization within these complex dynamical systems. The findings from our study can be used to design robotic materials that harness the materials' intrinsic, responsive properties to perform such functions as sensing, actuation, and information storage.
Phase models and clustering in networks of oscillators with delayed coupling
Campbell, Sue Ann; Wang, Zhen
2018-01-01
We consider a general model for a network of oscillators with time delayed coupling where the coupling matrix is circulant. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay enters as a phase shift. We use the phase model to determine model independent existence and stability results for symmetric cluster solutions. Our results extend previous work to systems with time delay and a more general coupling matrix. We show that the presence of the time delay can lead to the coexistence of multiple stable clustering solutions. We apply our analytical results to a network of Morris Lecar neurons and compare these results with numerical continuation and simulation studies.
Influences of adding negative couplings between cliques of Kuramoto-like oscillators
Yang, Li-xin; Lin, Xiao-lin; Jiang, Jun
2018-06-01
We study the dynamics in a clustered network of coupled oscillators by considering positive and negative coupling schemes. Second order oscillators can be interpreted as a model of consumers and generators working in a power network. Numerical results indicate that coupling strategies play an important role in the synchronizability of the clustered power network. It is found that the synchronizability can be enhanced as the positive intragroup connections increase. Meanwhile, when the intragroup interactions are positive and the probability p that two nodes belonging to different clusters are connected is increased, the synchronization has better performance. Besides, when the intragroup connections are negative, it is observed that the power network has poor synchronizability as the probability p increases. Our simulation results can help us understand the collective behavior of the power network with positive and negative couplings.
Coupled oscillators in identification of nonlinear damping of a real parametric pendulum
Olejnik, Paweł; Awrejcewicz, Jan
2018-01-01
A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.
Directory of Open Access Journals (Sweden)
Suhufa Alfarisa
2016-03-01
Full Text Available This research aims i to determine the density profile and calculate the ground state energy of a quantum dot in two dimensions (2D with a harmonic oscillator potential using orbital-free density functional theory, and ii to understand the effect of the harmonic oscillator potential strength on the electron density profiles in the quantum dot. This study determines the total energy functional of the quantum dot that is a functional of the density that depends only on spatial variables. The total energy functional consists of three terms. The first term is the kinetic energy functional, which is the Thomas–Fermi approximation in this case. The second term is the external potential. The harmonic oscillator potential is used in this study. The last term is the electron–electron interactions described by the Coulomb interaction. The functional is formally solved to obtain the electron density as a function of spatial variables. This equation cannot be solved analytically, and thus a numerical method is used to determine the profile of the electron density. Using the electron density profiles, the ground state energy of the quantum dot in 2D can be calculated. The ground state energies obtained are 2.464, 22.26, 90.1957, 252.437, and 496.658 au for 2, 6, 12, 20, and 56 electrons, respectively. The highest electron density is localized close to the middle of the quantum dot. The density profiles decrease with the increasing distance, and the lowest density is at the edge of the quantum dot. Generally, increasing the harmonic oscillator potential strength reduces the density profiles around the center of the quantum dot.
Electron screening and kinetic-energy oscillations in a strongly coupled plasma
International Nuclear Information System (INIS)
Chen, Y.C.; Simien, C.E.; Laha, S.; Gupta, P.; Martinez, Y.N.; Mickelson, P.G.; Nagel, S.B.; Killian, T.C.
2004-01-01
We study equilibration of strongly coupled ions in an ultracold neutral plasma produced by photoionizing laser-cooled and trapped atoms. By varying the electron temperature, we show that electron screening modifies the equilibrium ion temperature. Even with few electrons in a Debye sphere, the screening is well described by a model using a Yukawa ion-ion potential. We also observe damped oscillations of the ion kinetic energy that are a unique feature of equilibration of a strongly coupled plasma
Numerical study of unsteady flows past oscillating airfoils using direct zonal coupling method
International Nuclear Information System (INIS)
Zhang, F.; Khalid, M.
2005-01-01
A direct zonal coupling method was proposed for solving the flows past oscillating airfoils in this study. The entire computational domain was divided into inner and outer zones. The grid in the inner zone is moving with the oscillation of the airfoil, whereas the grid in the outer zone is artificially adjusted to the position consistent with the inner zone grid. The governing equations in the moving frame (the rotation potential energy is included) and those under the stationary frame were applied to inner and outer zones, respectively. By using this kind of treatment, the grid on the zonal interface is 1-to-1 matched. The coupling between the two zones is direct. Both the geometric and flow conservations are entirely satisfied. The NACA0012 and NLR7301 airfoils with oscillations were used as the test cases. The accuracy of the proposed method was demonstrated by the computational results compared with the experimental data.(author)
Du, Lei; Fan, Chu-Hui; Zhang, Han-Xiao; Wu, Jin-Hui
2017-11-20
We study the synchronization behaviors of two indirectly coupled mechanical oscillators of different frequencies in a doublecavity optomechanical system. It is found that quantum synchronization is roughly vanishing though classical synchronization seems rather good when each cavity mode is driven by an external field in the absence of temporal modulations. By periodically modulating cavity detunings or driving amplitudes, however, it is possible to observe greatly enhanced quantum synchronization accompanied with nearly perfect classical synchronization. The level of quantum synchronization observed here is, in particular, much higher than that for two directly coupled mechanical oscillators. Note also that the modulation on cavity detunings is more appealing than that on driving amplitudes when the robustness of quantum synchronization is examined against the bath's mean temperature or the oscillators' frequency difference.
Coupled Josephson local oscillator and detector experiments in the terahertz regime
International Nuclear Information System (INIS)
Robertazzi, R.P.; Hallen, H.D.; Buhrman, R.A.
1988-01-01
Recent coupled Josephson junction experiments in the authors' laboratory have demonstrated that high critical current density tunnel junctions can serve as effective local oscillators at frequencies up to and in excess of the gap sum frequency of the junction, i.e. well above 1 Terahertz for a niobium or niobium compound tunnel junction. While the details of the behavior of such a THz. oscillator were found not to be in accord with the predictions of the accepted theory of the A.C. Josephson effect in the gap region significant radiation could be capacitively coupled from the oscillator junction to an adjacent junction, sufficient for SIS mixer experiments at Terahertz frequencies. Research efforts are now under way to further extend and expand these studies. A high critical current density all NbN tunnel junction system is now under development for Terahertz applications and a new set of coupled Josephson oscillator - SIS detector experiments is being initiated using NbN tunnel junctions. In this paper the authors review the original coupled junction high frequency experiments and report on the recent progress of the current NbN tunnel junction experiments
Statistical properties of multiphoton time-dependent three-boson coupled oscillators
Czech Academy of Sciences Publication Activity Database
Abdalla, M. S.; Peřina, Jan; Křepelka, Jaromír
2006-01-01
Roč. 23, č. 6 (2006), s. 1146-1160 ISSN 0740-3224 R&D Projects: GA MŠk(CZ) OC P11.003 Institutional research plan: CEZ:AV0Z10100522 Keywords : quantum statistic * coupled oscillators * multiphoton Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.002, year: 2006
Two Coupled Oscillators : Simulations of the Circadian Pacemaker in Mammalian Activity Rhythms
Daan, Serge; Berde, Charles
1978-01-01
In the activity rhythms of captive small mammals a variety of features, most notably “splitting”, sugges that two coupled oscillators may constitute the pacemaker system which underlies the rhythms. A proposed phenomenological model is developed and expanded here using an explicit quantitative
Kuwahara, Jun; Miyata, Hajime; Konno, Hidetoshi
2017-09-01
Recently, complex dynamics of globally coupled oscillators have been attracting many researcher's attentions. In spite of their numerous studies, their features of nonlinear oscillator systems with global and local couplings in two-dimension (2D) are not understood fully. The paper focuses on 2D states of coherent, clustered and chaotic oscillation especially under the effect of negative global coupling (NGC) in 2D Alief-Panfilov model. It is found that the tuning NGC can cause various new coupling-parameter dependency on the features of oscillations. Then quantitative characterization of various states of oscillations (so called spiral wave turbulence) is examined by using the pragmatic information (PI) which have been utilized in analyzing multimode laser, solar activity and neuronal systems. It is demonstrated that the dynamics of the PI for various oscillations can be characterized successfully by the Hyper-Gamma stochastic process.
Ueki, Takeshi; Yoshida, Ryo
2014-06-14
Herein, we summarise the recent developments in self-oscillating polymeric materials based on the concepts of supramolecular chemistry, where aggregates of molecular building blocks with non-covalent bonds evolve the temporal or spatiotemporal structure. By utilising the rhythmic oscillation of the association/dissociation of molecular aggregates coupled with the redox oscillation by the BZ reaction, novel soft materials that express similar functions as those of living matter will be achieved. Further, from the viewpoint of materials science, our recent approach to prepare self-oscillating materials that operate long-term under mild conditions will be introduced.
Mathematical structure of Rabi oscillations in the strong coupling regime
International Nuclear Information System (INIS)
Fujii, Kazuyuki
2003-01-01
In this paper, we generalize the Jaynes-Cummings Hamiltonian by making use of some operators based on Lie algebras su(1, 1) and su(2), and study a mathematical structure of Rabi floppings of these models in the strong coupling regime. We show that Rabi frequencies are given by matrix elements of generalized coherent operators (Fujii K 2002 Preprint quant-ph/0202081) under the rotating-wave approximation. In the first half, we make a general review of coherent operators and generalized coherent ones based on Lie algebras su(1, 1) and su(2). In the latter half, we carry out a detailed examination of Frasca (Frasca M 2001 Preprint quant-ph/0111134) and generalize his method, and moreover present some related problems. We also apply our results to the construction of controlled unitary gates in quantum computation. Lastly, we make a brief comment on application to holonomic quantum computation
Synchronization ability of coupled cell-cycle oscillators in changing environments
2012-01-01
Background The biochemical oscillator that controls periodic events during the Xenopus embryonic cell cycle is centered on the activity of CDKs, and the cell cycle is driven by a protein circuit that is centered on the cyclin-dependent protein kinase CDK1 and the anaphase-promoting complex (APC). Many studies have been conducted to confirm that the interactions in the cell cycle can produce oscillations and predict behaviors such as synchronization, but much less is known about how the various elaborations and collective behavior of the basic oscillators can affect the robustness of the system. Therefore, in this study, we investigate and model a multi-cell system of the Xenopus embryonic cell cycle oscillators that are coupled through a common complex protein, and then analyze their synchronization ability under four different external stimuli, including a constant input signal, a square-wave periodic signal, a sinusoidal signal and a noise signal. Results Through bifurcation analysis and numerical simulations, we obtain synchronization intervals of the sensitive parameters in the individual oscillator and the coupling parameters in the coupled oscillators. Then, we analyze the effects of these parameters on the synchronization period and amplitude, and find interesting phenomena, e.g., there are two synchronization intervals with activation coefficient in the Hill function of the activated CDK1 that activates the Plk1, and different synchronization intervals have distinct influences on the synchronization period and amplitude. To quantify the speediness and robustness of the synchronization, we use two quantities, the synchronization time and the robustness index, to evaluate the synchronization ability. More interestingly, we find that the coupled system has an optimal signal strength that maximizes the synchronization index under different external stimuli. Simulation results also show that the ability and robustness of the synchronization for the square
Sato, Katsuhiko; Shima, Shin-ichiro
2015-10-01
We investigate a phase model that includes both locally attractive and globally repulsive coupling in one dimension. This model exhibits nontrivial spatiotemporal patterns that have not been observed in systems that contain only local or global coupling. Depending on the relative strengths of the local and global coupling and on the form of global coupling, the system can show a spatially uniform state (in-phase synchronization), a monotonically increasing state (traveling wave), and three types of oscillations of relative phase difference. One of the oscillations of relative phase difference has the characteristic of being locally unstable but globally attractive. That is, any small perturbation to the periodic orbit in phase space destroys its periodic motion, but after a long time the system returns to the original periodic orbit. This behavior is closely related to the emergence of saddle two-cluster states for global coupling only, which are connected to each other by attractive heteroclinic orbits. The mechanism of occurrence of this type of oscillation is discussed.
Time delay induced different synchronization patterns in repulsively coupled chaotic oscillators
Yao, Chenggui; Yi, Ming; Shuai, Jianwei
2013-09-01
Time delayed coupling plays a crucial role in determining the system's dynamics. We here report that the time delay induces transition from the asynchronous state to the complete synchronization (CS) state in the repulsively coupled chaotic oscillators. In particular, by changing the coupling strength or time delay, various types of synchronous patterns, including CS, antiphase CS, antiphase synchronization (ANS), and phase synchronization, can be generated. In the transition regions between different synchronous patterns, bistable synchronous oscillators can be observed. Furthermore, we show that the time-delay-induced phase flip bifurcation is of key importance for the emergence of CS. All these findings may light on our understanding of neuronal synchronization and information processing in the brain.
Synchronization in slowly switching networks of coupled oscillators
Zhou, Jie; Zou, Yong; Guan, Shuguang; Liu, Zonghua; Boccaletti, S.
2016-01-01
Networks whose structure of connections evolves in time constitute a big challenge in the study of synchronization, in particular when the time scales for the evolution of the graph topology are comparable with (or even longer than) those pertinent to the units’ dynamics. We here focus on networks with a slow-switching structure, and show that the necessary conditions for synchronization, i.e. the conditions for which synchronization is locally stable, are determined by the time average of the largest Lyapunov exponents of transverse modes of the switching topologies. Comparison between fast- and slow-switching networks allows elucidating that slow-switching processes prompt synchronization in the cases where the Master Stability Function is concave, whereas fast-switching schemes facilitate synchronization for convex curves. Moreover, the condition of slow-switching enables the introduction of a control strategy for inducing synchronization in networks with arbitrary structure and coupling strength, which is of evident relevance for broad applications in real world systems. PMID:27779253
Chimera states in coupled Kuramoto oscillators with inertia
International Nuclear Information System (INIS)
Olmi, Simona
2015-01-01
The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry
Chimera states in coupled Kuramoto oscillators with inertia
Energy Technology Data Exchange (ETDEWEB)
Olmi, Simona, E-mail: simona.olmi@fi.isc.cnr.it [CNR - Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); INFN Sez. Firenze, via Sansone, 1 - I-50019 Sesto Fiorentino (Italy)
2015-12-15
The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.
Chimera states in coupled Kuramoto oscillators with inertia.
Olmi, Simona
2015-12-01
The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.
Williams, Caitlin R. S.; Sorrentino, Francesco; Murphy, Thomas E.; Roy, Rajarshi
2013-12-01
We experimentally study the complex dynamics of a unidirectionally coupled ring of four identical optoelectronic oscillators. The coupling between these systems is time-delayed in the experiment and can be varied over a wide range of delays. We observe that as the coupling delay is varied, the system may show different synchronization states, including complete isochronal synchrony, cluster synchrony, and two splay-phase states. We analyze the stability of these solutions through a master stability function approach, which we show can be effectively applied to all the different states observed in the experiment. Our analysis supports the experimentally observed multistability in the system.
A weakly coupled semiconductor superlattice as a harmonic hypersonic-electrical transducer
International Nuclear Information System (INIS)
Poyser, C L; Akimov, A V; Campion, R P; Kent, A J; Balanov, A G
2015-01-01
We study experimentally and theoretically the effects of high-frequency strain pulse trains on the charge transport in a weakly coupled semiconductor superlattice. In a frequency range of the order of 100 GHz such excitation may be considered as single harmonic hypersonic excitation. While travelling along the axis of the SL, the hypersonic acoustic wavepacket affects the electron tunnelling, and thus governs the electrical current through the device. We reveal how the change of current depends on the parameters of the hypersonic excitation and on the bias applied to the superlattice. We have found that the changes in the transport properties of the superlattices caused by the acoustic excitation can be largely explained using the current–voltage relation of the unperturbed system. Our experimental measurements show multiple peaks in the dependence of the transferred charge on the repetition rate of the strain pulses in the train. We demonstrate that these resonances can be understood in terms of the spectrum of the applied acoustic perturbation after taking into account the multiple reflections in the metal film serving as a generator of hypersonic excitation. Our findings suggest an application of the semiconductor superlattice as a hypersonic-electrical transducer, which can be used in various microwave devices. (paper)
Mean-field behavior in coupled oscillators with attractive and repulsive interactions.
Hong, Hyunsuk; Strogatz, Steven H
2012-05-01
We consider a variant of the Kuramoto model of coupled oscillators in which both attractive and repulsive pairwise interactions are allowed. The sign of the coupling is assumed to be a characteristic of a given oscillator. Specifically, some oscillators repel all the others, thus favoring an antiphase relationship with them. Other oscillators attract all the others, thus favoring an in-phase relationship. The Ott-Antonsen ansatz is used to derive the exact low-dimensional dynamics governing the system's long-term macroscopic behavior. The resulting analytical predictions agree with simulations of the full system. We explore the effects of changing various parameters, such as the width of the distribution of natural frequencies and the relative strengths and proportions of the positive and negative interactions. For the particular model studied here we find, unexpectedly, that the mixed interactions produce no new effects. The system exhibits conventional mean-field behavior and displays a second-order phase transition like that found in the original Kuramoto model. In contrast to our recent study of a different model with mixed interactions [Phys. Rev. Lett. 106, 054102 (2011)], the π state and traveling-wave state do not appear for the coupling type considered here.
Spatiotemporal coding of inputs for a system of globally coupled phase oscillators
Wordsworth, John; Ashwin, Peter
2008-12-01
We investigate the spatiotemporal coding of low amplitude inputs to a simple system of globally coupled phase oscillators with coupling function g(ϕ)=-sin(ϕ+α)+rsin(2ϕ+β) that has robust heteroclinic cycles (slow switching between cluster states). The inputs correspond to detuning of the oscillators. It was recently noted that globally coupled phase oscillators can encode their frequencies in the form of spatiotemporal codes of a sequence of cluster states [P. Ashwin, G. Orosz, J. Wordsworth, and S. Townley, SIAM J. Appl. Dyn. Syst. 6, 728 (2007)]. Concentrating on the case of N=5 oscillators we show in detail how the spatiotemporal coding can be used to resolve all of the information that relates the individual inputs to each other, providing that a long enough time series is considered. We investigate robustness to the addition of noise and find a remarkable stability, especially of the temporal coding, to the addition of noise even for noise of a comparable magnitude to the inputs.
Plexcitons: The Role of Oscillator Strengths and Spectral Widths in Determining Strong Coupling
Energy Technology Data Exchange (ETDEWEB)
Thomas, Reshmi [School; Thomas, Anoop [School; Pullanchery, Saranya [School; Joseph, Linta [School; Somasundaran, Sanoop Mambully [School; Swathi, Rotti Srinivasamurthy [School; Gray, Stephen K. [Center; Thomas, K. George [School
2018-01-05
Strong coupling interactions between plasmon and exciton-based excitations have been proposed to be useful in the design of optoelectronic systems. However, the role of various optical parameters dictating the plasmon-exciton (plexciton) interactions is less understood. Herein, we propose an inequality for achieving strong coupling between plasmons and excitons through appropriate variation of their oscillator strengths and spectral widths. These aspects are found to be consistent with experiments on two sets of free-standing plexcitonic systems obtained by (i) linking fluorescein isothiocyanate on Ag nanoparticles of varying sizes through silane coupling and (ii) electrostatic binding of cyanine dyes on polystyrenesulfonate-coated Au nanorods of varying aspect ratios. Being covalently linked on Ag nanoparticles, fluorescein isothiocyanate remains in monomeric state, and its high oscillator strength and narrow spectral width enable us to approach the strong coupling limit. In contrast, in the presence of polystyrenesulfonate, monomeric forms of cyanine dyes exist in equilibrium with their aggregates: Coupling is not observed for monomers and H-aggregates whose optical parameters are unfavorable. The large aggregation number, narrow spectral width, and extremely high oscillator strength of J-aggregates of cyanines permit effective delocalization of excitons along the linear assembly of chromophores, which in turn leads to efficient coupling with the plasmons. Further, the results obtained from experiments and theoretical models are jointly employed to describe the plexcitonic states, estimate the coupling strengths, and rationalize the dispersion curves. The experimental results and the theoretical analysis presented here portray a way forward to the rational design of plexcitonic systems attaining the strong coupling limits.
Volcanic CO2 Emissions and Glacial Cycles: Coupled Oscillations
Burley, J. M.; Huybers, P. J.; Katz, R. F.
2016-12-01
Following the mid-Pleistocene transition, the dominant period of glacial cycles changed from 40 ka to 100 ka. It is broadly accepted that the 40 ka glacial cycles were driven by cyclical changes in obliquity. However, this forcing does not explain the 100 ka glacial cycles. Mechanisms proposed for 100 ka cycles include isostatic bed depression and proglacial lakes destabilising the Laurentide ice sheet, non-linear responses to orbital eccentricity, and Antarctic ice sheets influencing deep-ocean stratification. None of these are universally accepted. Here we investigate the hypothesis that variations in volcanic CO2 emissions can cause 100 ka glacial cycles. Any proposed mechanism for 100 ka glacial cycles must give the Earth's climate system a memory of 10^4 - 10^5years. This timescale is difficult to achieve for surface processes, however it is possible for the solid Earth. Recent work suggests volcanic CO2 emissions change in response to glacial cycles [1] and that there could be a 50 ka delay in that response [2]. Such a lagged response could drive glacial cycles from 40 ka cycles to an integer multiple of the forcing period. Under what conditions could the climate system admit such a response? To address this, we use a simplified climate model modified from Huybers and Tziperman [3]. Our version comprises three component models for energy balance, ice sheet growth and atmospheric CO2 concentration. The model is driven by insolation alone with other components varying according to a system of coupled, differential equations. The model is run for 500 ka to produce several glacial cycles and the resulting changes in global ice volume and atmospheric CO2 concentration.We obtain a switch from 40 ka to 100 ka cycles as the volcanic CO2 response to glacial cycles is increased. These 100 ka cycles are phase-locked to obliquity, lasting 80 or 120 ka. Whilst the MOR response required (in this model) is larger than plausible estimates based on [2], it illustrates the
Coupled opto electronic oscillator with a passively mode locked extended cavity diode laser
Energy Technology Data Exchange (ETDEWEB)
Lee, Jeongmin; Jang, Gwang Hoon; Yoon, Duseong; Song, Minsoo; Yoon, Tai Hyun [Korea Univ., Seoul (Korea, Republic of)
2008-11-15
An opto electronic oscillator(OEO)has very unique properties compared to the conventional quartz based microwave oscillators in that its oscillation frequency is determined by the beat note frequency of a phase coherent optical frequency comb generated as a side bands to an optical single mode carrier by using an electro optic modulator (EOM)or a direct current modulation of a semiconductor laser. Recently, a different type of OEO called a COEO has been demonstrated, where the optical carrier in the OEO system has been replaced by a mode locked laser so that an EOM or a direct current modulation are no longer necessary, but has potentially a much lower phase noise thanks to the high Q value of the optical frequency comb due to the mode locking mechanism. In this paper, we propose and demonstrate a COEO based on a passively mode locked ECDL at 852nm in which the fourth harmonic of the repetition frequency of the ECDL matched exactly the ground state hyperfine splitting frequency of the Cs atoms.
Coupled opto electronic oscillator with a passively mode locked extended cavity diode laser
International Nuclear Information System (INIS)
Lee, Jeongmin; Jang, Gwang Hoon; Yoon, Duseong; Song, Minsoo; Yoon, Tai Hyun
2008-01-01
An opto electronic oscillator(OEO)has very unique properties compared to the conventional quartz based microwave oscillators in that its oscillation frequency is determined by the beat note frequency of a phase coherent optical frequency comb generated as a side bands to an optical single mode carrier by using an electro optic modulator (EOM)or a direct current modulation of a semiconductor laser. Recently, a different type of OEO called a COEO has been demonstrated, where the optical carrier in the OEO system has been replaced by a mode locked laser so that an EOM or a direct current modulation are no longer necessary, but has potentially a much lower phase noise thanks to the high Q value of the optical frequency comb due to the mode locking mechanism. In this paper, we propose and demonstrate a COEO based on a passively mode locked ECDL at 852nm in which the fourth harmonic of the repetition frequency of the ECDL matched exactly the ground state hyperfine splitting frequency of the Cs atoms
Duggento, Andrea; Stankovski, Tomislav; McClintock, Peter V. E.; Stefanovska, Aneta
2012-12-01
Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.109.024101 109, 024101 (2012)] introduced a method based on dynamical Bayesian inference that facilitates the simultaneous detection of time-varying synchronization, directionality of influence, and coupling functions. It can distinguish unsynchronized dynamics from noise-induced phase slips. The method is based on phase dynamics, with Bayesian inference of the time-evolving parameters being achieved by shaping the prior densities to incorporate knowledge of previous samples. We now present the method in detail using numerically generated data, data from an analog electronic circuit, and cardiorespiratory data. We also generalize the method to encompass networks of interacting oscillators and thus demonstrate its applicability to small-scale networks.
Dynamical bifurcation in a system of coupled oscillators with slowly varying parameters
Directory of Open Access Journals (Sweden)
Igor Parasyuk
2016-08-01
Full Text Available This paper deals with a fast-slow system representing n nonlinearly coupled oscillators with slowly varying parameters. We find conditions which guarantee that all omega-limit sets near the slow surface of the system are equilibria and invariant tori of all dimensions not exceeding n, the tori of dimensions less then n being hyperbolic. We show that a typical trajectory demonstrates the following transient process: while its slow component is far from the stationary points of the slow vector field, the fast component exhibits damping oscillations; afterwards, the former component enters and stays in a small neighborhood of some stationary point, and the oscillation amplitude of the latter begins to increase; eventually the trajectory is attracted by an n-dimesional invariant torus and a multi-frequency oscillatory regime is established.
Two-step approach to the dynamics of coupled anharmonic oscillators
International Nuclear Information System (INIS)
Chung, N. N.; Chew, L. Y.
2009-01-01
We have further extended the two-step approach developed by Chung and Chew [N. N. Chung and L. Y. Chew, Phys. Rev. A 76, 032113 (2007)] to the solution of the quantum dynamics of general systems of N-coupled anharmonic oscillators. The idea is to employ an optimized basis set to represent the dynamical quantum states of these oscillator systems. The set is generated via the action of the optimized Bogoliubov transformed bosonic operators on the optimal squeezed vacuum product state. The procedure requires (i) applying the two-step approach to the eigendecomposition of the time evolution operator and (ii) transforming the representation of the initial state from the original to the optimal bases. We have applied the formalism to examine the dynamics of squeezing and entanglement of several anharmonic oscillator systems.
Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators
Energy Technology Data Exchange (ETDEWEB)
Wolfrum, Matthias; Omel' chenko, Oleh E. [Weierstrass Institute, Mohrenstrasse 39, Berlin 10117 (Germany); Sieber, Jan [College of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter EX4 4QF (United Kingdom)
2015-05-15
We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doubling cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.
International Nuclear Information System (INIS)
Gudkov, V.V.; Zhevstovskikh, I.V.; Zimbovskaya, N.A.; Okulov, V.I.
1991-01-01
The quantum oscillations are studied of ellipcity, the rotation angle of the ultrasound polarization plane, the velocity and absorption of waves polarized circularly at the 196 MHz frequency in a tungsten single crystal in magnetic field of 30-80 kOe at temperature 1,8 K. The oscillation amplitudes of ellipticity and rotation angle of the ultrasound polarization plane beyond the Doppler-shifted cyclotron resonance are found to vary nonmonotonously with field and to be large enough, so that they are not described by the simple expressions for high fields. The explanation for the oscillation amplification of the polarization parameters is given within the theory involving the ultrasound-spiral wave coupling predicted by Kaner and Skobov. The quantitative comparison in details demonstrates a good agreement in the theory and experimental data and allows to find the numerical values of new parameters characterizing the Fermi surface, electron relaxation frequency, and deformation potential
Spiral wave chimera states in large populations of coupled chemical oscillators
Totz, Jan Frederik; Rode, Julian; Tinsley, Mark R.; Showalter, Kenneth; Engel, Harald
2018-03-01
The coexistence of coherent and incoherent dynamics in a population of identically coupled oscillators is known as a chimera state1,2. Discovered in 20023, this counterintuitive dynamical behaviour has inspired extensive theoretical and experimental activity4-15. The spiral wave chimera is a particularly remarkable chimera state, in which an ordered spiral wave rotates around a core consisting of asynchronous oscillators. Spiral wave chimeras were theoretically predicted in 200416 and numerically studied in a variety of systems17-23. Here, we report their experimental verification using large populations of nonlocally coupled Belousov-Zhabotinsky chemical oscillators10,18 in a two-dimensional array. We characterize previously unreported spatiotemporal dynamics, including erratic motion of the asynchronous spiral core, growth and splitting of the cores, as well as the transition from the chimera state to disordered behaviour. Spiral wave chimeras are likely to occur in other systems with long-range interactions, such as cortical tissues24, cilia carpets25, SQUID metamaterials26 and arrays of optomechanical oscillators9.
Coupled-oscillator theory of dispersion and Casimir-Polder interactions
Energy Technology Data Exchange (ETDEWEB)
Berman, P. R.; Ford, G. W. [Physics Department, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109-1040 (United States); Milonni, P. W. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 (United States)
2014-10-28
We address the question of the applicability of the argument theorem (of complex variable theory) to the calculation of two distinct energies: (i) the first-order dispersion interaction energy of two separated oscillators, when one of the oscillators is excited initially and (ii) the Casimir-Polder interaction of a ground-state quantum oscillator near a perfectly conducting plane. We show that the argument theorem can be used to obtain the generally accepted equation for the first-order dispersion interaction energy, which is oscillatory and varies as the inverse power of the separation r of the oscillators for separations much greater than an optical wavelength. However, for such separations, the interaction energy cannot be transformed into an integral over the positive imaginary axis. If the argument theorem is used incorrectly to relate the interaction energy to an integral over the positive imaginary axis, the interaction energy is non-oscillatory and varies as r{sup −4}, a result found by several authors. Rather remarkably, this incorrect expression for the dispersion energy actually corresponds to the nonperturbative Casimir-Polder energy for a ground-state quantum oscillator near a perfectly conducting wall, as we show using the so-called “remarkable formula” for the free energy of an oscillator coupled to a heat bath [G. W. Ford, J. T. Lewis, and R. F. O’Connell, Phys. Rev. Lett. 55, 2273 (1985)]. A derivation of that formula from basic results of statistical mechanics and the independent oscillator model of a heat bath is presented.
Coupled-oscillator theory of dispersion and Casimir-Polder interactions
International Nuclear Information System (INIS)
Berman, P. R.; Ford, G. W.; Milonni, P. W.
2014-01-01
We address the question of the applicability of the argument theorem (of complex variable theory) to the calculation of two distinct energies: (i) the first-order dispersion interaction energy of two separated oscillators, when one of the oscillators is excited initially and (ii) the Casimir-Polder interaction of a ground-state quantum oscillator near a perfectly conducting plane. We show that the argument theorem can be used to obtain the generally accepted equation for the first-order dispersion interaction energy, which is oscillatory and varies as the inverse power of the separation r of the oscillators for separations much greater than an optical wavelength. However, for such separations, the interaction energy cannot be transformed into an integral over the positive imaginary axis. If the argument theorem is used incorrectly to relate the interaction energy to an integral over the positive imaginary axis, the interaction energy is non-oscillatory and varies as r −4 , a result found by several authors. Rather remarkably, this incorrect expression for the dispersion energy actually corresponds to the nonperturbative Casimir-Polder energy for a ground-state quantum oscillator near a perfectly conducting wall, as we show using the so-called “remarkable formula” for the free energy of an oscillator coupled to a heat bath [G. W. Ford, J. T. Lewis, and R. F. O’Connell, Phys. Rev. Lett. 55, 2273 (1985)]. A derivation of that formula from basic results of statistical mechanics and the independent oscillator model of a heat bath is presented
Wang, Peng-Fei; Ruan, Xiao-Dong; Xu, Zhong-Bin; Fu, Xin
2015-11-01
The Hong-Strogatz (HS) model of globally coupled phase oscillators with attractive and repulsive interactions reflects the fact that each individual (oscillator) has its own attitude (attractive or repulsive) to the same environment (mean field). Previous studies on HS model focused mainly on the stable states on Ott-Antonsen (OA) manifold. In this paper, the eigenvalues of the Jacobi matrix of each fixed point in HS model are explicitly derived, with the aim to understand the local dynamics around each fixed point. Phase transitions are described according to relative population and coupling strength. Besides, the dynamics off OA manifold is studied. Supported by the National Basic Research Program of China under Grant No. 2015CB057301, the Applied Research Project of Public Welfare Technology of Zhejiang Province under Grant No. 201SC31109 and China Postdoctoral Science Foundation under Grant No. 2014M560483
Nonstandard scaling law of fluctuations in finite-size systems of globally coupled oscillators.
Nishikawa, Isao; Tanaka, Gouhei; Aihara, Kazuyuki
2013-08-01
Universal scaling laws form one of the central issues in physics. A nonstandard scaling law or a breakdown of a standard scaling law, on the other hand, can often lead to the finding of a new universality class in physical systems. Recently, we found that a statistical quantity related to fluctuations follows a nonstandard scaling law with respect to the system size in a synchronized state of globally coupled nonidentical phase oscillators [I. Nishikawa et al., Chaos 22, 013133 (2012)]. However, it is still unclear how widely this nonstandard scaling law is observed. In the present paper, we discuss the conditions required for the unusual scaling law in globally coupled oscillator systems and validate the conditions by numerical simulations of several different models.
Explosive death of conjugate coupled Van der Pol oscillators on networks
Zhao, Nannan; Sun, Zhongkui; Yang, Xiaoli; Xu, Wei
2018-06-01
Explosive death phenomenon has been gradually gaining attention of researchers due to the research boom of explosive synchronization, and it has been observed recently for the identical or nonidentical coupled systems in all-to-all network. In this work, we investigate the emergence of explosive death in networked Van der Pol (VdP) oscillators with conjugate variables coupling. It is demonstrated that the network structures play a crucial role in identifying the types of explosive death behaviors. We also observe that the damping coefficient of the VdP system not only can determine whether the explosive death state is generated but also can adjust the forward transition point. We further show that the backward transition point is independent of the network topologies and the damping coefficient, which is well confirmed by theoretical analysis. Our results reveal the generality of explosive death phenomenon in different network topologies and are propitious to promote a better comprehension for the oscillation quenching behaviors.
Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators
Energy Technology Data Exchange (ETDEWEB)
Semenova, N.; Anishchenko, V. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Zakharova, A.; Schöll, E. [Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, 10623 Berlin (Germany)
2016-06-08
In this work we analyse nonlocally coupled networks of identical chaotic oscillators. We study both time-discrete and time-continuous systems (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of chaotic non-hyperbolic systems and cannot be found in networks of hyperbolic systems. This hypothesis is supported by numerical simulations for hyperbolic and non-hyperbolic cases.
A hybrid system of a membrane oscillator coupled to ultracold atoms
Kampschulte, Tobias
2015-05-01
The control over micro- and nanomechanical oscillators has recently made impressive progress. First experiments demonstrated ground-state cooling and single-phonon control of high-frequency oscillators using cryogenic cooling and techniques of cavity optomechanics. Coupling engineered mechanical structures to microscopic quantum system with good coherence properties offers new possibilities for quantum control of mechanical vibrations, precision sensing and quantum-level signal transduction. Ultracold atoms are an attractive choice for such hybrid systems: Mechanical can either be coupled to the motional state of trapped atoms, which can routinely be ground-state cooled, or to the internal states, for which a toolbox of coherent manipulation and detection exists. Furthermore, atomic collective states with non-classical properties can be exploited to infer the mechanical motion with reduced quantum noise. Here we use trapped ultracold atoms to sympathetically cool the fundamental vibrational mode of a Si3N4 membrane. The coupling of membrane and atomic motion is mediated by laser light over a macroscopic distance and enhanced by an optical cavity around the membrane. The observed cooling of the membrane from room temperature to 650 +/- 230 mK shows that our hybrid mechanical-atomic system operates at a large cooperativity. Our scheme could provide ground-state cooling and quantum control of low-frequency oscillators such as levitated nanoparticles, in a regime where purely optomechanical techniques cannot reach the ground state. Furthermore, we will present a scheme where an optomechanical system is coupled to internal states of ultracold atoms. The mechanical motion is translated into a polarization rotation which drives Raman transitions between atomic ground states. Compared to the motional-state coupling, the new scheme enables to couple atoms to high-frequency structures such as optomechanical crystals.
Kori, Hiroshi; Kiss, István Z.; Jain, Swati; Hudson, John L.
2018-04-01
Experiments and supporting theoretical analysis are presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation, where the coupling is repulsive in the electrode potential. While attractive coupling generates phase clusters and desynchronized states, repulsive coupling results in synchronized oscillations. The experiments are interpreted with a phenomenological model that captures the waveform of the oscillations (exponential increase) followed by a refractory period. The globally coupled autocatalytic integrate-and-fire model predicts the development of partially synchronized states that occur through attracting heteroclinic cycles between out-of-phase two-cluster states. Similar behavior can be expected in many other systems where the oscillations occur close to a saddle-loop bifurcation, e.g., with Morris-Lecar neurons.
Ghoshal, Gourab; Muñuzuri, Alberto P.; Pérez-Mercader, Juan
2016-01-01
Oscillatory phenomena are ubiquitous in Nature. The ability of a large population of coupled oscillators to synchronize constitutes an important mechanism to express information and establish communication among members. To understand such phenomena, models and experimental realizations of globally coupled oscillators have proven to be invaluable in settings as varied as chemical, biological and physical systems. A variety of rich dynamical behavior has been uncovered, although usually in the context of a single state of synchronization or lack thereof. Through the experimental and numerical study of a large population of discrete chemical oscillators, here we report on the unexpected discovery of a new phenomenon revealing the existence of dynamically distinct synchronized states reflecting different degrees of communication. Specifically, we discover a novel large-amplitude super-synchronized state separated from the conventionally reported synchronized and quiescent states through an unusual sharp jump transition when sampling the strong coupling limit. Our results assume significance for further elucidating globally coherent phenomena, such as in neuropathologies, bacterial cell colonies, social systems and semiconductor lasers.
Coupled Oscillator Model of the Business Cycle withFluctuating Goods Markets
Ikeda, Y.; Aoyama, H.; Fujiwara, Y.; Iyetomi, H.; Ogimoto, K.; Souma, W.; Yoshikawa, H.
The sectoral synchronization observed for the Japanese business cycle in the Indices of Industrial Production data is an example of synchronization. The stability of this synchronization under a shock, e.g., fluctuation of supply or demand, is a matter of interest in physics and economics. We consider an economic system made up of industry sectors and goods markets in order to analyze the sectoral synchronization observed for the Japanese business cycle. A coupled oscillator model that exhibits synchronization is developed based on the Kuramoto model with inertia by adding goods markets, and analytic solutions of the stationary state and the coupling strength are obtained. We simulate the effects on synchronization of a sectoral shock for systems with different price elasticities and the coupling strengths. Synchronization is reproduced as an equilibrium solution in a nearest neighbor graph. Analysis of the order parameters shows that the synchronization is stable for a finite elasticity, whereas the synchronization is broken and the oscillators behave like a giant oscillator with a certain frequency additional to the common frequency for zero elasticity.
Coherent oscillation in a linear quantum system coupled to a thermal bath
International Nuclear Information System (INIS)
Bell, N.F.; Volkas, R.R.; Sawyer, R.F.
2000-01-01
We consider the time development of the density matrix for a system coupled to a thermal bath, in models that go beyond the standard two-level systems through addition of an energy excitation degree of freedom and through the possibility of the replacement of the spin algebra by a more complex algebra. We find conditions under which increasing the coupling to the bath above a certain level decreases the rate of entropy production, and in which the limiting behavior is a dissipationless sinusoidal oscillation that could be interpreted as the synchronization of many modes of the uncoupled system
Optimum output coupling for a mid-infrared KTiOAsO4 optical parametric oscillator
International Nuclear Information System (INIS)
Li, Guochao; Gao, Yesheng; Zheng, Guangjin; Zhao, Yao; Chen, Kunfeng; Wang, Qingpu; Bai, Fen
2013-01-01
Taking into account the turn off time of the Q-switch, the coupled equations for a mid-infrared KTiOAsO 4 optical parametric oscillator (OPO) are given. These rate equations are solved numerically and some key parameters for designing the laser system are determined. The key parameters include the optimal coupling and nonlinear crystal length which maximize the output power and OPO conversion efficiency. We found that a low-loss singly resonant OPO cavity not only enhances the mid-infrared output but also decreases the optimal OPO crystal length. (paper)
Synchronization effects in two coupled one-dimensional lattices of phase oscillators
International Nuclear Information System (INIS)
Pando L, Carlos L.
2001-03-01
We study synchronization effects in a model consisting of two identical unidirectionally coupled 1-D arrays of phase oscillators. The master array is in the spatio-temporal chaos regime and the coupling across the two arrays is not strong enough in order to reach complete synchronization. The time series of the distance between the arrays is the main object of our study and this shows on-off intermittency. We can approximate the dynamics of the aforementioned time series with that of a first-order Markov process with two symbols. This model can be implemented in arrays of phase-locked loops (PPL) and Josephson junctions. (author)
Automatic Correction of Betatron Coupling in the LHC Using Injection Oscillations
Persson, T; Jacquet, D; Kain, V; Levinsen, Y; McAteer, M-J; Maclean, E; Skowronski, P; Tomas, R; Vanbavinckhove, G; Miyamoto, R
2013-01-01
The control of the betatron coupling at injection and during the energy ramp is critical for the safe operation of the tune feedback and for the dynamic aperture. In the LHC every fill is preceded by the injection of a pilot bunch with low intensity. Using the injection oscillations from the pilot bunch we are able to measure the coupling at each individual BPM. The measurement is used to calculate a global coupling correction. The correction is based on the use of two orthogonal knobs which correct the real and imaginary part of the difference resonance term f1001, respectively. This method to correct the betatron coupling has been proven successful during the normal operation of the LHC. This paper presents the method used to calculate the corrections and its performance.
International Nuclear Information System (INIS)
Luo Jian; Lu Di; Du Chaoling; Liu Youwen; Shi Daning; Lai Wei; Guo Chunlei; Gong Shangqing
2012-01-01
We theoretically investigate how to control the Rabi oscillation of excitons of the coupling quantum dots by manipulating static electric fields. Our results show that, for a single-photon process, when direct excitons change into indirect excitons with a bias applied on the sample, the Rabi oscillation rarely alters. However, for the two-photon process, a pronounced enhancement of Rabi oscillation is observed, which can be utilized as the logic gate in quantum information. (paper)
Periodic oscillations in linear continuous media coupled with nonlinear discrete systems
International Nuclear Information System (INIS)
Lupini, R.
1998-01-01
A general derivation of partial differential equations with boundary conditions in the form of ordinary differential equations is obtained using the principle of stationary action for a Lagrangian function composed of continuous plus discrete parts in interaction across the boundaries of a 1-dimensional medium. This approach leads directly to the theorem of energy conservation. For linear continuous medium, homogeneous Dirichlet condition at one boundary, and nonlinear oscillator at the other boundary, the entire differential problem reduces to a nonlinear differential-difference equation of neutral type and of the second order. The lag parameter is τ = l/c, where c is the phase speed, l the length of the continuum. The Author investigate the problem of the occurrence of periodic solutions of period integer multiple of the lag (super harmonic solutions) in the case of zero inertia of the boundary system. The problem for such oscillations is shown to reduce to systems of ordinary differential equations with matching conditions in a phase space of lower dimensionality: Phase-plane techniques are used to determine solutions of period 4τ, 8τ and 6τ
International Nuclear Information System (INIS)
Chuan-Sheng, Shen; Han-Shuang, Chen; Ji-Qian, Zhang
2008-01-01
We study the dynamic behaviour of two intracellular calcium oscillators that are coupled through gap junctions both to Ca 2+ and inositol(1,4,5)-trisphosphate (IP 3 ). It is found that synchronized anti-phase and in-phase oscillations of cytoplasmic calcium coexist in parameters space. Especially, synchronized anti-phase oscillations only occur near the onset of a Hopf bifurcation point when the velocity of IP 3 synthesis is increased. In addition, two kinds of coupling effects, i.e., the diffusions of Ca 2+ and IP 3 among cells on synchronous behaviour, are considered. We find that small coupling of Ca 2+ and large coupling of IP 3 facilitate the emergence of synchronized anti-phase oscillations. However, the result is contrary for the synchronized in-phase case. Our findings may provide a qualitative understanding about the mechanism of synchronous behaviour of intercellular calcium signalling
The intercellular synchronization of Ca2+ oscillations evaluates Cx36-dependent coupling.
Directory of Open Access Journals (Sweden)
Sabine Bavamian
Full Text Available Connexin36 (Cx36 plays an important role in insulin secretion by controlling the intercellular synchronization of Ca(2+ transients induced during stimulation. The lack of drugs acting on Cx36 channels is a major limitation in further unraveling the molecular mechanism underlying this effect. To screen for such drugs, we have developed an assay allowing for a semi-automatic, fluorimetric quantification of Ca(2+ transients in large populations of MIN6 cells. Here, we show that (1 compared to control cells, MIN6 cells with reduced Cx36 expression or function showed decreased synchrony of glucose-induced Ca(2+ oscillations; (2 glibenclamide, a sulphonylurea which promotes Cx36 junctions and coupling, increased the number of synchronous MIN6 cells, whereas quinine, an antimalarial drug which inhibits Cx36-dependent coupling, decreased this proportion; (3 several drugs were identified that altered the intercellular Ca(2+ synchronization, cell coupling and distribution of Cx36; (4 some of them also affected insulin content. The data indicate that the intercellular synchronization of Ca(2+ oscillations provides a reliable and non-invasive measurement of Cx36-dependent coupling, which is useful to identify novel drugs affecting the function of β-cells, neurons, and neuron-related cells that express Cx36.
Excitation transfer in two two-level systems coupled to an oscillator
International Nuclear Information System (INIS)
Hagelstein, P L; Chaudhary, I U
2008-01-01
We consider a generalization of the spin-boson model in which two different two-level systems are coupled to an oscillator, under conditions where the oscillator energy is much less than the two-level system energies, and where the oscillator is highly excited. We find that the two-level system transition energy is shifted, producing a Bloch-Siegert shift in each two-level system similar to what would be obtained if the other were absent. At resonances associated with energy exchange between a two-level system and the oscillator, the level splitting is about the same as would be obtained in the spin-boson model at a Bloch-Siegert resonance. However, there occur resonances associated with the transfer of excitation between one two-level system and the other, an effect not present in the spin-boson model. We use a unitary transformation leading to a rotated system in which terms responsible for the shift and splittings can be identified. The level splittings at the anticrossings associated with both energy exchange and excitation transfer resonances are accounted for with simple two-state models and degenerate perturbation theory using operators that appear in the rotated Hamiltonian
Directory of Open Access Journals (Sweden)
Po Hu
2016-06-01
Full Text Available The synchronous tuning of the self-oscillating wireless power transfer (WPT in a close-coupling condition is studied in this paper. The Hamel locus is applied to predict the self-oscillating points in the WPT system. In order to make the system operate stably at the most efficient point, which is the middle resonant point when there are middle resonant and split frequency points caused by frequency-splitting, the receiver (RX rather than the transmitter (TX current is chosen as the self-oscillating feedback variable. The automatic delay compensation is put forward to eliminate the influence of the intrinsic delay on frequency tuning for changeable parameters. In addition, the automatic circuit parameter tuning based on the phase difference is proposed to realize the synchronous tuning of frequency and circuit parameters. The experiments verified that the synchronous tuning proposed in this paper is effective, fully automatic, and more robust than the previous self-oscillating WPT system which use the TX current as the feedback variable.
International Nuclear Information System (INIS)
Wang, Chen-Wen; Zhu, Chaoyuan; Lin, Sheng-Hsien; Yang, Ling; Yu, Jian-Guo
2014-01-01
Damped harmonic oscillators are utilized to calculate Franck-Condon factors within displaced harmonic oscillator approximation. This is practically done by scaling unperturbed Hessian matrix that represents local modes of force constants for molecule in gaseous phase, and then by diagonalizing perturbed Hessian matrix it results in direct modification of Huang–Rhys factors which represent normal modes of solute molecule perturbed by solvent environment. Scaling parameters are empirically introduced for simulating absorption and fluorescence spectra of an isolated solute molecule in solution. The present method is especially useful for simulating vibronic spectra of polycyclic aromatic hydrocarbon molecules in which hydrogen atom vibrations in solution can be scaled equally, namely the same scaling factor being applied to all hydrogen atoms in polycyclic aromatic hydrocarbons. The present method is demonstrated in simulating solvent enhanced X 1 A g ↔ A 1 B 1u absorption and fluorescence spectra of perylene (medium-sized polycyclic aromatic hydrocarbon) in benzene solution. It is found that one of six active normal modes v 10 is actually responsible to the solvent enhancement of spectra observed in experiment. Simulations from all functionals (TD) B3LYP, (TD) B3LYP35, (TD) B3LYP50, and (TD) B3LYP100 draw the same conclusion. Hence, the present method is able to adequately reproduce experimental absorption and fluorescence spectra in both gas and solution phases
Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model
Energy Technology Data Exchange (ETDEWEB)
Freitas, Celso, E-mail: cbnfreitas@gmail.com; Macau, Elbert, E-mail: elbert.macau@inpe.br [Associate Laboratory for Computing and Applied Mathematics - LAC, Brazilian National Institute for Space Research - INPE (Brazil); Pikovsky, Arkady, E-mail: pikovsky@uni-potsdam.de [Department of Physics and Astronomy, University of Potsdam, Germany and Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2015-04-15
We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.
Coupled slow and fast surface dynamics in an electrocatalytic oscillator: Model and simulations
International Nuclear Information System (INIS)
Nascimento, Melke A.; Nagao, Raphael; Eiswirth, Markus; Varela, Hamilton
2014-01-01
The co-existence of disparate time scales is pervasive in many systems. In particular for surface reactions, it has been shown that the long-term evolution of the core oscillator is decisively influenced by slow surface changes, such as progressing deactivation. Here we present an in-depth numerical investigation of the coupled slow and fast surface dynamics in an electrocatalytic oscillator. The model consists of four nonlinear coupled ordinary differential equations, investigated over a wide parameter range. Besides the conventional bifurcation analysis, the system was studied by means of high-resolution period and Lyapunov diagrams. It was observed that the bifurcation diagram changes considerably as the irreversible surface poisoning evolves, and the oscillatory region shrinks. The qualitative dynamics changes accordingly and the chaotic oscillations are dramatically suppressed. Nevertheless, periodic cascades are preserved in a confined region of the resistance vs. voltage diagram. Numerical results are compared to experiments published earlier and the latter reinterpreted. Finally, the comprehensive description of the time-evolution in the period and Lyapunov diagrams suggests further experimental studies correlating the evolution of the system's dynamics with changes of the catalyst structure
Stability of phase locking in a ring of unidirectionally coupled oscillators
International Nuclear Information System (INIS)
Rogge, J A; Aeyels, D
2004-01-01
We discuss the dynamic behaviour of a finite group of phase oscillators unidirectionally coupled in a ring. The dynamics are based on the Kuramoto model. In the case of identical oscillators, all phase locking solutions and their stability properties are obtained. For nonidentical oscillators it is proven that there exist phase locking solutions for sufficiently strong coupling. An algorithm to obtain all phase locking solutions is proposed. These solutions can be classified into classes, each with its own stability properties. The stability properties are obtained by means of a novel extension of Gershgorin's theorem. One class of stable solutions has the property that all phase differences between neighbouring cells are contained in (-π/2, π/2). Contrary to intuition, a second class of stable solutions is established with exactly one of the phase differences contained in (π/2, 3π/2). The stability results are extended from sinusoidal interconnections to a class of odd functions. To conclude, a connection with the field of active antenna arrays is made, generalizing some results earlier obtained in this field
Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle.
Feillet, Céline; Krusche, Peter; Tamanini, Filippo; Janssens, Roel C; Downey, Mike J; Martin, Patrick; Teboul, Michèle; Saito, Shoko; Lévi, Francis A; Bretschneider, Till; van der Horst, Gijsbertus T J; Delaunay, Franck; Rand, David A
2014-07-08
Daily synchronous rhythms of cell division at the tissue or organism level are observed in many species and suggest that the circadian clock and cell cycle oscillators are coupled. For mammals, despite known mechanistic interactions, the effect of such coupling on clock and cell cycle progression, and hence its biological relevance, is not understood. In particular, we do not know how the temporal organization of cell division at the single-cell level produces this daily rhythm at the tissue level. Here we use multispectral imaging of single live cells, computational methods, and mathematical modeling to address this question in proliferating mouse fibroblasts. We show that in unsynchronized cells the cell cycle and circadian clock robustly phase lock each other in a 1:1 fashion so that in an expanding cell population the two oscillators oscillate in a synchronized way with a common frequency. Dexamethasone-induced synchronization reveals additional clock states. As well as the low-period phase-locked state there are distinct coexisting states with a significantly higher period clock. Cells transition to these states after dexamethasone synchronization. The temporal coordination of cell division by phase locking to the clock at a single-cell level has significant implications because disordered circadian function is increasingly being linked to the pathogenesis of many diseases, including cancer.
Parihar, Abhinav; Shukla, Nikhil; Datta, Suman; Raychowdhury, Arijit
2015-02-01
Computing with networks of synchronous oscillators has attracted wide-spread attention as novel materials and device topologies have enabled realization of compact, scalable and low-power coupled oscillatory systems. Of particular interest are compact and low-power relaxation oscillators that have been recently demonstrated using MIT (metal-insulator-transition) devices using properties of correlated oxides. Further the computational capability of pairwise coupled relaxation oscillators has also been shown to outperform traditional Boolean digital logic circuits. This paper presents an analysis of the dynamics and synchronization of a system of two such identical coupled relaxation oscillators implemented with MIT devices. We focus on two implementations of the oscillator: (a) a D-D configuration where complementary MIT devices (D) are connected in series to provide oscillations and (b) a D-R configuration where it is composed of a resistor (R) in series with a voltage-triggered state changing MIT device (D). The MIT device acts like a hysteresis resistor with different resistances in the two different states. The synchronization dynamics of such a system has been analyzed with purely charge based coupling using a resistive (RC) and a capacitive (CC) element in parallel. It is shown that in a D-D configuration symmetric, identical and capacitively coupled relaxation oscillator system synchronizes to an anti-phase locking state, whereas when coupled resistively the system locks in phase. Further, we demonstrate that for certain range of values of RC and CC, a bistable system is possible which can have potential applications in associative computing. In D-R configuration, we demonstrate the existence of rich dynamics including non-monotonic flows and complex phase relationship governed by the ratios of the coupling impedance. Finally, the developed theoretical formulations have been shown to explain experimentally measured waveforms of such pairwise coupled
Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure
International Nuclear Information System (INIS)
Jiang Hai-Bo; Zhang Li-Ping; Yu Jian-Jiang
2015-01-01
Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics. This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure. By constructing a proper Poincaré map of the non-smooth system, an analytical expression of the Jacobian matrix of Poincaré map is given. Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge–Kutta method. When the period is fixed and the coupling strength changes, the system undergoes stable, periodic, quasi-periodic, and hyper-chaotic solutions, etc. Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations. (paper)
Adiabatic approximation in the ultrastrong-coupling regime of an oscillator and two qubits
Energy Technology Data Exchange (ETDEWEB)
Yang, Ping; Zou, Ping [Laboratory of Nanophotonic Functional Materials and Devices, SIPSE and LQIT, South China Normal University, Guangzhou 510006 (China); Zhang, Zhi-Ming, E-mail: zmzhang@scnu.edu.cn [Laboratory of Nanophotonic Functional Materials and Devices, SIPSE and LQIT, South China Normal University, Guangzhou 510006 (China)
2012-10-01
We present a system composed of two flux qubits and a transmission-line resonator. Instead of using the rotating wave approximation (RWA), we analyze the system by the adiabatic approximation methods under two opposite extreme conditions. Basic properties of the system are calculated and compared under these two different conditions. Relative energy-level spectrum of the system in the adiabatic displaced oscillator basis is shown, and the theoretical result is compared with the numerical solution. -- Highlights: ► Our work shows that the adiabatic approximations may work also in the ultrastrong coupling limit. ► Both of the approximation methods are valid in a large range of coupling strength, including the ultrastrong coupling regime. ► The results of the approximate formula meet well the exact numerical solution.