An algebraic cluster model based on the harmonic oscillator basis
NASA Technical Reports Server (NTRS)
Levai, Geza; Cseh, J.
1995-01-01
We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.
A Simple Mechanical Model for the Isotropic Harmonic Oscillator
ERIC Educational Resources Information Center
Nita, Gelu M.
2010-01-01
A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)
Using Coupled Harmonic Oscillators to Model Some Greenhouse Gas Molecules
Go, Clark Kendrick C.; Maquiling, Joel T.
2010-07-28
Common greenhouse gas molecules SF{sub 6}, NO{sub 2}, CH{sub 4}, and CO{sub 2} are modeled as harmonic oscillators whose potential and kinetic energies are derived. Using the Euler-Lagrange equation, their equations of motion are derived and their phase portraits are plotted. The authors use these data to attempt to explain the lifespan of these gases in the atmosphere.
Covariant harmonic oscillators and coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, Daesoo; Kim, Young S.; Noz, Marilyn E.
1995-01-01
It is shown that the system of two coupled harmonic oscillators shares the basic symmetry properties with the covariant harmonic oscillator formalism which provides a concise description of the basic features of relativistic hadronic features observed in high-energy laboratories. It is shown also that the coupled oscillator system has the SL(4,r) symmetry in classical mechanics, while the present formulation of quantum mechanics can accommodate only the Sp(4,r) portion of the SL(4,r) symmetry. The possible role of the SL(4,r) symmetry in quantum mechanics is discussed.
Workshop on Harmonic Oscillators
NASA Technical Reports Server (NTRS)
Han, D. (Editor); Kim, Y. S. (Editor); Zachary, W. W. (Editor)
1993-01-01
Proceedings of a workshop on Harmonic Oscillators held at the College Park Campus of the University of Maryland on March 25 - 28, 1992 are presented. The harmonic oscillator formalism is playing an important role in many branches of physics. This is the simplest mathematical device which can connect the basic principle of physics with what is observed in the real world. The harmonic oscillator is the bridge between pure and applied physics.
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
ERIC Educational Resources Information Center
Lee, Keeyung
2009-01-01
The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…
ERIC Educational Resources Information Center
Parnis, J. Mark; Thompson, Matthew G. K.
2004-01-01
An introductory undergraduate physical organic chemistry exercise that introduces the harmonic oscillator's use in vibrational spectroscopy is developed. The analysis and modeling exercise begins with the students calculating the stretching modes of common organic molecules with the help of the quantum mechanical harmonic oscillator (QMHO) model.
Second harmonic FEL oscillation
NASA Astrophysics Data System (ADS)
Neil, George R.; Benson, S. V.; Biallas, G.; Freund, H. P.; Gubeli, J.; Jordan, K.; Myers, S.; Shinn, M. D.
2002-05-01
We have produced and measured for the first time second harmonic oscillation in the infrared region by the high-average-power Jefferson Lab Infrared Free Electron Laser. The finite geometry and beam emittance allows sufficient gain for lasing to occur. We were able to lase at pulse rates up to 74.85 MHz and could produce over 4.5 W average and 40 kW peak of IR power in a 40 nm FWHM bandwidth at 2925 nm. In agreement with predictions, the source preferentially lased in a TEM 01 mode. We present results of initial source performance measurements and comparisons with theory and simulation.
Second Harmonic FEL Oscillation
NASA Astrophysics Data System (ADS)
Neil, George R.; Benson, S. V.; Biallas, G.; Gubeli, J.; Jordan, K.; Myers, S.; Shinn, M. D.
2001-08-01
We have produced and measured for the first time second harmonic oscillation in the infrared region by a free electron laser. Although such lasing is ideally forbidden, since the gain of a plane wave is zero on axis for an electron beam perfectly aligned with a wiggler, a transverse mode antisymmetry allows sufficient gain in this experiment for lasing to occur. We lased at pulse rates up to 74.85 MHz and could produce over 4.5 W average and 40 kW peak of IR power in a 40 nm FWHM bandwidth at 2925 nm. In agreement with predictions, the source preferentially lased in a TEM01 mode.
Relativistic harmonic oscillator revisited
Bars, Itzhak
2009-02-15
The familiar Fock space commonly used to describe the relativistic harmonic oscillator, for example, as part of string theory, is insufficient to describe all the states of the relativistic oscillator. We find that there are three different vacua leading to three disconnected Fock sectors, all constructed with the same creation-annihilation operators. These have different spacetime geometric properties as well as different algebraic symmetry properties or different quantum numbers. Two of these Fock spaces include negative norm ghosts (as in string theory), while the third one is completely free of ghosts. We discuss a gauge symmetry in a worldline theory approach that supplies appropriate constraints to remove all the ghosts from all Fock sectors of the single oscillator. The resulting ghost-free quantum spectrum in d+1 dimensions is then classified in unitary representations of the Lorentz group SO(d,1). Moreover, all states of the single oscillator put together make up a single infinite dimensional unitary representation of a hidden global symmetry SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these new results in string theory and other areas of physics and mathematics are briefly mentioned.
Synchronous Discrete Harmonic Oscillator
Antippa, Adel F.; Dubois, Daniel M.
2008-10-17
We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2{pi} in phase space, is an integral multiple N of the discrete time step {delta}t. It is fully synchronous when N is even. It is pseudo-synchronous when T/{delta}t is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is ''blue shifted'' relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval {delta}t. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.
Galilean covariant harmonic oscillator
NASA Technical Reports Server (NTRS)
Horzela, Andrzej; Kapuscik, Edward
1993-01-01
A Galilean covariant approach to classical mechanics of a single particle is described. Within the proposed formalism, all non-covariant force laws defining acting forces which become to be defined covariantly by some differential equations are rejected. Such an approach leads out of the standard classical mechanics and gives an example of non-Newtonian mechanics. It is shown that the exactly solvable linear system of differential equations defining forces contains the Galilean covariant description of harmonic oscillator as its particular case. Additionally, it is demonstrated that in Galilean covariant classical mechanics the validity of the second Newton law of dynamics implies the Hooke law and vice versa. It is shown that the kinetic and total energies transform differently with respect to the Galilean transformations.
Symmetries of coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, D.; Kim, Y. S.
1993-01-01
It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).
Rigatos, Gerasimos G.
2007-09-06
Neural computation based on principles of quantum mechanics can provide improved models of memory processes and brain functioning and is of importance for the realization of quantum computing machines. To this end, this paper studies neural structures with weights that follow the model of the quantum harmonic oscillator. These weights correspond to diffusing particles, which interact to each other as the theory of Brownian motion predicts. The learning of the stochastic weights (convergence of the diffusing particles to an equilibrium) is analyzed. In the case of associative memories the proposed neural model results in an exponential increase of the number of attractors. Spectral analysis shows that the stochastic weights satisfy an equation which is analogous to the principle of uncertainty.
Quantum wormholes and harmonic oscillators
NASA Technical Reports Server (NTRS)
Garay, Luis J.
1993-01-01
The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface which divides the space time manifold into two disconnected parts. Minisuperspace models which consist of a homogeneous massless scalar field coupled to a Friedmann-Robertson-Walker space time are considered. Once the path integral over the lapse function is performed, the requirement that the space time be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is argued that there does not exist any wave function which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. Then, the wormhole wave functions can be written as linear combinations of harmonic oscillator wave functions.
Application of Elliott's SU(3) model to the triaxially deformed harmonic oscillators
NASA Astrophysics Data System (ADS)
Sugawara-Tanabe, Kazuko
2011-05-01
We have introduced new bosons corresponding to the integral ratio of three frequencies for a harmonic oscillator potential, by means of a non-linear transformation which realizes the SU(3) group as a dynamical symmetry group, and which leaves the anisotropic harmonic oscillator Hamiltonian invariant. The classification of the single-particle levels based on this covering group predicts magic numbers depending on the deformation parameters δ and γ. The special cases with tan γ = 1/√3 (γ = 30°) and √3 /5(γ˜19°) are discussed.
The harmonic oscillator and nuclear physics
NASA Technical Reports Server (NTRS)
Rowe, D. J.
1993-01-01
The three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It is shown that the three-dimensional harmonic oscillator features a rich variety of coherent states, including vibrations of the monopole, dipole, and quadrupole types, and rotations of the rigid flow, vortex flow, and irrotational flow types. Nuclear collective states exhibit all of these flows. It is also shown that the coherent state representations, which have their origins in applications to the dynamical groups of the simple harmonic oscillator, can be extended to vector coherent state representations with a much wider range of applicability. As a result, coherent state theory and vector coherent state theory become powerful tools in the application of algebraic methods in physics.
Second International Workshop on Harmonic Oscillators
NASA Technical Reports Server (NTRS)
Han, Daesoo (Editor); Wolf, Kurt Bernardo (Editor)
1995-01-01
The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as we explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory.
Making space for harmonic oscillators
Michelotti, Leo; /Fermilab
2004-11-01
If we restrict the number of harmonic oscillator energy eigenstates to some finite value, N, then the discrete spectrum of the corresponding position operator comprise the roots of the Hermite polynomial H{sub N+1}. Its range is just large enough to accommodate classical motion at high energy. A negative energy term must be added to the Hamiltonian which affects only the last eigenstate, |N>, suggesting it is concentrated at the extrema of this finite ''space''. Calculations support a conjecture that, in the limit of large N, the global distribution of points approaches the differential form for classical action.
Harmonic oscillator states in aberration optics
NASA Technical Reports Server (NTRS)
Wolf, Kurt Bernardo
1993-01-01
The states of the three-dimensional quantum harmonic oscillator classify optical aberrations of axis-symmetric systems due to the isomorphism between the two mathematical structures. Cartesian quanta and angular momentum classifications have their corresponding aberration classifications. The operation of concatenation of optical elements introduces a new operation between harmonic oscillator states.
Quantum phases for a generalized harmonic oscillator
NASA Astrophysics Data System (ADS)
Bracken, Paul
2008-03-01
An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator with this choice of parameters.
Harmonic Oscillators as Bridges between Theories
NASA Astrophysics Data System (ADS)
Kim, Y. S.; Noz, Marilyn E.
2005-03-01
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. It is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called SL(2, c). Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics.
On the moment of inertia of a quantum harmonic oscillator
Khamzin, A. A. Sitdikov, A. S.; Nikitin, A. S.; Roganov, D. A.
2013-04-15
An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.
Quantum harmonic oscillator with superoscillating initial datum
Buniy, R. V.; Struppa, D. C.; Colombo, F.; Sabadini, I.
2014-11-15
In this paper, we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the harmonic potential and that the analytic solution develops a singularity in finite time. We also show that for a large class of solutions of the Schrödinger equation, superoscillating behavior at any given time implies superoscillating behavior at any other time.
Quantum nondemolition measurements of harmonic oscillators
NASA Technical Reports Server (NTRS)
Thorne, K. S.; Caves, C. M.; Zimmermann, M.; Sandberg, V. D.; Drever, R. W. P.
1978-01-01
Measuring systems to determine the real component of the complex amplitude of a harmonic oscillator are described. This amplitude is constant in the absence of driving forces, and the uncertainty principle accounts for the fact that only the real component can be measured precisely and continuously ('quantum nondemolition measurement'). Application of the measuring systems to the detection of gravitational waves is considered.
Quantum harmonic oscillator in a thermal bath
NASA Technical Reports Server (NTRS)
Zhang, Yuhong
1993-01-01
The influence functional path-integral treatment of quantum Brownian motion is briefly reviewed. A newly derived exact master equation of a quantum harmonic oscillator coupled to a general environment at arbitrary temperature is discussed. It is applied to the problem of loss of quantum coherence.
Group Theory of Covariant Harmonic Oscillators
ERIC Educational Resources Information Center
Kim, Y. S.; Noz, Marilyn E.
1978-01-01
A simple and concrete example for illustrating the properties of noncompact groups is presented. The example is based on the covariant harmonic-oscillator formalism in which the relativistic wave functions carry a covariant-probability interpretation. This can be used in a group theory course for graduate students who have some background in…
Predicting charmonium and bottomonium spectra with a quark harmonic oscillator
NASA Technical Reports Server (NTRS)
Norbury, J. W.; Badavi, F. F.; Townsend, L. W.
1986-01-01
The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.
NASA Astrophysics Data System (ADS)
Scafetta, Nicola
2013-11-01
Power spectra of global surface temperature (GST) records (available since 1850) reveal major periodicities at about 9.1, 10-11, 19-22 and 59-62 years. Equivalent oscillations are found in numerous multisecular paleoclimatic records. The Coupled Model Intercomparison Project 5 (CMIP5) general circulation models (GCMs), to be used in the IPCC Fifth Assessment Report (AR5, 2013), are analyzed and found not able to reconstruct this variability. In particular, from 2000 to 2013.5 a GST plateau is observed while the GCMs predicted a warming rate of about 2 °C/century. In contrast, the hypothesis that the climate is regulated by specific natural oscillations more accurately fits the GST records at multiple time scales. For example, a quasi 60-year natural oscillation simultaneously explains the 1850-1880, 1910-1940 and 1970-2000 warming periods, the 1880-1910 and 1940-1970 cooling periods and the post 2000 GST plateau. This hypothesis implies that about 50% of the ~ 0.5 °C global surface warming observed from 1970 to 2000 was due to natural oscillations of the climate system, not to anthropogenic forcing as modeled by the CMIP3 and CMIP5 GCMs. Consequently, the climate sensitivity to CO2 doubling should be reduced by half, for example from the 2.0-4.5 °C range (as claimed by the IPCC, 2007) to 1.0-2.3 °C with a likely median of ~ 1.5 °C instead of ~ 3.0 °C. Also modern paleoclimatic temperature reconstructions showing a larger preindustrial variability than the hockey-stick shaped temperature reconstructions developed in early 2000 imply a weaker anthropogenic effect and a stronger solar contribution to climatic changes. The observed natural oscillations could be driven by astronomical forcings. The ~ 9.1 year oscillation appears to be a combination of long soli-lunar tidal oscillations, while quasi 10-11, 20 and 60 year oscillations are typically found among major solar and heliospheric oscillations driven mostly by Jupiter and Saturn movements. Solar models based
Factorization method for the truncated harmonic oscillator
NASA Astrophysics Data System (ADS)
Fernández C, D. J.; Morales-Salgado, V. S.
2015-04-01
Factorization procedures of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. Certain systems obtained in a straightforward way through said method possess differential ladder operators of both types, third and fourth order. Since systems with this kind of operators are linked with the Painlevé IV and V equations respectively, several solutions of these non-linear second-order differential equations will be simply found.
Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps
ERIC Educational Resources Information Center
Pendrill, Ann-Marie; Eager, David
2015-01-01
Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…
Improving Density Functionals with Quantum Harmonic Oscillators
NASA Astrophysics Data System (ADS)
Tkatchenko, Alexandre
2013-03-01
Density functional theory (DFT) is the most widely used and successful approach for electronic structure calculations. However, one of the pressing challenges for DFT is developing efficient functionals that can accurately capture the omnipresent long-range electron correlations, which determine the structure and stability of many molecules and materials. Here we show that, under certain conditions, the problem of computing the long-range correlation energy of interacting electrons can be mapped to a system of coupled quantum harmonic oscillators (QHOs). The proposed model allows us to synergistically combine concepts from DFT, quantum chemistry, and the widely discussed random-phase approximation for the correlation energy. In the dipole limit, the interaction energy for a system of coupled QHOs can be calculated exactly, thereby leading to an efficient and accurate model for the many-body dispersion energy of complex molecules and materials. The studied examples include intermolecular binding energies, the conformational hierarchy of DNA structures, the geometry and stability of molecular crystals, and supramolecular host-guest complexes (A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012); R. A. DiStasio Jr., A. von Lilienfeld, A. Tkatchenko, PNAS 109, 14791 (2012); A. Tkatchenko, D. Alfe, K. S. Kim, J. Chem. Theory and Comp. (2012), doi: 10.1021/ct300711r; A. Tkatchenko, A. Ambrosetti, R. A. DiStasio Jr., arXiv:1210.8343v1).
Complex metabolic oscillations in plants forced by harmonic irradiance.
Nedbal, Ladislav; Brezina, Vítezslav
2002-01-01
Plants exposed to harmonically modulated irradiance, approximately 1 + cos(omegat), exhibit a complex periodic pattern of chlorophyll fluorescence emission that can be deconvoluted into a steady-state component, a component that is modulated with the frequency of the irradiance (omega), and into at least two upper harmonic components (2omega and 3omega). A model is proposed that accounts for the upper harmonics in fluorescence emission by nonlinear negative feedback regulation of photosynthesis. In contrast to simpler linear models, the model predicts that the steady-state fluorescence component will depend on the frequency of light modulation, and that amplitudes of all fluorescence components will exhibit resonance peak(s) when the irradiance frequency is tuned to an internal frequency of a regulatory component. The experiments confirmed that the upper harmonic components appear and exhibit distinct resonant peaks. The frequency of autonomous oscillations observed earlier upon an abrupt increase in CO(2) concentration corresponds to the sharpest of the resonant peaks of the forced oscillations. We propose that the underlying principles are general for a wide spectrum of negative-feedback regulatory mechanisms. The analysis by forced harmonic oscillations will enable us to examine internal dynamics of regulatory processes that have not been accessible to noninvasive fluorescence monitoring to date. PMID:12324435
Fisher information of quantum damped harmonic oscillators
NASA Astrophysics Data System (ADS)
Aguiar, V.; Guedes, I.
2015-04-01
We calculate the time-dependent Fisher information in position ({{F}x}) and momentum ({{F}p}) for the lowest lying state ≤ft( n=0 \\right) of two classes of quantum damped (Lane-Emden (LE) and Caldirola-Kanai (CK)) harmonic oscillators. The expressions of {{F}x} and {{F}p} are written in terms of ρ , a c-number quantity satisfying a nonlinear differential equation. Analytical solutions of ρ were obtained. For the LE and CK oscillators, we observe that {{F}x} increases while {{F}p} decreases with increasing time. The product {{F}x}{{F}p} increases and tends to a constant value in the limit t\\to ∞ for the LE oscillator, while it is time-independent for the CK oscillator. Moreover, for the CK oscillator the product {{F}x}{{F}p} decreases as the damping ≤ft( γ \\right) increases. Relations among the Fisher information, Leipnik and Shannon entropies, and the Stam and Cramer-Rao inequalities are given. A discussion on the squeezing phenomenon in position for the oscillators is presented.
Harmonic oscillator interaction with squeezed radiation
NASA Technical Reports Server (NTRS)
Dodonov, V. V.; Nikonov, D. E.
1993-01-01
Although the problem of electromagnetic radiation by a quantum harmonic oscillator is considered in textbooks on quantum mechanics, some of its aspects have remained unclear until now. By this, we mean that usually the initial quantum states of both the oscillator and the field are assumed to be characterized by a definite energy level of the oscillator and definite occupation numbers of the field modes. In connection with growing interest in squeezed states, it would be interesting to analyze the general case when the initial states of both subsystems are arbitrary superpositions of energy eigenstates. This problem was considered in other work, where the power of the spontaneous emission was calculated in the case of an arbitrary oscillator's initial state, but the field was initially in a vacuum state. In the present article, we calculate the rate of the oscillator average energy, squeezing, and correlation parameter change under the influence of an arbitrary external radiation field. Some other problems relating to the interaction between quantum particles (atoms) or oscillators where the electromagnetic radiation is an arbitrary (in particular squeezed) state were investigated.
Random reverse-cyclic matrices and screened harmonic oscillator.
Srivastava, Shashi C L; Jain, Sudhir R
2012-04-01
We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an N-body exactly solvable model. We refer to this well-known model potential as a screened harmonic oscillator. The connection enables us to obtain all the correlations among the particle positions moving in a screened harmonic potential. The density of nontrivial eigenvalues of this ensemble is found to be of the Wigner form and admits a hole at the origin, in contrast to the semicircle law of the Gaussian orthogonal ensemble of random matrices. The spacing distributions assume different forms ranging from Gaussian-like to Wigner. PMID:22680453
Joint entropy of quantum damped harmonic oscillators
NASA Astrophysics Data System (ADS)
Aguiar, V.; Guedes, I.
2014-05-01
We use the dynamical invariant method and a unitary transformation to obtain the exact Schrödinger wave function, ψn(x,t), and calculate for n=0 the time-dependent joint entropy (Leipnik’s entropy) for two classes of quantum damped harmonic oscillators. We observe that the joint entropy does not vary in time for the Caldirola-Kanai oscillator, while it decreases and tends to a constant value (ln({e}/{2})) for asymptotic times for the Lane-Emden ones. This is due to the fact that for the latter, the damping factor decreases as time increases. The results show that the time dependence of the joint entropy is quite complex and does not obey a general trend of monotonously increase with time.
NASA Astrophysics Data System (ADS)
Lin, J. Y. Y.; Aczel, A. A.; Abernathy, D. L.; Nagler, S. E.; Buyers, W. J. L.; Granroth, G. E.
2014-04-01
Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of-flight chopper spectrometers [A. A. Aczel et al., Nat. Commun. 3, 1124 (2012), 10.1038/ncomms2117]. These modes are well described by three-dimensional isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states, and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature-dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T dependence of the scattering from these modes is strongly influenced by the uranium lattice.
Lin, J. Y. Y.; Aczel, Adam A; Abernathy, Douglas L; Nagler, Stephen E; Buyers, W. J. L.; Granroth, Garrett E
2014-01-01
Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of- flight chopper spectrometers [A.A. Aczel et al, Nature Communications 3, 1124 (2012)]. These modes are well described by 3D isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for the nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states (PDOS), and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T-dependence of the scattering from these modes is strongly influenced by the uranium lattice.
The Coupled Harmonic Oscillator: Not Just for Seniors Anymore.
ERIC Educational Resources Information Center
Preyer, Norris W.
1996-01-01
Presents experiments that use Microcomputer Based Laboratory (MBL) techniques to enable freshmen physics students to investigate complex systems, such as nonlinear oscillators or coupled harmonic oscillators, at a level appropriate for an independent project. (JRH)
BAYESIAN ANALYSIS OF MULTIPLE HARMONIC OSCILLATIONS IN THE SOLAR CORONA
Arregui, I.; Asensio Ramos, A.; Diaz, A. J.
2013-03-01
The detection of multiple mode harmonic kink oscillations in coronal loops enables us to obtain information on coronal density stratification and magnetic field expansion using seismology inversion techniques. The inference is based on the measurement of the period ratio between the fundamental mode and the first overtone and theoretical results for the period ratio under the hypotheses of coronal density stratification and magnetic field expansion of the wave guide. We present a Bayesian analysis of multiple mode harmonic oscillations for the inversion of the density scale height and magnetic flux tube expansion under each of the hypotheses. The two models are then compared using a Bayesian model comparison scheme to assess how plausible each one is given our current state of knowledge.
Effective field theory in the harmonic oscillator basis
NASA Astrophysics Data System (ADS)
Binder, S.; Ekström, A.; Hagen, G.; Papenbrock, T.; Wendt, K. A.
2016-04-01
We develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.
Effective field theory in the harmonic oscillator basis
Binder, S.; Ekström, Jan A.; Hagen, Gaute; Papenbrock, Thomas F.; Wendt, Kyle A.
2016-04-25
In this paper, we develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leadingmore » order. Finally, many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.« less
Free fall and harmonic oscillations: analyzing trampoline jumps
NASA Astrophysics Data System (ADS)
Pendrill, Ann-Marie; Eager, David
2015-01-01
Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is obtained in terms of maximum normalized force from the trampoline and the harmonic frequency. A simple expression is obtained for the ratio between air-time and harmonic period, and the maximum g-factor. The results are compared to experimental results, including accelerometer data showing 7g during bounces on a small trampoline in an amusement park play area. Similar results are obtained on a larger garden trampoline, and even larger accelerations have been measured for gymnastic trampolines.
Coherent states for the relativistic harmonic oscillator
NASA Technical Reports Server (NTRS)
Aldaya, Victor; Guerrero, J.
1995-01-01
Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.
A possible generalization of the harmonic oscillator potential
NASA Technical Reports Server (NTRS)
Levai, Geza
1995-01-01
A four-parameter potential is analyzed, which contains the three-dimensional harmonic oscillator as a special case. This potential is exactly solvable and retains several characteristics of the harmonic oscillator, and also of the Coulomb problem. The possibility of similar generalizations of other potentials is also pointed out.
Operation of higher harmonic oscillations in free-electron lasers.
Sei, N; Ogawa, H; Yamada, K
2012-01-01
We report for the first time the experimental achievement of a seventh-harmonic free-electron laser (FEL) oscillation. The measured FEL gains and average FEL powers for higher harmonics were identical to those calculated by a one-dimensional FEL theory. The measured linewidths of the higher-harmonic FELs were narrower than that of the fundamental FEL owing to the narrower spectral widths of the spontaneous emissions. By applying the higher-harmonic FEL oscillation to a resonator-type FEL with an advanced accelerator, an x-ray FEL oscillator can be realized at lower electron-beam energy. PMID:22274354
A Look at Damped Harmonic Oscillators through the Phase Plane
ERIC Educational Resources Information Center
Daneshbod, Yousef; Latulippe, Joe
2011-01-01
Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the…
Driven harmonic oscillator as a quantum simulator for open systems
Piilo, Jyrki; Maniscalco, Sabrina
2006-09-15
We show theoretically how a driven harmonic oscillator can be used as a quantum simulator for the non-Markovian damped harmonic oscillator. In the general framework, our results demonstrate the possibility to use a closed system as a simulator for open quantum systems. The quantum simulator is based on sets of controlled drives of the closed harmonic oscillator with appropriately tailored electric field pulses. The non-Markovian dynamics of the damped harmonic oscillator is obtained by using the information about the spectral density of the open system when averaging over the drives of the closed oscillator. We consider single trapped ions as a specific physical implementation of the simulator, and we show how the simulator approach reveals physical insight into the open system dynamics, e.g., the characteristic quantum mechanical non-Markovian oscillatory behavior of the energy of the damped oscillator, usually obtained by the non-Lindblad-type master equation, can have a simple semiclassical interpretation.
Harmonic and Anharmonic Behaviour of a Simple Oscillator
ERIC Educational Resources Information Center
O'Shea, Michael J.
2009-01-01
We consider a simple oscillator that exhibits harmonic and anharmonic regimes and analyse its behaviour over the complete range of possible amplitudes. The oscillator consists of a mass "m" fixed at the midpoint of a horizontal rope. For zero initial rope tension and small amplitude the period of oscillation, tau, varies as tau is approximately…
Non-Markovian quantum Brownian motion of a harmonic oscillator
Tang, J.
1994-02-01
We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.
Optimal control of a harmonic oscillator: Economic interpretations
NASA Astrophysics Data System (ADS)
Janová, Jitka; Hampel, David
2013-10-01
Optimal control is a popular technique for modelling and solving the dynamic decision problems in economics. A standard interpretation of the criteria function and Lagrange multipliers in the profit maximization problem is well known. On a particular example, we aim to a deeper understanding of the possible economic interpretations of further mathematical and solution features of the optimal control problem: we focus on the solution of the optimal control problem for harmonic oscillator serving as a model for Phillips business cycle. We discuss the economic interpretations of arising mathematical objects with respect to well known reasoning for these in other problems.
Quantum Dynamics of a Harmonic Oscillator in a Defomed Bath in the Presence of Lamb Shift
NASA Astrophysics Data System (ADS)
Daeimohamad, M.; Mohammadi, M.
2012-10-01
In this paper, we investigate the dissipative quantum dynamics of a harmonic oscillator in the presence a deformed bath by considering the Lamb shift term. The deformed bath is modelled by a collection of deformed quantum harmonic oscillators as a generalization of Hopfield model. The Langevin equation for both the photon number and the fluctuation spectrum under the Weisskopf-Winger approximation are obtained and discussed.
Probing deformed commutators with macroscopic harmonic oscillators
Bawaj, Mateusz; Biancofiore, Ciro; Bonaldi, Michele; Bonfigli, Federica; Borrielli, Antonio; Di Giuseppe, Giovanni; Marconi, Lorenzo; Marino, Francesco; Natali, Riccardo; Pontin, Antonio; Prodi, Giovanni A.; Serra, Enrico; Vitali, David; Marin, Francesco
2015-01-01
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters have just been extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high-quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass mP (≈22 μg). The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation. PMID:26088965
Probing deformed commutators with macroscopic harmonic oscillators.
Bawaj, Mateusz; Biancofiore, Ciro; Bonaldi, Michele; Bonfigli, Federica; Borrielli, Antonio; Di Giuseppe, Giovanni; Marconi, Lorenzo; Marino, Francesco; Natali, Riccardo; Pontin, Antonio; Prodi, Giovanni A; Serra, Enrico; Vitali, David; Marin, Francesco
2015-01-01
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters have just been extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high-quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass mP (≈ 22 μg). The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation. PMID:26088965
Harmonic oscillator in quantum rotational spectra: Molecules and nuclei
NASA Technical Reports Server (NTRS)
Pavlichenkov, Igor M.
1995-01-01
The mapping of a rotational dynamics on a harmonic oscillator is considered. The method used for studying the stabilization of the rigid top rotation around the intermediate moment of inertial axix by orbiting particle is described.
A harmonic oscillator having “volleyball damping”
NASA Astrophysics Data System (ADS)
Mickens, R. E.; Oyedeji, K.; Rucker, S. A.
2006-05-01
Volleyball damping corresponds to linear damping up to a certain critical velocity, with zero damping above this value. The dynamics of a linear harmonic oscillator is investigated with this damping mechanism.
Kraus representation of a damped harmonic oscillator and its application
Liu Yuxi; Oezdemir, Sahin K.; Miranowicz, Adam; Imoto, Nobuyuki
2004-10-01
By definition, the Kraus representation of a harmonic oscillator suffering from the environment effect, modeled as the amplitude damping or the phase damping, is directly given by a simple operator algebra solution. As examples and applications, we first give a Kraus representation of a single qubit whose computational basis states are defined as bosonic vacuum and single particle number states. We further discuss the environment effect on qubits whose computational basis states are defined as the bosonic odd and even coherent states. The environment effects on entangled qubits defined by two different kinds of computational basis are compared with the use of fidelity.
Phase of the quantum harmonic oscillator with applications to optical polarization
NASA Technical Reports Server (NTRS)
Shepard, Scott R.
1993-01-01
The phase of the quantum harmonic oscillator, the temporal distribution of a particle in a square-well potential, and a quantum theory of angles are derived from a general theory of complementarity. Schwinger's harmonic oscillator model of angular momenta is modified for the case of photons. Angular distributions for systems of identical and distinguishable particles are discussed. Unitary and antiunitary time reversal operators are then presented and applied to optical polarization states in birefringent media.
The Study of Damped Harmonic Oscillations Using an Electronic Counter
ERIC Educational Resources Information Center
Wadhwa, Ajay
2009-01-01
We study damped harmonic oscillations in mechanical systems like the loaded spring and simple pendulum with the help of an oscillation measuring electronic counter. The experimental data are used in a software program that solves the differential equation for damped vibrations of any system and determines its position, velocity and acceleration as…
Calculation of four-particle harmonic-oscillator transformation brackets
NASA Astrophysics Data System (ADS)
Germanas, D.; Kalinauskas, R. K.; Mickevičius, S.
2010-02-01
A procedure for precise calculation of the three- and four-particle harmonic-oscillator (HO) transformation brackets is presented. The analytical expressions of the four-particle HO transformation brackets are given. The computer code for the calculations of HO transformation brackets proves to be quick, efficient and produces results with small numerical uncertainties. Program summaryProgram title: HOTB Catalogue identifier: AEFQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1247 No. of bytes in distributed program, including test data, etc.: 6659 Distribution format: tar.gz Programming language: FORTRAN 90 Computer: Any computer with FORTRAN 90 compiler Operating system: Windows, Linux, FreeBSD, True64 Unix RAM: 8 MB Classification: 17.17 Nature of problem: Calculation of the three-particle and four-particle harmonic-oscillator transformation brackets. Solution method: The method is based on compact expressions of the three-particle harmonics oscillator brackets, presented in [1] and expressions of the four-particle harmonics oscillator brackets, presented in this paper. Restrictions: The three- and four-particle harmonic-oscillator transformation brackets up to the e=28. Unusual features: Possibility of calculating the four-particle harmonic-oscillator transformation brackets. Running time: Less than one second for the single harmonic-oscillator transformation bracket. References:G.P. Kamuntavičius, R.K. Kalinauskas, B.R. Barret, S. Mickevičius, D. Germanas, Nuclear Physics A 695 (2001) 191.
Petrenko, Taras; Neese, Frank
2012-12-21
In this work, an improved method for the efficient automatic simulation of optical band shapes and resonance Raman (rR) intensities within the "independent mode displaced harmonic oscillator" is described. Despite the relative simplicity of this model, it is able to account for the intensity distribution in absorption (ABS), fluorescence, and rR spectra corresponding to strongly dipole allowed electronic transitions with high accuracy. In order to include temperature-induced effects, we propose a simple extension of the time dependent wavepacket formalism developed by Heller which enables one to derive analytical expressions for the intensities of hot bands in ABS and rR spectra from the dependence of the wavepacket evolution on its initial coordinate. We have also greatly optimized the computational procedures for numerical integration of complicated oscillating integrals. This is important for efficient simulations of higher-order rR spectra and excitation profiles, as well as for the fitting of experimental spectra of large molecules. In particular, the multimode damping mechanism is taken into account for efficient reduction of the upper time limit in the numerical integration. Excited state energy gradient as well as excited state geometry optimization calculations are employed in order to determine excited state dimensionless normal coordinate displacements. The gradient techniques are highly cost-effective provided that analytical excited state derivatives with respect to nuclear displacements are available. Through comparison with experimental spectra of some representative molecules, we illustrate that the gradient techniques can even outperform the geometry optimization method if the harmonic approximation becomes inadequate. PMID:23267471
Noninvariance groups for many-particle systems: Coupled harmonic oscillators
NASA Astrophysics Data System (ADS)
Kellman, Michael E.
1984-07-01
Noninvariance groups for many-particle systems are investigated in the context of the model problem of the coupling of a pair of harmonic oscillators to give normal modes. First, a recent paper analyzing normal modes in terms of breaking of the SU(2) invariance symmetry of the uncoupled system is reviewed. Next, the noninvariance group description of the one-dimensional oscillator spectrum in terms of infinite-dimensional unitary representations of SU(1,1) is summarized. Then, the analysis of normal modes in terms of a broken noninvariance SU(2,1) group for the two-dimensional problem is carried out. First, the T, U, and V SU(2) subgroup classifications of SU(3) are reviewed in the context of representations for the three-dimensional oscillator. Second, the analogous SU(2) and SU(1,1) subgroup classification of the infinite two-dimensional spectrum is presented. The SU(1,1) groups classify infinite sequences of excitation of the symmetric and antisymmetric stretch, respectively. Then, in an alternate approach, SU(1,1) representations for the spectra of the individual oscillators are coupled, analogous to vector coupling of angular momentum. Normal modes can be obtained in this manner, but only in the limit in which an arbitrary parameter labeling the group representations takes the value infinity. The relation of these results to the theory of group contractions and their implications for the description of truncated spectra (such as coupled Morse oscillators or π-electron spectra of linear polyenes) are briefly discussed.
First-harmonic approximation in nonlinear chirped-driven oscillators.
Uzdin, Raam; Friedland, Lazar; Gat, Omri
2014-01-01
Nonlinear classical oscillators can be excited to high energies by a weak driving field provided the drive frequency is properly chirped. This process is known as autoresonance (AR). We find that for a large class of oscillators, it is sufficient to consider only the first harmonic of the motion when studying AR, even when the dynamics is highly nonlinear. The first harmonic approximation is also used to relate AR in an asymmetric potential to AR in a "frequency equivalent" symmetric potential and to study the autoresonance breakdown phenomenon. PMID:24580292
Single trapped ion as a time-dependent harmonic oscillator
Menicucci, Nicolas C.; Milburn, G. J.
2007-11-15
We show how a single trapped ion may be used to test a variety of important physical models realized as time-dependent harmonic oscillators. The ion itself functions as its own motional detector through laser-induced electronic transitions. Alsing et al., [Phys. Rev. Lett. 94, 220401 (2005)] proposed that an exponentially decaying trap frequency could be used to simulate (thermal) Gibbons-Hawking radiation in an expanding universe, but the Hamiltonian used was incorrect. We apply our general solution to this experimental proposal, correcting the result for a single ion and showing that while the actual spectrum is different from the Gibbons-Hawking case, it nevertheless shares an important experimental signature with this result.
34 GHz second-harmonic peniotron oscillator
NASA Astrophysics Data System (ADS)
Dressman, Lawrence Jude
Harmonic operation of gyro-devices has been proposed as a way to lower the magnetic field required to a level feasible with normal (i.e., non-superconducting) magnets. The problem is, however, that gyrotron efficiency drops dramatically at harmonics greater than two, making development of such a device of limited utility. A promising solution to this quandary is the development of a related device, the peniotron, which is believed capable of achieving both high efficiency and harmonic operation resulting in a reduction of the required axial magnetic field. Although the physics of the peniotron interaction, including its high electronic conversion efficiency, has been understood and experimentally verified, demonstration of characteristics consistent with a practical device has been more elusive. This is the goal of this effort---specifically, to demonstrate high device efficiency (defined as the actual power output as a fraction of the electron beam power) with an electron beam generated by a compact cusp electron gun consistent in size and performance with other microwave vacuum electron devices. The cavity design process revealed that the pi/2 mode couples easily to the output circular waveguide. In fact, the transition to circular waveguide produced such a low reflection coefficient that an iris was needed at the cavity output to achieve the desired Q. Integral couplers were also designed to couple directly into the slotted cavity for diagnostic purposes for simplicity in this proof-of-principle physics experiment. This eliminated the need for a high-power circular vacuum window and allowed the diagnostic coupling to be made in standard WR-28 rectangular waveguide. Although mode competition did prevent the second-harmonic peniotron mode from being tuned over its entire range of magnetic field, the peniotron mode was stable over a range sufficient to allow useful experimental data to be obtained. However, another unexpected problem which occurred during execution
Asymptotic Formula for Quantum Harmonic Oscillator Tunneling Probabilities
NASA Astrophysics Data System (ADS)
Jadczyk, Arkadiusz
2015-10-01
Using simple methods of asymptotic analysis it is shown that for a quantum harmonic oscillator in n-th energy eigenstate the probability of tunneling into the classically forbidden region obeys an unexpected but simple asymptotic formula: the leading term is inversely proportional to the cube root of n.
Simulating Harmonic Oscillator and Electrical Circuits: A Didactical Proposal
ERIC Educational Resources Information Center
Albano, Giovannina; D'Apice, Ciro; Tomasiello, Stefania
2002-01-01
A Mathematica[TM] package is described that uses simulations and animations to illustrate key concepts in harmonic oscillation and electric circuits for students not majoring in physics or mathematics. Students are not required to know the Mathematica[TM] environment: a user-friendly interface with buttons functionalities and on-line help allows…
The One-Dimensional Damped Forced Harmonic Oscillator Revisited
ERIC Educational Resources Information Center
Flores-Hidalgo, G.; Barone, F. A.
2011-01-01
In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.
Symmetry algebra of a generalized anisotropic harmonic oscillator
NASA Technical Reports Server (NTRS)
Castanos, O.; Lopez-Pena, R.
1993-01-01
It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.
Franck-Condon factors for multidimensional harmonic oscillators
NASA Astrophysics Data System (ADS)
Malmqvist, Per-Åke; Forsberg, Niclas
1998-03-01
We present a simple formula for the overlap integrals of two sets of multi-dimensional harmonic oscillators. The oscillators have in general different equilibrium points, force constants, and natural vibration modes. The formula expresses the overlap matrix in the one-dimensional case, < m'| n''>, as a so-called LU decomposition,
New stochastic equation for a harmonic oscillator: Brownian motion with adhesion
NASA Astrophysics Data System (ADS)
Gitterman, M.
2010-11-01
In addition to the usually considered stochastic harmonic oscillator with an external random force (Brownian motion) or with random frequency and random damping, we consider an oscillator with a random mass for which the particles of the surrounding medium adhere to the oscillator for some (random) time after the collision, thereby changing the oscillator mass. We have calculated the first two moments and the Lyapunov exponent, which describes the stability of the fixed point. This model can be useful for the analysis of chemical and biological solutions as well as for nano-technological devices.
The q-harmonic oscillators, q-coherent states and the q-symplecton
NASA Technical Reports Server (NTRS)
Biedenharn, L. C.; Lohe, M. A.; Nomura, Masao
1993-01-01
The recently introduced notion of a quantum group is discussed conceptually and then related to deformed harmonic oscillators ('q-harmonic oscillators'). Two developments in applying q-harmonic oscillators are reviewed: q-coherent states and the q-symplecton.
Harmonic oscillations and their switching in elliptical optical waveguide arrays
NASA Astrophysics Data System (ADS)
Jie Zheng, Ming; San Chan, Yun; Yu, Kin Wah
2011-03-01
We have studied harmonic oscillations in an elliptical optical waveguide array in which the coupling between neighboring waveguides is varied in accord with a Kac matrix so that the propagation constant eigenvalues can take equally spaced values. As a result, long-living Bloch oscillations (BO) and dipole oscillations (DO) are obtained when a linear gradient in the propagation constant is applied. Moreover, we achieve a switching from DO to BO or vice versa by ramping up the gradient profile. The various optical oscillations as well as their switching are investigated by field-evolution analysis and confirmed by Hamiltonian optics. The equally spaced eigenvalues in the propagation constant allow viable applications in transmitting images, switching and routing of optical signals.
Time-Dependent Coupled Harmonic Oscillators: Classical and Quantum Solutions
NASA Astrophysics Data System (ADS)
Macedo, Diego Ximenes; Guedes, Ilde
2015-10-01
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 invariant method. The exact wave functions are obtained by solving the respective Milne-Pinney equation for each system. We obtain the solutions for the system with m1 = m2 = m0eγt, ω1 = ω01e-γt/2, ω2 = ω02e-γt/2 and k = k0.
Time-dependent coupled harmonic oscillators: Classical and quantum solutions
NASA Astrophysics Data System (ADS)
Macedo, D. X.; Guedes, I.
2014-08-01
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 m1 = m2 = m0eγt, ω1 = ω01e-γt/2, ω2 = ω02e-γt/2 and k = k0.
Reaching Synchronization in Networked Harmonic Oscillators With Outdated Position Data.
Song, Qiang; Yu, Wenwu; Cao, Jinde; Liu, Fang
2016-07-01
This paper studies the synchronization problem for a network of coupled harmonic oscillators by proposing a distributed control algorithm based only on delayed position states, i.e., outdated position states stored in memory. The coupling strength of the network is conveniently designed according to the absolute values and the principal arguments of the nonzero eigenvalues of the network Laplacian matrix. By analyzing a finite number of stability switches of the network with respect to the variation in the time delay, some necessary and sufficient conditions are derived for reaching synchronization in networked harmonic oscillators with positive and negative coupling strengths, respectively, and it is shown that the time delay should be taken from a set of intervals bounded by some critical values. Simulation examples are given to illustrate the effectiveness of the theoretical analysis. PMID:26241985
First, Second Quantization and Q-Deformed Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Van Ngu, Man; Gia Vinh, Ngo; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Viet, Nguyen Ai
2015-06-01
Relations between the first, the second quantized representations and deform algebra are investigated. In the case of harmonic oscillator, the axiom of first quantization (the commutation relation between coordinate and momentum operators) and the axiom of second quantization (the commutation relation between creation and annihilation operators) are equivalent. We shown that in the case of q-deformed harmonic oscillator, a violence of the axiom of second quantization leads to a violence of the axiom of first quantization, and inverse. Using the coordinate representation, we study fine structures of the vacuum state wave function depend in the deformation parameter q. A comparison with fine structures of Cooper pair of superconductivity in the coordinate representation is also performed.
High gain amplifiers: Power oscillations and harmonic generation
Dattoli, G.; Ottaviani, P. L.; Pagnutti, S.
2007-08-01
We discuss the power oscillations in saturated high gain free electron laser amplifiers and show that the relevant period can be written in terms of the gain length. We use simple arguments following from the solution of the pendulum equation in terms of Jacobi elliptic functions. Nontrivial effects due to nonlinear harmonic generation and inhomogeneous broadening are discussed too, as well as the saturated dynamics of short pulses.
Fisher Information and Shannon Entropy in Confined 1D Harmonic Oscillator
Stevanovic, Ljiljana
2010-01-21
Study of the linear harmonic oscillator confined in the square well with impenetrable walls is of great interest since its application for modeling parabolic quantum well semiconductor heterostructures. Fisher information and Shannon entropy, as a complexity measure for its ground and some excited energy levels are reported here.
Decoherence and dissipation of a quantum harmonic oscillator coupled to two-level systems
Schlosshauer, Maximilian; Hines, A. P.; Milburn, G. J.
2008-02-15
We derive and analyze the Born-Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a fundamental role as one of the four 'canonical' system-environment models for decoherence and dissipation. To investigate the influence of further couplings of the environmental spins to a dissipative bath, we also derive the master equation for a harmonic oscillator interacting with a single spin coupled to a bosonic bath. Our models are experimentally motivated by quantum-electromechanical systems and micron-scale ion traps. Decoherence and dissipation rates are found to exhibit temperature dependencies significantly different from those in quantum Brownian motion. In particular, the systematic dissipation rate for the central oscillator decreases with increasing temperature and goes to zero at zero temperature, but there also exists a temperature-independent momentum-diffusion (heating) rate.
Pisot q-coherent states quantization of the harmonic oscillator
Gazeau, J.P.; Olmo, M.A. del
2013-03-15
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories. - Highlights: Black-Right-Pointing-Pointer Quantized version of the harmonic oscillator (HO) through a q-family of coherent states. Black-Right-Pointing-Pointer For q,0
oscillator.
The time-dependent quantum harmonic oscillator revisited: Applications to quantum field theory
Gomez Vergel, Daniel Villasenor, Eduardo J.S.
2009-06-15
In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a single one-dimensional time-dependent oscillator, for which we first summarize some basic results concerning the unitary implementability of the dynamics. This is done by employing techniques different from those used so far to derive the Feynman propagator. In particular, we calculate the transition amplitudes for the usual harmonic oscillator eigenstates and define suitable semiclassical states for some physically relevant models. We then explore the possible extension of this study to infinite dimensional dynamical systems. Specifically, we construct Schroedinger functional representations in terms of appropriate probability spaces, analyze the unitarity of the time evolution, and probe the existence of semiclassical states for a wide range of physical systems, particularly, the well-known Minkowskian free scalar fields and Gowdy cosmological models.
MODEL HARMONIZATION POTENTIAL AND BENEFITS
The IPCS Harmonization Project, which is currently ongoing under the auspices of the WHO, in the context of chemical risk assessment or exposure modeling, does not imply global standardization. Instead, harmonization is thought of as an effort to strive for consistency among appr...
Information theories for time-dependent harmonic oscillator
Choi, Jeong Ryeol; Kim, Min-Soo; Kim, Daeyeoul; Maamache, Mustapha; Menouar, Salah; Nahm, In Hyun
2011-06-15
Highlights: > Information theories for the general time-dependent harmonic oscillator based on invariant operator method. > Time dependence of entropies and entropic uncertainty relation. > Characteristics of Shannon information and Fisher information. > Application of information theories to particular systems that have time-dependent behavior. - Abstract: Information theories for the general time-dependent harmonic oscillator are described on the basis of invariant operator method. We obtained entropic uncertainty relation of the system and discussed whether it is always larger than or equal to the physically allowed minimum value. Shannon information and Fisher information are derived by means of density operator that satisfies Liouville-von Neumann equation and their characteristics are investigated. Shannon information is independent of time, but Fisher information is explicitly dependent on time as the time functions of the Hamiltonian vary. We can regard that the Fisher information is a local measure since its time behavior is largely affected by local arrangements of the density, whilst the Shannon information plays the role of a global measure of the spreading of density. To promote the understanding, our theory is applied to special systems, the so-called quantum oscillator with time-dependent frequency and strongly pulsating mass system.
Argand diagrams, harmonic oscillators, and record-playing tonearms
NASA Astrophysics Data System (ADS)
Piccard, Richard D.
1986-04-01
The complex analysis of the driven, damped, harmonic oscillator is reviewed for the specific case that the driving force is produced by ``wiggling the other end of the spring,'' a case which many find intuitively appealing. The solution is examined using the Cartesian and polar presentations in the complex plane. The record-playing tonearm is particularly suited as a ``practical example'' because it naturally leads to a question that is much easier to answer in terms of the Argand diagram: What will the cartridge output be?
Quantum entanglement in coupled harmonic oscillator systems: from micro to macro
NASA Astrophysics Data System (ADS)
Kao, Jhih-Yuan; Chou, Chung-Hsien
2016-07-01
We investigate the entanglement dynamics of several models of coupled harmonic oscillators, whereby a number of properties concerning entanglement have been scrutinized, such as how the environment affects entanglement of a system, and death and revival of entanglement. Among them, there are two models for which we are able to vary their particle numbers easily by assuming identicalness, thereby examining how the particle number affects entanglement. We have found that the upper bound of entanglement between identical oscillators is approximately inversely proportional to the particle number.
A 95 GHz, 4th harmonic gyro-oscillator
Hargreaves, T.A.; Scheitrum, G.P.; Bemis, T.; Higgins, L.
1994-12-31
There is currently an interest in medium power ({approximately}100 kW), compact 95 GHz amplifiers for future radar applications. Size, weight, and efficiency are critical for airborne applications. Litton has been investigating a 4th harmonic, 4-cavity gyro-amplifier. The key to success of the amplifier is the axis-encircling electron beam from a new type of electron gun, the advanced center post (ACP) gun. Gun simulations incorporating the actual magnetic field and thermal velocity spread in the emitted electrons show that axial velocity spreads of less than 2% are attainable, which is significantly better than other gun concepts. The amplifier utilizes coaxial-magnetron-type cavities operating in the {pi} mode. In this cavity, vanes extend nearly down to the electron beam`s outside diameter. The majority of the RF stored energy in the system is in the coaxial cavity, so that the resonant frequency and quality factor of each coaxial magnetron cavity may be adjusted by varying only the coaxial cavity. Several components are being tested individually. To test the cavity design, a 4th harmonic oscillator based on a coaxial magnetron cavity has been designed. Results of the oscillator testing will be presented.
Non-unique monopole oscillations of harmonically confined Yukawa systems
NASA Astrophysics Data System (ADS)
Ducatman, Samuel; Henning, Christian; Kaehlert, Hanno; Bonitz, Michael
2008-11-01
Recently it was shown that the Breathing Mode (BM), the mode of uniform radial expansion and contraction, which is well known from harmonically confined Coulomb systems [1], does not exist in general for other systems [2]. As a consequence the monopole oscillation (MO), the radial collective excitation, is not unique, but there are several MO with different frequencies. Within this work we show simulation results of those monopole oscillations of 2-dimensional harmonically confined Yukawa systems, which are known from, e.g., dusty plasma crystals [3,4]. We present the corresponding spectrum of the particle motion, including analysis of the frequencies found, and compare with theoretical investigations.[1] D.H.E. Dubin and J.P. Schiffer, Phys. Rev. E 53, 5249 (1996)[2] C. Henning at al., accepted for publication in Phys. Rev. Lett. (2008)[3] A. Melzer et al., Phys. Rev. Lett. 87, 115002 (2001)[4] M. Bonitz et al., Phys. Rev. Lett. 96, 075001 (2006)
Entanglement dynamics for a conditionally kicked harmonic oscillator
NASA Astrophysics Data System (ADS)
Arrais, Eric G.; Sales, J. S.; de Almeida, N. G.
2016-08-01
The time evolution of the quantum kicked harmonic oscillator (KHO) is described by the Floquet operator which maps the state of the system immediately before one kick onto the state at a time immediately after the next. Quantum KHO is characterized by three parameters: the coupling strength V 0, the so-called Lamb–Dicke parameter η whose square is proportional to the effective Planck constant {{\\hslash }}{{eff}}, and the ratio T of the natural frequency of the oscillator and the kick frequency. To a given coupling strength and depending on T being a natural or irrational number, the phase space of the classical kicked oscillator can display different behaviors, as for example, stochastic webs or quasicrystal structures, thus showing a chaotic or localized behavior that is mirrored in the quantum phase space. On the other hand, the classical limit is studied letting {{\\hslash }}{{eff}} become negligible. In this paper we investigate how the ratio T, considered as integer, rational or irrational, influences the entanglement dynamics of the quantum KHO and study how the entanglement dynamics behaves when varying either V 0 or {{\\hslash }}{{eff}} parameters.
Oscillator Seeding of a High Gain Harmonic Generation FEL in a Radiator-First Configuration
Gandhi, P.; Wurtele, J.; Penn, G.; Reinsch, M.
2012-05-20
A longitudinally coherent X-ray pulse from a high repetition rate free electron laser (FEL) is desired for a wide variety of experimental applications. However, generating such a pulse with a repetition rate greater than 1 MHz is a significant challenge. The desired high repetition rate sources, primarily high harmonic generation with intense lasers in gases or plasmas, do not exist now, and, for the multi-MHz bunch trains that superconducting accelerators can potentially produce, are likely not feasible with current technology. In this paper, we propose to place an oscillator downstream of a radiator. The oscillator generates radiation that is used as a seed for a high gain harmonic generation (HGHG) FEL which is upstream of the oscillator. For the first few pulses the oscillator builds up power and, until power is built up, the radiator has no HGHG seed. As power in the oscillator saturates, the HGHG is seeded and power is produced. The dynamics and stability of this radiator-first scheme is explored analytically and numerically. A single-pass map is derived using a semi-analytic model for FEL gain and saturation. Iteration of the map is shown to be in good agreement with simulations. A numerical example is presented for a soft X-ray FEL.
Fastest Effectively Adiabatic Transitions for a Collection of Harmonic Oscillators.
Boldt, Frank; Salamon, Peter; Hoffmann, Karl Heinz
2016-05-19
We discuss fastest effectively adiabatic transitions (FEATs) for a collection of noninteracting harmonic oscillators with shared controllable real frequencies. The construction of such transitions is presented for given initial and final equilibrium states, and the dependence of the minimum time control on the interval of achievable frequencies is discussed. While the FEAT times and associated FEAT processes are important in their own right as optimal controls, the FEAT time is an added feature which provides a measure of the quality of a shortcut to adiabaticity (STA). The FEAT time is evaluated for a previously reported experiment, wherein a cloud of Rb atoms is cooled following a STA recipe that took about twice as long as the FEAT speed limit, a time efficiency of 50%. PMID:26811863
Quantum Harmonic Oscillator Subjected to Quantum Vacuum Fluctuations
NASA Astrophysics Data System (ADS)
Gevorkyan, A. S.; Burdik, C.; Oganesyan, K. B.
2010-05-01
Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy level, as well as many other phenomena in real nonrelativistic quantum systems are connected with the influence of quantum vacuum fluctuations which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum harmonic oscillator (QHO) + environment" is described in terms of complex probabilistic processes (CPP) which satisfies a stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type. On the basis of orthogonal CPP, the method of stochastic density matrix (SDM) is developed. The energy spectrum of QHO and a possibility of infringement of detailed balance of transitions between quantum levels including spontaneous decay of ≪ground state≫ are investigated by the SDM method.
ERIC Educational Resources Information Center
Earl, Boyd L.
2008-01-01
A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…
Exact solution of a quantum forced time-dependent harmonic oscillator
NASA Technical Reports Server (NTRS)
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
1992-01-01
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
Feinberg-Horodecki states of a time-dependent mass distribution harmonic oscillator
NASA Astrophysics Data System (ADS)
Eshghi, M.; Sever, R.; Ikhdair, S. M.
2016-07-01
The solution of the Feinberg-Horodecki (FH) equation for a time-dependent mass (TDM) harmonic oscillator quantum system is studied. A certain interaction is applied to a mass m(t) to provide a particular spectrum of stationary energies. The related spectrum of the harmonic oscillator potential V(t) acting on the TDM m(t) oscillators is found. We apply the time version of the asymptotic iteration method (AIM) to calculate analytical expressions of the TDM stationary state energies and their wave functions. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the time-dependent mass reduces to m0.
Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator
NASA Astrophysics Data System (ADS)
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.
Cooper pair of superconductivity in the coordinate representation and q-deformed harmonic oscillator
NASA Astrophysics Data System (ADS)
Van Ngu, Man; Gia Vinh, Ngo; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Viet, Nguyen Ai
2016-06-01
In this work we study the similarity between the wave functions of q -deformed harmonic oscillator and wave functions of Cooper pair. The wave functions of Cooper pairs in coordinate-space have an “onion-like” layered structure with exponent decay (Boltzmann) envelope modulation. The ground state wave function of q -deform harmonic oscillator has the form of oscillate functions with Gaussian decay envelope modulation. The corresponding between Boltzmann and Gaussian forms of envelope functions and their quantum similarity are discussed.
Novel Approach for Solving the Equation of Motion of a Simple Harmonic Oscillator. Classroom Notes
ERIC Educational Resources Information Center
Gauthier, N.
2004-01-01
An elementary method, based on the use of complex variables, is proposed for solving the equation of motion of a simple harmonic oscillator. The method is first applied to the equation of motion for an undamped oscillator and it is then extended to the more important case of a damped oscillator. It is finally shown that the method can readily be…
Inverse Problem for Harmonic Oscillator Perturbed by Potential, Characterization
NASA Astrophysics Data System (ADS)
Chelkak, Dmitri; Kargaev, Pavel; Korotyaev, Evgeni
Consider the perturbed harmonic oscillator Ty=-y''+x2y+q(x)y in L2(R), where the real potential q belongs to the Hilbert space H={q', xq∈ L2(R)}. The spectrum of T is an increasing sequence of simple eigenvalues λn(q)=1+2n+μn, n >= 0, such that μn--> 0 as n-->∞. Let ψn(x,q) be the corresponding eigenfunctions. Define the norming constants νn(q)=limx↑∞log |ψn (x,q)/ψn (-x,q)|. We show that for some real Hilbert space and some subspace Furthermore, the mapping ψ:q|-->ψ(q)=({λn(q)}0∞, {νn(q)}0∞) is a real analytic isomorphism between H and is the set of all strictly increasing sequences s={sn}0∞ such that The proof is based on nonlinear functional analysis combined with sharp asymptotics of spectral data in the high energy limit for complex potentials. We use ideas from the analysis of the inverse problem for the operator -y''py, p∈ L2(0,1), with Dirichlet boundary conditions on the unit interval. There is no literature about the spaces We obtain their basic properties, using their representation as spaces of analytic functions in the disk.
Optical-parametric-oscillator solitons driven by the third harmonic.
Lutsky, Vitaly; Malomed, Boris A
2004-12-01
We introduce a model of a lossy second-harmonic-generating (chi(2)) cavity externally pumped at the third harmonic, which gives rise to driving terms of a new type, corresponding to a cross-parametric gain. The equation for the fundamental-frequency (FF) wave may also contain a quadratic self-driving term, which is generated by the cubic nonlinearity of the medium. Unlike previously studied phase-matched models of chi(2) cavities driven at the second harmonic or at FF, the present one admits an exact analytical solution for the soliton, at a special value of the gain parameter. Two families of solitons are found in a numerical form, and their stability area is identified through numerical computation of the perturbation eigenvalues (stability of the zero solution, which is a necessary condition for the soliton's stability, is investigated in an analytical form). One family is a continuation of the special analytical solution. At given values of the parameters, one soliton is stable and the other one is not; they swap their stability at a critical value of the mismatch parameter. The stability of the solitons is also verified in direct simulations, which demonstrate that an unstable pulse rearranges itself into a stable one, or into a delocalized state, or decays to zero. A soliton which was given an initial boost C starts to move but quickly comes to a halt, if the boost is smaller than a critical value C(cr) . If C > C(cr) , the boost destroys the soliton (sometimes, through splitting into two secondary pulses). Interactions between initially separated solitons are investigated, too. It is concluded that stable solitons always merge into a single one. In the system with weak loss, it appears in a vibrating form, slowly relaxing to the static shape. With stronger loss, the final soliton emerges in the stationary form. PMID:15697523
Optical-parametric-oscillator solitons driven by the third harmonic
NASA Astrophysics Data System (ADS)
Lutsky, Vitaly; Malomed, Boris A.
2004-12-01
We introduce a model of a lossy second-harmonic-generating (χ(2)) cavity externally pumped at the third harmonic, which gives rise to driving terms of a new type, corresponding to a cross-parametric gain. The equation for the fundamental-frequency (FF) wave may also contain a quadratic self-driving term, which is generated by the cubic nonlinearity of the medium. Unlike previously studied phase-matched models of χ(2) cavities driven at the second harmonic or at FF, the present one admits an exact analytical solution for the soliton, at a special value of the gain parameter. Two families of solitons are found in a numerical form, and their stability area is identified through numerical computation of the perturbation eigenvalues (stability of the zero solution, which is a necessary condition for the soliton’s stability, is investigated in an analytical form). One family is a continuation of the special analytical solution. At given values of the parameters, one soliton is stable and the other one is not; they swap their stability at a critical value of the mismatch parameter. The stability of the solitons is also verified in direct simulations, which demonstrate that an unstable pulse rearranges itself into a stable one, or into a delocalized state, or decays to zero. A soliton which was given an initial boost C starts to move but quickly comes to a halt, if the boost is smaller than a critical value Ccr . If C>Ccr , the boost destroys the soliton (sometimes, through splitting into two secondary pulses). Interactions between initially separated solitons are investigated, too. It is concluded that stable solitons always merge into a single one. In the system with weak loss, it appears in a vibrating form, slowly relaxing to the static shape. With stronger loss, the final soliton emerges in the stationary form.
ERIC Educational Resources Information Center
Nicolaides, Cleanthes A.; Constantoudis, Vasilios
2009-01-01
In Planck's model of the harmonic oscillator (HO) a century ago, both the energy and the phase space were quantized according to epsilon[subscript n] = nhv, n = 0, 1, 2..., and [double integral]dp[subscript x] dx = h. By referring to just these two relations, we show how the adoption of "cycle-averaged phase-space states" (CAPSSs) leads to the…
Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons
Menikoff, Ralph
2014-09-02
A complete equation of state (EOS) for a molecular solid is derived utilizing a Helmholtz free energy. Assuming that the solid is nonconducting, phonon excitations dominate the specific heat. Phonons are approximated as independent quasi-harmonic oscillators with vibrational frequencies depending on the specific volume. The model is suitable for calibrating an EOS based on isothermal compression data and infrared/Raman spectroscopy data from high pressure measurements utilizing a diamond anvil cell. In contrast to a Mie-Gruneisen EOS developed for an atomic solid, the specific heat and Gruneisen coefficient depend on both density and temperature.
Wood, William E.; Osseward, Peter J.; Roseberry, Thomas K.; Perkel, David J.
2013-01-01
Complex motor skills are more difficult to perform at certain points in the day (for example, shortly after waking), but the daily trajectory of motor-skill error is more difficult to predict. By undertaking a quantitative analysis of the fundamental frequency (FF) and amplitude of hundreds of zebra finch syllables per animal per day, we find that zebra finch song follows a previously undescribed daily oscillation. The FF and amplitude of harmonic syllables rises across the morning, reaching a peak near mid-day, and then falls again in the late afternoon until sleep. This oscillation, although somewhat variable, is consistent across days and across animals and does not require serotonin, as animals with serotonergic lesions maintained daily oscillations. We hypothesize that this oscillation is driven by underlying physiological factors which could be shared with other taxa. Song production in zebra finches is a model system for studying complex learned behavior because of the ease of gathering comprehensive behavioral data and the tractability of the underlying neural circuitry. The daily oscillation that we describe promises to reveal new insights into how time of day affects the ability to accomplish a variety of complex learned motor skills. PMID:24312654
Dynamics in the Kuramoto model with a bi-harmonic coupling function
NASA Astrophysics Data System (ADS)
Yuan, Di; Cui, Haitao; Tian, Junlong; Xiao, Yi; Zhang, Yingxin
2016-09-01
We study a variant of the Kuramoto model with a bi-harmonic coupling function, in which oscillators with positive first harmonic coupling strength are conformists and oscillators with negative first harmonic coupling strength are contrarians. We show that the model displays different synchronous dynamics and different dynamics may be characterized by the phase distributions of oscillators. There exist stationary synchronous states, travelling wave states, π state and, most interestingly, another type of nonstationary state: an oscillating π state. The phase distribution oscillates in a confined region and the phase difference between conformists and contrarians oscillates around π with a constant amplitude and a constant period in oscillating π state. Finally, the bifurcation diagram of the model in the parameter space is presented.
Purity and decoherence in the theory of a damped harmonic oscillator.
Isar, A; Sandulescu, A; Scheid, W
1999-12-01
For the generalized master equations derived by Karrlein and Grabert for the microscopic model of a damped harmonic oscillator, the conditions for purity of states are written, in particular for different initial conditions and different types of damping, including Ohmic, Drude, and weak coupling cases, and the Agarwal and Weidlich-Haake models. It is shown that the states which remain pure are the squeezed states with variances that are constant in time. For pure states, generalized nonlinear Schrödinger-type equations corresponding to these master equations are also obtained. Then the condition for purity of states of a damped harmonic oscillator is considered in the framework of Lindblad theory for open quantum systems. For a special choice of the environment coefficients, correlated coherent states with constant variances and covariance are shown to be the only states which remain pure all the time during the evolution of the considered system. In Karrlein-Grabert and Lindblad models, as well as in the particular models considered, expressions for the rate of entropy production are written, and it is shown that state which preserve their purity in time are also states which minimize entropy production and, therefore, are the most stable state under evolution in the presence of the environment, and play an important role in the description of decoherence phenomenon. PMID:11970551
Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators
NASA Astrophysics Data System (ADS)
Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong
2016-03-01
Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO.
Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators
Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong
2016-01-01
Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO. PMID:26961962
Floquet topological system based on frequency-modulated classical coupled harmonic oscillators
NASA Astrophysics Data System (ADS)
Salerno, Grazia; Ozawa, Tomoki; Price, Hannah M.; Carusotto, Iacopo
2016-02-01
We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time. Making use of Floquet theory in the high-frequency limit, we identify a regime in which the system is accurately described by a Harper-Hofstadter model where the synthetic magnetic field can be externally tuned via the phase of the frequency modulation of the different oscillators. We illustrate how the topologically protected chiral edge states, as well as the Hofstadter butterfly of bulk bands, can be observed in the driven-dissipative steady state under a monochromatic drive. In analogy with the integer quantum Hall effect, we show how the topological Chern numbers of the bands can be extracted from the mean transverse shift of the steady-state oscillation amplitude distribution. Finally, we discuss the regime where the analogy with the Harper-Hofstadter model breaks down.
The Adiabatic Invariant of the n-Degree-of-Freedom Harmonic Oscillator
ERIC Educational Resources Information Center
Devaud, M.; Leroy, V.; Bacri, J.-C.; Hocquet, T.
2008-01-01
In this graduate-level theoretical paper, we propose a general derivation of the adiabatic invariant of the n-degree-of-freedom harmonic oscillator, available whichever the physical nature of the oscillator and of the parametrical excitation it undergoes. This derivation is founded on the use of the classical Glauber variables and ends up with…
On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress
Bocko, M.F.; Onofrio, R.
1996-07-01
Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them, have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves {ital et} {ital al}., 1980, Rev. Mod. Phys. {bold 52}, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review. {copyright} {ital 1996 The American Physical Society.}
NASA Astrophysics Data System (ADS)
Egorov, A. G.; Kamalutdinov, A. M.; Paimushin, V. N.; Firsov, V. A.
2016-03-01
A method for determining the drag coefficient of a thin plate harmonically oscillating in a viscous incompressible fluid is proposed. The method is based on measuring the amplitude of deflections of cantilever-fixed thin plates exhibiting damping flexural oscillations with a frequency corresponding to the first mode and on solving an inverse problem of calculating the drag coefficient on the basis of the experimentally found logarithmic decrement of beam oscillations.
Microwave Imaging Reflectometry for the study of Edge Harmonic Oscillations on DIII-D
NASA Astrophysics Data System (ADS)
Ren, X.; Chen, M.; Chen, X.; Domier, C. W.; Ferraro, N. M.; Kramer, G. J.; Luhmann, N. C., Jr.; Muscatello, C. M.; Nazikian, R.; Shi, L.; Tobias, B. J.; Valeo, E.
2015-10-01
Quiescent H-mode (QH-mode) is an ELM free mode of operation in which edge-localized harmonic oscillations (EHOs) are believed to enhance particle transport, thereby stabilizing ELMs and preventing damage to the divertor and plasma facing components. Microwave Imaging Reflectometer (MIR) enabling direct comparison between the measured and simulated 2D images of density fluctuations near the edge can determine the 2D structure of density oscillation, which can help to explain the physics behind EHO modes. MIR data sometimes indicate a counter-propagation between dominant (n=1) and higher harmonic modes of coherent EHOs in the steep gradient regions of the pedestal. To preclude diagnostic artifacts, we have performed forward modeling that includes possible optical mis-alignments to show that offsets between transmitting and receiving antennas do not account for this feature. We have also simulated the non-linear structure of the EHO modes, which induces multiple harmonics that are properly charaterized in the synthetic diagnostic. By excluding mis-alignments of optics as well as patially eliminating non-linearity of EHO mode structure as possible explanation for the data, counter-propagation observed in MIR data, which is not corroborated by external Mirnov coil array measurements, may be due to subtleties of the eigenmode structure, such as an inversion radius consistent with a magnetic island. Similar effects are observed in analysis of internal ECE-Imaging and BES data. The identification of a non-ideal structure motivates further exploration of nonlinear models of this instability. A shorter version of this contribution is due to be published in PoS at: 1st EPS conference on Plasma Diagnostics
NASA Astrophysics Data System (ADS)
De Rosis, Alessandro
2014-11-01
In this paper, the fluid dynamics induced by a rigid lamina undergoing harmonic oscillations in a non-Newtonian calm fluid is investigated. The fluid is modelled through the lattice Boltzmann method and the flow is assumed to be nearly incompressible. An iterative viscosity-correction based procedure is proposed to properly account for the non-Newtonian fluid feature and its accuracy is evaluated. In order to handle the mutual interaction between the lamina and the encompassing fluid, the Immersed Boundary method is adopted. A numerical campaign is performed. In particular, the effect of the non-Newtonian feature is highlighted by investigating the fluid forces acting on a harmonically oscillating lamina for different values of the Reynolds number. The findings prove that the non-Newtonian feature can drastically influence the behaviour of the fluid and, as a consequence, the forces acting upon the lamina. Several considerations are carried out on the time history of the drag coefficient and the results are used to compute the added mass through the hydrodynamic function. Moreover, the computational cost involved in the numerical simulations is discussed. Finally, two applications concerning water resources are investigated: the flow through an obstructed channel and the particle sedimentation. Present findings highlight a strong coupling between the body shape, the Reynolds number, and the flow behaviour index.
NASA Astrophysics Data System (ADS)
Dixon, George Jefferies
Spike-mode oscillation of a single-frequency, internally-doubled Nd:YAG laser under conditions of square -wave pump modulation is a potentially interesting technique for increasing the average harmonic conversion efficiency. To investigate this mode of operation, we have designed and built a unidirectional, Nd:YAG ring laser prototype which is capable of single-longitudinal mode oscillation at pump powers which are substantially above threshold. Initial study of this laser with diode-laser-array pumping yielded a maximum continuous-wave (cw) 1064-nm output power of 72 mW at an optical conversion efficiency exceeding 14%. Intracavity second harmonic generation was studied by inserting a crystal of potassium titanyl phosphate (KTP) inside the resonator and replacing the infrared output coupler with a mirror which was highly reflecting at 1064 nm and had high transmission at the 532-nm second harmonic. A maximum cw harmonic output power of 12 mW was observed from the laser at a pump power of 473 mW. Spike-mode oscillation could be achieved in the intracavity-doubled laser through square wave current modulation of the diode laser pump. Under optimal conditions, the average harmonic conversion efficiency was increased by over 100% under spiked conditions. Spike-mode oscillation with significant intracavity nonlinear coupling was observed to differ substantially from that of laser without the nonlinear crystal. The power-dependent harmonic output coupling had the effect of damping out relaxation oscillations and substantially limiting the peak spiked power. It was also observed to increase the amplitude and temporal stability of the spike pulse train and significantly increase the frequency range over which spiked oscillation would occur. A set of coupled rate equations relating the single -mode intracavity field to the gain in the laser medium was used to model the spike-mode oscillations of the intracavity -doubled ring. Numerical methods were used to obtain solutions
On harmonic oscillators and their Kemmer relativistic forms
NASA Technical Reports Server (NTRS)
Debergh, Nathalie; Beckers, Jules
1993-01-01
It is shown that Dirac (Kemmer) equations are intimately connected with (para)supercharges coming from (para)supersymmetric quantum mechanics, a nonrelativistic theory. The dimensions of the irreducible representations of Clifford (Kemmer) algebras play a fundamental role in such an analysis. These considerations are illustrated through oscillator like interactions, leading to (para)relativistic oscillators.
A neural network model of harmonic detection
NASA Astrophysics Data System (ADS)
Lewis, Clifford F.
2003-04-01
Harmonic detection theories postulate that a virtual pitch is perceived when a sufficient number of harmonics is present. The harmonics need not be consecutive, but higher harmonics contribute less than lower harmonics [J. Raatgever and F. A. Bilsen, in Auditory Physiology and Perception, edited by Y. Cazals, K. Horner, and L. Demany (Pergamon, Oxford, 1992), pp. 215-222 M. K. McBeath and J. F. Wayand, Abstracts of the Psychonom. Soc. 3, 55 (1998)]. A neural network model is presented that has the potential to simulate this operation. Harmonics are first passed through a bank of rounded exponential filters with lateral inhibition. The results are used as inputs for an autoassociator neural network. The model is trained using harmonic data for symphonic musical instruments, in order to test whether it can self-organize by learning associations between co-occurring harmonics. It is shown that the trained model can complete the pattern for missing-fundamental sounds. The Performance of the model in harmonic detection will be compared with experimental results for humans.
On the Mössbauer studies of harmonically bound quantum oscillators in Brownian motion
NASA Astrophysics Data System (ADS)
Razdan, A.
1999-03-01
In many biological systems like whole cells, membranes or proteins and some of the polymeric systems, dynamics reveals itself in Mössbauer spectra as a non Lorentzian behaviour above some particular temperature which is characteristic of the system. Moreover mean square displacement and line width show temperature dependence above the characteristic temperature. Brownian motion of harmonically bound oscillator has been able to explain the non-Lorentzian behaviour. In the present paper, a quantum picture of the above model is discussed and lineshape is expressed as the closed form for the extreme overdamping case. In addition to the non-Lorentzian behaviour, the present model also predicts a temperature dependence of mean square displacement and linewidth.
Thermodynamics of trajectories of a quantum harmonic oscillator coupled to N baths
NASA Astrophysics Data System (ADS)
Pigeon, Simon; Fusco, Lorenzo; Xuereb, André; De Chiara, Gabriele; Paternostro, Mauro
2015-07-01
We undertake a thorough analysis of the thermodynamics of the trajectories followed by a quantum harmonic oscillator coupled to N dissipative baths by using an approach to large-deviation theory inspired by phase-space quantum optics. As an illustrative example, we study the archetypal case of a harmonic oscillator coupled to two thermal baths, allowing for a comparison with the analogous classical result. In the low-temperature limit, we find a significant quantum suppression in the rate of work exchanged between the system and each bath. We further show how the presented method is capable of giving analytical results even for the case of a driven harmonic oscillator. Based on that result, we analyze the laser cooling of the motion of a trapped ion or optomechanical system, illustrating how the emission statistics can be controllably altered by the driving force.
The finite harmonic oscillator and its associated sequences
Gurevich, Shamgar; Hadani, Ronny; Sochen, Nir
2008-01-01
A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication theory are explained. PMID:18635684
The finite harmonic oscillator and its associated sequences.
Gurevich, Shamgar; Hadani, Ronny; Sochen, Nir
2008-07-22
A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication theory are explained. PMID:18635684
Entanglement scaling in classical and quantum harmonic oscillator lattices
Audenaert, K.; Eisert, J.; Plenio, M. B.; Cramer, M.
2006-11-15
We consider entanglement properties of ground and thermal states of harmonic lattice systems. A theorem connecting entanglement between a region and the rest of the lattice with the surface area of the boundary between the two regions is presented for systems in arbitrary spatial dimensions. The behavior of the block entanglement in the field limit is analysed and a logarithmic divergence is recovered.
On the effects of a screw dislocation and a linear potential on the harmonic oscillator
NASA Astrophysics Data System (ADS)
Bueno, M. J.; Furtado, C.; Bakke, K.
2016-09-01
Quantum effects on the harmonic oscillator due to the presence of a linear scalar potential and a screw dislocation are investigated. By searching for bound states solutions, it is shown that an Aharonov-Bohm-type effect for bound states and a restriction of the values of the angular frequency of the harmonic oscillator can be obtained, where the allowed values are determined by the topology of the screw dislocation and the quantum numbers associated with the radial modes and the angular momentum. As particular cases, the angular frequency and the energy levels associated with the ground state and the first excited state of the system are obtained.
NASA Astrophysics Data System (ADS)
Falaye, B. J.; Dong, Shi-Hai; Oyewumi, K. J.; Ilaiwi, K. F.; Ikhdair, S. M.
2015-10-01
We derive the relativistic energy spectrum for the modified Dirac equation by adding a harmonic oscillator potential where the coordinates and momenta are assumed to obey the commutation relation [x̂,p̂] = iℏ(1 + ηp2). In the nonrelativistic (NR) limit, our results are in agreement with the ones obtained previously. Furthermore, the extension to the construction of creation and annihilation operators for the harmonic oscillators with minimal length uncertainty relation is presented. Finally, we show that the commutation relation of the SU(1, 1) ˜SO(2, 1) algebra is satisfied by the operators ℒ±̂ and ℒẑ.
A high-fidelity harmonic drive model.
Preissner, C.; Royston, T. J.; Shu, D.
2012-01-01
In this paper, a new model of the harmonic drive transmission is presented. The purpose of this work is to better understand the transmission hysteresis behavior while constructing a new type of comprehensive harmonic drive model. The four dominant aspects of harmonic drive behavior - nonlinear viscous friction, nonlinear stiffness, hysteresis, and kinematic error - are all included in the model. The harmonic drive is taken to be a black box, and a dynamometer is used to observe the input/output relations of the transmission. This phenomenological approach does not require any specific knowledge of the internal kinematics. In a novel application, the Maxwell resistive-capacitor hysteresis model is applied to the harmonic drive. In this model, sets of linear stiffness elements in series with Coulomb friction elements are arranged in parallel to capture the hysteresis behavior of the transmission. The causal hysteresis model is combined with nonlinear viscous friction and spectral kinematic error models to accurately represent the harmonic drive behavior. Empirical measurements are presented to quantify all four aspects of the transmission behavior. These measurements motivate the formulation of the complete model. Simulation results are then compared to additional measurements of the harmonic drive performance.
Harmonic oscillator representation in the theory of scattering and nuclear reactions
NASA Technical Reports Server (NTRS)
Smirnov, Yuri F.; Shirokov, A. M.; Lurie, Yuri, A.; Zaitsev, S. A.
1995-01-01
The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.
Vibrational spectroscopy of a harmonic oscillator system nonlinearly coupled to a heat bath
NASA Astrophysics Data System (ADS)
Kato, Tsuyoshi; Tanimura, Yoshitaka
2002-10-01
Vibrational relaxation of a harmonic oscillator nonlinearly coupled to a heat bath is investigated by the Gaussian-Markovian quantum Fokker-Planck equation approach. The system-bath interaction is assumed to be linear in the bath coordinate, but linear plus square in the system coordinate modeling the elastic and inelastic relaxation mechanisms. Interplay of the two relaxation processes induced by the linear-linear and square-linear interactions in Raman or infrared spectra is discussed for various system-bath couplings, temperatures, and correlation times for the bath fluctuations. The one-quantum coherence state created through the interaction with the pump laser pulse relaxes through different pathways in accordance with the mechanisms of the system-bath interactions. Relations between the present theory, Redfield theory, and stochastic theory are also discussed.
Some properties of an infinite family of deformations of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Quesne, Christiane
2010-12-01
In memory of Marcos Moshinsky, who promoted the algebraic study of the harmonic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed. This set, which was introduced by Tremblay, Turbiner, and Winternitz, consists in some Hamiltonians Hk on the plane, depending on a positive real parameter k. Two algebraic extensions of Hk are described. The first one, based on the elements of the dihedral group D2k and a Dunkl operator formalism, provides a convenient tool to prove the superintegrability of Hk for odd integer k. The second one, employing two pairs of fermionic operators, leads to a supersymmetric extension of Hk of the same kind as the familiar Freedman and Mende super-Calogero model. Some connection between both extensions is also outlined.
Some properties of an infinite family of deformations of the harmonic oscillator
Quesne, Christiane
2010-12-23
In memory of Marcos Moshinsky, who promoted the algebraic study of the harmonic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed. This set, which was introduced by Tremblay, Turbiner, and Winternitz, consists in some Hamiltonians H{sub k} on the plane, depending on a positive real parameter k. Two algebraic extensions of H{sub k} are described. The first one, based on the elements of the dihedral group D{sub 2k} and a Dunkl operator formalism, provides a convenient tool to prove the superintegrability of H{sub k} for odd integer k. The second one, employing two pairs of fermionic operators, leads to a supersymmetric extension of H{sub k} of the same kind as the familiar Freedman and Mende super-Calogero model. Some connection between both extensions is also outlined.
Revised calculation of four-particle harmonic-oscillator transformation brackets matrix
NASA Astrophysics Data System (ADS)
Mickevičius, S.; Germanas, D.; Kalinauskas, R. K.
2013-02-01
In this article we present a new, considerably enhanced and more rapid method for calculation of the matrix of four-particle harmonic-oscillator transformation brackets (4HOB). The new method is an improved version of 4HOB matrix calculations which facilitates the matrix calculation by finding the eigenvectors of the 4HOB matrix explicitly. Using this idea the new Fortran code for fast and 4HOB matrix calculation is presented. The calculation time decreases more than a few hundred times for large matrices. As many problems of nuclear and hadron physics structure are modeled on the harmonic oscillator (HO) basis our presented method can be useful for large-scale nuclear structure and many-particle identical fermion systems calculations. Program summaryTitle of program: HOTB_M Catalogue identifier: AEFQ_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFQ_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 2149 No. of bytes in distributed program, including test data, etc.: 17576 Distribution format: tar.gz Programming language: Fortran 90. Computer: Any computer with Fortran 90 compiler. Operating system: Windows, Linux, FreeBSD, True64 Unix. RAM: Up to a few Gigabytes (see Tables 1 and 2 included in the distribution package) Classification: 17.16, 17.17. Catalogue identifier of previous version: AEFQ_v2_0 Journal reference of previous version: Comput. Phys. Comm. 182(2011)1377 Does the new version supersede the previous version?: Yes Nature of problem: Calculation of the matrix of the 4HOB in a more effective way, which allows us to calculate the matrix of the brackets up to a few hundred times more rapidly than in a previous version. Solution method: The method is based on compact expressions of 4HOB, presented in [1] and its simplifications presented in this paper. Reasons for new version
The impact damped harmonic oscillator in free decay
NASA Technical Reports Server (NTRS)
Brown, G. V.; North, C. M.
1987-01-01
The impact-damped oscillator in free decay is studied by using time history solutions. A large range of oscillator amplitude is covered. The amount of damping is correlated with the behavior of the impacting mass. There are three behavior regimes: (1) a low amplitude range with less than one impact per cycle and very low damping, (2) a useful middle amplitude range with a finite number of impacts per cycle, and (3) a high amplitude range with an infinite number of impacts per cycle and progressively decreasing damping. For light damping the impact damping in the middle range is: (1) proportional to impactor mass, (2) additive to proportional damping, (3) a unique function of vibration amplitude, (4) proportional to 1-epsilon, where epsilon is the coefficient of restitution, and (5) very roughly inversely proportional to amplitude. The system exhibits jump phenomena and period doublings. An impactor with 2 percent of the oscillator's mass can produce a loss factor near 0.1.
Quantum optics. Quantum harmonic oscillator state synthesis by reservoir engineering.
Kienzler, D; Lo, H-Y; Keitch, B; de Clercq, L; Leupold, F; Lindenfelser, F; Marinelli, M; Negnevitsky, V; Home, J P
2015-01-01
The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to generate squeezed, coherent, and displaced-squeezed states as steady states in the presence of noise. We verify the created state by generating two-state correlated spin-motion Rabi oscillations, resulting in high-contrast measurements. For both cooling and measurement, we use spin-oscillator couplings that provide transitions between oscillator states in an engineered Fock state basis. Our approach should facilitate studies of entanglement, quantum computation, and open-system quantum simulations in a wide range of physical systems. PMID:25525161
Multivariable harmonic balance analysis of the neuronal oscillator for leech swimming.
Chen, Zhiyong; Zheng, Min; Friesen, W Otto; Iwasaki, Tetsuya
2008-12-01
Biological systems, and particularly neuronal circuits, embody a very high level of complexity. Mathematical modeling is therefore essential for understanding how large sets of neurons with complex multiple interconnections work as a functional system. With the increase in computing power, it is now possible to numerically integrate a model with many variables to simulate behavior. However, such analysis can be time-consuming and may not reveal the mechanisms underlying the observed phenomena. An alternative, complementary approach is mathematical analysis, which can demonstrate direct and explicit relationships between a property of interest and system parameters. This paper introduces a mathematical tool for analyzing neuronal oscillator circuits based on multivariable harmonic balance (MHB). The tool is applied to a model of the central pattern generator (CPG) for leech swimming, which comprises a chain of weakly coupled segmental oscillators. The results demonstrate the effectiveness of the MHB method and provide analytical explanations for some CPG properties. In particular, the intersegmental phase lag is estimated to be the sum of a nominal value and a perturbation, where the former depends on the structure and span of the neuronal connections and the latter is roughly proportional to the period gradient, communication delay, and the reciprocal of the intersegmental coupling strength. PMID:18663565
Vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to harmonic bath.
Joutsuka, Tatsuya; Ando, Koji
2011-05-28
The vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to a harmonic bath are examined to assess the applicability of the time correlation function (TCF), the response function, and the semiclassical frequency modulation (SFM) model to the calculation of infrared (IR) spectra. These three approaches are often used in connection with the molecular dynamics simulations but have not been compared in detail. We also analyze the vibrational energy relaxation (VER), which determines the line shape and is itself a pivotal process in energy transport. The IR spectra and VER are calculated using the generalized Langevin equation (GLE), the Gaussian wavepacket (GWP) method, and the quantum master equation (QME). By calculating the vibrational frequency TCF, a detailed analysis of the frequency fluctuation and correlation time of the model is provided. The peak amplitude and width in the IR spectra calculated by the GLE with the harmonic quantum correction are shown to agree well with those by the QME though the vibrational frequency is generally overestimated. The GWP method improves the peak position by considering the zero-point energy and the anharmonicity although the red-shift slightly overshoots the QME reference. The GWP also yields an extra peak in the higher-frequency region than the fundamental transition arising from the difference frequency of the center and width oscillations of a wavepacket. The SFM approach underestimates the peak amplitude of the IR spectra but well reproduces the peak width. Further, the dependence of the VER rate on the strength of an excitation pulse is discussed. PMID:21639460
Generation of high power sub-terahertz radiation from a gyrotron with second harmonic oscillation
Saito, Teruo; Yamada, Naoki; Ikeuti, Shinji; Tatematsu, Yoshinori; Ikeda, Ryosuke; Ogawa, Isamu; Idehara, Toshitaka; Ogasawara, Shinya; Manuilov, Vladimir N.; Shimozuma, Takashi; Kubo, Shin; Nishiura, Masaki; Tanaka, Kenji; Kawahata, Kazuo
2012-06-15
New power records of second harmonic gyrotron oscillation have been demonstrated in the sub-THz band. The first step gyrotron of demountable type had succeeded in oscillation with power more than 50 kW at 350 GHz and nearly 40 kW at 390 GHz [T. Notake et al., Phys. Rev. Lett. 103, 225002 (2009)]. Then, the second step gyrotron of sealed-off type was manufactured. A cavity mode was carefully selected to avoid mode competition with a neighboring fundamental harmonic mode. Matching of the selected mode with the electron gun was also circumspectly considered. The second step gyrotron has attained higher power radiation than the first gyrotron. The maximum single mode power was 62 kW at 388 GHz. Then, the electron gun was modified for use of a different cavity mode with a higher coupling coefficient than that for the 62 kW mode. The new mode proved single mode oscillation power of 83 kW at about 389 GHz. These results are new second-harmonic-oscillation power records for sub-THz gyrotrons. The present study constitutes foundations of development of high power second harmonic sub-THz gyrotron for application to collective Thomson scattering measurement on fusion plasmas, especially on high-density plasmas such as those produced in LHD [N. Ohyabu et al., Phys. Rev. Lett. 97, 055002 (2006)]. This paper reports the design consideration to realize high power single mode gyrotron oscillation at second harmonic and the examination of oscillation characteristics of the gyrotron.
Schulze-Halberg, Axel E-mail: xbataxel@gmail.com; Wang, Jie
2015-07-15
We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system.
NASA Astrophysics Data System (ADS)
Leadenham, S.; Erturk, A.
2014-11-01
Over the past few years, nonlinear oscillators have been given growing attention due to their ability to enhance the performance of energy harvesting devices by increasing the frequency bandwidth. Duffing oscillators are a type of nonlinear oscillator characterized by a symmetric hardening or softening cubic restoring force. In order to realize the cubic nonlinearity in a cantilever at reasonable excitation levels, often an external magnetic field or mechanical load is imposed, since the inherent geometric nonlinearity would otherwise require impractically high excitation levels to be pronounced. As an alternative to magnetoelastic structures and other complex forms of symmetric Duffing oscillators, an M-shaped nonlinear bent beam with clamped end conditions is presented and investigated for bandwidth enhancement under base excitation. The proposed M-shaped oscillator made of spring steel is very easy to fabricate as it does not require extra discrete components to assemble, and furthermore, its asymmetric nonlinear behavior can be pronounced yielding broadband behavior under low excitation levels. For a prototype configuration, linear and nonlinear system parameters extracted from experiments are used to develop a lumped-parameter mathematical model. Quadratic damping is included in the model to account for nonlinear dissipative effects. A multi-term harmonic balance solution is obtained to study the effects of higher harmonics and a constant term. A single-term closed-form frequency response equation is also extracted and compared with the multi-term harmonic balance solution. It is observed that the single-term solution overestimates the frequency of upper saddle-node bifurcation point and underestimates the response magnitude in the large response branch. Multi-term solutions can be as accurate as time-domain solutions, with the advantage of significantly reduced computation time. Overall, substantial bandwidth enhancement with increasing base excitation is
Harmonic mode competition in a terahertz gyrotron backward-wave oscillator
Kao, S. H.; Chiu, C. C.; Chang, P. C.; Wu, K. L.; Chu, K. R.
2012-10-15
Electron cyclotron maser interactions at terahertz (THz) frequencies require a high-order-mode structure to reduce the wall loss to a tolerable level. To generate THz radiation, it is also essential to employ cyclotron harmonic resonances to reduce the required magnetic field strength to a value within the capability of the superconducting magnets. However, much weaker harmonic interactions in a high-order-mode structure lead to serious mode competition problems. The current paper addresses harmonic mode competition in the gyrotron backward wave oscillator (gyro-BWO). We begin with a comparative study of the mode formation and oscillation thresholds in the gyro-BWO and gyromonotron. Differences in linear features result in far fewer 'windows' for harmonic operation of the gyro-BWO. Nonlinear consequences of these differences are examined in particle simulations of the multimode competition processes in the gyro-BWO, which shed light on the competition criteria between modes of different as well as the same cyclotron harmonic numbers. The viability of a harmonic gyro-BWO is assessed on the basis of the results obtained.
NASA Astrophysics Data System (ADS)
Stepšys, A.; Mickevicius, S.; Germanas, D.; Kalinauskas, R. K.
2014-11-01
This new version of the HOTB program for calculation of the three and four particle harmonic oscillator transformation brackets provides some enhancements and corrections to the earlier version (Germanas et al., 2010) [1]. In particular, new version allows calculations of harmonic oscillator transformation brackets be performed in parallel using MPI parallel communication standard. Moreover, higher precision of intermediate calculations using GNU Quadruple Precision and arbitrary precision library FMLib [2] is done. A package of Fortran code is presented. Calculation time of large matrices can be significantly reduced using effective parallel code. Use of Higher Precision methods in intermediate calculations increases the stability of algorithms and extends the validity of used algorithms for larger input values. Catalogue identifier: AEFQ_v4_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFQ_v4_0.html Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 Number of lines in programs, including test data, etc.: 1711 Number of bytes in distributed programs, including test data, etc.: 11667 Distribution format: tar.gz Program language used: FORTRAN 90 with MPI extensions for parallelism Computer: Any computer with FORTRAN 90 compiler Operating system: Windows, Linux, FreeBSD, True64 Unix Has the code been vectorized of parallelized?: Yes, parallelism using MPI extensions. Number of CPUs used: up to 999 RAM(per CPU core): Depending on allocated binomial and trinomial matrices and use of precision; at least 500 MB Catalogue identifier of previous version: AEFQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181, Issue 2, (2010) 420-425 Does the new version supersede the previous version? Yes Nature of problem: Calculation of matrices of three-particle harmonic oscillator brackets (3HOB) and four-particle harmonic oscillator brackets (4HOB) in a more
Modelling Ultradian Oscillations and Segmentation
NASA Astrophysics Data System (ADS)
Jensen, Mogens
2008-03-01
We model ultradian oscillations in four different eucaryotic systems: Hes1, p53-mdm2, NF-kB and Wnt-Notch. In each of the systems we identify the feed-back loops for the genetic regulations. Oscillations are possible when time delays are present, either by directly introducing a delay, by many steps in the loops or by saturated degradation. The oscillations are important for apoptosis and control of inflammation. The Wnt-Notch system is essential in embryo segmentation and we introduce a model in which the Wnt oscillates by itself but drives the Notch cycle out of phase with the Wnt cycle, in good agreement with experimental observations.
Vignat, C.; Lamberti, P. W.
2009-10-15
Recently, Carinena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.
Coherent dynamics of a flux qubit coupled to a harmonic oscillator.
Chiorescu, I; Bertet, P; Semba, K; Nakamura, Y; Harmans, C J P M; Mooij, J E
2004-09-01
In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits (qubits). Single-qubit operations, direct coupling between two qubits and the realization of a quantum gate have been reported. However, complex manipulation of entangled states-such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments and cavity quantum electrodynamics-has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux qubit (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic oscillator. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi oscillations of the coupled system. PMID:15356624
NASA Astrophysics Data System (ADS)
Gokhale, M. H.
A spherical harmonic Fourier analysis of the maximum areas of sunspot groups listed in Ledgers I and II of Greenwich photoheliographic results for 1933 - 1954 yield significant peaks at the 11 y periodicity for some spherical harmonic modes: especially the mode (l = 6, m = 0). A similar analysis of the daily areas of the spotgroups during 1944 - 1954 yields 11 y periodicity peaks only for some non-axisymmetric modes. These results suggest that the sunspot activity may be physically related to long period global oscillations of the sun.
Quenching of vortex breakdown oscillations via harmonic modulation
NASA Astrophysics Data System (ADS)
Lopez, J. M.; Cui, Y. D.; Marques, F.; Lim, T. T.
Vortex breakdown is a phenomenon inherent to many practical problems, such as leading-edge vortices on aircraft, atmospheric tornadoes, and flame-holders in combustion devices. The breakdown of these vortices is associated with the stagnation of the axial velocity on the vortex axis and the development of a near-axis recirculation zone. For large enough Reynolds number, the breakdown can be time-dependent. The unsteadiness can have serious consequences in some applications, such as tail-buffeting in aircraft flying at high angles of attack. There has been much interest in controlling the vortex breakdown phenomenon, but most efforts have focused on either shifting the threshold for the onset of steady breakdown or altering the spatial location of the recirculation zone. There has been much less attention paid to the problem of controlling unsteady vortex breakdown. Here we present results from a combined experimental and numerical investigation of vortex breakdown in an enclosed cylinder in which low-amplitude modulations of the rotating endwall that sets up the vortex are used as an open-loop control. As expected, for very low amplitudes of the modulation, variation of the modulation frequency reveals typical resonance tongues and frequency locking, so that the open-loop control allows us to drive the unsteady vortex breakdown to a prescribed periodicity within the resonance regions. For modulation amplitudes above a critical level that depends on the modulation frequency (but still very low), the result is a periodic state synchronous with the forcing frequency over an extensive range of forcing frequencies. Of particular interest is the spatial form of this forced periodic state: for modulation frequencies less than about twice the natural frequency of the unsteady breakdown, the oscillations of the near-axis recirculation zone are amplified, whereas for modulation frequencies larger than about twice the natural frequency the oscillations of the recirculation
NASA Astrophysics Data System (ADS)
Quesne, C.
2016-02-01
The classical and quantum solutions of a nonlinear model describing harmonic oscillators on the sphere and the hyperbolic plane, derived in polar coordinates in a recent paper (Quesne, 2015) [1], are extended by the inclusion of an isotonic term.
Evading surface and detector frequency noise in harmonic oscillator measurements of force gradients
Moore, Eric W.; Lee, SangGap; Hickman, Steven A.; Harrell, Lee E.; Marohn, John A.
2010-01-01
We introduce and demonstrate a method of measuring small force gradients acting on a harmonic oscillator in which the force-gradient signal of interest is used to parametrically up-convert a forced oscillation below resonance into an amplitude signal at the oscillator’s resonance frequency. The approach, which we demonstrate in a mechanically detected electron spin resonance experiment, allows the force-gradient signal to evade detector frequency noise by converting a slowly modulated frequency signal into an amplitude signal. PMID:20733934
Coherent states for nonlinear harmonic oscillator and some of its properties
Amir, Naila E-mail: naila.amir@sns.nust.edu.pk; Iqbal, Shahid E-mail: siqbal@sns.nust.edu.pk
2015-06-15
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
The Harmonic Oscillator Influenced by Gravitational Wave in Noncommutative Quantum Phase Space
NASA Astrophysics Data System (ADS)
Yakup, Rehimhaji; Dulat, Sayipjamal; Li, Kang; Hekim, Mamatabdulla
2014-04-01
Dynamical property of harmonic oscillator affected by linearized gravitational wave (LGW) is studied in a particular case of both position and momentum operators which are noncommutative to each other. By using the generalized Bopp's shift, we, at first, derived the Hamiltonian in the noncommutative phase space (NPS) and, then, calculated the time evolution of coordinate and momentum operators in the Heisenberg representation. Tiny vibration of flat Minkowski space and effect of NPS let the Hamiltonian of harmonic oscillator, moving in the plain, get new extra terms from it's original and noncommutative space partner. At the end, for simplicity, we take the general form of the LGW into gravitational plain wave, obtain the explicit expression of coordinate and momentum operators.
Corrections to the Born-Oppenheimer approximation for a harmonic oscillator
NASA Astrophysics Data System (ADS)
Patterson, Chris W.
1993-02-01
We derive simple expressions for the energy corrections to the Born-Oppenheimer approximation valid for a harmonic oscillator. We apply these corrections to the electronic and rotational ground state of H+2 and show that the diabatic energy corrections are linearly dependent on the vibrational quantum numbers as seen in recent variational calculations [D. A. Kohl and E. J. Shipsey, J. Chem. Phys. 84, 2707 (1986)].
Truncated harmonic oscillator and Painlevé IV and V equations
NASA Astrophysics Data System (ADS)
Fernández C, David J.; Morales-Salgado, V. S.
2015-06-01
Quantum systems described by second and third order polynomial Heisenberg algebras are obtained applying supersymmetric quantum mechanics to the harmonic oscillator with an infinite potential barrier. These systems are linked with the Painlevé IV and V equations, respectively, thus several solutions of these non-linear second-order differential equations will be found, along with a chain of Bäcklund transformations connecting such solutions.
RLC circuit realization of a q-deformed harmonic oscillator with time dependent mass
NASA Astrophysics Data System (ADS)
Batouli, J.; El Baz, M.; Maaouni, A.
2015-08-01
We consider an RLC circuit type realization of a q-deformed harmonic oscillator. The differential equations of motion characterizing this circuit are derived, and it is shown that the RLC circuit gets modified as a result of the q-deformation. The natural frequency, the capacitance and the external power source are all modified and become q-dependent. The energy aspects of the circuit are also studied and the effects of the deformation are shown.
Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator
Chen Xi; Muga, J. G.
2010-11-15
We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes ('shortcuts to adiabaticity') designed to reproduce the initial populations at some predetermined final frequency and time. We provide lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.
NASA Technical Reports Server (NTRS)
Bgattacharyya, Sudip; Strohmayer, E.
2005-01-01
We report on a study of the evolution of burst oscillation properties during the rising phase of X-ray bursts from 4U 1636-536 observed with the proportional counter array (PCA) on board the Rossi X-Ray Timing Explorer (RXTE) . We present evidence for significant harmonic structure of burst oscillation pulses during the early rising phases of bursts. This is the first such detection in burst rise oscillations, and is very important for constraining neutron star structure parameters and the equation of state models of matter at the core of a neutron star. The detection of harmonic content only during the initial portions of the burst rise is consistent with the theoretical expectation that with time the thermonuclear burning region becomes larger, and hence the fundamental and harmonic amplitudes both diminish. We also find, for the first time from this source, strong evidence of oscillation frequency increase during the burst rise. The timing behavior of harmonic content, amplitude, and frequency of burst rise oscillations may be important in understanding the spreading of thermonuclear flames under the extreme physical conditions on neutron star surfaces.
Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators
NASA Astrophysics Data System (ADS)
Demarie, Tommaso F.; Linjordet, Trond; Menicucci, Nicolas C.; Brennen, Gavin K.
2014-08-01
The Kitaev surface code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy (TEE), but due to low signal to noise, it is extremely difficult to observe in these systems, and one usually resorts to measuring anyonic statistics of excitations or non-local string operators to reveal the order. We describe a continuous-variable analog to the surface code using quantum harmonic oscillators on a two-dimensional lattice, which has the distinctive property of needing only two-body nearest-neighbor interactions for its creation. Though such a model is gapless, it satisfies an area law and the ground state can be simply prepared by measurements on a finitely squeezed and gapped two-dimensional cluster-state without topological order. Asymptotically, the continuous variable surface code TEE grows linearly with the squeezing parameter and a recently discovered non-local quantity, the topological logarithmic negativity, behaves analogously. We also show that the mixed-state generalization of the TEE, the topological mutual information, is robust to some forms of state preparation error and can be detected simply using single-mode quadrature measurements. Finally, we discuss scalable implementation of these methods using optical and circuit-QED technology.
Rotational Shear Effects on Edge Harmonic Oscillations in DIII-D Quiescent H-mode Discharges
NASA Astrophysics Data System (ADS)
Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, Wm.; Tobias, B. J.; Yan, Z.
2015-11-01
In quiescent H-mode (QH) regime, the edge harmonic oscillations (EHO) play an important role in avoiding the transient ELM power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n <= 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended MHD code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-I and MIR diagnostics, as well as the kink/peeling mode properties of the ideal MHD code ELITE. The numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by the toroidal rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that the low-n EHO can be destabilized in principle with rotation in both directions. These modeling results are consistent with experimental observations of the EHO and support the proposed theory of the EHO as a rotational shear driven kink/peeling mode.
NASA Astrophysics Data System (ADS)
Fidler, Andrew F.; Engel, Gregory S.
2013-10-01
We present a theory for a bath model in which we approximate the adiabatic nuclear potential surfaces on the ground and excited electronic states by displaced harmonic oscillators that differ in curvature. Calculations of the linear and third-order optical response functions employ an effective short-time approximation coupled with the cumulant expansion. In general, all orders of correlation contribute to the optical response, indicating that the solvation process cannot be described as Gaussian within the model. Calculations of the linear absorption and fluorescence spectra resulting from the theory reveal a stronger temperature dependence of the Stokes shift along with a general asymmetry between absorption and fluorescence line shapes, resulting purely from the difference in the phonon side band. We discuss strategies for controlling spectral tuning and energy-transfer dynamics through the manipulation of the excited-state and ground-state curvature. Calculations of the nonlinear response also provide insights into the dynamics of the system-bath interactions and reveal that multidimensional spectroscopies are sensitive to a difference in curvature between the ground- and excited-state adiabatic surfaces. This extension allows for the elucidation of short-time dynamics of dephasing that are accessible in nonlinear spectroscopic methods.
Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges
NASA Astrophysics Data System (ADS)
Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, W. M.; Tobias, B. J.; Yan, Z.
2016-07-01
In the quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHOs) play an important role in avoiding transient edge localized mode (ELM) power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n ⩽ 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended magentoohydrodynamics (MHD) code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-Imaging and microwave imaging reflectometer (MIR) diagnostics, as well as the kink/peeling mode properties found by the ideal MHD code ELITE. Numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by rotation and/or rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that EHOs can be destabilized in principle with rotation in either direction. The modeling results are consistent with observations of EHO, support the proposed theory of the EHO as a low-n kink/peeling mode destabilized by edge E × B rotational shear, and improve our understanding and confidence in creating and sustaining QH-mode in present and future devices.
The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Rañada, Manuel F.; Santander, Mariano
2008-03-01
The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and metric of any signature, either Riemannian (definite positive) or Lorentzian (indefinite). In this paper we study the main properties of these "curved" harmonic oscillators simultaneously on any such configuration space, using a Cayley-Klein (CK)-type approach, with two free parameters κ1,κ2 which altogether correspond to the possible values for curvature and signature type: the generic Riemannian and Lorentzian spaces of constant curvature (sphere S2, hyperbolic plane H2, AntiDeSitter sphere AdS1+1, and DeSitter sphere dS1+1) appear in this family, with Euclidean and Minkowski spaces as flat particular cases. We solve the equations of motion for the curved harmonic oscillator and obtain explicit expressions for the orbits by using three different methods: by direct integration, by obtaining the general CK version of Binet's equation, and finally as a consequence of its superintegrable character. The orbits are conics with center at the potential origin on any CK space, thereby extending this well known Euclidean property to any constant curvature configuration space. The final part of the article, that has a more geometric character, presents pertinent results of the theory of conics on spaces of constant curvature.
NASA Astrophysics Data System (ADS)
Wang, Fei; Nie, Wei; Feng, Xunli; Oh, C. H.
2016-07-01
The correlated emission lasing (CEL) is experimentally demonstrated in harmonic oscillators coupled via a single three-level artificial atom [Phys. Rev. Lett. 115, 223603 (2015), 10.1103/PhysRevLett.115.223603] in which two-mode entanglement only exists in a certain time period when the harmonic oscillators are resonant with the atomic transitions. Here we examine this system and show that it is possible to obtain the steady-state entanglement when the two harmonic oscillators are resonant with Rabi sidebands. Applying dressed atomic states and Bogoliubov-mode transformation, we obtain the analytical results of the variance sum of a pair of Einstein-Podolsky-Rosen (EPR)-like operators. The stable entanglement originates from the dissipation process of the Bogoliubov modes because the atomic system can act as a reservoir in dressed state representation. We also show that the entanglement is robust against the dephasing rates of the superconducing atom, which is expected to have important applications in quantum information processing.
Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams
NASA Technical Reports Server (NTRS)
Steely, Sidney L.
1993-01-01
The similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite-Gaussian laser beams is illustrated. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite-Gaussian laser beams. The classical limits of a corresponding two-dimensional harmonic oscillator provide a definition of the spot size of Hermite-Gaussian laser beams. The classical limits of the harmonic oscillator provide integration limits for the photon probability densities of the laser beam modes to determine the fraction of photons detected therein. Mathematica is used to integrate the probability densities for large-order beam modes and to illustrate the functional similarities. The probabilities of detecting photons within the classical limits of Hermite-Gaussian laser beams asymptotically approach unity in the limit of large-order modes, in agreement with the Correspondence Principle. The classical limits for large-order modes include all of the nodes for Hermite Gaussian laser beams; Sturm's theorem provides a direct proof.
Containment control for coupled harmonic oscillators with multiple leaders under directed topology
NASA Astrophysics Data System (ADS)
Xu, Chengjie; Zheng, Ying; Su, Housheng; Wang, Hua O.
2015-02-01
This paper investigates the problem of containment control for coupled harmonic oscillators with multiple leaders under directed topology. Using tools from matrix, graph and stability theories, necessary and sufficient conditions are obtained for coupled harmonic oscillators under continuous-time and sampled-data-based protocols, respectively. When the continuous-time protocol is used, it is proved that every follower will ultimately converge to the convex hull spanned by the leaders if and only if there exists at least one leader that has a directed path to that follower at any time. When the sampled-data-based protocol is used, it is shown that the containment can be achieved if and only if: (1) an appropriate sampling period is chosen and (2) for every follower, there exists at least one leader that has a directed path to that follower at any time. And we also give the containment conditions for coupled harmonic oscillators under undirected topology as a special case. Finally, numerical simulations are presented to illustrate the theoretical findings.
Quantum spatial-periodic harmonic model for daily price-limited stock markets
NASA Astrophysics Data System (ADS)
Meng, Xiangyi; Zhang, Jian-Wei; Xu, Jingjing; Guo, Hong
2015-11-01
We investigate the behaviors of stocks in daily price-limited stock markets by purposing a quantum spatial-periodic harmonic model. The stock price is considered to be oscillating and damping in a quantum spatial-periodic harmonic oscillator potential well. A complicated non-linear relation including inter-band positive correlation and intra-band negative correlation between the volatility and trading volume of a stock is numerically derived with the energy band structure of the model concerned. The effectiveness of price limit is re-examined, with some observed characteristics of price-limited stock markets in China studied by applying our quantum model.
ERIC Educational Resources Information Center
Andrews, David L.; Romero, Luciana C. Davila
2009-01-01
The dynamical behaviour of simple harmonic motion can be found in numerous natural phenomena. Within the quantum realm of atomic, molecular and optical systems, two main features are associated with harmonic oscillations: a finite ground-state energy and equally spaced quantum energy levels. Here it is shown that there is in fact a one-to-one…
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators.
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
2016-07-01
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time. PMID:27575089
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators
NASA Astrophysics Data System (ADS)
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
2016-07-01
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.
Properties of infrared extrapolations in a harmonic oscillator basis
NASA Astrophysics Data System (ADS)
Coon, Sidney A.; Kruse, Michael K. G.
2016-02-01
The success and utility of effective field theory (EFT) in explaining the structure and reactions of few-nucleon systems has prompted the initiation of EFT-inspired extrapolations to larger model spaces in ab initio methods such as the no-core shell model (NCSM). In this contribution, we review and continue our studies of infrared (ir) and ultraviolet (uv) regulators of NCSM calculations in which the input is phenomenological NN and NNN interactions fitted to data. We extend our previous findings that an extrapolation in the ir cutoff with the uv cutoff above the intrinsic uv scale of the interaction is quite successful, not only for the eigenstates of the Hamiltonian but also for expectation values of operators, such as r2, considered long range. The latter results are obtained with Hamiltonians transformed by the similarity renormalization group (SRG) evolution. On the other hand, a possible extrapolation of ground state energies in the uv cutoff when the ir cutoff is below the intrinsic ir scale is not robust and does not agree with the ir extrapolation of the same data or with independent calculations using other methods.
NASA Astrophysics Data System (ADS)
Stepšys, A.; Mickevicius, S.; Germanas, D.; Kalinauskas, R. K.
2014-11-01
This new version of the HOTB program for calculation of the three and four particle harmonic oscillator transformation brackets provides some enhancements and corrections to the earlier version (Germanas et al., 2010) [1]. In particular, new version allows calculations of harmonic oscillator transformation brackets be performed in parallel using MPI parallel communication standard. Moreover, higher precision of intermediate calculations using GNU Quadruple Precision and arbitrary precision library FMLib [2] is done. A package of Fortran code is presented. Calculation time of large matrices can be significantly reduced using effective parallel code. Use of Higher Precision methods in intermediate calculations increases the stability of algorithms and extends the validity of used algorithms for larger input values. Catalogue identifier: AEFQ_v4_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFQ_v4_0.html Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 Number of lines in programs, including test data, etc.: 1711 Number of bytes in distributed programs, including test data, etc.: 11667 Distribution format: tar.gz Program language used: FORTRAN 90 with MPI extensions for parallelism Computer: Any computer with FORTRAN 90 compiler Operating system: Windows, Linux, FreeBSD, True64 Unix Has the code been vectorized of parallelized?: Yes, parallelism using MPI extensions. Number of CPUs used: up to 999 RAM(per CPU core): Depending on allocated binomial and trinomial matrices and use of precision; at least 500 MB Catalogue identifier of previous version: AEFQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181, Issue 2, (2010) 420-425 Does the new version supersede the previous version? Yes Nature of problem: Calculation of matrices of three-particle harmonic oscillator brackets (3HOB) and four-particle harmonic oscillator brackets (4HOB) in a more
Schutt, Carolyn E; Ibsen, Stuart; Benchimol, Michael; Hsu, Mark; Esener, Sadik
2015-06-15
A new optical contrast agent has been developed by exposing dye-loaded microbubbles to a rapidly-cooled thermal treatment to homogenize the dye distribution across the surface. Ultrasound causes these microbubbles to oscillate in size which changes the self-quenching efficiency of the dye molecules creating a "blinking" signal. We demonstrate for the first time that these microbubbles can reproducibly generate second, third, and even fourth harmonic fluorescence intensity modulations, in addition to the fundamental frequency of the driving ultrasound. Detecting these harmonic signals could produce a higher signal-to-noise ratio for fluorescence imaging in medical applications by allowing fundamental frequency interference and artifacts to be filtered out. PMID:26076274
A TE{sub 21} second-harmonic gyrotron backward-wave oscillator with slotted structure
Chen, N. C.; Yu, C. F.; Chang, T. H.
2007-12-15
Second-harmonic gyrotron backward-wave oscillator (gyro-BWO) with a reduced magnetic field strength is a tunable source in the millimeter wave regime, but it has long been impeded by the severe mode competition as a result of low efficiency and narrow bandwidth. This study employs a slotted structure functioning as a mode selective circuit to suppress the lower order transverse modes. In addition, a two-step tapered waveguide is adopted to stabilize the higher-order transverse modes and axial modes. Some important characteristics of the slotted gyro-BWO will be analyzed and discussed. As a calculated result, the interaction efficiency is improved and the stable tuning range is broadened. A stable, Ka-band, slotted second-harmonic gyro-BWO is capable of producing an efficiency of 23% with a 3 dB tuning bandwidth of 9% at 5 A and 100 kV.
Generalized Hopf Fibration and Geometric SO(3) Reduction of the 4DOF Harmonic Oscillator
NASA Astrophysics Data System (ADS)
van der Meer, J. C.; Crespo, F.; Ferrer, S.
2016-04-01
It is shown that the generalized Hopf map ℍ × ℍ → ℍ × ℝ × ℝ quaternion formulation can be interpreted as an SO(3) orbit map for a symplectic SO(3) action. As a consequence the generalized Hopf fibration S7 → S4 appears in the SO(3) geometric symplectic reduction of the 4DOF isotropic harmonic oscillator. Furthermore it is shown how the Hopf fibration and associated twistor fibration play a role in the geometry of the Kepler problem and the rigid body problem.
Protective measurement of the wave function of a single squeezed harmonic-oscillator state
NASA Astrophysics Data System (ADS)
Alter, Orly; Yamamoto, Yoshihisa
1996-05-01
A scheme for the "protective measurement"
Harmonic oscillators and resonance series generated by a periodic unstable classical orbit
NASA Technical Reports Server (NTRS)
Kazansky, A. K.; Ostrovsky, Valentin N.
1995-01-01
The presence of an unstable periodic classical orbit allows one to introduce the decay time as a purely classical magnitude: inverse of the Lyapunov index which characterizes the orbit instability. The Uncertainty Relation gives the corresponding resonance width which is proportional to the Planck constant. The more elaborate analysis is based on the parabolic equation method where the problem is effectively reduced to the multidimensional harmonic oscillator with the time-dependent frequency. The resonances form series in the complex energy plane which is equidistant in the direction perpendicular to the real axis. The applications of the general approach to various problems in atomic physics are briefly exposed.
NASA Astrophysics Data System (ADS)
Hoover, Wm. G.; Hoover, Carol G.
2012-02-01
We compare the Gram-Schmidt and covariant phase-space-basis-vector descriptions for three time-reversible harmonic oscillator problems, in two, three, and four phase-space dimensions respectively. The two-dimensional problem can be solved analytically. The three-dimensional and four-dimensional problems studied here are simultaneously chaotic, time-reversible, and dissipative. Our treatment is intended to be pedagogical, for use in an updated version of our book on Time Reversibility, Computer Simulation, and Chaos. Comments are very welcome.
NASA Astrophysics Data System (ADS)
Afshar, Davood; Motamedinasab, Amin; Anbaraki, Azam; Jafarpour, Mojtaba
2016-02-01
In this paper, we have constructed even and odd superpositions of supercoherent states, similar to the standard even and odd coherent states of the harmonic oscillator. Then, their nonclassical properties, that is, squeezing and entanglement have been studied. We have observed that even supercoherent states show squeezing behavior for some values of parameters involved, while odd supercoherent states do not show squeezing at all. Also sub-Poissonian statistics have been observed for some ranges of the parameters in both states. We have also shown that these states may be considered as logical qubits which reduce to the Bell states at a limit, with concurrence equal to 1.
Harmonic Pinnacles in the Discrete Gaussian Model
NASA Astrophysics Data System (ADS)
Lubetzky, Eyal; Martinelli, Fabio; Sly, Allan
2016-06-01
The 2 D Discrete Gaussian model gives each height function {η : Z^2to{Z}} a probability proportional to {exp(-β {H}(η))}, where {β} is the inverse-temperature and {{H}(η) = sum_{x˜ y}(η_x-η_y)^2} sums over nearest-neighbor bonds. We consider the model at large fixed {β}, where it is flat unlike its continuous analog (the Discrete Gaussian Free Field). We first establish that the maximum height in an {L× L} box with 0 boundary conditions concentrates on two integers M, M + 1 with {M˜ √{(1/2πβ)log Llog log L}}. The key is a large deviation estimate for the height at the origin in {{Z}2}, dominated by "harmonic pinnacles", integer approximations of a harmonic variational problem. Second, in this model conditioned on {η≥ 0} (a floor), the average height rises, and in fact the height of almost all sites concentrates on levels H, H + 1 where {H˜ M/√{2}}. This in particular pins down the asymptotics, and corrects the order, in results of Bricmont et al. (J. Stat. Phys. 42(5-6):743-798, 1986), where it was argued that the maximum and the height of the surface above a floor are both of order {√{log L}}. Finally, our methods extend to other classical surface models (e.g., restricted SOS), featuring connections to p-harmonic analysis and alternating sign matrices.
NASA Astrophysics Data System (ADS)
Kato, Tsuyoshi; Tanimura, Yoshitaka
2004-01-01
Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model.
Kato, Tsuyoshi; Tanimura, Yoshitaka
2004-01-01
Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model. PMID:15267286
The sojourn time of the inverted harmonic oscillator on the noncommutative plane
NASA Astrophysics Data System (ADS)
Guo, Guang-Jie; Ren, Zhong-Zhou; Ju, Guo-Xing; Long, Chao-Yun
2011-10-01
The sojourn time of the Gaussian wavepacket that is stationed at the center of the inverted harmonic oscillator is investigated on the noncommutative plane in detail. In ordinary commutative space quantum mechanics, the sojourn time of the Gaussian wavepacket is always a monotonically decreasing function of the curvature parameter ω of the potential. However, in this paper, we find that the spatial noncommutativity makes the sojourn time a concave function of ω with a minimum at an inflection point ω0. Furthermore, if ω is larger than a certain critical value the sojourn time will become infinity. Thus, the ordinary intuitive physical picture about the relation between the sojourn time and the shape of the inverted oscillator potential is changed when the spatial noncommutativity is considered.
Fox, Ronald F.; Vela-Arevalo, Luz V.
2002-11-01
The problem of multiphoton processes for intense, long-wavelength irradiation of atomic and molecular electrons is presented. The recently developed method of quasiadiabatic time evolution is used to obtain a nonperturbative analysis. When applied to the standard vector potential coupling, an exact auxiliary equation is obtained that is in the electric dipole coupling form. This is achieved through application of the Goeppert-Mayer gauge. While the analysis to this point is general and aimed at microwave irradiation of Rydberg atoms, a Floquet analysis of the auxiliary equation is presented for the special case of the periodically driven harmonic oscillator. Closed form expressions for a complete set of Floquet states are obtained. These are used to demonstrate that for the oscillator case there are no multiphoton resonances.
Pyragas, Viktoras; Pyragas, Kestutis
2015-08-01
In a recent paper [Phys. Rev. E 91, 012920 (2015)] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation. PMID:26382493
Confined One Dimensional Harmonic Oscillator as a Two-Mode System
Gueorguiev, V G; Rau, A P; Draayer, J P
2005-07-11
The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two limits has a characteristic spectral structure describing the two different excitation modes of the system. Near each of these limits, one can use perturbation theory to achieve an accurate description of the eigenstates. Away from the exact limits, however, one has to carry out a matrix diagonalization because the basis-state mixing that occurs is typically too large to be reproduced in any other way. An alternative to casting the problem in terms of one or the other basis set consists of using an ''oblique'' basis that uses both sets. Through a study of this alternative in this one-dimensional problem, we are able to illustrate practical solutions and infer the applicability of the concept for more complex systems, such as in the study of complex nuclei where oblique-basis calculations have been successful.
NASA Technical Reports Server (NTRS)
Defacio, B.; Vannevel, Alan; Brander, O.
1993-01-01
A formulation is given for a collection of phonons (sound) in a fluid at a non-zero temperature which uses the simple harmonic oscillator twice; one to give a stochastic thermal 'noise' process and the other which generates a coherent Glauber state of phonons. Simple thermodynamic observables are calculated and the acoustic two point function, 'contrast' is presented. The role of 'coherence' in an equilibrium system is clarified by these results and the simple harmonic oscillator is a key structure in both the formulation and the calculations.
NASA Astrophysics Data System (ADS)
Zhao, Liyun; Zhou, Jin; Wu, Quanjun
2016-01-01
This paper considers the sampled-data synchronisation problems of coupled harmonic oscillators with communication and input delays subject to controller failure. A synchronisation protocol is proposed for such oscillator systems over directed network topology, and then some general algebraic criteria on exponential convergence for the proposed protocol are established. The main features of the present investigation include: (1) both the communication and input delays are simultaneously addressed, and the directed network topology is firstly considered and (2) the effects of time delays on synchronisation performance are theoretically and numerically investigated. It is shown that in the absence of communication delays, coupled harmonic oscillators can achieve synchronisation oscillatory motion. Whereas if communication delays are nonzero at infinite multiple sampled-data instants, its synchronisation (or consensus) state is zero. This conclusion can be used as an effective control strategy to stabilise coupled harmonic oscillators in practical applications. Furthermore, it is interesting to find that increasing either communication or input delays will enhance the synchronisation performance of coupled harmonic oscillators. Subsequently, numerical examples illustrate and visualise theoretical results.
Harmonic oscillator states with integer and non-integer orbital angular momentum
NASA Astrophysics Data System (ADS)
Land, Martin
2011-12-01
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
Squeezing induced in a harmonic oscillator by a sudden change in mass or frequency
NASA Astrophysics Data System (ADS)
Abdalla, M. Sebawe; Colegrave, R. K.
1993-08-01
The Kanai-Caldirola (Bateman) Hamiltonian is used to derive the dynamics of a simple harmonic oscillator, initially in a minimum uncertainty state, under the influence of an external agency which causes the mass parameter to change from M0 to M1 in a short time ɛ. Then the frequency changes from ω0 to ω1=(M0/M1)ω0+O(ɛ2). In the limit ɛ-->0, no squeezing or loss of coherence occurs. If M1/M0=1+/-η (0<η<<1), then a squeezing of order ɛ2η occurs. If M1/M0 is appreciably different from unity, then the quadrature variances are unequal but the state no longer has minimum uncertainty. An application could be made in quantum optics.
NASA Astrophysics Data System (ADS)
Kuwata, S.
2016-02-01
For the Fourier transform: ℱ of a non-integrablefunction φ, we exploit theresolvent ℛ forthe harmonic oscillator Hamiltonian, where the integral kernel for ℛ can be represented using the confluent hypergeometric function. Due to the commutativity of ℱ and ℛ, ℱ can be regarded by ℛ-1ℱℛ. In the case of φ(x) = 1, for example, it follows that(ℛφ)(x) is continuous on ℝ and that (ℛφ)(x) ≃ x-2(|x| → ∞)), so that ℛφ turns outto be integrable over ℝ. The finding that(ℱℛ)φ is exponentially localized indicatesthat the mapℱℛ:φ ↦ ¢ can be used as data compression of φ. Moreover, the inverse map:ℛ-1ℱ-1:¢ ↦ φ is well defined, which implies that the data decompression into φ can be made in a numerical calculation friendly way.
Song, Yongli; Zhang, Tonghua; Tadé, Moses O
2008-12-01
We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov-Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved. PMID:19123623
Alternative descriptions of wave and particle aspects of the harmonic oscillator
NASA Technical Reports Server (NTRS)
Schuch, Dieter
1993-01-01
The dynamical properties of the wave and particle aspects of the harmonic oscillator can be studied with the help of the time-dependent Schroedinger equation (SE). Especially the time-dependence of maximum and width of Gaussian wave packet solutions allow to show the evolution and connections of those two complementary aspects. The investigation of the relations between the equations describing wave and particle aspects leads to an alternative description of the considered systems. This can be achieved by means of a Newtonian equation for a complex variable in connection with a conservation law for a nonclassical angular momentum-type quantity. With the help of this complex variable, it is also possible to develop a Hamiltonian formalism for the wave aspect contained in the SE, which allows to describe the dynamics of the position and momentum uncertainties. In this case the Hamiltonian function is equivalent to the difference between the mean value of the Hamiltonian operator and the classical Hamiltonian function.
GENERAL: Solving Dirac Equation with New Ring-Shaped Non-Spherical Harmonic Oscillator Potential
NASA Astrophysics Data System (ADS)
Hu, Xian-Quan; Luo, Guang; Wu, Zhi-Min; Niu, Lian-Bin; Ma, Yan
2010-02-01
A new ring-shaped non-harmonic oscillator potential is proposed. The precise hound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 (2005) 94. The positive energy states of system are discussed and the conclusions are made properly.
Bose–Einstein condensation in a two-component Bose gas with harmonic oscillator interaction
NASA Astrophysics Data System (ADS)
Abulseoud, A. A.; Abbas, A. H.; Galal, A. A.; El-Sherbini, Th M.
2016-07-01
In this article a system containing two species of identical bosons interacting via a harmonic oscillator potential is considered. It is assumed that the number of bosons of each species is the same and that bosons belonging to the same species repel each other while those belonging to different species attract. The Hamiltonian is diagonalized and the energy spectrum of the system is written down. The behaviour of the system in the thermodynamic limit is studied within the framework of the grand canonical ensemble, and thermodynamic parameters, such as the internal energy, entropy and specific heat capacity are calculated. It is shown that the system exhibits a single species Bose–Einstein condensation when the coupling strengths are equal and a dual species condensation when they are different.
ERIC Educational Resources Information Center
Viana-Gomes, J.; Peres, N. M. R.
2011-01-01
We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…
High efficiency fourth-harmonic generation from nanosecond fiber master oscillator power amplifier
NASA Astrophysics Data System (ADS)
Mu, Xiaodong; Steinvurzel, Paul; Rose, Todd S.; Lotshaw, William T.; Beck, Steven M.; Clemmons, James H.
2016-03-01
We demonstrate high power, deep ultraviolet (DUV) conversion to 266 nm through frequency quadrupling of a nanosecond pulse width 1064 nm fiber master oscillator power amplifier (MOPA). The MOPA system uses an Yb-doped double-clad polarization-maintaining large mode area tapered fiber as the final gain stage to generate 0.5-mJ, 10 W, 1.7- ns single mode pulses at a repetition rate of 20 kHz with measured spectral bandwidth of 10.6 GHz (40 pm), and beam qualities of Mx 2=1.07 and My 2=1.03, respectively. Using LBO and BBO crystals for the second-harmonic generation (SHG) and fourth-harmonic generation (FHG), we have achieved 375 μJ (7.5 W) and 92.5 μJ (1.85 W) at wavelengths of 532 nm and 266 nm, respectively. To the best of our knowledge these are the highest narrowband infrared, green and UV pulse energies obtained to date from a fully spliced fiber amplifier. We also demonstrate high efficiency SHG and FHG with walk-off compensated (WOC) crystal pairs and tightly focused pump beam. An SHG efficiency of 75%, FHG efficiency of 47%, and an overall efficiency of 35% from 1064 nm to 266 nm are obtained.
Continuous-Wave Operation of a 460-GHz Second Harmonic Gyrotron Oscillator.
Hornstein, Melissa K; Bajaj, Vikram S; Griffin, Robert G; Temkin, Richard J
2006-06-01
We report the regulated continuous-wave (CW) operation of a second harmonic gyrotron oscillator at output power levels of over 8 W (12.4 kV and 135 mA beam voltage and current) in the TE(0,6,1) mode near 460 GHz. The gyrotron also operates in the second harmonic TE(2,6,1) mode at 456 GHz and in the TE(2,3,1) fundamental mode at 233 GHz. CW operation was demonstrated for a one-hour period in the TE(0,6,1) mode with better than 1% power stability, where the power was regulated using feedback control. Nonlinear simulations of the gyrotron operation agree with the experimentally measured output power and radio-frequency (RF) efficiency when cavity ohmic losses are included in the analysis. The output radiation pattern was measured using a pyroelectric camera and is highly Gaussian, with an ellipticity of 4%. The 460-GHz gyrotron will serve as a millimeter-wave source for sensitivity-enhanced nuclear magnetic resonance (dynamic nuclear polarization) experiments at a magnetic field of 16.4 T. PMID:17710187
Continuous-Wave Operation of a 460-GHz Second Harmonic Gyrotron Oscillator
Hornstein, Melissa K.; Bajaj, Vikram S.; Griffin, Robert G.; Temkin, Richard J.
2007-01-01
We report the regulated continuous-wave (CW) operation of a second harmonic gyrotron oscillator at output power levels of over 8 W (12.4 kV and 135 mA beam voltage and current) in the TE0,6,1 mode near 460 GHz. The gyrotron also operates in the second harmonic TE2,6,1 mode at 456 GHz and in the TE2,3,1 fundamental mode at 233 GHz. CW operation was demonstrated for a one-hour period in the TE0,6,1 mode with better than 1% power stability, where the power was regulated using feedback control. Nonlinear simulations of the gyrotron operation agree with the experimentally measured output power and radio-frequency (RF) efficiency when cavity ohmic losses are included in the analysis. The output radiation pattern was measured using a pyroelectric camera and is highly Gaussian, with an ellipticity of 4%. The 460-GHz gyrotron will serve as a millimeter-wave source for sensitivity-enhanced nuclear magnetic resonance (dynamic nuclear polarization) experiments at a magnetic field of 16.4 T. PMID:17710187
NASA Technical Reports Server (NTRS)
Ehlers, F. E.; Weatherill, W. H.; Yip, E. L.
1984-01-01
A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.
Oscillating water column structural model
Copeland, Guild; Bull, Diana L; Jepsen, Richard Alan; Gordon, Margaret Ellen
2014-09-01
An oscillating water column (OWC) wave energy converter is a structure with an opening to the ocean below the free surface, i.e. a structure with a moonpool. Two structural models for a non-axisymmetric terminator design OWC, the Backward Bent Duct Buoy (BBDB) are discussed in this report. The results of this structural model design study are intended to inform experiments and modeling underway in support of the U.S. Department of Energy (DOE) initiated Reference Model Project (RMP). A detailed design developed by Re Vision Consulting used stiffeners and girders to stabilize the structure against the hydrostatic loads experienced by a BBDB device. Additional support plates were added to this structure to account for loads arising from the mooring line attachment points. A simplified structure was designed in a modular fashion. This simplified design allows easy alterations to the buoyancy chambers and uncomplicated analysis of resulting changes in buoyancy.
NASA Astrophysics Data System (ADS)
Lorenz, Ulf; Saalfrank, Peter
2015-02-01
System-bath problems in physics and chemistry are often described by Markovian master equations. However, the Markov approximation, i.e., neglect of bath memory effects is not always justified, and different measures of non-Markovianity have been suggested in the literature to judge the validity of this approximation. Here we calculate several computable measures of non-Markovianity for the non-trivial problem of a harmonic oscillator coupled to a large number of bath oscillators. The Multi Configurational Time Dependent Hartree method is used to provide a numerically converged solution of the system-bath Schrödinger equation, from which the appropriate quantities can be calculated. In particular, we consider measures based on trace-distances and quantum discord for a variety of initial states. These quantities have proven useful in the case of two-level and other small model systems typically encountered in quantum optics, but are less straightforward to interpret for the more complex model systems that are relevant for chemical physics. Supplementary material in the form of one zip file available from the Journal web page at http://dx.doi.org/10.1140/epjd/e2014-50727-8
NASA Astrophysics Data System (ADS)
Ita, B. I.; Obong, H. P.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.
2014-11-01
The solutions of the Klein-Gordon equation with equal scalar and vector harmonic oscillator plus inverse quadratic potential for S-waves have been presented using the Nikiforov-Uvarov method. The bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms of the Laguerre polynomials.
Cari, C. Suparmi, A.
2014-09-30
Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.
On oscillations in the Social Force Model
NASA Astrophysics Data System (ADS)
Kretz, Tobias
2015-11-01
The Social Force Model is one of the most prominent models of pedestrian dynamics. As such naturally much discussion and criticism have spawned around it, some of which concerns the existence of oscillations in the movement of pedestrians. This contribution is investigating under which circumstances, parameter choices, and model variants oscillations do occur and how this can be prevented. It is shown that oscillations can be excluded if the model parameters fulfill certain relations. The fact that with some parameter choices oscillations occur and with some not is exploited to verify a specific computer implementation of the model.
Quantization and instability of the damped harmonic oscillator subject to a time-dependent force
Majima, H. Suzuki, A.
2011-12-15
We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity (-{gamma}x) and a time-dependent external force (K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman's system, which is described by the Lagrangian: L=mxy-U(x+1/2 y)+U(x-1/2 y)+({gamma})/2 (xy-yx)-xK(t)+yK(t), which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting U(x{+-}y/2)=1/2 k(x{+-}y/2){sup 2} specifically for a dual extended damped-amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman's Hamiltonian H. The Heisenberg equations of motion utilizing the quantized Hamiltonian H surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped-amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force. - Highlights: > A method of quantizing dissipative systems is presented. > In order to obtain the method, we apply Bateman's dual system approach. > A formula for a transition amplitude is derived. > We use the formula to study the instability of the dissipative systems.
NASA Astrophysics Data System (ADS)
Ashhab, Sahel
2015-03-01
The Landau-Zener (LZ) problem is a standard paradigm for studying energy transfer and adiabatic passage protocols. We consider the LZ problem for a two level system when this system interacts with one harmonic oscillator mode that is initially set to a finite-temperature thermal equilibrium state. The oscillator could represent an external mode that is strongly coupled to the system, e.g. an ionic oscillation mode in a molecule, or it could represent a prototypical uncontrolled environment. We analyze the system's occupation probabilities at the final time in a number of different regimes, varying the system and oscillator frequencies, their coupling strength and the temperature. In particular we find some surprising non-monotonic dependence on the coupling strength and temperature.
NASA Technical Reports Server (NTRS)
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Building Mathematical Models of Simple Harmonic and Damped Motion.
ERIC Educational Resources Information Center
Edwards, Thomas
1995-01-01
By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)
NASA Astrophysics Data System (ADS)
Wang, W.-M.
2008-01-01
We prove that the 1- d quantum harmonic oscillator is stable under spatially localized, time quasi-periodic perturbations on a set of Diophantine frequencies of positive measure. This proves a conjecture raised by Enss-Veselic in their 1983 paper [EV] in the general quasi-periodic setting. The motivation of the present paper also comes from construction of quasi-periodic solutions for the corresponding nonlinear equation.
Teaching Oscillations by a Model of Nanoresonator
ERIC Educational Resources Information Center
Lindell, A.; Viiri, J.
2009-01-01
Nanoscience offers fascinating opportunities for science education as it links the achievements of modern technology to traditional models of science. In this article we present a nanotechnology orientated lesson on oscillations, suitable for physics courses at high schools and universities. The focus of the lesson is in forced oscillations on a…
NASA Astrophysics Data System (ADS)
Muralidhar, K.
2014-03-01
Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass and bivector spin has been derived in the form . Where, is the angular velocity bivector of complex rotations, is the velocity of light. The unit vector acts as an operator on the idempotents and to give the eigen values The constant represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed.
NASA Astrophysics Data System (ADS)
Monnier, B.; Naguib, A. M.; Koochesfahani, M. M.
2015-04-01
Reported herein is an investigation of the influence of the structural flexibility of sinusoidally pitching airfoils on the pattern of vorticity shed into the wake. For rigid airfoils, it is well known that, depending on the oscillation frequency and amplitude, this pattern takes the form of the classical or reverse von Kármán vortex street. The pattern may be characterized by the vortex circulation ( Γ o ), vortex-to-vortex streamwise and cross-stream spacing ( a and b, respectively), and vortex core radius ( R). In the present work, these four parameters are obtained from particle image velocimetry measurements in the wake of airfoils consisting of a rigid "head" and flexible "tail" at chord Reynolds number of 2010 for different tail flexibilities. The results show that flexible airfoils exhibit the switch from classical to reverse von Kármán vortex street (i.e., change in the sign of b) at a reduced frequency of oscillation lower than their rigid counterpart. At a given oscillation frequency, the Strouhal number at which this switch occurs is smallest for a given airfoil structural flexibility; which becomes stiffer with increasing frequency. Using Strouhal number based on the actual trailing edge oscillation amplitude, reasonable scaling is found of the dependence of not only b but also Γ o , a and R on the motion and structure parameters for all airfoils investigated. These results are complemented with analyses using a vortex array model, which together with the identified scaling of the wake vortex parameters, provide basis for the computation of the net thrust acting on the airfoil.
NASA Astrophysics Data System (ADS)
Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.
1995-08-01
The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.
NASA Astrophysics Data System (ADS)
Papangelo, A.; Ciavarella, M.
2015-03-01
Due to the nonlinearity of the Coulomb friction law, even the simplest models of interfaces in contact show a very rich dynamic solution. It is often desirable, especially if the frequency of loading is only a fraction of the first natural frequency of the system, to replace a full dynamic analysis with a quasi-static one, which obviously is much simpler to obtain. In this work, we study a simple Coulomb frictional oscillator with harmonic tangential load, but with constant normal load. It is found that the quasi-static solution (which has only 2 stops) captures approximately the displacement peak as long as the forcing frequency is low enough for the dynamic solution to have 2 or, even better, more than 2 stops. Instead, the velocity peak is not correctly estimated, since the velocity becomes highly irregular due to the stick-slip stops, whose number increases without limit for zero frequency. In this sense, the classical quasi-static solution, obtaining by cancelling inertia terms in the equilibrium equations, does not coincide with the limit of the full dynamic solution at low frequencies. The difference is not eliminated by adding a small amount of viscous damping, as only with critical damping, the dynamic solution is very close to the quasi-static one. Additional discrepancies arise above a limit frequency whose value depends on the ratio of the tangential load to the limit one for sliding, and correspond to when the dynamic solution turns from 2 to 0 stop per cycle.
Gasulla, Ivana; Sancho, Juan; Capmany, José; Lloret, Juan; Sales, Salvador
2010-12-01
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. PMID:21164914
A Model for Generative Harmonic Dictation.
ERIC Educational Resources Information Center
Bales, W. Kenton
This BASIC computer program designed to help music theory students practice harmonic dictation generates examples for students to use in a drill and practice approach in developing aural skills. To facilitate the implementation of effective generative algorithms, the author has used a non-linear analytical technique similar to the chord symbol…
Spherical harmonic analysis for verfication of a global atmospheric model
NASA Technical Reports Server (NTRS)
Christidis, Z.; Spar, J.
1979-01-01
Surface spherical harmonics were used to analyze the horizontal fields of various quantities generated by a global climate model. Also, the computed monthly mean forecast fields were compared with the corresponding observed fields.
Modeling cardiac pacemakers with relaxation oscillators
NASA Astrophysics Data System (ADS)
Grudziński, Krzysztof; Żebrowski, Jan J.
2004-05-01
A modified van der Pol oscillator model was designed in order to reproduce the time series of the action potential generated by a natural pacemaker of the heart (i.e., the SA or the AV node). The main motivation was that the models published up to now were not altogether adequate for research on the heart. Based on either the classical van der Pol oscillator or other nonlinear oscillators, these models were interesting rather because of the physical phenomena that could be obtained (chaos and synchronization). However, they were unable to simulate many important physiological features of true physiological action potentials. We based our research on the experience of other groups which modeled neuronal oscillators. There complex nonlinear oscillators were used whose most important feature was a certain topology of the phase space. In our case, we modified the phase space of the classical van der Pol oscillator by adding two fixed points: a saddle and a node. In addition, a damping term asymmetric with respect to the voltage was introduced. Introduction of these new features into the van der Pol oscillator allowed to change the firing frequency of the pacemaker node without changing the length of the refractory period - an important physiological detail. We also show different ways of changing the pacemaker rhythm. A comparison of the properties of the signal obtained from our model with the features of the action potentials measured by other groups is made.
Oscillations in SIRS model with distributed delays
NASA Astrophysics Data System (ADS)
Gonçalves, S.; Abramson, G.; Gomes, M. F. C.
2011-06-01
The ubiquity of oscillations in epidemics presents a long standing challenge for the formulation of epidemic models. Whether they are external and seasonally driven, or arise from the intrinsic dynamics is an open problem. It is known that fixed time delays destabilize the steady state solution of the standard SIRS model, giving rise to stable oscillations for certain parameters values. In this contribution, starting from the classical SIRS model, we make a general treatment of the recovery and loss of immunity terms. We present oscillation diagrams (amplitude and period) in terms of the parameters of the model, showing how oscillations can be destabilized by the shape of the distributions of the two characteristic (infectious and immune) times. The formulation is made in terms of delay equations which are both numerically integrated and linearized. Results from simulations are included showing where they support the linear analysis and explaining why not where they do not. Considerations and comparison with real diseases are presented along.
Nonlinear oscillator metamaterial model: numerical and experimental verification.
Poutrina, E; Huang, D; Urzhumov, Y; Smith, D R
2011-04-25
We verify numerically and experimentally the accuracy of an analytical model used to derive the effective nonlinear susceptibilities of a varactor-loaded split ring resonator (VLSRR) magnetic medium. For the numerical validation, a nonlinear oscillator model for the effective magnetization of the metamaterial is applied in conjunction with Maxwell equations and the two sets of equations solved numerically in the time-domain. The computed second harmonic generation (SHG) from a slab of a nonlinear material is then compared with the analytical model. The computed SHG is in excellent agreement with that predicted by the analytical model, both in terms of magnitude and spectral characteristics. Moreover, experimental measurements of the power transmitted through a fabricated VLSRR metamaterial at several power levels are also in agreement with the model, illustrating that the effective medium techniques associated with metamaterials can accurately be transitioned to nonlinear systems. PMID:21643082
On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator
ERIC Educational Resources Information Center
Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru
2009-01-01
The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.
Coupled Oscillator Model for Nonlinear Gravitational Perturbations
NASA Astrophysics Data System (ADS)
Yang, Huan; Zhang, Fan; Green, Stephen; Lehner, Luis
2015-04-01
Motivated by the fluid/gravity correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein's equation to the equations of motion of a series of nonlinearly-coupled harmonic oscillators. These oscillators correspond to the quasinormal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism with an asymptotically AdS black-brane spacetime, where the equations of motion for the oscillators are shown to be equivalent to the Navier-Stokes equation for the boundary fluid in the mode-expansion picture. We thereby expand on the explicit correspondence connecting the fluid and gravity sides for this particular physical set-up. Perhaps more importantly, we expect this formalism to remain valid in more general spacetimes, including those without a fluid/gravity correspondence. In other words, although born out of the correspondence, the formalism survives independently of it and has a much wider range of applicability.
Teaching Oscillations by a Model of Nanoresonator
NASA Astrophysics Data System (ADS)
Lindell, A.; Viiri, J.
2009-12-01
Nanoscience offers fascinating opportunities for science education as it links the achievements of modern technology to traditional models of science. In this article we present a nanotechnology orientated lesson on oscillations, suitable for physics courses at high schools and universities. The focus of the lesson is in forced oscillations on a cantilever beam used as a sensor in scanning probe microscopy or as an independent micro mechanical force sensor.
NASA Technical Reports Server (NTRS)
Isar, Aurelian
1995-01-01
The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.
Teichmann, Karen; Wenderoth, Martin; Prüser, Henning; Pierz, Klaus; Schumacher, Hans W; Ulbrich, Rainer G
2013-08-14
InAs quantum dots embedded in an AlAs matrix inside a double barrier resonant tunneling diode are investigated by cross-sectional scanning tunneling spectroscopy. The wave functions of the bound quantum dot states are spatially and energetically resolved. These bound states are known to be responsible for resonant tunneling phenomena in such quantum dot diodes. The wave functions reveal a textbook-like one-dimensional harmonic oscillator behavior showing up to five equidistant energy levels of 80 meV spacing. The derived effective oscillator mass of m* = 0.24m0 is 1 order of magnitude higher than the effective electron mass of bulk InAs that we attribute to the influence of the surrounding AlAs matrix. This underlines the importance of the matrix material for tailored QD devices with well-defined properties. PMID:23777509
NASA Astrophysics Data System (ADS)
KartaloğLu, Tolga; Figen, Z. Gürkan; Aytür, Orhan
2003-02-01
We report a simple ad hoc method for designing an aperiodic grating structure to quasi-phase match two arbitrary second-order nonlinear processes simultaneously within the same electric-field-poled crystal. This method also allows the relative strength of the two processes to be adjusted freely, thereby enabling maximization of the overall conversion efficiency. We also report an experiment that is based on an aperiodically poled lithium niobate crystal that was designed by use of our method. In this crystal, parametric oscillation and second-harmonic generation are simultaneously phase matched for upconversion of a femtosecond Ti:sapphire laser to 570 nm. This self-doubling optical parametric oscillator provides an experimental verification of our design method.
Steele, Richard H
2008-03-01
This article introduces quantum physics into biology in an intuitive and non-intimidating manner. It extends the quantum aspects of harmonic oscillators, and electromagnetic fields, to their functional roles in biology. Central to this process are the De Broglie wave-particle duality equation, and the adiabatic invariant parameters, magnetic moment, angular momentum and magnetic flux, determined by Ehrenfest as imposing quantum constraints on the dynamics of charges in motion. In mechanisms designed to explain the generation of low-level light emissions in biology we have adopted a biological analog of the electrical circuitry modeled on the parallel plated capacitor, traversed by helical protein structures, capable of generating electromagnetic radiation in the optical spectral region. The charge carrier required for the emissions is an accelerating electron driven, in a cyclotron-type mechanism, by ATP-induced reverse electron transfer with the radial, emission, components, mediated by coulombic forces within the helical configurations. Adenine, an essential nucleotide constituent of DNA, was examined with its long wavelength absorption maximum determining the energetic parameters for the calculations. The calculations were made for a virtual 5-turn helix where each turn of the helix emits a different frequency, generating a biological quantum series. The components of six adiabatic invariant equations were found to be embedded in Planck's constant rendering them discrete, finite, non-random, non-statistical-Planck's constant precludes probability. A mechanism for drug-induced hallucination is described that might provide insights as to the possible role of electromagnetic fields in consciousness. Sodium acceleration through a proposed nerve membrane helical channel generated electromagnetic emissions in the microwave region in confirmation of reported microwave emission for active nerves and may explain saltatory nerve conduction. Theoretical calculations for a
NASA Astrophysics Data System (ADS)
Bamler, Robert; Rosch, Achim
2015-06-01
The presence of (approximate) conservation laws can prohibit the fast relaxation of interacting many-particle quantum systems. We investigate this physics by studying the center-of-mass oscillations of two species of fermionic ultracold atoms in a harmonic trap. If their trap frequencies are equal, a dynamical symmetry (spectrum-generating algebra), closely related to Kohn's theorem, prohibits the relaxation of center-of-mass oscillations. A small detuning δ ω of the trap frequencies for the two species breaks the dynamical symmetry and ultimately leads to a damping of dipole oscillations driven by interspecies interactions. Using memory-matrix methods, we calculate the relaxation as a function of frequency difference, particle number, temperature, and strength of interspecies interactions. When interactions dominate, there is almost perfect drag between the two species and the dynamical symmetry is approximately restored. The drag can either arise from Hartree potentials or from friction. In the latter case (hydrodynamic limit), the center-of-mass oscillations decay with a tiny rate, 1 /τ ∝(δω ) 2/Γ , where Γ is a single-particle scattering rate.
Structure and Behavior of the Edge Harmonic Oscillation in Quiescent H-Mode Plasmas on DIII-D
NASA Astrophysics Data System (ADS)
McKee, G. R.; Yan, Z.; Burrell, K. H.; Garofalo, A. M.; Grierson, B. A.; Solomon, W. M.
2013-10-01
The edge harmonic oscillation (EHO) is a steady-state, pedestal-localized instability that is observed in high-performance, ELM-free Quiescent H-mode plasmas. The spatiotemporal characteristics of the EHO have been measured in QH-mode plasmas with a 2D BES array that measures low-k density fluctuations. The skewness of the fluctuation distribution increases radially from -0.5 to +1 near the separatrix, consistent with the radially varying and highly non-sinusoidal harmonic structure. These fluctuation characteristics are qualitatively consistent with an outward particle transport driven by the EHO. The density fluctuation (ñ / n) profile peaks inside the pedestal, near ρ = 0.90-0.95, and is observed from ρ = 0 . 85 to the separatrix; the fundamental frequency is typically in the range of 5-15 kHz. The radial structure of the oscillation has a monotonically varying phase shift of approximately 180 degrees across the outer plasma region that changes direction with plasma current, suggesting that the mode structure is impacted by the high edge toroidal rotation velocity. Work supported by the US Department of Energy under DE-FG02-08ER54999, DE-FC02-04ER54698, and DE-AC02-09CH11466.
Coupled oscillator model for nonlinear gravitational perturbations
NASA Astrophysics Data System (ADS)
Yang, Huan; Zhang, Fan; Green, Stephen R.; Lehner, Luis
2015-04-01
Motivated by the gravity-fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a collection of nonlinearly coupled harmonic oscillators. These oscillators correspond to the quasinormal or normal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism within the context of perturbed asymptotically anti-de Sitter black brane spacetimes. We confirm in this case that the boundary fluid dynamics are equivalent to those of the hydrodynamic quasinormal modes of the bulk spacetime. We expect this formalism to remain valid in more general spacetimes, including those without a fluid dual. In other words, although born out of the gravity-fluid correspondence, the formalism is fully independent and it has a much wider range of applicability. In particular, as this formalism inspires an especially transparent physical intuition, we expect its introduction to simplify the often highly technical analytical exploration of nonlinear gravitational dynamics.
Polynomial harmonic GMDH learning networks for time series modeling.
Nikolaev, Nikolay Y; Iba, Hitoshi
2003-12-01
This paper presents a constructive approach to neural network modeling of polynomial harmonic functions. This is an approach to growing higher-order networks like these build by the multilayer GMDH algorithm using activation polynomials. Two contributions for enhancement of the neural network learning are offered: (1) extending the expressive power of the network representation with another compositional scheme for combining polynomial terms and harmonics obtained analytically from the data; (2) space improving the higher-order network performance with a backpropagation algorithm for further gradient descent learning of the weights, initialized by least squares fitting during the growing phase. Empirical results show that the polynomial harmonic version phGMDH outperforms the previous GMDH, a Neurofuzzy GMDH and traditional MLP neural networks on time series modeling tasks. Applying next backpropagation training helps to achieve superior polynomial network performances. PMID:14622880
A Computer Model for Soda Bottle Oscillations: "The Bottelator".
ERIC Educational Resources Information Center
Soltzberg, Leonard J.; And Others
1997-01-01
Presents a model to explain the behavior of oscillatory phenomena found in the soda bottle oscillator. Describes recording the oscillations, and the design of the model based on the qualitative explanation of the oscillations. Illustrates a variety of physiochemical concepts including far-from-equilibrium oscillations, feedback, solubility and…
3/4-Fractional Superdiffusion in a System of Harmonic Oscillators Perturbed by a Conservative Noise
NASA Astrophysics Data System (ADS)
Bernardin, Cédric; Gonçalves, Patrícia; Jara, Milton
2016-05-01
We consider a harmonic chain perturbed by an energy conserving noise and show that after a space-time rescaling the energy-energy correlation function is given by the solution of a skew-fractional heat equation with exponent 3/4.
A model El Nino-Southern Oscillation
NASA Technical Reports Server (NTRS)
Zebiak, Stephen E.; Cane, Mark A.
1987-01-01
A coupled atmosphere-ocean model is developed and used to study the ENSO (El Nino/Southern Oscillation) phenomenon. With no anomalous external forcing, the coupled model reproduces certain key features of the observed phenomenon, including the recurrence of warm events at irregular intervals with a preference for three to four years. It is shown that the mean sea surface temperature, wind and ocean current fields determine the characteristic spatial structure of ENSO anomalies. The tendency for phase-locking of anomalies is explained in terms of a variation in coupling strength associated with the annual cycle in the mean fields. Sensitivity studies reveal that both the amplitude and the time scale of the oscillation are sensitive to several parameters that affect the strength of the atmosphere-ocean coupling. Stronger coupling implies larger oscillations with a longer timescale. A critical element of the model oscillation is the variability in the equatorial heat content of the upper ocean. Equatorial heat content increases prior to warm events and decreases sharply during the events. A theory for this variability and the associated transitions between non-El Nino and El Nino states is presented. Implications of the model results for the prediction of El Nino events are discussed.
Four mass coupled oscillator guitar model.
Popp, John E
2012-01-01
Coupled oscillator models have been used for the low frequency response (50 to 250 Hz) of a guitar. These 2 and 3 mass models correctly predict measured resonance frequency relationships under various laboratory boundary conditions, but did not always represent the true state of a guitar in the players' hands. The model presented has improved these models in three ways, (1) a fourth oscillator includes the guitar body, (2) plate stiffnesses and other fundamental parameters were measured directly and effective areas and masses used to calculate the responses, including resonances and phases, directly, and (3) one of the three resultant resonances varies with neck and side mass and can also be modeled as a bar mode of the neck and body. The calculated and measured resonances and phases agree reasonably well. PMID:22280705
A Comprehensive and Harmonized Digital Forensic Investigation Process Model.
Valjarevic, Aleksandar; Venter, Hein S
2015-11-01
Performing a digital forensic investigation (DFI) requires a standardized and formalized process. There is currently neither an international standard nor does a global, harmonized DFI process (DFIP) exist. The authors studied existing state-of-the-art DFIP models and concluded that there are significant disparities pertaining to the number of processes, the scope, the hierarchical levels, and concepts applied. This paper proposes a comprehensive model that harmonizes existing models. An effort was made to incorporate all types of processes proposed by the existing models, including those aimed at achieving digital forensic readiness. The authors introduce a novel class of processes called concurrent processes. This is a novel contribution that should, together with the rest of the model, enable more efficient and effective DFI, while ensuring admissibility of digital evidence. Ultimately, the proposed model is intended to be used for different types of DFI and should lead to standardization. PMID:26258644
Modelling the Madden Julian Oscillation
Slingo, J M; Inness, P M; Sperber, K R
2004-05-21
The MJO has long been an aspect of the global climate that has provided a tough test for the climate modelling community. Since the 1980s there have been numerous studies of the simulation of the MJO in atmospheric general circulation models (GCMs), ranging from Hayashi and Golder (1986, 1988) and Lau and Lau (1986), through to more recent studies such as Wang and Schlesinger (1999) and Wu et al. (2002). Of course, attempts to reproduce the MJO in climate models have proceeded in parallel with developments in our understanding of what the MJO is and what drives it. In fact, many advances in understanding the MJO have come through modeling studies. In particular, failure of climate models to simulate various aspects of the MJO has prompted investigations into the mechanisms that are important to its initiation and maintenance, leading to improvements both in our understanding of, and ability to simulate, the MJO. The initial focus of this chapter will be on modeling the MJO during northern winter, when it is characterized as a predominantly eastward propagating mode and is most readily seen in observations. Aspects of the simulation of the MJO will be discussed in the context of its sensitivity to the formulation of the atmospheric model, and the increasing evidence that it may be a coupled ocean-atmosphere phenomenon. Later, we will discuss the challenges regarding the simulation of boreal summer intraseasonal variability, which is more complex since it is a combination of the eastward propagating MJO and the northward propagation of the tropical convergence zone. Finally some concluding remarks on future directions in modeling the MJO and its relationship with other timescales of variability in the tropics will be made.
A representation of Jacchia's thermospheric models in spherical harmonics
NASA Technical Reports Server (NTRS)
Blum, P.; Harris, I.
1973-01-01
The Jacchia models are represented in terms of spherical harmonic functions. This representation has the advantages of ease of comparison with theoretical and other observational models and data, mathematical analyticity and relative simplicity. The symmetry properties of the models are emphasized by this representation and some physical characteristics like the increase of the amplitude of the diurnal density variation with decreasing solar activity become more apparent.
NASA Astrophysics Data System (ADS)
Marquette, Ian; Quesne, Christiane
2016-05-01
The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent PIV, obtained in the context of second-order supersymmetric quantum mechanics and third-order ladder operators, with a hierarchy of families of quantum systems called k-step rational extensions of the harmonic oscillator and related with multi-indexed Xm1,m2,…,mk Hermite exceptional orthogonal polynomials of type III. The connection between these exactly solvable models is established at the level of the equivalence of the Hamiltonians using rational solutions of the fourth Painlevé equation in terms of generalized Hermite and Okamoto polynomials. We also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving Darboux-Crum and Krein-Adler supercharges, their zero modes and the corresponding energies. These results will demonstrate and clarify the relation observed for a particular case in previous papers.
NASA Astrophysics Data System (ADS)
Aghaei, S.; Chenaghlou, A.
2015-01-01
In this paper, we study the Dirac equation with spin and pseudospin symmetry by the quadratic algebra approach for the 4-dimensional harmonic oscillator. By realization of the quadratic algebras in the deformed oscillator algebra, we obtain the relativistic energy spectrum. Also, by regarding the generalized Kustaanheimo-Stiefel transformation, we obtain the relativistic energy spectrum for the charge-dyon system with the U(1) monopole.
Speech synthesis with pitch modification using harmonic plus noise model
NASA Astrophysics Data System (ADS)
Lehana, Parveen K.; Pandey, Prem C.
2003-10-01
In harmonic plus noise model (HNM) based speech synthesis, the input signal is modeled as two parts: the harmonic part using amplitudes and phases of the harmonics of the fundamental and the noise part using an all-pole filter excited by random white Gaussian noise. This method requires relatively less number of parameters and computations, provides good quality output, and permits pitch and time scaling without explicit estimation of vocal tract parameters. Pitch scaling to synthesize the speech with interpolated original amplitudes and phases at the multiples of the scaled pitch frequency results in an unnatural quality. Our investigation for obtaining natural quality output showed that the frequency scale of the amplitudes and phases of the harmonics of the original signal needed to be modified by a speaker dependent warping function. The function was obtained by studying the relationship between pitch frequency and formant frequencies for the three cardinal vowels naturally occurring with different pitches in a passage with intonation. Listening tests showed that good quality speech was obtained by linear frequency scaling of the amplitude and phase spectra, by the same factor as the pitch-scaling.
Modeling of solar oscillation power spectra
NASA Technical Reports Server (NTRS)
Anderson, Edwin R.; Duvall, Thomas L., Jr.; Jefferies, Stuart M.
1990-01-01
To produce accurate estimates of the line-profile parameters of a model used to represent the spectral features in a solar oscillation power spectrum, it is necessary to (1) select the appropriate probability density function when deriving the maximum-likelihood function to be employed for the parameter estimation and (2) allow for the redistribution of spectral power caused by gaps in the data string. This paper describes a maximum-likelihood method for estimating the model parameters (based on the observed power spectrum statistics) that accounts for redistribution of spectral power caused by gaps in the data string, by convolving the model with the power spectrum of the observed window function. The accuracy and reliability of the method were tested using both artificial and authentic solar oscillation power spectrum data. A comparison of this method with various least-squares techniques is also presented.
Ayvaz, Muzaffer; Demiralp, Metin
2012-12-10
This study focuses on the construction of the optimal control equations for one dimensional quantum harmonic oscillator under the influence of external dipol effects and the solution of these equations by using Fluctuationlessness Theorem and a recently developed scheme called Characteristic Evolutions Method. The dipole function of the system has been taken as odd cubic spatial polynomial. Optimal control equations of the system under consideration are constructed by using expectation values of the position and the momentum operators instead of the wave and costate evolutions. It is shown that, the resulting equations are systems of ordinary differential equations and there are infinitely many ODEs. The solution strategy is based on the approximation of the expectation values for the operator products in the sense of Fluctuationlessness Theorem.
An Ultrahigh-order-mode, Higher-harmonic Coaxial Gyrotron Oscillator in Sub-terahertz Wave Range
NASA Astrophysics Data System (ADS)
Zhang, Hui-Bo; Zhang, Shi-Chang
2013-12-01
A coaxial cavity gyrotron oscillator at a frequency of 0.34 THz is studied, which operates with a quite low magnetic field of 4.55 Tesla at the third cyclotron harmonic of the ultrahigh-order mode TE43,4. Properly choosing the depth of the longitudinal corrugations on the inner rod and optimizing the electron-beam position significantly suppress the mode competition. Nonlinear multimode simulations show the feasibility of the single-mode operation with an output power of 163 kW by using an electron beam with a voltage of 70kV and a current of 30A, which corresponds to an interaction efficiency of 9.2 % with maxim density of ohmic losses 2.9 kW/cm2.
NASA Astrophysics Data System (ADS)
Carlos Castro-Palacio, Juan; Velázquez-Abad, Luisberis; Giménez, Marcos H.; Monsoriu, Juan A.
2013-06-01
We have used a mobile phone acceleration sensor, and the Accelerometer Monitor application for Android, to collect data in physics experiments on free and damped oscillations. Results for the period, frequency, spring constant, and damping constant agree very well with measurements obtained by other methods. These widely available sensors are likely to find increased use in instructional laboratories.
NASA Astrophysics Data System (ADS)
Castellanos-Gomez, A.
2013-01-01
A simple strobe setup with the potential to study higher-order eigenmodes and multifrequency oscillations in micromechanical resonators is described. It requires standard equipment, commonly found in many laboratories, and it can thus be employed for public demonstrations of mechanical resonances. Moreover, the work presented here can be used by undergraduate students and/or teachers to prepare practical work in laboratory courses at physics or engineering universities. The dynamics of a micromachined cantilever is analysed as an example. In fact, using our stroboscopic setup, the first and second flexural eigenmodes, as well as a multifrequency oscillation composed by a superposition of both modes, have been successfully filmed with a conventional optical microscope equipped with a digital camera.
A quantum quasi-harmonic nonlinear oscillator with an isotonic term
Rañada, Manuel F.
2014-08-01
The properties of a nonlinear oscillator with an additional term k{sub g}/x², characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, κ and k{sub g}, in such a way that for κ = 0 all the characteristics of the standard isotonic system are recovered. The first part is devoted to the classical system and the second part to the quantum system. This is a problem of quantization of a system with position-dependent mass of the form m(x) = 1/(1 − κx²), with a κ-dependent non-polynomial rational potential and with an additional isotonic term. The Schrödinger equation is exactly solved and the (κ, k{sub g})-dependent wave functions and bound state energies are explicitly obtained for both κ < 0 and κ > 0.
NASA Astrophysics Data System (ADS)
Hegedűs, Ferenc
2016-03-01
The topology of the stable periodic orbits of a harmonically driven bubble oscillator, the Rayleigh-Plesset equation, in the space of the excitation parameters (pressure amplitude and frequency) has been revealed numerically. This topology is governed by a hierarchy of two-sided Farey trees initiated from a unique primary structure defined also by a simple asymmetric Farey tree. The sub-topology of each of these building blocks is driven by a homoclinic tangency of a periodic saddle. This self-similar organisation is a suitable basis for a general description, since it is in good agreement with partial results obtained in other periodically forced oscillators and iterated maps. The applied ambient pressure in the model is near but still below Blake's critical threshold. Therefore, this paper is also a straightforward continuation of the work of Hegedűs [1], who first found numerical evidence for the existence of stable, period 1 solutions beyond Blake's threshold. The present findings are crucial for the extension of the available numerical results from period 1 to arbitrary periodicity.
Numerical linearized MHD model of flapping oscillations
NASA Astrophysics Data System (ADS)
Korovinskiy, D. B.; Ivanov, I. B.; Semenov, V. S.; Erkaev, N. V.; Kiehas, S. A.
2016-06-01
Kink-like magnetotail flapping oscillations in a Harris-like current sheet with earthward growing normal magnetic field component Bz are studied by means of time-dependent 2D linearized MHD numerical simulations. The dispersion relation and two-dimensional eigenfunctions are obtained. The results are compared with analytical estimates of the double-gradient model, which are found to be reliable for configurations with small Bz up to values ˜ 0.05 of the lobe magnetic field. Coupled with previous results, present simulations confirm that the earthward/tailward growth direction of the Bz component acts as a switch between stable/unstable regimes of the flapping mode, while the mode dispersion curve is the same in both cases. It is confirmed that flapping oscillations may be triggered by a simple Gaussian initial perturbation of the Vz velocity.
A Model for Semantic Equivalence Discovery for Harmonizing Master Data
NASA Astrophysics Data System (ADS)
Piprani, Baba
IT projects often face the challenge of harmonizing metadata and data so as to have a "single" version of the truth. Determining equivalency of multiple data instances against the given type, or set of types, is mandatory in establishing master data legitimacy in a data set that contains multiple incarnations of instances belonging to the same semantic data record . The results of a real-life application define how measuring criteria and equivalence path determination were established via a set of "probes" in conjunction with a score-card approach. There is a need for a suite of supporting models to help determine master data equivalency towards entity resolution—including mapping models, transform models, selection models, match models, an audit and control model, a scorecard model, a rating model. An ORM schema defines the set of supporting models along with their incarnation into an attribute based model as implemented in an RDBMS.
Testing the Model of Oscillating Magnetic Traps
NASA Astrophysics Data System (ADS)
Szaforz, Ż.; Tomczak, M.
2015-01-01
The aim of this paper is to test the model of oscillating magnetic traps (the OMT model), proposed by Jakimiec and Tomczak ( Solar Phys. 261, 233, 2010). This model describes the process of excitation of quasi-periodic pulsations (QPPs) observed during solar flares. In the OMT model energetic electrons are accelerated within a triangular, cusp-like structure situated between the reconnection point and the top of a flare loop as seen in soft X-rays. We analyzed QPPs in hard X-ray light curves for 23 flares as observed by Yohkoh. Three independent methods were used. We also used hard X-ray images to localize magnetic traps and soft X-ray images to diagnose thermal plasmas inside the traps. We found that the majority of the observed pulsation periods correlates with the diameters of oscillating magnetic traps, as was predicted by the OMT model. We also found that the electron number density of plasma inside the magnetic traps in the time of pulsation disappearance is strongly connected with the pulsation period. We conclude that the observations are consistent with the predictions of the OMT model for the analyzed set of flares.
Condition for equivalence of q-deformed and anharmonic oscillators
NASA Technical Reports Server (NTRS)
Artoni, M.; Zang, Jun; Birman, Joseph L.
1993-01-01
The equivalence between the q-deformed harmonic oscillator and a specific anharmonic oscillator model, by which some new insight into the problem of the physical meaning of the parameter q can be attained, are discussed.
Stanislavsky, A A
2004-11-01
We consider a fractional oscillator which is a generalization of the conventional linear oscillator in the framework of fractional calculus. It is interpreted as an ensemble average of ordinary harmonic oscillators governed by a stochastic time arrow. The intrinsic absorption of the fractional oscillator results from the full contribution of the harmonic oscillator ensemble: these oscillators differ a little from each other in frequency so that each response is compensated by an antiphase response of another harmonic oscillator. This allows one to draw a parallel in the dispersion analysis for media described by a fractional oscillator and an ensemble of ordinary harmonic oscillators with damping. The features of this analysis are discussed. PMID:15600586
Three oscillator model of the heartbeat generator
NASA Astrophysics Data System (ADS)
Suchorsky, Meghan; Rand, Richard
2009-05-01
The sinoatrial (SA) node is a group of self-oscillatory cells in the heart which beat rhythmically and initiate electric potentials, producing a wave of contraction that travels through the heart resulting in the circulation of blood. The SA node is an inhomogeneous collection of cells which have varying intrinsic frequencies. Experimental measurements of these frequencies have shown that the peripheral cells of the SA node have a higher natural frequency than do the interior cells. This is surprising to us since in 1:1 phase-locked motion of two oscillators of different frequency, the oscillator with the higher frequency leads the other oscillator by a phase angle. If the wave originates in the center of the SA node as one expects, then the interior cells would be leading in a 1:1 phase-locked motion and should therefore have a higher frequency than the peripheral cells. Our objective in this work is to explain this discrepancy between intuition and the measured results, and to determine possible advantages of having cells of lower frequency in the interior. Using a model of the SA node consisting of three coupled phase-only oscillators, we show that increased robustness of synchronized behavior (represented by a larger region of parameter space) comes as a result of the experimentally observed distribution of frequencies in the SA node. Associated with the loss of synchronized behavior is a complicated series of bifurcations called the "devil's staircase". We use our system to derive a 1D discontinuous map which exhibits the devil's staircase, and we analyze its dynamics.
NASA Astrophysics Data System (ADS)
Amro, Rami M.; Neiman, Alexander B.
2013-03-01
Sensory hair cells are the first stage in conveying the mechanical stimuli into the electrical signals in auditory and vestibular organs of vertebrates. Experiments showed that hair cells rely on active processes in hair bundles to achieve high selective sensitivity, e.g. due to myosin molecular motors inside stereocilia. In lower vertebrates these active processes result in spontaneous oscillations of hair bundles which can be accompanied by oscillations of the cells' membrane potentials. We use modeling to study how the dynamics of both the membrane potential and the hair bundle interact to produce coherent self-sustained oscillations and how this interaction contributes to the cell's sensitivity to external mechanical perturbations. The model incorporates a mechanical stochastic hair bundle system coupled to a Hodgkin-Huxley type system for the membrane potential. We show that oscillatory regimes result in enhanced sensitivity and selectivity to harmonic stimuli.
NASA Astrophysics Data System (ADS)
Haxton, Wick; Lunardini, Cecilia
2008-09-01
Semi-leptonic electroweak interactions in nuclei—such as β decay, μ capture, charged- and neutral-current neutrino reactions, and electron scattering—are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |p→|/M, where p→ and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q, where q is the magnitude of the three-momentum transfer. While results for such matrix elements are available in tabular form, with certain restriction on quantum numbers, the task of determining the analytic form of a response function can still be quite tedious, requiring the folding of the tabulated matrix elements with the nuclear density matrix, and subsequent algebra to evaluate products of operators. Here we provide a Mathematica script for generating these matrix elements, which will allow users to carry out all such calculations by symbolic manipulation. This will eliminate the errors that may accompany hand calculations and speed the calculation of electroweak nuclear cross sections and rates. We illustrate the use of the new script by calculating the cross sections for charged- and neutral-current neutrino scattering in 12C. Program summaryProgram title: SevenOperators Catalogue identifier: AEAY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
NASA Astrophysics Data System (ADS)
Hernandez Tenorio, C.; Villagran Vargas, E.; Serkin, Vladimir N.; Aguero Granados, M.; Belyaeva, T. L.; Pena Moreno, R.; Morales Lara, L.
2005-10-01
The dynamics of dark solitons is studied within the framework of the mathematical model of nonlinear Schrödinger equation (NSE) with an external harmonic potential. A comparative analysis of the solutions of nonstationary problems is performed for a linear harmonic oscillator and the NSE model with a harmonic potential for different signs of the self-action potential. It is shown that the main specific feature of the dynamics of dark NSE solitons in a parabolic trap is the formation of solitons with dynamically changing form factors producing the periodic variation in the modulation depth (the degree of 'blackness') of dark solitons. The oscillation period of the dark soliton does not coincide with the oscillation period of a linear quantum-mechanical oscillator, which is caused by the periodic transformation of the black soliton to the grey one and vice versa. The conditions of applicability of the method of inverse scattering problem are presented, the generalised Lax pair is found, and exact soliton solutions are given for the mathematical NSE model with an external harmonic potential.
Phase of the Riemann ζ function and the inverted harmonic oscillator
NASA Astrophysics Data System (ADS)
Bhaduri, R. K.; Khare, Avinash; Law, J.
1995-07-01
The Argand diagram is used to display some characteristics of the Riemann ζ function. The zeros of the ζ function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram. The behavior of the phase of the ζ function on and off the line of zeros is studied. Up to some distance from the line of the complex zeros, the phase angle is shown to still retain their memory. The Argand plots also lead to an analogy with the scattering amplitude and an approximate rule for the location of the zeros. The smooth phase of the ζ function along the line of the zeros is related to the quantum density of states of an inverted oscillator.
NASA Technical Reports Server (NTRS)
Durisen, R. H.
1978-01-01
The structure and stability of Maclaurin spheroids embedded in rigid uniform-density oblate spheroidal halos are determined by the tensor virial-equation method. These spheroid-halo systems can be thought of as crude fluid analogs of disk galaxies with halos. The halos are assumed to have the same center, the same axis of symmetry, and the same equatorial radius as the Maclaurin spheroids. Only halos with lower eccentricity than the Maclaurin spheroids are considered. The dynamic instability of the toroidal (barlike) modes is suppressed when m, the ratio of the halo mass to Maclaurin spheroid mass, is greater than 3 pi/8 for spherical halos and when m is greater than 1/2 for halos congruent to the Maclaurin spheroids. Intermediate halo flattenings yield intermediate critical m-values. On the other hand, a neutral point of the toroidal modes in the rotating and inertial frames occurs for all m and for all allowed halo flattenings. Growth rates for secular instability beyond the neutral point are calculated, and the eigenfrequencies of all second-harmonic modes are given for select cases. The Ostriker-Peebles (1973) conjecture concerning the stability of disk galaxies against barlike perturbations appears to be incorrect.
NASA Astrophysics Data System (ADS)
Hu, Xuanyu
2016-06-01
The spherical and ellipsoidal harmonic series of the external gravitational potential for a given mass distribution are equivalent in their mutual region of uniform convergence. In an instructive case, the equality of the two series on the common coordinate surface of an infinitely large sphere reveals the exact correspondence between the spherical and ellipsoidal harmonic coefficients. The transformation between the two sets of coefficients can be accomplished via the numerical methods by Walter (Celest Mech 2:389-397, 1970) and Dechambre and Scheeres (Astron Astrophys 387:1114-1122, 2002), respectively. On the other hand, the harmonic coefficients are defined by the integrals of mass density moments in terms of the respective solid harmonics. This paper presents general algebraic formulas for expressing the solid ellipsoidal harmonics as a linear combination of the corresponding solid spherical harmonics. An exact transformation from spherical to ellipsoidal harmonic coefficients is found by incorporating these connecting expressions into the density integral. A computational procedure is proposed for the transformation. Numerical results based on the nearly ellipsoidal Martian moon, Phobos, are presented for validation of the method.
Core-oscillator model of Caulobacter crescentus
NASA Astrophysics Data System (ADS)
Vandecan, Yves; Biondi, Emanuele; Blossey, Ralf
2016-06-01
The gram-negative bacterium Caulobacter crescentus is a powerful model organism for studies of bacterial cell cycle regulation. Although the major regulators and their connections in Caulobacter have been identified, it still is a challenge to properly understand the dynamics of its circuitry which accounts for both cell cycle progression and arrest. We show that the key decision module in Caulobacter is built from a limit cycle oscillator which controls the DNA replication program. The effect of an induced cell cycle arrest is demonstrated to be a key feature to classify the underlying dynamics.
NASA Astrophysics Data System (ADS)
Harko, Tiberiu; Liang, Shi-Dong
2016-06-01
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\\'enard and generalized Li\\'enard type, which physically describe important oscillator systems. By using a method inspired by quantum mechanics, and which consist on the deformation of the phase space coordinates of the harmonic oscillator, we generalize the equation of motion of the classical linear harmonic oscillator to several classes of strongly non-linear differential equations. The first integrals, and a number of exact solutions of the corresponding equations are explicitly obtained. The devised method can be further generalized to derive explicit general solutions of nonlinear second order differential equations unrelated to the harmonic oscillator. Applications of the obtained results for the study of the travelling wave solutions of the reaction-convection-diffusion equations, and of the large amplitude free vibrations of a uniform cantilever beam are also presented.
Model reduction for networks of coupled oscillators
NASA Astrophysics Data System (ADS)
Gottwald, Georg A.
2015-05-01
We present a collective coordinate approach to describe coupled phase oscillators. We apply the method to study synchronisation in a Kuramoto model. In our approach, an N-dimensional Kuramoto model is reduced to an n-dimensional ordinary differential equation with n ≪ N , constituting an immense reduction in complexity. The onset of both local and global synchronisation is reproduced to good numerical accuracy, and we are able to describe both soft and hard transitions. By introducing two collective coordinates, the approach is able to describe the interaction of two partially synchronised clusters in the case of bimodally distributed native frequencies. Furthermore, our approach allows us to accurately describe finite size scalings of the critical coupling strength. We corroborate our analytical results by comparing with numerical simulations of the Kuramoto model with all-to-all coupling networks for several distributions of the native frequencies.
Are Collapse Models Testable via Flavor Oscillations?
NASA Astrophysics Data System (ADS)
Donadi, Sandro; Bassi, Angelo; Curceanu, Catalina; Di Domenico, Antonio; Hiesmayr, Beatrix C.
2013-07-01
Collapse models predict the spontaneous collapse of the wave function, in order to avoid the emergence of macroscopic superpositions. In their mass-dependent formulation, they claim that the collapse of any system's wave function depends on its mass. Neutral K, D, B mesons are oscillating systems that are given by Nature as superposition of two distinct mass eigenstates. Thus they are unique laboratory for testing collapse models that are sensitive to the mass. In this paper we derive—for the single mesons and bipartite entangled mesons—the effect of the mass-proportional CSL (Continuous Spontaneous Localization) collapse model on the dynamics on neutral mesons. We compare the theoretical prediction with experimental data from different accelerator facilities.
NASA Astrophysics Data System (ADS)
StankevičiÅ«tÄ--, K.; PipinytÄ--, I.; Vengelis, J.; MarcinkevičiÅ«tÄ--, A.; Å uminas, R.; Grigonis, R.; Eckardt, R. C.; Sirutkaitis, V.
2013-09-01
We present experimental data obtained during investigation of synchronously pumped optical parametric oscillators (SPOPO's) pumped by fundamental (1030 nm) and second harmonic (515 nm) radiation of mode-locked Yb:KGW laser, providing 105 fs pulses at 76 MHz repetition rate with an average power of 4 W. Different nonlinear crystals such as beta barium borate (BBO), and periodically poled lithium niobate (PPLN) and MgO doped PPLN (MgO:PPLN) were tested to estimate wavelength tuning capabilities and SPOPO's efficiency. Rotation of BBO nonlinear crystal and SPOPO's cavity length variation and, in the case of SPOPO based on PPLN, change of grating period and cavity length allowed signal wavelength tuning in 630 - 1030 nm and 1350 - 1700 nm spectral ranges, respectively. Parametric light conversion from pump power to signal power efficiency was as high as 25 %. Including the idler pulses the tuning ranges were from 630 to 2400 nm and from 1350 to 4000 nm in case of BBO and PPLN crystals, respectively. SPOPO based on BBO wsithout intracavity group velocity dispersion (GVD) compensation generates longer than transform limited pulses, so SPOPO based on BBO with dispersive prisms were investigated.
Neural network solution of the Schrödinger equation for a two-dimensional harmonic oscillator
NASA Astrophysics Data System (ADS)
Androsiuk, J.; Kułak, L.; Sienicki, K.
1993-07-01
We present computer simulations of a neural network capable of learning to perform transformations generated by the Schrödinger equation required to find eigenenergies of a two-dimensional harmonic oscillator. We show that this task can be achieved by a not fully connected back-propagation neural network containing 49 input neurons, 3 hidden layer neurons and 1 output neuron. The investigated neural network turns out to be capable of predicting eigenenergies with an average error of less than one percent. We demonstrate that the CPU time required to teach a neural network of performing the transformation produced by the Schrödinger equation is about 2 min to reach 41000 learning iterations, thus making foreseeable a direct application of a neural network in this and other more complex physical and chemical problems. A discussion of the errors due to the generalization of acquired knowledge is presented and related to a limited number of examples in learning mode and the number of neurons in the hidden layer. Decreasing the number of neurons in the hidden layer increases the apparent ability of the neural network for generalization.
NASA Technical Reports Server (NTRS)
Weatherill, W. H.; Ehlers, F. E.; Yip, E.; Sebastian, J. D.
1980-01-01
Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.
Raindrop Oscillations: Evaluation of a Potential Flow Model with Gravity.
NASA Astrophysics Data System (ADS)
Beard, Kennethi V.
1984-05-01
Potential flow oscillations about an equilibrium raindrop distortion were modeled for ellipsoidal variations driven by changes in surface and gravitational potential energy with linear dissipation of kinetic energy. The model was found to be quantitatively similar to the Navier-Stokes results of G. B. Foote for axisymmetric oscillations without gravity. Computed frequencies and average axis ratios for vertical and horizontal oscillations with gravity were compared to wind tunnel observations of oscillating water drops and raindrop camera data. Simple formulas with good accuracy were developed for the time variation and time average axis ratios as a function of oscillation amplitude.
Quantitative Modeling of Single Atom High Harmonic Generation
Gordon, Ariel; Kaertner, Franz X.
2005-11-25
It is shown by comparison with numerical solutions of the Schroedinger equation that the three step model (TSM) of high harmonic generation (HHG) can be improved to give a quantitatively reliable description of the process. Excellent agreement is demonstrated for the H atom and the H{sub 2}{sup +} molecular ion. It is shown that the standard TSM heavily distorts the HHG spectra, especially of H{sub 2}{sup +}, and an explanation is presented for this behavior. Key to the improvement is the use of the Ehrenfest theorem in the TSM.
A model of nonautonomous dynamics driven by repeated harmonic interaction
NASA Astrophysics Data System (ADS)
Zagrebnov, V. A.; Tamura, H.
2016-06-01
We consider an exactly solvable model of nonautonomous W*-dynamics driven by repeated harmonic interaction. The dynamics is Hamiltonian and quasifree. Because of inelastic interaction in the large-time limit, it leads to relaxation of initial states to steady states. We derive the explicit entropy production rate accompanying this relaxation. We also study the evolution of different subsystems to elucidate their eventual correlations and convergence to equilibriums. In conclusion, we prove that the W*-dynamics manifests a universal stationary behavior in a short-time interaction limit.
Noguera, Norman; Rózga, Krzysztof
2015-07-15
In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case of a slightly more general potential than the one for harmonic oscillator.
NASA Astrophysics Data System (ADS)
Taghipour, Javad; Dardel, Morteza
2015-10-01
Steady state dynamical behavior of two degrees of freedom (DOF) system composed of a harmonically excited nonlinear oscillator coupled with a single DOF nonlinear energy sink (NES) is studied in comparison with the behavior of a system consisting of a nonlinear oscillator coupled with a two-DOF NES subjected to external harmonic excitation. First, an optimized set of parameters was obtained using optimization for the two-DOF system. Results show that the system with one NES has low robustness to the changes of the parameters and external force. By adding a degree of freedom to the first system, the steady state behavior of the resulting three-DOF system was investigated. Conclusions illustrated that increasing the degrees of freedom of the NES would increase the robustness of the system to the changes in system parameters and amplitude of external force.
Modeling Airborne Gravimetry with High-Degree Harmonic Expansions
NASA Astrophysics Data System (ADS)
Holmes, Simon; Wang, Yan Ming; Roman, Daniel
2010-05-01
Since its official unveiling at the 2008 General Assembly of the European Geosciences Union, EGM2008 has demonstrated that high-degree harmonic expansions constitute a useful and effective final representation for high-resolution global gravitational models. However, such expansions also provide a versatile means of capturing (modeling), inter-comparing, and optimally combining local and regional high-resolution terrestrial data sets of different types. Here we present a general recipe for using high-degree expansions to capture, downward-continue and assimilate airborne survey data. This approach relies on the production of two ‘competing' high-degree expansions. A first, ‘terrestrial-only' expansion incorporates EGM2008 globally, and high-resolution terrestrial gravimetry regionally. This expansion can be used to upward-continue the regional terrestrial data to the flight level of the airborne survey, such that the terrestrial gravimetry outside the survey area can be merged with the airborne data inside the survey area, all at flight level. Harmonic analysis of this merged data set, also at flight level, yields a second ‘airborne-augmented' expansion, which closely matches the ‘terrestrial-only' expansion outside the survey area, but which also closely reproduces the airborne survey data inside the survey area. Capturing the airborne and terrestrial data in this way means that downward-continuation of the airborne data, as well as spectral/spatial comparison (and ultimate combination) of the airborne data with the terrestrial (and satellite) data, can all be achieved through spherical- and ellipsoidal-harmonic synthesis of these two competing expansions, and their spectral combination. This general approach is illustrated with a worked example.
A model for premixed combustion oscillations
Janus, M.C.; Richards, G.A.
1996-03-01
Combustion oscillations are receiving renewed research interest due to increasing application of lean premix (LPM) combustion to gas turbines. A simple, nonlinear model for premixed combustion is described; it was developed to explain experimental results and to provide guidance for developing active control schemes based on nonlinear concepts. The model can be used to quickly examine instability trends associated with changes in equivalence ratio, mass flow rate, geometry, ambient conditions, etc. The model represents the relevant processes occurring in a fuel nozzle and combustor analogous to current LPM turbine combustors. Conservation equations for the nozzle and combustor are developed from simple control volume analysis, providing ordinary differential equations that can be solved on a PC. Combustion is modeled as a stirred reactor, with bimolecular reaction between fuel and air. Although focus is on the model, it and experimental results are compared to understand effects of inlet air temperature and open loop control schemes. The model shows that both are related to changes in transport time.
A one-dimensional basic oscillator model of the vircator
NASA Astrophysics Data System (ADS)
Biswas, Debabrata
2009-06-01
A one-dimensional model of the virtual cathode oscillator (vircator) is proposed keeping only the essential physical processes. The basic model consists of a radiating charge in an oscillating electric field. Using parameters from (realistic) particle-in-cell simulations such as the charge Q and amplitude E1 of the oscillating electric field, the model correctly predicts the amplitude of virtual cathode oscillation and the power radiated. The basic model is then extended to incorporate beam-cavity interaction and the resonance effect.
Oscillation models for predicting raindrop axis and backscatter ratios
NASA Astrophysics Data System (ADS)
Beard, K. V.
1984-01-01
Raindrop oscillations have been modeled using a potential flow, ellipsoidal variation about an equilibrium distortion along with a potential energy function that includes surface and gravitational energy. Two degenerate modes were investigated, the axisymmetric (vertical) oscillation and the ellipsoidal (horizontal) oscillation, and found to have different time-averaged axis ratios and oscillation frequencies. Averaged axis and backscatter ratios were calculated for oscillations in a steady state balance between collisional energy and viscous dissipation. The results indicate that the polarization properties of rain are significantly affected by the nonequilibrium distortion of large drops in heavy rainfall.
Majority orienting model for the oscillation of market price
NASA Astrophysics Data System (ADS)
Takahashi, H.; Itoh, Y.
2004-01-01
The present paper introduces a majority orienting model in which the dealers' behavior changes based on the influence of the price to show the oscillation of stock price in the stock market. We show the oscillation of the price for the model by applying the vanderPol equation which is a deterministic approximation of our model.
A Computer Model for Soda Bottle Oscillations: "The Bottelator"
NASA Astrophysics Data System (ADS)
Soltzberg, Leonard J.; Bowers, Peter G.; Hofstetter, Christine
1997-06-01
Oscillatory release of gas sometimes occurs when a small pinhole is made in a bottle of commercial soda water. We present experimental documentation of these oscillations, and have modeled them using the Stella II modeling package. The oscillations arise because the headspace above the liquid in the bottle is repressurized by escaping bubbles, thereby temporarily shutting off further bubble nucleation. The system makes an extremely simple demonstration of far-from-equilibrium oscillations.
Numerical Modeling of High Harmonic Fast Wave Heating on NSTX
NASA Astrophysics Data System (ADS)
Phillips, C. K.; Hosea, J. C.; Bell, R. E.; Leblanc, B. P.; Parker, J. B.; Valeo, E. J.; Wilson, J. R.; Ryan, P. M.; Jaeger, E. F.; Wilgen, J. B.; Sabbagh, S. A.; Bonoli, P. T.; Wright, J. C.; Harvey, R. W.; Dumont, R. J.
2007-11-01
High harmonic fast wave (HHFW) heating and current drive processes, at frequencies up to 15 times the fundamental deuterium cyclotron frequency, are being studied on NSTX. Recent experiments indicate that the core heating efficiency depends strongly on the antenna phasing and plasma conditions [1]. The wave propagation and absorption characteristics for select NSTX discharges will be analyzed using a variety of rf modeling codes, including both ray tracing and full wave models. Both core power deposition profiles and rf power flow in the edge regions will be considered. The possibility of off-axis mode conversion of the HHFW to shorter wavelength modes and the subsequent impact on power deposition will be explored. [1] See invited talk by J. C. Hosea this meeting for details
ABJM models in Script N = 3 harmonic superspace
NASA Astrophysics Data System (ADS)
Buchbinder, I. L.; Ivanov, E. A.; Lechtenfeld, O.; Pletnev, N. G.; Samsonov, I. B.; Zupnik, B. M.
2009-03-01
We construct the classical action of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model in the Script N = 3, d = 3 harmonic superspace. In such a formulation three out of six supersymmetries are realized off shell while the other three mix the superfields and close on shell. The superfield action involves two hypermultiplet superfields in the bifundamental representation of the gauge group and two Chern-Simons gauge superfields corresponding to the left and right gauge groups. The Script N = 3 superconformal invariance allows only for a minimal gauge interaction of the hypermultiplets. Amazingly, the correct sextic scalar potential of ABJM emerges after the elimination of auxiliary fields. Besides the original U(N) × U(N) ABJM model, we also construct Script N = 3 superfield formulations of some generalizations. For the SU(2) × SU(2) case we give a simple superfield proof of its enhanced Script N = 8 supersymmetry and SO(8) R-symmetry.
Experimental investigation and model development for a harmonic drive transmission.
Preissner, C.; Shu, D.; Royston, T. J.; Univ. of Illinois at Chicago
2007-01-01
Harmonic drive transmissions (HDTs) are compact, low-backlash, high-ratio, high-resolution rotary motion transmissions. One application to benefit from these attributes is the revolute joint robot. Engineers at the Advanced Photon Source (APS) are investigating the use of this type of robot for the positioning of an x-ray detector; understanding the properties of the robot components is crucial to modeling positioner behavior. The robot bearing elements had been investigated previously, leaving the transmission as the missing component. While the benefits of HDTs are well known, the disadvantages, including fluctuating dissipation characteristics and nonlinear stiffness, are not understood as well. These characteristics can contribute uncontrolled dynamics to the overall robot performance. A dynamometer has been constructed at the APS to experimentally measure the HDT's response. Empirical torque and position data were recorded for multiple transmission load cases and input conditions. In turn, a computer model of the dynamometer HDT system was constructed to approximate the observed response.
Polymerization and oscillation stuttering in a filamentous model of the subcellular Min oscillation
NASA Astrophysics Data System (ADS)
Rutenberg, Andrew; Sengupta, Supratim; Sain, Anirban; Derr, Julien
2011-03-01
We present a computational model of the E. coli Min oscillation that involves polymerization of MinD filaments followed by depolymerization stimulated by filament-end zones of MinE. Our stochastic model is fully three-dimensional, and tracks the diffusion and interactions of every MinD and MinE molecule. We recover self-organized Min oscillations. We investigate the experimental phenomenon of oscillation stuttering, which we relate to the disruption of MinE tip-binding at the filament scale.
Multiple Bifurcations in a Polynomial Model of Bursting Oscillations
NASA Astrophysics Data System (ADS)
de Vries, G.
1998-06-01
Bursting oscillations are commonly seen to be the primary mode of electrical behaviour in a variety of nerve and endocrine cells, and have also been observed in some biochemical and chemical systems. There are many models of bursting. This paper addresses the issue of being able to predict the type of bursting oscillation that can be produced by a model. A simplified model capable of exhibiting a wide variety of bursting oscillations is examined. By considering the codimension-2 bifurcations associated with Hopf, homoclinic, and saddle-node of periodics bifurcations, a bifurcation map in two-dimensional parameter space is created. Each region on the map is characterized by a qualitatively distinct bifurcation diagram and, hence, represents one type of bursting oscillation. The map elucidates the relationship between the various types of bursting oscillations. In addition, the map provides a different and broader view of the current classification scheme of bursting oscillations.
Investigation of self-oscillation using particle balance model
Bae, Inshik; Na, Byungkeun Chang, Hongyoung
2015-08-15
Self-oscillation obtained using a DC-only power supply under specific anode voltage conditions is investigated in a cylindrical system with thermal electrons using tungsten filaments. Analysis of the obtained oscillation profiles reveals that the experimental data are consistent with a model derived from the particle balance model. The self-oscillation period characteristics with respect to the pressure and gas species are also analyzed. As the physics and particle motion of self-oscillation near the plasma transition region are analyzed from different perspectives, this paper may advance the study of this phenomenon.
Investigation of Self-Oscillation using Particle Balance Model
NASA Astrophysics Data System (ADS)
Bae, Inshik; Na, Byungkeun; Chang, Hongyoung
2015-09-01
Self-oscillation, which is obtained by using a DC-only power supply with specific anode voltage conditions, is investigated in a cylindrical system with thermal electrons using tungsten filaments. From analysis of the obtained oscillation profiles, the experimental data is consistent with the model derived from the particle balance model. The self-oscillation period characteristics with respect to the pressure and gas species are also analyzed. As the physics and particle motion of self-oscillation near the electron avalanche is analyzed in different perspective, this study may advance the understanding of this phenomenon. This research was supported by the Ministry of Knowledge Economy (MKE) of Korea (Grant No. 10041681).
A numerical modelling of stator rotor interaction in a turbine stage with oscillating blades
NASA Astrophysics Data System (ADS)
Gnesin, V. I.; Kolodyazhnaya, L. V.; Rzadkowski, R.
2004-11-01
In real flows unsteady phenomena connected with the circumferential non-uniformity of the main flow and those caused by oscillations of blades are observed only jointly. An understanding of the physics of the mutual interaction between gas flow and oscillating blades and the development of predictive capabilities are essential for improved overall efficiency, durability and reliability. In the study presented, the algorithm proposed involves the coupled solution of 3D unsteady flow through a turbine stage and the dynamics problem for rotor-blade motion by the action of aerodynamic forces, without separating the outer and inner flow fluctuations. The partially integrated method involves the solution of the fluid and structural equations separately, but information is exchanged at each time step, so that solution from one domain is used as a boundary condition for the other domain. 3-D transonic gas flow through the stator and rotor blades in relative motion with periodicity on the whole annulus is described by the unsteady Euler conservation equations, which are integrated using the explicit monotonous finite volume difference scheme of Godunov Kolgan. The structural analysis uses the modal approach and a 3-D finite element model of a blade. The blade motion is assumed to be constituted as a linear combination of the first natural modes of blade oscillations, with the modal coefficients depending on time. A calculation has been done for the last stage of the steam turbine, under design and off-design regimes. The numerical results for unsteady aerodynamic forces due to stator rotor interaction are compared with results obtained while taking into account blade oscillations. The mutual influence of both outer flow non-uniformity and blade oscillations has been investigated. It is shown that the amplitude-frequency spectrum of blade oscillations contains the high-frequency harmonics, corresponding to the rotor moving past one stator blade pitch, and low
Analytical modelling and x-ray imaging of oscillations of a single magnetic domain wall
Bocklage, Lars; Kruger, Benjamin; Fischer, Peter; Meier, Guido
2009-07-10
Domain-wall oscillation in a pinnig potential is described analytically in a one dimensional model for the feld-driven case. For a proper description the pinning potential has to be extended by nonharmonic contributions. Oscillations of a domain wall are observed on its genuine time scale by magnetic X-ray microscopy. It is shown that the nonharmonic terms are present in real samples with a strong restoring potential. In the framework of our model we gain deep insight into the domain-wall motion by looking at different phase spaces. The corrections of the harmonic potential can change the motion of the domain wall significantly. The damping parameter of permalloy is determined via the direct imaging technique.
Modeling and analysis of aircraft non-linear components for harmonics analysis
Karimi, K.J.; Voss, J.
1995-12-31
Modern commercial aircraft Electric Power Systems (EPS) include many nonlinear components which produce harmonics. The addition of all the current harmonics could result in a power system with unacceptable levels of voltage distortion. It is important to be able to predict the levels of voltage distortion at early program stages to correct any potential problems and avoid costly redesigns. In this paper the nature and sources of harmonic producing equipment are described. These sources of harmonics and their effect on aircraft power system operation are described. Models for various aircraft non-linear components are developed in this paper. These component models are used in a model of the Boeing 777 EPS which is used to calculate voltage harmonics for various airplane configurations and flight conditions. A description of this model and the models used for various components are given. Tests performed to validate these models are described. Comparison of experimental results with analytical model predictions are given.
Misra, Ranjeev; Mandal, Soma E-mail: soma@iucaa.ernet.in
2013-12-10
A generic model for alternating lags in quasi-periodic oscillation (QPO) harmonics is presented where variations in the photon spectrum are caused by oscillations in two parameters that characterize the spectrum. It is further assumed that variations in one of the parameters are linearly driven by variations in the other after a time delay t{sub d} . It is shown that alternating lags will be observed for a range of t{sub d} values. A phenomenological model based on this generic one is developed that can explain the amplitude and phase lag variation with energy of the fundamental and the next three harmonics of the 67 mHz QPO observed in GRS 1915+105. The phenomenological model also predicts the variation of the Bicoherence phase with energy, which can be checked by further analysis of the observational data.
Discrete Harmonic Model for Stacked Membranes: Theory and Experiment
NASA Astrophysics Data System (ADS)
Lei, Ning; Safinya, C. R.; Bruinsma, R. F.
1995-08-01
The discrete harmonic (DH) model has been developed which describes the static structure factor of stacked membranes. The (DH) model was used to analyze a synchrotron small-angle X-ray scattering study in stacked membranes. We studied lyotropic lamellar Lα phase samples in a quaternary mixture consisting of thin water layers coated with surfactant sodium dodecyl sulfate (SDS) and cosurfactant (pentanol) molecules, separated by oil. The experiments on highly oriented Lα phase samples covered a large interlayer spacing range from d=49.1 to 255.8 Å produced by dodecane dilution, which considerably exceeded those of previous high resolution synchrotron scattering studies of powder samples. Two significant differences emerge between the (DH) model and the continuum Caillé model description of smectic-A liquid crystals and multilayer membranes. First, whereas the continuum model is necessarily restricted to the vicinity of the Bragg peaks of the structure factor, the discrete nature of the (DH) model allowed us to fit the experimentally measured X-ray structure factor over the full range of wave-vectors and dilutions. This enabled measurements of the membrane bending and multilayer compressiblity elastic constants kappa and B separately, in contrast to the continuum model which gives reliable measurement of the product kappa B. Second, the (DH) model is able to account for the universally observed anomalously large small angle scattering (SAS) in strongly fluctuating dilute fluid multilayer membranes. The (SAS) is shown to contain contributions both due to concentration fluctuations described previously by Porte et al. and Nallet et al. and unexpectedly from a divergent thermal-coherent diffraction effect which dominates in single crystal multilayers.
The analysis of solar models: Neutrinos and oscillations
NASA Technical Reports Server (NTRS)
Ulrich, R. K.; Rhodes, E. J., Jr.; Tomczyk, S.; Dumont, P. J.; Brunish, W. M.
1983-01-01
Tests of solar neutrino flux and solar oscillation frequencies were used to assess standard stellar structure theory. Standard and non-standard solar models are enumerated and discussed. The field of solar seismology, wherein the solar interior is studied from the measurement of solar oscillations, is introduced.
Spherical Calogero model with oscillator/Coulomb potential: Quantum case
NASA Astrophysics Data System (ADS)
Correa, Francisco; Hakobyan, Tigran; Lechtenfeld, Olaf; Nersessian, Armen
2016-06-01
We consider the quantum mechanics of Calogero models in an oscillator or Coulomb potential on the N -dimensional sphere. Their Hamiltonians are obtained by an appropriate Dunkl deformation of the oscillator/Coulomb system on the sphere and its restriction to (Coxeter reflection) symmetric wave functions. By the same method we also find the symmetry generators and compute their algebras.
Oishi, T.; Kado, S.; Yoshinuma, M.; Ida, K.; Akiyama, T.; Minami, T.; Nagaoka, K.; Shimizu, A.; Okamura, S.; Tanaka, S.
2006-10-15
In the present study, a coherent density fluctuation similar to the edge harmonic oscillation (EHO) in tokamaks was observed in the edge transport barrier discharge in the Compact Helical System (CHS) [K. Matsuoka et al., Plasma Physics and Controlled Nuclear Fusion Research, 1988 (International Atomic Energy Agency, Vienna, 1989), Vol. 2, pp. 441] using beam emission spectroscopy (BES). The fluctuation had both fundamental (f=4.5 kHz) and second-harmonic (2f=9 kHz) frequencies. EHO in CHS had a peak amplitude at approximately {rho}=0.95. The mode has a continuous phase shift in the radial direction. If this is interpreted as the radial propagation, the mode propagates in the outer radial direction at an apparent phase velocity of several hundreds of meters per second, which is a characteristic similar to the radial phase shift of EHO in tokamaks.
Guo, H.Z.; Rodgers, J.; Hoppe, D.J.
1995-12-31
Phase-locking in a 34.5 GHz special complex cavity gyrotron oscillator operating at the second harmonic of the electron cyclotron frequency was studied. Injection of the locking power was made via a quasi-optical circulator connected to the gyrotron output. Locking bandwidth was measured by comparing the phase of the injection signal and output signal using a balanced mixer. Locking was observed with input power level as low as 40 dB below the gyrotron output power. The locking bandwidth is, however, narrower than in gyrotrons operating at the fundamental cyclotron frequency which may be attributed to the longer resonant cavity in the second harmonic gyrotron and the corresponding larger value of external quality factor. The measurements are roughly in agreement with predictions of Adler`s phase-locking equation which is given for the system in terms of powers propagating in the output waveguide toward and away from the gyrotron cavity.
NASA Astrophysics Data System (ADS)
Stoitsov, M. V.; Dobaczewski, J.; Nazarewicz, W.; Ring, P.
2005-04-01
We describe the program HFBTHO for axially deformed configurational Hartree-Fock-Bogolyubov calculations with Skyrme-forces and zero-range pairing interaction using Harmonic-Oscillator and/or Transformed Harmonic-Oscillator states. The particle-number symmetry is approximately restored using the Lipkin-Nogami prescription, followed by an exact particle number projection after the variation. The program can be used in a variety of applications, including systematic studies of wide ranges of nuclei, both spherical and axially deformed, extending all the way out to nucleon drip lines. Program summaryTitle of the program: HFBTHO (v1.66p) Catalogue number: ADUI Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI Licensing provisions: none Computers on which the program has been tested: Pentium-III, Pentium-IV, AMD-Athlon, IBM Power 3, IBM Power 4, Intel Xeon Operating systems: LINUX, Windows Programming language used: FORTRAN-95 Memory required to execute with typical data: 59 MB when using N=20 No. of bits in a word: 64 No. of processors used: 1 Has the code been vectorized?: No No. of bytes in distributed program, including test data, etc.: 195 285 No. of lines in distributed program: 12 058 Distribution format: tar.gz Nature of physical problem: The solution of self-consistent mean-field equations for weakly bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasiparticle wave functions. In the present implementation, this is achieved by using the single-particle wave functions of the Transformed Harmonic Oscillator, which allows for an accurate description of deformation effects and pairing correlations in nuclei arbitrarily close to the particle drip lines. Method of solution: The program uses the axially Transformed Harmonic Oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes
NASA Astrophysics Data System (ADS)
Aeschlimann, Martin; Brixner, Tobias; Fischer, Alexander; Hensen, Matthias; Huber, Bernhard; Kilbane, Deirdre; Kramer, Christian; Pfeiffer, Walter; Piecuch, Martin; Thielen, Philip
2016-07-01
We reconstruct the optical response of nanostructures of increasing complexity by fitting interferometric time-resolved photoemission electron microscopy (PEEM) data from an ultrashort (21 fs) laser excitation source with different harmonic oscillator-based models. Due to its high spatial resolution of ~40 nm, PEEM is a true near-field imaging system and enables in normal incidence mode a mapping of plasmon polaritons and an intuitive interpretation of the plasmonic behaviour. Using an actively stabilized Mach-Zehnder interferometer, we record two-pulse correlation signals with 50 as time resolution that contain information about the temporal plasmon polariton evolution. Spectral amplitude and phase of excited plasmon polaritons are extracted from the recorded phase-resolved interferometric two-pulse correlation traces. We show that the optical response of a plasmon polariton generated at a gold nanoparticle can be reconstructed from the interferometric two-pulse correlation signal using a single harmonic oscillator model. In contrast, for a corrugated silver surface, a system with increased plasmonic complexity, in general an unambiguous reconstruction of the local optical response based on coupled and uncoupled harmonic oscillators, fails. Whereas for certain local responses different models can be discriminated, this is impossible for other positions. Multidimensional spectroscopy offers a possibility to overcome this limitation.
Bierbach, Jana; Yeung, Mark; Eckner, Erich; Roedel, Christian; Kuschel, Stephan; Zepf, Matt; Paulus, Gerhard G.
2015-05-01
Surface high-harmonic generation in the relativistic regime is demonstrated as a source of extreme ultra-violet (XUV) pulses with extended operation time. Relativistic high-harmonic generation is driven by a frequency-doubled high-power Ti:Sapphire laser focused to a peak intensity of 3·1019 W/cm2 onto spooling tapes. We demonstrate continuous operation over up to one hour runtime at a repetition rate of 1 Hz. Harmonic spectra ranging from 20 eV to 70 eV (62 nm to 18 nm) were consecutively recorded by an XUV spectrometer. An average XUV pulse energy in the µJ range is measured. With the presented setup, relativistic surface high-harmonic generation becomes a powerful source of coherent XUV pulses that might enable applications in, e.g. attosecond laser physics and the seeding of free-electron lasers, when the laser issues causing 80-% pulse energy fluctuations are overcome.
D3-Equivariant coupled advertising oscillators model
NASA Astrophysics Data System (ADS)
Zhang, Chunrui; Zheng, Huifeng
2011-04-01
A ring of three coupled advertising oscillators with delay is considered. Using the symmetric functional differential equation theories, the multiple Hopf bifurcations of the equilibrium at the origin are demonstrated. The existence of multiple branches of bifurcating periodic solution is obtained. Numerical simulation supports our analysis results.
Modeling Wave Driven Non-linear Flow Oscillations: The Terrestrial QBO and a Solar Analog
NASA Technical Reports Server (NTRS)
Mayr, Hans G.; Bhartia, P. K. (Technical Monitor)
2001-01-01
The Quasi Biennial Oscillation (QBO) of the zonal circulation observed in the terrestrial atmosphere at low latitudes is driven by wave mean flow interaction as was demonstrated first by Lindzen and Holton (1968), shown in a laboratory experiment by Plumb and McEwan (1978), and modeled by others (e.g., Plumb, Dunkerton). Although influenced by the seasonal cycle of solar forcing, the QBO, in principle, represents a nonlinear flow oscillation that can be maintained by a steady source of upward propagating waves. The wave driven non-linearity is of third or odd order in the flow velocity, which regenerates the fundamental harmonic itself to keep the oscillation going - the fluid dynamical analog of the displacement mechanism in the mechanical clock. Applying Hines' Doppler Spread Parameterization (DSP) for gravity waves (GW), we discuss with a global-scale spectral model numerical experiments that elucidate some properties of the QBO and its possible effects on the climatology of the atmosphere. Depending on the period of the QBO, wave filtering can cause interaction with the seasonal variations to produce pronounced oscillations with beat periods around 10 years. Since the seasonal cycle and its variability influence the period of the QBO, it may also be a potent conduit of solar activity variations to lower altitudes. Analogous to the terrestrial QBO, we propose that a flow oscillation may account for the 22-year periodicity of the solar magnetic cycle, potentially answering Dicke (1978) who asked, "Is there a chronometer hidden deep inside the Sun?" The oscillation would occur below the convection region, where gravity waves can propagate. Employing a simplified, analytic model, Hines' DSP is applied to estimate the flow oscillation. Depending on the adopted horizontal wavelengths of GW's, wave amplitudes less than 10 m/s can be made to produce oscillating zonal flows of about 20 m/s that should be large enough to generate a significant oscillation in the magnetic
Quantum oscillations in a minimal model for pyrochlore iridates
NASA Astrophysics Data System (ADS)
Rhim, Jun Won; Kim, Yong Baek
2015-03-01
Motivated by recent experiments on Pr2Ir2O7, we provide a theory of quantum oscillations in a minimal model for pyrochlore iridates. Focusing on the conduction electron degrees of freedom with strong spin-orbit coupling and considering the electronic structure near the Fermi level, we compute quantum oscillation signals in the paramagnetic state of the model. We compare our theoretical results with existing experimental data on Pr2Ir2O7 and discuss implication to future experiments.
Self-oscillation in electrochemical transistors: An RLC modeling approach
NASA Astrophysics Data System (ADS)
Tu, Deyu; Forchheimer, Robert
2012-03-01
We propose an RLC model for PEDOT:PSS electrochemical transistors to interpret the persistent oscillating currents observed in experiments. The electrochemical reaction is represented by an inductor in the equivalent circuit. The simulation results show that an electrochemical device can be operated as normal transistors or oscillators under different voltage bias. This model predicts that analog circuit functions can be realized with "inductor-like" electrochemical devices.
Atomic Oscillator Strengths for Stellar Atmosphere Modeling
NASA Astrophysics Data System (ADS)
Ruffoni, Matthew; Pickering, Juliet C.
2015-08-01
In order to correctly model stellar atmospheres, fundamental atomic data must be available to describe atomic lines observed in their spectra. Accurate, laboratory-measured oscillator strengths (f-values) for Fe peak elements in neutral or low-ionisation states are particularly important for determining chemical abundances.However, advances in astronomical spectroscopy in recent decades have outpaced those in laboratory astrophysics, with the latter frequently being overlooked at the planning stages of new projects. As a result, numerous big-budget astronomy projects have been, and continue to be hindered by a lack of suitable, accurately-measured reference data to permit the analysis of expensive astronomical spectra; a problem only likely to worsen in the coming decades as spectrographs at new facilities increasingly move to infrared wavelengths.At Imperial College London - and in collaboration with NIST, Wisconsin University and Lund University - we have been working with the astronomy community in an effort to provide new accurately-measured f-values for a range of projects. In particular, we have been working closely with the Gaia-ESO (GES) and SDSS-III/APOGEE surveys, both of which have discovered that many lines that would make ideal candidates for inclusion in their analyses have poorly defined f-values, or are simply absent from the database. Using high-resolution Fourier transform spectroscopy (R ~ 2,000,000) to provide atomic branching fractions, and combining these with level lifetimes measured with laser induced fluorescence, we have provided new laboratory-measured f-values for a range of Fe-peak elements, most recently including Fe I, Fe II, and V I. For strong, unblended lines, uncertainties are as low as ±0.02 dex.In this presentation, I will describe how experimental f-values are obtained in the laboratory and present our recent work for GES and APOGEE. In particular, I will also discuss the strengths and limitations of current laboratory
Modelling of photo-thermal control of biological cellular oscillators
Assanov, Gani S.; Zhanabaev, Zeinulla Zh.; Govorov, Alexander O.; Neiman, Alexander B.
2015-01-01
We study the transient dynamics of biological oscillators subjected to brief heat pulses. A prospective well-defined experimental system for thermal control of oscillators is the peripheral electroreceptors in paddlefish. Epithelial cells in these receptors show spontaneous voltage oscillations which are known to be temperature sensitive. We use a computational model to predict the effect of brief thermal pulses in this system. In our model thermal stimulation is realized through the light excitation of gold nanoparticles delivered in close proximity to epithelial cells and generating heat due to plasmon resonance. We use an ensemble of modified Morris-Lecar systems to model oscillatory epithelial cells. First, we validate that the model quantitatively reproduces the dynamics of epithelial oscillations in paddlefish electroreceptors, including responses to static and slow temperature changes. Second, we use the model to predict transient responses to short heat pulses generated by the light actuated gold nanoparticles. The model predicts that the epithelial oscillators can be partially synchronized by brief 5 – 15 ms light stimuli resulting in a large-amplitude oscillations of the mean field potential. PMID:25685293
Evaluation of Turbulence Models for Unsteady Flows of an Oscillating Airfoil
NASA Technical Reports Server (NTRS)
Srinivasan, G. R.; Ekaterinaris, J. A.; McCroskey, W. J.
1995-01-01
Unsteady flowfields of a two-dimensional oscillating airfoil are calculated using an implicit, finite-difference, Navier Stokes numerical scheme. Five widely used turbulence models are used with the numerical scheme to assess the accuracy and suitability of the models for simulating the retreating blade stall of helicopter rotor in forward flight. Three unsteady flow conditions corresponding to an essentially attached flow, light-stall, and deep-stall cases of an oscillating NACA 0015 wing experiment were chosen as test cases for computations. Results of unsteady airloads hysteresis curves, harmonics of unsteady pressures, and instantaneous flowfield patterns are presented. Some effects of grid density, time-step size, and numerical dissipation on the unsteady solutions relevant to the evaluation of turbulence models are examined. Comparison of unsteady airloads with experimental data show that all models tested are deficient in some sense and no single model predicts airloads consistently and in agreement with experiment for the three flow regimes. The chief findings are that the simple algebraic model based on the renormalization group theory (RNG) offers some improvement over the Baldwin Lomax model in all flow regimes with nearly same computational cost. The one-equation models provide significant improvement over the algebraic and the half-equation models but have their own limitations. The Baldwin-Barth model overpredicts separation and underpredicts reattachment. In contrast, the Spalart-Allmaras model underpredicts separation and overpredicts reattachment.
Fractional Relativistic Yamaleev Oscillator Model and Its Dynamical Behaviors
NASA Astrophysics Data System (ADS)
Luo, Shao-Kai; He, Jin-Man; Xu, Yan-Li; Zhang, Xiao-Tian
2016-07-01
In the paper we construct a new kind of fractional dynamical model, i.e. the fractional relativistic Yamaleev oscillator model, and explore its dynamical behaviors. We will find that the fractional relativistic Yamaleev oscillator model possesses Lie algebraic structure and satisfies generalized Poisson conservation law. We will also give the Poisson conserved quantities of the model. Further, the relation between conserved quantities and integral invariants of the model is studied and it is proved that, by using the Poisson conserved quantities, we can construct integral invariants of the model. Finally, the stability of the manifold of equilibrium states of the fractional relativistic Yamaleev oscillator model is studied. The paper provides a general method, i.e. fractional generalized Hamiltonian method, for constructing a family of fractional dynamical models of an actual dynamical system.
Systematical bifurcation analysis of an intracellular calcium oscillation model.
Liu, Xijun; Li, Xiang
2016-07-01
As a very important second messenger, Ca(2+) plays the role of adjusting various cellular physiological processes through calcium oscillations. In this paper, a further theoretical study is conducted to explore the kinetic behavior of the calcium signals based on a mathematical model. At first, the causes behind the appearance and disappearance of calcium oscillations are strictly verified from the theoretical level and a comparative analysis between the improved model and the original model is also made. Then, it is found that with the increase of relaxation time, the second bifurcation point of the system moves towards the increasing direction of the stimulus intensity and the oscillation interval displays gradual increase. It is also found that under given stimulus intensity, with the relaxation time getting longer, both the peak value and the period of the calcium oscillations display significant increase. Combining the results from the comparative analysis between the improved model and the original model with the results from the analysis of the relaxation time, it shows that the calcium pump activity exerts a direct impact on the calcium oscillation interval. Finally, the calcium leakage item is introduced into the improved model and it is found that as the calcium leakage increases, the two Hopf bifurcation points of the system both move towards the decreasing direction of the stimulus intensity and the oscillation interval gradually narrows down. The study also shows that under given stimulus intensity, as the calcium leakage increases, the peak value of the calcium oscillations displays slow increase and the oscillation period displays gradual decline. PMID:27172874
Neutrino oscillations in a model with a source and detector
NASA Astrophysics Data System (ADS)
Kiers, Ken; Weiss, Nathan
1998-03-01
We study the oscillations of neutrinos in a model in which the neutrino is coupled to a localized, idealized source and detector. By varying the spatial and temporal resolution of the source and detector we are able to model the full range of source and detector types ranging from coherent to incoherent. We find that this approach is useful in understanding the interface between the quantum mechanical nature of neutrino oscillations on the one hand and the production and detection systems on the other hand. This method can easily be extended to study the oscillations of other particles such as the neutral K and B mesons. We find that this approach gives a reliable way to treat the various ambiguities which arise when one examines the oscillations from a wave packet point of view. We demonstrate that the conventional oscillation formula is correct in the relativistic limit and that several recent claims of an extra factor of 2 in the oscillation length are incorrect. We also demonstrate explicitly that the oscillations of neutrinos which have separated spatially may be ``revived'' by a long coherent measurement.
Nonlinear propagation in ultrasonic fields: measurements, modelling and harmonic imaging.
Humphrey, V F
2000-03-01
In high amplitude ultrasonic fields, such as those used in medical ultrasound, nonlinear propagation can result in waveform distortion and the generation of harmonics of the initial frequency. In the nearfield of a transducer this process is complicated by diffraction effects associated with the source. The results of a programme to study the nonlinear propagation in the fields of circular, focused and rectangular transducers are described, and comparisons made with numerical predictions obtained using a finite difference solution to the Khokhlov-Zabolotskaya-Kuznetsov (or KZK) equation. These results are extended to consider nonlinear propagation in tissue-like media and the implications for ultrasonic measurements and ultrasonic heating are discussed. The narrower beamwidths and reduced side-lobe levels of the harmonic beams are illustrated and the use of harmonics to form diagnostic images with improved resolution is described. PMID:10829672
Modeling of a bipedal robot using mutually coupled Rayleigh oscillators.
Filho, Armando C de Pina; Dutra, Max S; Raptopoulos, Luciano S C
2005-01-01
The objective of the work presented here was the modeling of a bipedal robot using a central pattern generator (CPG) formed by a set of mutually coupled Rayleigh oscillators. We analyzed a 2D model, with the three most important determinants of gait, that performs only motions parallel to the sagittal plane. Using oscillators with integer relation of frequency, we determined the transient motion and the stable limit cycles of the network formed by the three oscillators, showing the behavior of the knee angles and the hip angle. A comparison of the plotted graphs revealed that the system provided excellent results when compared to experimental analysis. Based on the results of the study, we come to the conclusion that the use of mutually coupled Rayleigh oscillators can represent an excellent method of signal generation, allowing their application for feedback control of a walking machine. PMID:15580522
Bennett, Charles L.; Sewall, Noel; Boroa, Carl
2014-08-19
An engine based on a reciprocating piston engine that extracts work from pressurized working fluid. The engine includes a harmonic oscillator inlet valve capable of oscillating at a resonant frequency for controlling the flow of working fluid into of the engine. In particular, the inlet valve includes an inlet valve head and a spring arranged together as a harmonic oscillator so that the inlet valve head is moveable from an unbiased equilibrium position to a biased closed position occluding an inlet. Upon releasing the inlet valve the inlet valve head undergoes a single oscillation past the equilibrium positio to a maximum open position and returns to a biased return position close to the closed position to choke the flow and produce a pressure drop across the inlet valve causing the inlet valve to close. Protrusions carried either by the inlet valve head or piston head are used to bump open the inlet valve from the closed position and initiate the single oscillation of the inlet valve head, and protrusions carried either by the outlet valve head or piston head are used to close the outlet valve ahead of the bump opening of the inlet valve.
Relaxation oscillations in an idealized ocean circulation model
NASA Astrophysics Data System (ADS)
Roberts, Andrew; Saha, Raj
2016-06-01
This work is motivated by a desire to understand transitions between stable equilibria observed in Stommel's 1961 thermohaline circulation model. We adapt the model, including a forcing parameter as a dynamic slow variable. The resulting model is a piecewise-smooth, three time-scale system. The model is analyzed using geometric singular perturbation theory to demonstrate the existence of attracting periodic orbits. The system is capable of producing classical relaxation oscillations as expected, but there is also a parameter regime in which the model exhibits small amplitude oscillations known as canard cycles. Forcing the model with obliquity variations from the last 100,000 years produces oscillations that are modulated in amplitude and frequency. The output shows similarities with important features of the climate proxy data of the same period.
Bennett, Charles L.
2009-10-20
A high efficiency harmonic engine based on a resonantly reciprocating piston expander that extracts work from heat and pressurizes working fluid in a reciprocating piston compressor. The engine preferably includes harmonic oscillator valves capable of oscillating at a resonant frequency for controlling the flow of working fluid into and out of the expander, and also preferably includes a shunt line connecting an expansion chamber of the expander to a buffer chamber of the expander for minimizing pressure variations in the fluidic circuit of the engine. The engine is especially designed to operate with very high temperature input to the expander and very low temperature input to the compressor, to produce very high thermal conversion efficiency.
Bierbach, Jana; Yeung, Mark; Eckner, Erich; Roedel, Christian; Kuschel, Stephan; Zepf, Matt; Paulus, Gerhard G.
2015-05-01
Surface high-harmonic generation in the relativistic regime is demonstrated as a source of extreme ultra-violet (XUV) pulses with extended operation time. Relativistic high-harmonic generation is driven by a frequency-doubled high-power Ti:Sapphire laser focused to a peak intensity of 3·1019 W/cm2 onto spooling tapes. We demonstrate continuous operation over up to one hour runtime at a repetition rate of 1 Hz. Harmonic spectra ranging from 20 eV to 70 eV (62 nm to 18 nm) were consecutively recorded by an XUV spectrometer. An average XUV pulse energy in the µJ range is measured. With the presented setup, relativistic surface high-harmonic generationmore » becomes a powerful source of coherent XUV pulses that might enable applications in, e.g. attosecond laser physics and the seeding of free-electron lasers, when the laser issues causing 80-% pulse energy fluctuations are overcome.« less
NASA Astrophysics Data System (ADS)
Ping, J.; Heki, K.; Matumoto, K.; Rise Group
2003-03-01
A topography model, NLT360 is estimated by using spherical harmonic function through 360-orders and degrees. The corresponding lunar Moho topography and crustal thickness are also estimated by assuming a single layered crust on the top of Moho.
The NASA/MSFC global reference atmospheric model: MOD 3 (with spherical harmonic wind model)
NASA Technical Reports Server (NTRS)
Justus, C. G.; Fletcher, G. R.; Gramling, F. E.; Pace, W. B.
1980-01-01
Improvements to the global reference atmospheric model are described. The basic model includes monthly mean values of pressure, density, temperature, and geostrophic winds, as well as quasi-biennial and small and large scale random perturbations. A spherical harmonic wind model for the 25 to 90 km height range is included. Below 25 km and above 90 km, the GRAM program uses the geostrophic wind equations and pressure data to compute the mean wind. In the altitudes where the geostrophic wind relations are used, an interpolation scheme is employed for estimating winds at low latitudes where the geostrophic wind relations being to mesh down. Several sample wind profiles are given, as computed by the spherical harmonic model. User and programmer manuals are presented.
Spherical Calogero model with oscillator/Coulomb potential: Classical case
NASA Astrophysics Data System (ADS)
Correa, Francisco; Hakobyan, Tigran; Lechtenfeld, Olaf; Nersessian, Armen
2016-06-01
We construct the Hamiltonians and symmetry generators of Calogero-oscillator and Calogero-Coulomb models on the N -dimensional sphere within the matrix-model reduction approach. Our method also produces the integrable Calogero-Coulomb-Stark model on the sphere and proves the integrability of the spin extensions of all these systems.
Closed form solution of the itinerant oscillator model of molecular libration
NASA Astrophysics Data System (ADS)
Coffey, W. T.; Walsh, M. E.
1997-05-01
It is shown by using self-consistent (so that action and reaction torques are fully accounted for) expressions for the viscous drag and white noise terms in the equations of motion of the fixed axis rotator version of the itinerant oscillator model that the characteristic (secular) equation of the system automatically factorizes. Hence all the correlation functions of the model (which consists of a "cage" of dipolar molecules surrounding a tagged molecule) may be given in closed form. In particular, the orientational correlation functions of the tagged molecule become the products of single particle ones namely those of a free Brownian rotator and a damped harmonic oscillator while the orientational correlation functions of the cage are simply those of the free Brownian rotator. The equations of motion of the system likewise decouple when the restrictions of small oscillations and of rotation about a fixed axis are removed. Thus, irrespective of the form of the interaction potential between the cage and the tagged molecule, the relaxation modes of the system separate into those of the tagged molecule and those of its surroundings which behave as an inertia corrected free Brownian rotator.
Computational-Model-Based Analysis of Context Effects on Harmonic Expectancy.
Morimoto, Satoshi; Remijn, Gerard B; Nakajima, Yoshitaka
2016-01-01
Expectancy for an upcoming musical chord, harmonic expectancy, is supposedly based on automatic activation of tonal knowledge. Since previous studies implicitly relied on interpretations based on Western music theory, the underlying computational processes involved in harmonic expectancy and how it relates to tonality need further clarification. In particular, short chord sequences which cannot lead to unique keys are difficult to interpret in music theory. In this study, we examined effects of preceding chords on harmonic expectancy from a computational perspective, using stochastic modeling. We conducted a behavioral experiment, in which participants listened to short chord sequences and evaluated the subjective relatedness of the last chord to the preceding ones. Based on these judgments, we built stochastic models of the computational process underlying harmonic expectancy. Following this, we compared the explanatory power of the models. Our results imply that, even when listening to short chord sequences, internally constructed and updated tonal assumptions determine the expectancy of the upcoming chord. PMID:27003807
Computational-Model-Based Analysis of Context Effects on Harmonic Expectancy
Morimoto, Satoshi; Remijn, Gerard B.; Nakajima, Yoshitaka
2016-01-01
Expectancy for an upcoming musical chord, harmonic expectancy, is supposedly based on automatic activation of tonal knowledge. Since previous studies implicitly relied on interpretations based on Western music theory, the underlying computational processes involved in harmonic expectancy and how it relates to tonality need further clarification. In particular, short chord sequences which cannot lead to unique keys are difficult to interpret in music theory. In this study, we examined effects of preceding chords on harmonic expectancy from a computational perspective, using stochastic modeling. We conducted a behavioral experiment, in which participants listened to short chord sequences and evaluated the subjective relatedness of the last chord to the preceding ones. Based on these judgments, we built stochastic models of the computational process underlying harmonic expectancy. Following this, we compared the explanatory power of the models. Our results imply that, even when listening to short chord sequences, internally constructed and updated tonal assumptions determine the expectancy of the upcoming chord. PMID:27003807
Fan, Li; Ding, Jin; Zhu, Jun-jie; Chen, Zhe; Zhang, Shu-yi; Zhang, Hui; Li, Xiao-juan
2015-10-01
A model of thermoacoustic refrigerator on the basis of an acoustic metamaterial is presented, in which an array of side pipes is adopted to suppress harmonic waves in the thermoacoustic resonator. The array of side pipes traps the acoustic waves with Fabry-Perot resonant frequencies and induces narrow forbidden bands of transmission. When the resonant frequency of the thermoacoustic refrigerator is chosen as the operating frequency, the harmonic wave can be exactly located in the forbidden band by properly adapting the structural parameters of the system. Therefore, the component of the harmonic wave in the thermoacoustic resonator can be efficiently suppressed. PMID:26520357
NASA Technical Reports Server (NTRS)
Watkins, Charles E
1951-01-01
This report treats the effect of aspect ratio on the air forces and moments of an oscillating flat rectangular wing in supersonic potential flow. The linearized velocity potential for the wing undergoing sinusoidal torsional oscillations simultaneously with sinusoidal vertical translations is derived in the form of a power series in terms of a frequency parameter. The series development is such that the differential equation for the velocity potential is satisfied to the required power of the frequency parameter considered and the linear boundary conditions are satisfied exactly. The method of solution can be utilized for other plan forms, that is, plan forms for which certain steady-state solutions are known.
The development and analysis of geopotential coefficient models to spherical harmonic degree 360
NASA Astrophysics Data System (ADS)
Rapp, Richard H.; Pavlis, Nikolaos K.
1990-12-01
Two new geopotential coefficient models to spherical harmonic degree 360 are developed using recent advances made in theoretical modeling methods, satellite gravitational models, and expanded and improved terrestrial data. The new models are based on the combination of a satellite potential coefficient model (GEM-T2) to degree 50 with 30-arc mean gravity anomalies, yielding an adjusted set of coefficients and gravity anomalies, which were then harmonically analyzed to yield a set of potential coefficients to degree 360. The models were verified in several ways including satellite orbit residual analysis, demonstrating a substantial improvement over previous high-degree expansions.
The development and analysis of geopotential coefficient models to spherical harmonic degree 360
NASA Technical Reports Server (NTRS)
Rapp, Richard H.; Pavlis, Nikolaos K.
1990-01-01
Two new geopotential coefficient models to spherical harmonic degree 360 are developed using recent advances made in theoretical modeling methods, satellite gravitational models, and expanded and improved terrestrial data. The new models are based on the combination of a satellite potential coefficient model (GEM-T2) to degree 50 with 30-arc mean gravity anomalies, yielding an adjusted set of coefficients and gravity anomalies, which were then harmonically analyzed to yield a set of potential coefficients to degree 360. The models were verified in several ways including satellite orbit residual analysis, demonstrating a substantial improvement over previous high-degree expansions.
Vector model for polarized second-harmonic generation microscopy under high numerical aperture
NASA Astrophysics Data System (ADS)
Wang, Xiang-Hui; Chang, Sheng-Jiang; Lin, Lie; Wang, Lin-Rui; Huo, Bing-Zhong; Hao, Shu-Jian
2010-04-01
Based on the vector diffraction theory and the generalized Jones matrix formalism, a vector model for polarized second-harmonic generation (SHG) microscopy is developed, which includes the roles of the axial component Pz, the weight factor and the cross-effect between the lateral components. The numerical results show that as the relative magnitude of Pz increases, the polarization response of the second-harmonic signal will vary from linear polarization to elliptical polarization and the polarization orientation of the second-harmonic signal is different from that under the paraxial approximation. In addition, it is interesting that the polarization response of the detected second-harmonic signal can change with the value of the collimator lens NA. Therefore, it is more advantageous to adopt the vector model to investigate the property of polarized SHG microscopy for a variety of cases.
Numerical modeling of cavitational resonant oscillations of a liquid
NASA Astrophysics Data System (ADS)
Iakovtsov, A. V.
Using the method of differential approximation, the dispersion characteristics of the Lax-Wendroff (LW) schemes and LW schemes with correction of Boris-Book flows are analyzed. It is shown that the combined Lax-Wendroff-Boris-Books scheme is capable of suppressing variance errors. Several fluid models are analyzed. Using three models of the combined scheme, the induced oscillations of a water column are calculated, and it is shown that the amplitude-frequency characteristics of oscillations calculated using a model of a liquid with bubbles are in good agreement with experimental data. Special attention is given to estimating boundary conditions and to determinations of the behavior of an oscillation process with increasing excitation frequencies.
Skin temperature oscillation model for assessing vasomotion of microcirculation
NASA Astrophysics Data System (ADS)
Tang, Yuan-Liang; He, Ying; Shao, Hong-Wei; Mizeva, Irina
2015-02-01
It has been proved that there exists a certain correlation between fingertip temperature oscillations and blood flow oscillations. In this work, a porous media model of human hand is presented to investigate how the blood flow oscillation in the endothelial frequency band influences fingertip skin temperature oscillations. The porosity which represents the density of micro vessels is assumed to vary periodically and is a function of the skin temperature. Finite element analysis of skin temperature for a contra lateral hand under a cooling test was conducted. Subsequently, wavelet analysis was carried out to extract the temperature oscillations of the data through the numerical analysis and experimental measurements. Furthermore, the oscillations extracted from both numerical analyses and experiments were statistically analyzed to compare the amplitude. The simulation and experimental results show that for the subjects in cardiovascular health, the skin temperature fluctuations in endothelial frequency decrease during the cooling test and increase gradually after cooling, implying that the assumed porosity variation can represent the vasomotion in the endothelial frequency band.
Reply to Steele & Ferrer: Modeling Oscillation, Approximately or Exactly?
ERIC Educational Resources Information Center
Oud, Johan H. L.; Folmer, Henk
2011-01-01
This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure…
Ayvaz, Muzaffer; Demiralp, Metin
2011-09-14
In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.
Improvement of the low frequency oscillation model for Hall thrusters
NASA Astrophysics Data System (ADS)
Wang, Chunsheng; Wang, Huashan
2016-08-01
The low frequency oscillation of the discharge current in Hall thrusters is a major aspect of these devices that requires further study. While the existing model captures the ionization mechanism of the low frequency oscillation, it unfortunately fails to express the dynamic characteristics of the ion acceleration. The analysis in this paper shows this is because of the simplification of the electron equation, which affects both the electric field distribution and the ion acceleration process. Additionally, the electron density equation is revised and a new model that is based on the physical properties of ion movement is proposed.
NASA Technical Reports Server (NTRS)
Christidis, Z. D.; Spar, J.
1980-01-01
Spherical harmonic analysis was used to analyze the observed climatological (C) fields of temperature at 850 mb, geopotential height at 500 mb, and sea level pressure. The spherical harmonic method was also applied to the corresponding "model climatological" fields (M) generated by a general circulation model, the "GISS climate model." The climate model was initialized with observed data for the first of December 1976 at 00. GMT and allowed to generate five years of meteorological history. Monthly means of the above fields for the five years were computed and subjected to spherical harmonic analysis. It was found from the comparison of the spectral components of both sets, M and C, that the climate model generated reasonable 500 mb geopotential heights. The model temperature field at 850 mb exhibited a generally correct structure. However, the meridional temperature gradient was overestimated and overheating of the continents was observed in summer.
Direct measurement of clarinet air column oscillations
NASA Astrophysics Data System (ADS)
Jones, Jesse; Rogers, Chris; French, Chris
2003-10-01
The internal oscillation of a clarinet air column has been directly measured through the implementation of hot-wire anemometry. By taking a series of measurements down the centerline of the bore, velocity and pressure modal shapes of individual harmonics are separated, measured, and plotted. Finally, composite averaged power spectra of the internal oscillation are presented and compared to acoustic measurements acquired outside the clarinet. In many cases, the even harmonics of the internal oscillation dominate over the power found in the odd harmonics. This contradicts the classic model of the clarinet as a cylindrical pipe closed at one end and open at the other (where only odd harmonics are produced). Further, the data from the direct velocity measurements also contradict the externally acquired acoustic data, where odd harmonics generally dominate for the lowest 5-9 harmonics. Thus the clarinet, in theory and practice, is generally considered incapable of generating strong even harmonics. In this research, however, it is seen that dominate even harmonics are generated, but the energy for these frequencies is largely trapped inside the clarinet, whereas the energy associated with the odd harmonics is released to the ambient. [This research was conducted with the support of Selmer Musical Instruments.
Nonequilibrium simulations of model ionomers in an oscillating electric field
Ting, Christina L.; Sorensen-Unruh, Karen E.; Stevens, Mark J.; Frischknecht, Amalie L.
2016-07-25
Here, we perform molecular dynamics simulations of a coarse-grained model of ionomer melts in an applied oscillating electric field. The frequency-dependent conductivity and susceptibility are calculated directly from the current density and polarization density, respectively. At high frequencies, we find a peak in the real part of the conductivity due to plasma oscillations of the ions. At lower frequencies, the dynamic response of the ionomers depends on the ionic aggregate morphology in the system, which consists of either percolated or isolated aggregates. We show that the dynamic response of the model ionomers to the applied oscillating field can be understoodmore » by comparison with relevant time scales in the systems, obtained from independent calculations.« less
Nonequilibrium simulations of model ionomers in an oscillating electric field.
Ting, Christina L; Sorensen-Unruh, Karen E; Stevens, Mark J; Frischknecht, Amalie L
2016-07-28
We perform molecular dynamics simulations of a coarse-grained model of ionomer melts in an applied oscillating electric field. The frequency-dependent conductivity and susceptibility are calculated directly from the current density and polarization density, respectively. At high frequencies, we find a peak in the real part of the conductivity due to plasma oscillations of the ions. At lower frequencies, the dynamic response of the ionomers depends on the ionic aggregate morphology in the system, which consists of either percolated or isolated aggregates. We show that the dynamic response of the model ionomers to the applied oscillating field can be understood by comparison with relevant time scales in the systems, obtained from independent calculations. PMID:27475392
Kurihara, Eru; Hay, Todd A; Ilinskii, Yurii A; Zabolotskaya, Evgenia A; Hamilton, Mark F
2011-11-01
Interaction between acoustically driven or laser-generated bubbles causes the bubble surfaces to deform. Dynamical equations describing the motion of two translating, nominally spherical bubbles undergoing small shape oscillations in a viscous liquid are derived using Lagrangian mechanics. Deformation of the bubble surfaces is taken into account by including quadrupole and octupole perturbations in the spherical-harmonic expansion of the boundary conditions on the bubbles. Quadratic terms in the quadrupole and octupole amplitudes are retained, and surface tension and shear viscosity are included in a consistent manner. A set of eight coupled second-order ordinary differential equations is obtained. Simulation results, obtained by numerical integration of the model equations, exhibit qualitative agreement with experimental observations by predicting the formation of liquid jets. Simulations also suggest that bubble-bubble interactions act to enhance surface mode instability. PMID:22088009
Memcapacitor model and its application in a chaotic oscillator
NASA Astrophysics Data System (ADS)
Guang-Yi, Wang; Bo-Zhen, Cai; Pei-Pei, Jin; Ti-Ling, Hu
2016-01-01
A memcapacitor is a new type of memory capacitor. Before the advent of practical memcapacitor, the prospective studies on its models and potential applications are of importance. For this purpose, we establish a mathematical memcapacitor model and a corresponding circuit model. As a potential application, based on the model, a memcapacitor oscillator is designed, with its basic dynamic characteristics analyzed theoretically and experimentally. Some circuit variables such as charge, flux, and integral of charge, which are difficult to measure, are observed and measured via simulations and experiments. Analysis results show that besides the typical period-doubling bifurcations and period-3 windows, sustained chaos with constant Lyapunov exponents occurs. Moreover, this oscillator also exhibits abrupt chaos and some novel bifurcations. In addition, based on the digital signal processing (DSP) technology, a scheme of digitally realizing this memcapacitor oscillator is provided. Then the statistical properties of the chaotic sequences generated from the oscillator are tested by using the test suit of the National Institute of Standards and Technology (NIST). The tested randomness definitely reaches the standards of NIST, and is better than that of the well-known Lorenz system. Project supported by the National Natural Science Foundation of China (Grant Nos. 61271064, 61401134, and 60971046), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LZ12F01001 and LQ14F010008), and the Program for Zhejiang Leading Team of S&T Innovation, China (Grant No. 2010R50010).
Algebraic approach to the projected deformed oscillator model
NASA Astrophysics Data System (ADS)
Asherova, R. M.; Smirnov, Yu. F.; Tolstoy, V. N.; Shustov, A. P.
1981-03-01
A new method of calculation in terms of the projected deformed oscillator model is proposed. The method involves expansion of its wave functions in terms of the wave functions of an isotropic oscillator potential. Only overlap integrals between projected wave functions and reduced probabilities B(E2) of E2 transitions are examined. B(E2) values are expressed as a series containing the corresponding values of the Elliott SU(3) scheme. The convergence of these expansions is shown to be fairly good. The expectation values of operators ( QQ) and ( QQQ), which characterize the effective internal non-sphericity and non-axiality of the nucleus, are also calculated and discussed.
NASA Astrophysics Data System (ADS)
Albeverio, Sergio; Fassari, Silvestro; Rinaldi, Fabio
2013-09-01
We rigorously define the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive δ‧-interaction, of strength β, centred at 0 (the bottom of the confining parabolic potential), by explicitly providing its resolvent. Our approach is based on a ‘coupling constant renormalization’, related to a technique originated in quantum field theory and implemented in the rigorous mathematical construction of the self-adjoint operator representing the negative Laplacian perturbed by the δ-interaction in two and three dimensions. The way the δ‧-interaction enters in our Hamiltonian corresponds to the one originally discussed for the free Hamiltonian (instead of the harmonic oscillator one) by P Sěba. It should not be confused with the δ‧-potential perturbation of the harmonic oscillator discussed, e.g., in a recent paper by Gadella, Glasser and Nieto (also introduced by P Sěba as a perturbation of the one-dimensional free Laplacian and recently investigated in that context by Golovaty, Hryniv and Zolotaryuk). We investigate in detail the spectrum of our perturbed harmonic oscillator. The spectral structure differs from that of the one-dimensional harmonic oscillator perturbed by an attractive δ-interaction centred at the origin: the even eigenvalues are not modified at all by the δ‧-interaction. Moreover, all the odd eigenvalues, regarded as functions of β, exhibit the rather remarkable phenomenon called ‘level crossing’ after first producing the double degeneracy of all the even eigenvalues for the value \\beta = \\beta _0 = \\frac{{2\\sqrt \\pi }}{{B\\left( {\\frac{3}{4},\\frac{1}{2}} \\right)}} \\cong 1.47934(B( ·, ·) being the beta function). Dedicated to Professor Gianfausto Dell'Antonio on the occasion of his 80th birthday.
Bennett, Charles L.
2016-03-22
A reciprocating-piston uniflow engine includes a harmonic oscillator inlet valve capable of oscillating at a resonant frequency for controlling the flow of working fluid into the engine. In particular, the inlet valve includes an inlet valve head and a spring arranged together as a harmonic oscillator so that the inlet valve head is moveable from an unbiased equilibrium position to a biased closed position occluding an inlet. When released, the inlet valve head undergoes a single oscillation past the equilibrium position to a maximum open position and returns to a biased return position close to the closed position to choke the flow and produce a pressure drop across the inlet valve causing the inlet valve to close. In other embodiments, the harmonic oscillator arrangement of the inlet valve enables the uniflow engine to be reversibly operated as a uniflow compressor.
NASA Astrophysics Data System (ADS)
Hernandez Tenorio, C.; Villagran Vargas, E.; Serkin, Vladimir N.; Aguero Granados, M.; Belyaeva, T. L.; Pena Moreno, R.; Morales Lara, L.
2005-09-01
The dynamics of nonlinear solitary waves is studied by using the model of nonlinear Schrödinger equation (NSE) with an external harmonic potential. The model allows one to analyse on the general basis a variety of nonlinear phenomena appearing both in a Bose—Einstein condensate in a magnetic trap, whose profile is described by a quadratic function of coordinates, and in nonlinear optics, physics of lasers, and biophysics. It is shown that exact solutions for a quantum-mechanical particle in a harmonic potential and solutions obtained within the framework of the adiabatic perturbation theory for bright solitons in a parabolic trap are completely identical. This fact not only proves once more that solitons behave like particles but also that they can preserve such properties in different traps for which the parabolic approximation is valid near potential energy minima. The conditions are found for formation of stable stationary states of antiphase solitons in a harmonic potential. The interaction dynamics of solitons in nonstationary potentials is studied and the possibility of the appearance of a soliton parametric resonance at which the amplitude of soliton oscillations in a trap exponentially increases with time is shown. It is shown that exact solutions of the problem found using the Miura transformation open up the possibility to control the dynamics of solitons. New effects are predicted, which are called the reversible and irreversible denaturation of solitons in a nonstationary harmonic potential.
Results of a model for premixed combustion oscillation
Janus, M.C.; Richards, G.A.
1996-12-31
Combustion oscillations are receiving renewed research interest due to the increasing application of lean premix (LPM) combustion to gas turbines. A simple, nonlinear model for premixed combustion is described in this paper. The model was developed to help explain specific experimental observations, and to provide guidance for the development of active control schemes based on nonlinear concepts. The model can be used to quickly examine instability trends associated with changes in equivalence ratio, mass flow rate, geometry, ambient conditions, and other pertinent factors. The model represents the relevant processes occurring in a fuel nozzle and combustor which are analogous to current LPM turbine combustors. Conservation equations for the fuel nozzle and combustor are developed from simple control volume analysis, providing a set of ordinary differential equations that can be solved on a personal computer. Combustion is modeled as a stirred reactor, with a bi- molecular reaction rate between fuel and air. A variety of numerical results and comparisons to experimental data are presented to demonstrate the utility of the model. Model results are used to understand the fundamental mechanisms which drive combustion oscillations, the effects of inlet air temperature and nozzle geometry on instability, and the effectiveness of active control schemes. The technique used in the model may also be valuable to understand oscillations in low NO{sub x} industrial burners.
NASA Astrophysics Data System (ADS)
Ruderman, M. S.; Petrukhin, N. S.; Pelinovsky, E.
2016-04-01
We study kink oscillations of thin magnetic tubes. We assume that the density inside and outside the tube (and possibly also the cross-section radius) can vary along the tube. This variation is assumed to be of such a form that the kink speed is symmetric with respect to the tube centre and varies monotonically from the tube ends to the tube centre. Then we prove a theorem stating that the ratio of periods of the fundamental mode and first overtone is a monotonically increasing function of the ratio of the kink speed at the tube centre and the tube ends. In particular, it follows from this theorem that the period ratio is lower than two when the kink speed increases from the tube ends to its centre, while it is higher than two when the kink speed decreases from the tube ends to its centre. The first case is typical for non-expanding coronal magnetic loops, and the second for prominence threads. We apply the general results to particular problems. First we consider kink oscillations of coronal magnetic loops. We prove that, under reasonable assumptions, the ratio of the fundamental period to the first overtone is lower than two and decreases when the loop size increases. The second problem concerns kink oscillations of prominence threads. We consider three internal density profiles: generalised parabolic, Gaussian, and Lorentzian. Each of these profiles contain the parameter α that is responsible for its sharpness. We calculate the dependence of the period ratio on the ratio of the mean to the maximum density. For all considered values of α we find that a formula relating the period ratio and the ratio of the mean and maximum density suggested by Soler, Goossens, and Ballester ( Astron. Astrophys. 575, A123, 2015) gives a sufficiently good approximation to the exact dependence.
Anomalies in high-order harmonic generation at relativistic intensities
Teubner, U.; Foerster, E.; Pretzler, G.; Eidmann, K.; Witte, K.; Schlegel, Th.
2003-01-01
High-order harmonic generation from a solid target surface has been investigated using femtosecond laser pulses focused to intensities greater than 10{sup 18} W/cm{sup 2}. The experiments show that the harmonics are very intense, with a conversion efficiency that is one or two orders of magnitude larger than that of harmonics generated in gases. Beside the observation of presently the shortest wavelength harmonics from femtosecond-laser solid target interaction, i.e., down to 22 nm, an anomaly has been observed in the harmonic spectrum. In contrast to the expected well-known continuous 'roll off' of the high-harmonic orders, the harmonic intensity decreases with the increase of harmonic order, but in between shows minima which are significantly less intense than the neighboring harmonics. Furthermore, the order of the harmonic minima depend on target material. Additional calculations using numerical kinetic particle simulations and a simpler oscillating mirror model show that the physical origin of these modulations is an intricate interplay of resonance absorption and ponderomotive force which leads to a complex electron density profile evolution. Furthermore, this is emphasized by a spectral line analysis of the harmonics. In agreement with the theory, broad lines have been observed and, in particular for the harmonics in the minima, a complex interference structure is present.
A model for premixed combustion oscillations
Janus, M.C.; Richards, G.A.
1996-09-01
This paper describes a simulation based on a time dependent, nonlinear control volume analysis. The combustion is modeled as a well-stirred reactor having finite kinetics. Flow properties and species in the nozzle, combustion, and tailpipe regions are determined using a control volume formulation of the conservation equation.
Oscillations in a simple climate-vegetation model
NASA Astrophysics Data System (ADS)
Rombouts, J.; Ghil, M.
2015-05-01
We formulate and analyze a simple dynamical systems model for climate-vegetation interaction. The planet we consider consists of a large ocean and a land surface on which vegetation can grow. The temperature affects vegetation growth on land and the amount of sea ice on the ocean. Conversely, vegetation and sea ice change the albedo of the planet, which in turn changes its energy balance and hence the temperature evolution. Our highly idealized, conceptual model is governed by two nonlinear, coupled ordinary differential equations, one for global temperature, the other for vegetation cover. The model exhibits either bistability between a vegetated and a desert state or oscillatory behavior. The oscillations arise through a Hopf bifurcation off the vegetated state, when the death rate of vegetation is low enough. These oscillations are anharmonic and exhibit a sawtooth shape that is characteristic of relaxation oscillations, as well as suggestive of the sharp deglaciations of the Quaternary. Our model's behavior can be compared, on the one hand, with the bistability of even simpler, Daisyworld-style climate-vegetation models. On the other hand, it can be integrated into the hierarchy of models trying to simulate and explain oscillatory behavior in the climate system. Rigorous mathematical results are obtained that link the nature of the feedbacks with the nature and the stability of the solutions. The relevance of model results to climate variability on various timescales is discussed.
Relaxation oscillation model of hemodynamic parameters in the cerebral vessels
NASA Astrophysics Data System (ADS)
Cherevko, A. A.; Mikhaylova, A. V.; Chupakhin, A. P.; Ufimtseva, I. V.; Krivoshapkin, A. L.; Orlov, K. Yu
2016-06-01
Simulation of a blood flow under normality as well as under pathology is extremely complex problem of great current interest both from the point of view of fundamental hydrodynamics, and for medical applications. This paper proposes a model of Van der Pol - Duffing nonlinear oscillator equation describing relaxation oscillations of a blood flow in the cerebral vessels. The model is based on the patient-specific clinical experimental data flow obtained during the neurosurgical operations in Meshalkin Novosibirsk Research Institute of Circulation Pathology. The stability of the model is demonstrated through the variations of initial data and coefficients. It is universal and describes pressure and velocity fluctuations in different cerebral vessels (arteries, veins, sinuses), as well as in a laboratory model of carotid bifurcation. Derived equation describes the rheology of the ”blood stream - elastic vessel wall gelatinous brain environment” composite system and represents the state equation of this complex environment.
A Comparison between a GFDL General Circulation Model and Observations using Harmonic Analysis
NASA Astrophysics Data System (ADS)
Taghavi, F.
2010-09-01
One of the most important features in analyzing the climatology of any region is to study the precipitation and its periodicity of different harmonics in order to investigate the behavior of the observed data. In this study using precipitation values obtained from the 20C3M (run1) experiment of the GFDL general circulation model (CM2.1) and CPC Merged Analysis of Precipitation (CMAP) from NCEP, harmonic analysis has been employed to study the seasonal variation of precipitation over the Middle East (20°-40°N, 30°-65°E).The monthly precipitation values were averaged over a 25-year integration, producing a dataset 12 monthly for each grid locations. The annual mean and seasonal variance for each grid obtained from two dataset. Maps of the first, second and third harmonic amplitudes and phases provide a useful source of comparison between model output and observational data. Results show that the method of harmonic analysis allows a more analytical comparison between model predictions and data than the conventional approach of representing the annual march in the form of a curve of mean monthly rainfall amounts. The method delineates regional boundaries of the various precipitation regimes in the Middle East.A comparison of the simulated and observed values indicate that the GCM fails to capture a significant amount of the regional detail in precipitation climatology in the South of Middle East when its results are decomposed by harmonic analysis.
Sudden lateral asymmetry and torsional oscillations of section models of suspension bridges
NASA Astrophysics Data System (ADS)
Plaut, R. H.; Davis, F. M.
2007-11-01
Cable-supported bridges typically exhibit minimal torsional motion under traffic and wind loads. If symmetry of the bridge about the deck's centerline is suddenly lost, such as by the failure of one or more cables or hangers (suspenders), torsional motion of the deck may grow and angles of twist may become large. The initiation of the disastrous torsional oscillations of the original Tacoma Narrows Bridge involved a sudden lateral asymmetry due to loosening of a cable band at midspan. The effects of these types of events on two-degree-of-freedom and four-degree-of-freedom section models of suspension bridges are analyzed. Vertical and rotational motions of the deck, along with vertical motions of the cables, are considered. A harmonic vertical force and an aerodynamic moment proportional to angular velocity are applied to the deck. Resistance is provided by translational and rotational springs and dashpots. Flutter instability and large oscillations occur under the aerodynamic moment, which provides "negative damping." In order to model the occurrence of limit cycles, nonlinear damping of the van der Pol type is included in one case, and nonlinear stiffness of the hangers in others. The frequencies of the limit cycles are compared to the natural frequencies of the system.
Model of Wave Driven Flow Oscillation for Solar Cycle
NASA Technical Reports Server (NTRS)
Mayr, Hans G.; Wolff, Charles L.; Einaudi, Franco (Technical Monitor)
2001-01-01
At low latitudes in the Earth's atmosphere, the observed zonal flow velocities are dominated by the semi-annual and quasi-biennial oscillations with periods of 6 months and 20 to 32 months respectively. These terrestrial oscillations, the SAO and QBO respectively, are driven by wave-mean flow interactions due to upward propagating planetary-scale waves (periods of days) and small-scale gravity waves (periods of hours). We are proposing (see also Mayr et al., GRL, 2001) that such a mechanism may drive long period oscillations (reversing flows) in stellar and planetary interiors, and we apply it to the Sun. The reversing flows would occur below the convective envelope where waves can propagate. We apply a simplified, one dimensional, analytical flow model that incorporates a gravity wave parameterization due to Hines (1997). Based on this analysis, our estimates show that relatively small wave amplitudes less than 10 m/s can produce zonal flow amplitudes of 20 m/s, which should be sufficient to generate the observed variations in the magnetic field. To produce the 22-year period of oscillation, a low buoyancy frequency must be chosen, and this places the proposed flow in a region that is close to (and below) the base of the convective envelope. Enhanced turbulence associated with this low stability should help to generate the dynamo currents. With larger stability at deeper levels in the solar interior, the model can readily produce also oscillations with much longer periods. To provide an understanding of the fluid dynamics involved, we present numerical results from a 2D model for the terrestrial atmosphere that exemplify the non-linear nature of the wave interaction for which a mechanical analog is the escapement mechanism of the clock.
NASA Technical Reports Server (NTRS)
Chakrabarti, S.; Martin, J. J.; Pearson, J. B.; Lewis, R. A.
2003-01-01
The NASA MSFC Propulsion Research Center (PRC) is conducting a research activity examining the storage of low energy antiprotons. The High Performance Antiproton Trap (HiPAT) is an electromagnetic system (Penning-Malmberg design) consisting of a 4 Tesla superconductor, a high voltage confinement electrode system, and an ultra high vacuum test section; designed with an ultimate goal of maintaining charged particles with a half-life of 18 days. Currently, this system is being experimentally evaluated using normal matter ions which are cheap to produce and relatively easy to handle and provide a good indication of overall trap behavior, with the exception of assessing annihilation losses. Computational particle-in-cell plasma modeling using the XOOPIC code is supplementing the experiments. Differing electrode voltage configurations are employed to contain charged particles, typically using flat, modified flat and harmonic potential wells. Ion cloud oscillation frequencies are obtained experimentally by amplification of signals induced on the electrodes by the particle motions. XOOPIC simulations show that for given electrode voltage configurations, the calculated charged particle oscillation frequencies are close to experimental measurements. As a two-dimensional axisymmetric code, XOOPIC cannot model azimuthal plasma variations, such as those induced by radio-frequency (RF) modulation of the central quadrupole electrode in experiments designed to enhance ion cloud containment. However, XOOPIC can model analytically varying electric potential boundary conditions and particle velocity initial conditions. Application of these conditions produces ion cloud axial and radial oscillation frequency modes of interest in achieving the goal of optimizing HiPAT for reliable containment of antiprotons.
Nonresonant holeburning in the Terahertz range: Brownian oscillator model.
Haberle, Uli; Diezemann, Gregor
2004-01-15
The response to the field sequence of nonresonant hole burning, a pump-wait-probe experiment originally designed to investigate slow relaxation in complex systems, is calculated for a model of Brownian oscillators, thus including inertial effects. In the overdamped regime the model predictions are very similar to those of the purely dissipative stochastic models investigated earlier, including the possibility to discriminate between dynamic homogeneous and heterogeneous relaxation. The case of underdamped oscillations is of particular interest when low-frequency excitations in glassy systems are considered. We show that also in this situation a frequency selective modification of the response should be feasable. This means that it is possible to specifically address various parts of the spectrum. An experimental realization of nonresonant holeburning in the Terahertz regime therefore is expected to shed further light on the nature of the vibrations around the so-called boson peak. PMID:15268272
Nonresonant holeburning in the Terahertz range: Brownian oscillator model
NASA Astrophysics Data System (ADS)
Häberle, Uli; Diezemann, Gregor
2004-01-01
The response to the field sequence of nonresonant hole burning, a pump-wait-probe experiment originally designed to investigate slow relaxation in complex systems, is calculated for a model of Brownian oscillators, thus including inertial effects. In the overdamped regime the model predictions are very similar to those of the purely dissipative stochastic models investigated earlier, including the possibility to discriminate between dynamic homogeneous and heterogeneous relaxation. The case of underdamped oscillations is of particular interest when low-frequency excitations in glassy systems are considered. We show that also in this situation a frequency selective modification of the response should be feasable. This means that it is possible to specifically address various parts of the spectrum. An experimental realization of nonresonant holeburning in the Terahertz regime therefore is expected to shed further light on the nature of the vibrations around the so-called boson peak.
Multivariable Harmonic Balance for Central Pattern Generators★
Iwasaki, Tetsuya
2009-01-01
The central pattern generator (CPG) is a nonlinear oscillator formed by a group of neurons, providing a fundamental control mechanism underlying rhythmic movements in animal locomotion. We consider a class of CPGs modeled by a set of interconnected identical neurons. Based on the idea of multivariable harmonic balance, we show how the oscillation profile is related to the connectivity matrix that specifies the architecture and strengths of the interconnections. Specifically, the frequency, amplitudes, and phases are essentially encoded in terms of a pair of eigenvalue and eigenvector. This basic principle is used to estimate the oscillation profile of a given CPG model. Moreover, a systematic method is proposed for designing a CPG-based nonlinear oscillator that achieves a prescribed oscillation profile. PMID:19956774
Hasegawa, Hideo
2011-07-01
Responses of small open oscillator systems to applied external forces have been studied with the use of an exactly solvable classical Caldeira-Leggett model in which a harmonic oscillator (system) is coupled to finite N-body oscillators (bath) with an identical frequency (ω(n) = ω(o) for n = 1 to N). We have derived exact expressions for positions, momenta, and energy of the system in nonequilibrium states and for work performed by applied forces. A detailed study has been made on an analytical method for canonical averages of physical quantities over the initial equilibrium state, which is much superior to numerical averages commonly adopted in simulations of small systems. The calculated energy of the system which is strongly coupled to a finite bath is fluctuating but nondissipative. It has been shown that the Jarzynski equality is valid in nondissipative nonergodic open oscillator systems regardless of the rate of applied ramp force. PMID:21867150
Kohira, Masahiro I; Kitahata, Hiroyuki; Magome, Nobuyuki; Yoshikawa, Kenichi
2012-02-01
An oscillatory system called a plastic bottle oscillator is studied, in which the downflow of water and upflow of air alternate periodically in an upside-down plastic bottle containing water. It is demonstrated that a coupled two-bottle system exhibits in- and antiphase synchronization according to the nature of coupling. A simple ordinary differential equation is deduced to interpret the characteristics of a single oscillator. This model is also extended to coupled oscillators, and the model reproduces the essential features of the experimental observations. PMID:22463297
NASA Astrophysics Data System (ADS)
Kohira, Masahiro I.; Kitahata, Hiroyuki; Magome, Nobuyuki; Yoshikawa, Kenichi
2012-02-01
An oscillatory system called a plastic bottle oscillator is studied, in which the downflow of water and upflow of air alternate periodically in an upside-down plastic bottle containing water. It is demonstrated that a coupled two-bottle system exhibits in- and antiphase synchronization according to the nature of coupling. A simple ordinary differential equation is deduced to interpret the characteristics of a single oscillator. This model is also extended to coupled oscillators, and the model reproduces the essential features of the experimental observations.
Model for relaxation oscillations in a helicon discharge
NASA Astrophysics Data System (ADS)
Degeling, A. W.; Sheridan, T. E.; Boswell, R. W.
1999-05-01
Relaxation oscillations observed in the large-volume, helicon plasma experiment WOMBAT (Waves on Magnetized Beams and Turbulence) [R. W. Boswell and R. K. Porteous, Appl. Phys. Lett. 50, 1130 (1987)] are modeled. These oscillations have a period of several milliseconds and have been identified as transitions between a low-density, inductive discharge and a high-density, helicon-wave discharge. In the model, it is assumed that the mode transitions are triggered by variations in the neutral density in the source region. The neutral density decreases due to ionization augmented by ion pumping and increases due to refilling of the source chamber from the much larger diffusion chamber. The system is modeled using two, coupled, nonlinear, ordinary differential equations that describe the neutral and plasma densities in the source chamber. Ionization by inductively-coupled fields and ionization due to electrons accelerated by helicon waves with phase velocities near the threshold electron velocity for ionization are considered. The model is found to reproduce experimentally measured variations of the plasma density and helicon wave phase velocity with rf power, neutral pressure and magnetic field. The negative impedance needed for the existence of a relaxation oscillation is provided by the helicon-wave coupling mechanism.
A Lattice Boltzmann Model for Oscillating Reaction-Diffusion
NASA Astrophysics Data System (ADS)
Rodríguez-Romo, Suemi; Ibañez-Orozco, Oscar; Sosa-Herrera, Antonio
2016-07-01
A computational algorithm based on the lattice Boltzmann method (LBM) is proposed to model reaction-diffusion systems. In this paper, we focus on how nonlinear chemical oscillators like Belousov-Zhabotinsky (BZ) and the chlorite-iodide-malonic acid (CIMA) reactions can be modeled by LBM and provide with new insight into the nature and applications of oscillating reactions. We use Gaussian pulse initial concentrations of sulfuric acid in different places of a bidimensional reactor and nondiffusive boundary walls. We clearly show how these systems evolve to a chaotic attractor and produce specific pattern images that are portrayed in the reactions trajectory to the corresponding chaotic attractor and can be used in robotic control.
NASA Astrophysics Data System (ADS)
Ibarra-Sierra, V. G.; Sandoval-Santana, J. C.; Cardoso, J. L.; Kunold, A.
2015-11-01
We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai-Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators.
Model of high-order harmonic generation from laser interaction with a plasma grating
NASA Astrophysics Data System (ADS)
Zhang, S. J.; Zhuo, H. B.; Zou, D. B.; Gan, L. F.; Zhou, H. Y.; Li, X. Z.; Yu, M. Y.; Yu, W.
2016-05-01
Harmonic generation from linearly polarized high-intensity short-pulse laser normally impacting a solid plasma grating is investigated using analytical modeling and particle-in-cell simulation. It is found that when the radiation excited by the relativistic electron quiver motion in the laser fields suitably matches a harmonic of the grating periodicity, it will be significantly enhanced and peak with narrow angular spread in specific directions. The corresponding theory shows that the phenomenon can be attributed to an interference effect of the periodic grating on the excitation.
Modeling of large aperture third harmonic frequency conversion of high power Nd:glass laser systems
Henesian, M.A.; Wegner, P.J.; Speck, D.R.; Bibeau, C.; Ehrlich, R.B.; Laumann, C.W.; Lawson, J.K.; Weiland, T.L.
1991-03-13
To provide high-energy, high-power beams at short wavelengths for inertial-confinement-fusion experiments, we routinely convert the 1.053-{mu}m output of the Nova, Nd:phosphate-glass, laser system to its third-harmonic wavelength. We describe performance and conversion efficiency modeling of the 3 {times} 3 arrays potassium-dihydrogen-phosphate crystal plates used for type II/type II phase-matched harmonic conversion of Nova 0.74-m diameter beams, and an alternate type I/type II phase-matching configuration that improves the third-harmonic conversion efficiency. These arrays provide energy conversion of up to 65% and intensity conversion to 70%. 19 refs., 11 figs.
Oscillation threshold of a clarinet model: a numerical continuation approach.
Karkar, Sami; Vergez, Christophe; Cochelin, Bruno
2012-01-01
This paper focuses on the oscillation threshold of single reed instruments. Several characteristics such as blowing pressure at threshold, regime selection, and playing frequency are known to change radically when taking into account the reed dynamics and the flow induced by the reed motion. Previous works have shown interesting tendencies, using analytical expressions with simplified models. In the present study, a more elaborated physical model is considered. The influence of several parameters, depending on the reed properties, the design of the instrument or the control operated by the player, are studied. Previous results on the influence of the reed resonance frequency are confirmed. New results concerning the simultaneous influence of two model parameters on oscillation threshold, regime selection and playing frequency are presented and discussed. The authors use a numerical continuation approach. Numerical continuation consists in following a given solution of a set of equations when a parameter varies. Considering the instrument as a dynamical system, the oscillation threshold problem is formulated as a path following of Hopf bifurcations, generalizing the usual approach of the characteristic equation, as used in previous works. The proposed numerical approach proves to be useful for the study of musical instruments. It is complementary to analytical analysis and direct time-domain or frequency-domain simulations since it allows to derive information that is hardly reachable through simulation, without the approximations needed for analytical approach. PMID:22280691
Oscillation threshold of a clarinet model: A numerical continuation approach
NASA Astrophysics Data System (ADS)
Karkar, Sami; Vergez, Christophe; Cochelin, Bruno
This paper focuses on the oscillation threshold of single reed instruments. Several characteristics such as blowing pressure at threshold, regime selection, and playing frequency are known to change radically when taking into account the reed dynamics and the flow induced by the reed motion. Previous works have shown interesting tendencies, using analytical expressions with simplified models. In the present study, a more elaborated physical model is considered. The influence of several parameters, depending on the reed properties, the design of the instrument or the control operated by the player, are studied. Previous results on the influence of the reed resonance frequency are confirmed. New results concerning the simultaneous influence of two model parameters on oscillation threshold, regime selection and playing frequency are presented and discussed. The authors use a numerical continuation approach. Numerical continuation consists in following a given solution of a set of equations when a parameter varies. Considering the instrument as a dynamical system, the oscillation threshold problem is formulated as a path following of Hopf bifurcations, generalizing the usual approach of the characteristic equation, as used in previous works. The proposed numerical approach proves to be useful for the study of musical instruments. It is complementary to analytical analysis and direct time-domain or frequency-domain simulations since it allows to derive information that is hardly reachable through simulation, without the approximations needed for analytical approach.
Region Spherical Harmonic Magnetic Modeling from Near-Surface and Satellite-Altitude Anomlaies
NASA Technical Reports Server (NTRS)
Kim, Hyung Rae; von Frese, Ralph R. B.; Taylor, Patrick T.
2013-01-01
The compiled near-surface data and satellite crustal magnetic measured data are modeled with a regionally concentrated spherical harmonic presentation technique over Australia and Antarctica. Global crustal magnetic anomaly studies have used a spherical harmonic analysis to represent the Earth's magnetic crustal field. This global approach, however is best applied where the data are uniformly distributed over the entire Earth. Satellite observations generally meet this requirement, but unequally distributed data cannot be easily adapted in global modeling. Even for the satellite observations, due to the errors spread over the globe, data smoothing is inevitable in the global spherical harmonic presentations. In addition, global high-resolution modeling requires a great number of global spherical harmonic coefficients for the regional presentation of crustal magnetic anomalies, whereas a lesser number of localized spherical coefficients will satisfy. We compared methods in both global and regional approaches and for a case where the errors were propagated outside the region of interest. For observations from the upcoming Swarm constellation, the regional modeling will allow the production a lesser number of spherical coefficients that are relevant to the region of interest
NASA Technical Reports Server (NTRS)
Ehlers, F. E.; Sebastian, J. D.; Weatherill, W. H.
1979-01-01
Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.
NASA Astrophysics Data System (ADS)
Constantinou, Chrysovalantis; Caprio, Mark A.; Vary, James P.; Maris, Pieter
2014-03-01
It has recently been found that when no-core configuration interaction (NCCI) calculations of low-mass nuclei are plotted against an infrared momentum cutoff λsc (scaling cutoff), a universal curve is obtained for the energy and the RMS radius. The plotted results must have an ultraviolet (UV) cutoff ΛUV greater than or equal to the intrinsic cutoff ΛNN of the interaction. This assures that UV convergence is reached. The scaling property then allows for the performance of extrapolations in the IR limit. Here we conduct NCCI calculations in the harmonic oscillator basis with the JISP16 potential. In the IR limit we obtain universal curves for N = Z nuclei up to and including 8Be . An extrapolation in the IR limit for the ground state energy and the RMS radius is performed, and extrapolated results are obtained. Supported by US DOE (DE-FG02-95ER-40934, DESC0008485 SciDAC/NUCLEI, DE-FG02-87ER40371), US NSF (0904782), and Research Corporation for Science Advancement (Cottrell Scholar Award). Computational resources provided by NERSC (US DOE DE-AC02-05CH11231).
Including slot harmonics to mechanical model of two-pole induction machine with a force actuator
NASA Astrophysics Data System (ADS)
Sinervo, Anssi; Arkkio, Antero
2012-10-01
A simple mechanical model is identified for a two-pole induction machine that has a four-pole extra winding as a force actuator. The actuator can be used to suppress rotor vibrations. Forces affecting the rotor of the induction machine are separated into actuator force, purely mechanical force due to mass unbalance, and force caused by unbalanced magnetic pull from higher harmonics and unipolar flux. The force due to higher harmonics is embedded to the mechanical model. Parameters of the modified mechanical model are identified from measurements and the modifications are shown to be necessary. The force produced by the actuator is calculated using the mechanical model, direct flux measurements, and voltage and current of the force actuator. All three methods are shown to give matching results proving that the mechanical model can be used in vibration control. The test machine is shown to have time periodic behavior and discrete Fourier analysis is used to obtain time-invariant model parameters.
RSRM Chamber Pressure Oscillations: Transit Time Models and Unsteady CFD
NASA Technical Reports Server (NTRS)
Nesman, Tom; Stewart, Eric
1996-01-01
Space Shuttle solid rocket motor low frequency internal pressure oscillations have been observed since early testing. The same type of oscillations also are present in the redesigned solid rocket motor (RSRM). The oscillations, which occur during RSRM burn, are predominantly at the first three motor cavity longitudinal acoustic mode frequencies. Broadband flow and combustion noise provide the energy to excite these modes at low levels throughout motor burn, however, at certain times during burn the fluctuating pressure amplitude increases significantly. The increased fluctuations at these times suggests an additional excitation mechanism. The RSRM has inhibitors on the propellant forward facing surface of each motor segment. The inhibitors are in a slot at the segment field joints to prevent burning at that surface. The aft facing segment surface at a field joint slot burns and forms a cavity of time varying size. Initially the inhibitor is recessed in the field joint cavity. As propellant burns away the inhibitor begins to protrude into the bore flow. Two mechanisms (transit time models) that are considered potential pressure oscillation excitations are cavity-edge tones, and inhibitor hole-tones. Estimates of frequency variation with time of longitudinal acoustic modes, cavity edge-tones, and hole-tones compare favorably with frequencies measured during motor hot firing. It is believed that the highest oscillation amplitudes occur when vortex shedding frequencies coincide with motor longitudinal acoustic modes. A time accurate computational fluid dynamic (CFD) analysis was made to replicate the observations from motor firings and to observe the transit time mechanisms in detail. FDNS is the flow solver used to detail the time varying aspects of the flow. The fluid is approximated as a single-phase ideal gas. The CFD model was an axisymmetric representation of the RSRM at 80 seconds into burn.Deformation of the inhibitors by the internal flow was determined
Harmonization and translation of crop modeling data to ensure interoperability
Technology Transfer Automated Retrieval System (TEKTRAN)
The Agricultural Model Intercomparison and Improvement Project (AgMIP, www.agmip.org) seeks to improve the capability of ecophysiological and economic models to describe the potential impacts of climate change on agricultural systems. AgMIP protocols emphasize the use of multiple models; consequentl...
Reference Model 6 (RM6): Oscillating Wave Energy Converter.
Bull, Diana L; Smith, Chris; Jenne, Dale Scott; Jacob, Paul; Copping, Andrea; Willits, Steve; Fontaine, Arnold; Brefort, Dorian; Gordon, Margaret Ellen; Copeland, Robert; Jepsen, Richard Alan
2014-10-01
This report is an addendum to SAND2013-9040: Methodology for Design and Economic Analysis of Marine Energy Conversion (MEC) Technologies. This report describes an Oscillating Water Column Wave Energy Converter reference model design in a complementary manner to Reference Models 1-4 contained in the above report. In this report, a conceptual design for an Oscillating Water Column Wave Energy Converter (WEC) device appropriate for the modeled reference resource site was identified, and a detailed backward bent duct buoy (BBDB) device design was developed using a combination of numerical modeling tools and scaled physical models. Our team used the methodology in SAND2013-9040 for the economic analysis that included costs for designing, manufacturing, deploying, and operating commercial-scale MEC arrays, up to 100 devices. The methodology was applied to identify key cost drivers and to estimate levelized cost of energy (LCOE) for this RM6 Oscillating Water Column device in dollars per kilowatt-hour ($/kWh). Although many costs were difficult to estimate at this time due to the lack of operational experience, the main contribution of this work was to disseminate a detailed set of methodologies and models that allow for an initial cost analysis of this emerging technology. This project is sponsored by the U.S. Department of Energy's (DOE) Wind and Water Power Technologies Program Office (WWPTO), within the Office of Energy Efficiency & Renewable Energy (EERE). Sandia National Laboratories, the lead in this effort, collaborated with partners from National Laboratories, industry, and universities to design and test this reference model.
Noise Cancelling of Multichannel MRS Signals with a Time Dependent Harmonic Model
NASA Astrophysics Data System (ADS)
Larsen, J.; Dalgaard, E.; Auken, E.
2013-12-01
Magnetic resonance sounding (MRS) is a non-invasive geophysical technique applicable to groundwater investigations and provides a direct quantification of the subsurface water content from surface measurements. The technique is susceptible to electromagnetic noise and signal processing must be employed to retrieve the NMR signal from noisy measurements. The latest generation of MRS equipment is multichannel systems where a primary coil records the noisy NMR signal. Additional coils, physically displaced from the primary coil, synchronously measure the noise which is then subtracted from the primary coil with multichannel Wiener filtering. Unfortunately, this approach fails to take into account that noise can originate from several sources and as a result the noise cancelling is not always optimum. To remedy this problem it can be utilized that one of the major noise components in MRS signals is powerline harmonics, i.e. the noise is a sum of sinusoidal signals all harmonically related to the same fundamental powerline frequency. This implies that it is possible to create a model of the powerline harmonic noise that can be fitted to the MRS recordings and subtracted from these before employing multichannel Wiener filtering as we have recently demonstrated. A fundamental assumption in that work was that the powerline frequency and the amplitude and phase of each harmonic remained constant throughout a signal record of approximately 1 s duration. This assumption is often valid, but not always. In this study we present an extension of this method where the variations in the powerline signal are accounted for by a time dependent model. The signal records from each coil are divided into short overlapping segments, with a typical duration of 100 ms, and a harmonic model with time independent parameters is fitted to each segment. The fitting parameters from each segment are subsequently splined to a full harmonic model where all parameters; fundamental powerline frequency
Results of a model for premixed combustion oscillations
Janus, M.C.; Richards, G.A.
1996-09-01
Combustion oscillations are receiving renewed research interest due to increasing use of lean premix (LPM) combustion to gas turbines. A simple, nonlinear model for premixed combustion is described in this paper. The model was developed to help explain specific experimental observations and to provide guidance for development of active control schemes based on nonlinear concepts. The model can be used to quickly examine instability trends associated with changes in equivalence ratio, mass flow rate, geometry, ambient conditions, etc. The model represents the relevant processes occurring in a fuel nozzle and combustor which are analogous to current LPM turbine combustors. Conservation equations for the fuel nozzle and combustor are developed from simple control volume analysis, providing a set of ordinary differential equations that can be solved on a personal computer. Combustion is modeled as a stirred reactor, with a bimolecular reaction rate between fuel and air. A variety of numerical results and comparisons to experimental data are presented to demonstrate the utility of the model. Model results are used to understand the fundamental mechanisms which drive combustion oscillations, effects of inlet air temperature and nozzle geometry on instability, and effectiveness of open loop control schemes.
Tao, Cui; Jiang, Guoqian; Wei, Weiqi; Solbrig, Harold R.; Chute, Christopher G.
2011-01-01
In this paper, we introduce our case studies for representing clinical study meta-data models such as the HL7 Detailed Clinical Models (DCMs) and the ISO11179 model in a framework that is based on the Semantic-Web technology. We consider such a harmonization would provide computable semantics of the models, thus facilitate the model reuse, model harmonization and data integration.1 PMID:22211181
The pulsar magnetic field oscillation model and the verification method
NASA Astrophysics Data System (ADS)
Liang, Z. X.; Liang, Y.
The characteristics of pulsar have been most commonly explained using lighthouse model However our research has demonstrated that the characteristics of pulsar can be better described using a magnetic oscillating model hereafter MO model built by analogising the reversing phenomenon of the solar magnetic field to pulsar Although the mechanism why the magnetic field can oscillate has not been known yet no observed oppositions to it MO model have been found either After comparing with the lighthouse model the MO model has the following advantages 1 The prediction of the MO model differs significantly from the prediction of the lighthouse model The MO model predicts that the geodetic precession of the spin axis in binary pulsar system may result in some slight changes of the amplitude and shape of profile but it is impossible that they disappear from our line of sight The observed results of PSR B1913 16 PSR J0737-3039 and other binary pulsar system have shown obviously such tendency 2 The lighthouse model can be ruled out by the result from calculating the micropulse of PSR B1133 16 The wheel-axis structure of the image of Crab Nebula taken by Chandra X-ray Observatory correlates precisely with the prediction of the MO model 3 The MO model is more appropriate to explain the polarization characteristics glitch the interpulse and the generation rate of the pulsar than the lighthouse model The MO model also gives satisfactory results to explain the other characteristics eg the spin-down the pulse nulling the beat and pulse
Modeling grain size and dislocation density effects on harmonics of the magnetic induction
Sablik, M. J.; Stegemann, D.; Krys, A.
2001-06-01
Microstructural attributes of steels affect hysteretic magnetic properties because the microstructure affects domain wall movement and pinning. Two important features are grain size and dislocation density. The consensus experimentally is that the coercivity tends to be linearly related to the inverse of the average grain diameter and to the square root of the dislocation density. In this article, these experimental tendencies are utilized in formulating the dependence of the hysteresis parameters of the Jiles{endash}Atherton model as a function of grain size and dislocation density. The results are then used in computing the first and third harmonics of the magnetic induction as a function of grain size and dislocation density. This is done via an adaptation of a hysteresis model formulated by Jiles for higher excitation frequencies. The results indicate that the harmonic amplitudes decrease monotonically with inverse grain size and the square root of dislocation density. Since increasing inverse grain size and dislocation density are correlated with increasing tensile strength, the results are consistent with experimental results for the decrease of the harmonic amplitudes with increasing tensile strength in automotive steels. Also, the harmonic amplitudes decrease with increasing excitation frequency, consistent with experiment. {copyright} 2001 American Institute of Physics.
Modeling grain size and dislocation density effects on harmonics of the magnetic induction
NASA Astrophysics Data System (ADS)
Sablik, M. J.; Stegemann, D.; Krys, A.
2001-06-01
Microstructural attributes of steels affect hysteretic magnetic properties because the microstructure affects domain wall movement and pinning. Two important features are grain size and dislocation density. The consensus experimentally is that the coercivity tends to be linearly related to the inverse of the average grain diameter and to the square root of the dislocation density. In this article, these experimental tendencies are utilized in formulating the dependence of the hysteresis parameters of the Jiles-Atherton model as a function of grain size and dislocation density. The results are then used in computing the first and third harmonics of the magnetic induction as a function of grain size and dislocation density. This is done via an adaptation of a hysteresis model formulated by Jiles for higher excitation frequencies. The results indicate that the harmonic amplitudes decrease monotonically with inverse grain size and the square root of dislocation density. Since increasing inverse grain size and dislocation density are correlated with increasing tensile strength, the results are consistent with experimental results for the decrease of the harmonic amplitudes with increasing tensile strength in automotive steels. Also, the harmonic amplitudes decrease with increasing excitation frequency, consistent with experiment.
Oscillator models of the solar cycle and the Waldmeier effect
NASA Astrophysics Data System (ADS)
Nagy, M.; Petrovay, K.
2013-11-01
We study the behaviour of the van der Pol oscillator when either its damping parameter μ or its nonlinearity parameter ξ is subject to additive or multiplicative random noise. Assuming various power law exponents for the relation between the oscillating variable and the sunspot number, for each case we map the parameter plane defined by the amplitude and the correlation time of the perturbation and mark the parameter regime where the sunspot number displays solar-like behaviour. Solar-like behaviour is defined here as a good correlation between the rise rate and cycle amplitude and the lack of a good correlation between the decay rate and amplitude, together with significant ({⪆ 10} %) r.m.s. variation in cycle lengths and cycle amplitudes. It is found that perturbing μ alone the perturbed van der Pol oscillator does not show solar-like behaviour. When the perturbed variable is ξ, solar-like behaviour is displayed for perturbations with a correlation time of about 3-4 years and significant amplitude. Such studies may provide useful constraints on solar dynamo models and their parameters.
Modelling soil erosion at European scale: towards harmonization and reproducibility
NASA Astrophysics Data System (ADS)
Bosco, C.; de Rigo, D.; Dewitte, O.; Poesen, J.; Panagos, P.
2015-02-01
Soil erosion by water is one of the most widespread forms of soil degradation. The loss of soil as a result of erosion can lead to decline in organic matter and nutrient contents, breakdown of soil structure and reduction of the water-holding capacity. Measuring soil loss across the whole landscape is impractical and thus research is needed to improve methods of estimating soil erosion with computational modelling, upon which integrated assessment and mitigation strategies may be based. Despite the efforts, the prediction value of existing models is still limited, especially at regional and continental scale, because a systematic knowledge of local climatological and soil parameters is often unavailable. A new approach for modelling soil erosion at regional scale is here proposed. It is based on the joint use of low-data-demanding models and innovative techniques for better estimating model inputs. The proposed modelling architecture has at its basis the semantic array programming paradigm and a strong effort towards computational reproducibility. An extended version of the Revised Universal Soil Loss Equation (RUSLE) has been implemented merging different empirical rainfall-erosivity equations within a climatic ensemble model and adding a new factor for a better consideration of soil stoniness within the model. Pan-European soil erosion rates by water have been estimated through the use of publicly available data sets and locally reliable empirical relationships. The accuracy of the results is corroborated by a visual plausibility check (63% of a random sample of grid cells are accurate, 83% at least moderately accurate, bootstrap p ≤ 0.05). A comparison with country-level statistics of pre-existing European soil erosion maps is also provided.
Modelling soil erosion at European scale: towards harmonization and reproducibility
NASA Astrophysics Data System (ADS)
Bosco, C.; de Rigo, D.; Dewitte, O.; Poesen, J.; Panagos, P.
2014-04-01
Soil erosion by water is one of the most widespread forms of soil degradation. The loss of soil as a result of erosion can lead to decline in organic matter and nutrient contents, breakdown of soil structure and reduction of the water holding capacity. Measuring soil loss across the whole landscape is impractical and thus research is needed to improve methods of estimating soil erosion with computational modelling, upon which integrated assessment and mitigation strategies may be based. Despite the efforts, the prediction value of existing models is still limited, especially at regional and continental scale. A new approach for modelling soil erosion at large spatial scale is here proposed. It is based on the joint use of low data demanding models and innovative techniques for better estimating model inputs. The proposed modelling architecture has at its basis the semantic array programming paradigm and a strong effort towards computational reproducibility. An extended version of the Revised Universal Soil Loss Equation (RUSLE) has been implemented merging different empirical rainfall-erosivity equations within a climatic ensemble model and adding a new factor for a better consideration of soil stoniness within the model. Pan-European soil erosion rates by water have been estimated through the use of publicly available datasets and locally reliable empirical relationships. The accuracy of the results is corroborated by a visual plausibility check (63% of a random sample of grid cells are accurate, 83% at least moderately accurate, bootstrap p ≤ 0.05). A comparison with country level statistics of pre-existing European maps of soil erosion by water is also provided.
Secondary flow structures under simple harmonic inflow in a bent pipe model for curved arteries
NASA Astrophysics Data System (ADS)
Glenn, Autumn; Seagrave, Penelope; Shu, Fangjun; Bulusu, Kartik; Plesniak, Michael W.
2010-11-01
Inward centrifuging of fluid in the inviscid core of a 180 degree curved pipe leads to Lyne-type vortices under zero-mean harmonic oscillations, along with the formation of vortices in the Stokes' layer, that rotate in the same directional sense as their steady flow counterpart (Dean vortices). Under physiological conditions, the development of the Lyne-type vortices is believed to be influenced by the systolic pulse, and its associated rapid acceleration and deceleration. Experimental data acquired using Particle Image Velocimetry (PIV) for three harmonic waveforms of different frequencies clarify the conditions under which Lyne vortices form. Multiple vortex pairs were observed for all waveforms and frequencies investigated, including Dean and Lyne-type vortex structures at a Womersley number of 4.22, much lower than previously reported. Hence, frequency alone is not an adequate governing parameter to characterize secondary flow structures in pulsatile flows. A regime map of the secondary flow was sought by using an acceleration-based parameter and the Dean number.
Spherical Cap Harmonic Modelling of 400 Years of Secular Variation in the South-west Pacific
NASA Astrophysics Data System (ADS)
Ingham, M.; Alfheid, M.; Ingham, E. M.; Turner, G. M.
2014-12-01
Historical magnetic data recorded in ship's logs on voyages of exploration and trade in the south-west Pacific have been used as a basis for constructing a model of secular variation in the region using spherical cap harmonic (SCH) analysis. The spherical cap used is centred on colatitude 115° and longitude 160° and has a radius of 50°, thus covering New Zealand, Australia and parts of Antarctica. Gaps in the observational data have been filled by an iterative procedure started by using IGRF field values to obtain SCH models for 2000, 1950 and 1900 and assuming that the spherical cap coefficients have a linear variation in time over the 400 year time period of the model, as is observed to a first approximation for Gauss coefficients calculated from a global spherical harmonic analysis. The resulting field models have generally smooth spatial and temporal variations in declination, inclination and intensity which show some differences from the variations calculated using the global spherical harmonic model gufm1. The technique clearly shows promise for producing more refined models of secular variation in the south-west Pacific when the historical data are supplemented by archeomagnetic and paleomagnetic data.
Dynamic stall of an oscillating wing. Part 1: Evaluation of turbulence models
NASA Technical Reports Server (NTRS)
Srinivasan, G. R.; Ekaterinaris, J. A.; Mccroskey, W. J.
1993-01-01
Unsteady flowfields of a two-dimensional oscillating wing are calculated using an implicit, finite-difference, Navier-Stokes numerical scheme using five widely used turbulence models. The objective of this study is to identify an appropriate turbulence model for accurate simulation of three-dimensional dynamic stall. Three unsteady flow conditions corresponding to attached flow, light-stall, and deep-stall of an oscillating wing experiment were chosen as test cases for computations. Results of unsteady airload hysteresis curves, harmonics of unsteady pressures, and instantaneous flow pictures are presented. Comparison of unsteady airloads with experiment show that all models are deficient in some sense and not a single model predicts all airloads consistently and in agreement with experiment for all flow conditions. For the attached flow condition, the Renormalization Group Theory (RNG), the Johnoson-King (J-K), and the Spalart-Allmaras (S-A) models have better performance. The Baldwin-Lomax (B-L) and the Baldwin-Barth (B-B) models fair poorly. At the light-stall condition, the results for the RNG, the J-K, and S-A models are in agreement with experiment for the upstroke but they all over predict the separation shown by the experiment and therefore have bigger hysteresis loops than experimental results. The B-B model results are also in good agreement for upstroke but have poor lift hysteresis for downstroke. It has superior drag and pitching-moment predictions. For deep-stall conditions, the airloads for the RNG, the B -B, and the S-A models have fair agreement with experiment, but the B-B model performed better at the extreme deep-stall condition. Overall, the RNG model provides significant improvement over the B-L model in all flow regimes with no additional computational cost. The Baldwin-Barth model is the most expensive of the models considered here, costing about 2.5 times that of the Baldwin-Lomax model. Finally, a brief discussion of the effects of grid
Numerical-analytical modeling of the Earth's pole oscillations
NASA Astrophysics Data System (ADS)
Markov, Y.; Filippova, A.
2015-08-01
For the purpose of more accurate forecasting the oscillatory process of the Earth pole in time periods with significant anomalies (irregular deviations) a numerical-analytical approach is presented for the combined modeling of the interdependent dynamical processes - the oscillatory-rotational motion of the Earth and the time dependent coefficients of the geopotential. The oscillations of the inertia tensor components of the Earth depend on various factors such as mechanical and physical parameters of the planet, the motions of the tide-generating bodies and observed large scale natural events. Time variations of these and some other factors affect the Earth orientation parameters. The generalization of the previously researched mathematical model of Chandler and annual oscillations of the Earth pole is being held with the use of celestial mechanics methods and the mathematical description of the Earth gravitational field's temporal variations. The latter makes possible to improve the forecast precision of the Earth pole trajectory. Also the more precise model is to have small number of parameters and to agree with the previously developed one (to have the same structural features and to have a correspondence between the averaged dynamical parameters and the parameters of the basic model).
MAVRIC Flutter Model Transonic Limit Cycle Oscillation Test
NASA Technical Reports Server (NTRS)
Edwards, John W.; Schuster, David M.; Spain, Charles V.; Keller, Donald F.; Moses, Robert W.
2001-01-01
The Models for Aeroelastic Validation Research Involving Computation semi-span wind-tunnel model (MAVRIC-I), a business jet wing-fuselage flutter model, was tested in NASA Langley's Transonic Dynamics Tunnel with the goal of obtaining experimental data suitable for Computational Aeroelasticity code validation at transonic separation onset conditions. This research model is notable for its inexpensive construction and instrumentation installation procedures. Unsteady pressures and wing responses were obtained for three wingtip configurations clean, tipstore, and winglet. Traditional flutter boundaries were measured over the range of M = 0.6 to 0.9 and maps of Limit Cycle Oscillation (LCO) behavior were made in the range of M = 0.85 to 0.95. Effects of dynamic pressure and angle-of-attack were measured. Testing in both R134a heavy gas and air provided unique data on Reynolds number, transition effects, and the effect of speed of sound on LCO behavior. The data set provides excellent code validation test cases for the important class of flow conditions involving shock-induced transonic flow separation onset at low wing angles, including Limit Cycle Oscillation behavior.
On the Asymmetric Longitudinal Oscillations of a Pikelner's Model Prominence
NASA Astrophysics Data System (ADS)
Kraśkiewicz, J.; Murawski, K.; Solov'ev, A.; Srivastava, A. K.
2016-02-01
We present analytical and numerical models of a normal-polarity quiescent prominence that are based on the model of Pikelner (Solar Phys. 17, 44, 1971). We derive the general analytical expressions for the two-dimensional (2D) equilibrium plasma quantities such as the mass density and gas pressure, and we specify magnetic-field components for the prominence, which corresponds to a dense and cold plasma residing in the dip of curved magnetic-field lines. Adapting of these expressions, we numerically solve the 2D, nonlinear, ideal MHD equations for the Pikelner model of a prominence that is initially perturbed by reducing the gas pressure at the dip of magnetic-field lines. Our findings reveal that as a result of pressure perturbations, the prominence plasma starts evolving in time. This leads to antisymmetric magnetoacoustic-gravity oscillations and to the mass-density growth at the magnetic dip, and the magnetic-field lines subside there. This growth depends on the depth of the magnetic dip. For a shallower dip, less plasma is condensed, and vice versa. We conjecture that the observed long-period magnetoacoustic-gravity oscillations in various prominence systems are in general the consequence of the internal-pressure perturbations of the plasma residing in equilibrium at the prominence dip.
Neutrino oscillations and uncertainty in the solar model
NASA Astrophysics Data System (ADS)
Dearborn, D. S.; Fuller, G. M.
1989-06-01
The Mikheyev-Smirnov-Wolfenstein (MSW) resonant neutrino oscillation mechanism is investigated for the Sun using a detailed numerical solar model and a modified version of the Parke-Walker technique for following the neutrino phases through the oscillation resonance. We present overall solar-neutrino spectra and the associated expected neutrino count rates for the 37Cl, 71Ga, and Kamiokande detectors for ranges of masses and vacuum mixing angles for two neutrino species. We also investigate the effects of uncertainties in the solar model. In particular, we examine the effect of opacity changes on the expected solar-neutrino spectrum and resulting parameter space for the MSW mechanism. We find that plausible uncertainties in the standard solar model, and in particular the opacity, translate into significant expansion in the constraints on neutrino masses and vacuum mixing angles from neutrino experiments. It is shown, however, that forthcoming results from the Kamiokande solar-neutrino experiment could put stringent constraints on even the expanded MSW parameter space.
NASA Astrophysics Data System (ADS)
Xin, Cui; Di-Yu, Zhang; Gao, Chen; Ji-Gen, Chen; Si-Liang, Zeng; Fu-Ming, Guo; Yu-Jun, Yang
2016-03-01
We demonstrate that the interference minima in the linear molecular harmonic spectra can be accurately predicted by a modified two-center model. Based on systematically investigating the interference minima in the linear molecular harmonic spectra by the strong-field approximation (SFA), it is found that the locations of the harmonic minima are related not only to the nuclear distance between the two main atoms contributing to the harmonic generation, but also to the symmetry of the molecular orbital. Therefore, we modify the initial phase difference between the double wave sources in the two-center model, and predict the harmonic minimum positions consistent with those simulated by SFA. Project supported by the National Basic Research Program of China (Grant No. 2013CB922200) and the National Natural Science Foundation of China (Grant Nos. 11274001, 11274141, 11304116, 11247024, and 11034003), and the Jilin Provincial Research Foundation for Basic Research, China (Grant Nos. 20130101012JC and 20140101168JC).
NASA Astrophysics Data System (ADS)
Zhong, Jianghong; Tian, Jie; Yang, Xin; Qin, Chenghu
2011-03-01
Applying Cerenkov luminescence tomography (CLT) to localizing Cerenkov light sources in situ is still in its nascent stage. One of the obstacles hindering the development of the CLT is the lack of dedicated imaging mode. In this contribution, the paper presented a Cerenkov optical imaging mode, in which the propagation of optical photons inside tissues generated by the Vavilov-Cerenkov effect is modeled based on simplified spherical harmonics approximation. As a significantly more transport-like and computational-efficient approximation theory, the performance of the third-order simplified spherical harmonics approximation (SP3) in the CLT forward is investigated in stages. Finally, the performance of the proposed forward model is validated using numerical phantoms and compared with the simulation data based on the Monte Carlo method.
A Time-Distinguished Analysis of the Harmonic Structure from a Model Molecular Ion
NASA Astrophysics Data System (ADS)
Yang, Yu-Jun; Chen, Gao; Chen, Ji-Gen; Zhu, Qi-Ren
2004-04-01
We present high-order harmonic generation spectra resulted from a single-electron model molecular ion exposed to intense laser fields by numerically solving a one-dimensional time-dependent Schrödinger equation. There are three plateaus in the spectra and the maximal cutoff energy is Ip+8.5Up, when the inter-nuclear distance R equals pialpha0/2. Here Ip is the ionization potential and Up = E02/(4omega2) is the ponderomotive potential with E0 and omega being the laser electric field amplitude and the central frequency. The harmonic structures are well interpreted by a modified three-step model in which the effects of the electron reflected by the non-parent ion are stressed.
Linear and nonlinear aspects of the tropical 30-60 day oscillation: A modeling study
NASA Technical Reports Server (NTRS)
Stevens, Duane E.; Stephens, Graeme L.
1991-01-01
The scientific problem focused on study of the tropical 30-60 day oscillation and explanation for this phenomenon is discussed. The following subject areas are covered: the scientific problem (the importance of low frequency oscillations; suggested mechanisms for developing the tropical 30-60 day oscillation); proposed research and its objective; basic approach to research; and results (satellite data analysis and retrieval development; thermodynamic model of the oscillation; the 5-level GCM).
Modeling Tides, Planetary Waves, and Equatorial Oscillations in the MLT
NASA Technical Reports Server (NTRS)
Mengel, J. G.; Mayr, H. G.; Drob, D. P.; Porter, H. S.; Bhartia, P. K. (Technical Monitor)
2001-01-01
Applying Hines Doppler Spread Parameterization for gravity waves (GW), our 3D model reproduces some essential features that characterize the observed seasonal variations of tides and planetary waves in the upper mesosphere. In 2D, our model also reproduces the large Semi-Annual Oscillation (SAO) and Quasi Biennial Oscillation (QBO) observed in this region at low latitudes. It is more challenging to describe these features combined in a more comprehensive self consistent model, and we give a progress report that outlines the difficulties and reports some success. In 3D, the GW's are partially absorbed by tides and planetary waves to amplify them. Thus the waves are less efficient in generating the QBO and SAO at equatorial latitudes. Some of this deficiency is compensated by the fact that the GW activity is observed to be enhanced at low latitudes. Increasing the GW source has the desired effect to boost the QBO, but the effect is confined primarily to the stratosphere. With increasing altitude, the meridional circulation becomes more important in redistributing the momentum deposited in the background flow by the GW's. Another factor involved is the altitude at which the GW's originate, which we had originally chosen to be the surface. Numerical experiments show that moving this source altitude to the top of the troposphere significantly increases the efficiency for generating the QBO without affecting much the tides and planetary waves in the model. Attention to the details in which the GW source comes into play thus appears to be of critical importance in modeling the phenomenology of the MLT. Among the suite of numerical experiments reported, we present a simulation that produced significant variations of tides and planetary waves in the upper mesosphere. The effect is related to the QBO generated in the model, and GW filtering is the likely cause.
Flow separation in a computational oscillating vocal fold model
NASA Astrophysics Data System (ADS)
Alipour, Fariborz; Scherer, Ronald C.
2004-09-01
A finite-volume computational model that solves the time-dependent glottal airflow within a forced-oscillation model of the glottis was employed to study glottal flow separation. Tracheal input velocity was independently controlled with a sinusoidally varying parabolic velocity profile. Control parameters included flow rate (Reynolds number), oscillation frequency and amplitude of the vocal folds, and the phase difference between the superior and inferior glottal margins. Results for static divergent glottal shapes suggest that velocity increase caused glottal separation to move downstream, but reduction in velocity increase and velocity decrease moved the separation upstream. At the fixed frequency, an increase of amplitude of the glottal walls moved the separation further downstream during glottal closing. Increase of Reynolds number caused the flow separation to move upstream in the glottis. The flow separation cross-sectional ratio ranged from approximately 1.1 to 1.9 (average of 1.47) for the divergent shapes. Results suggest that there may be a strong interaction of rate of change of airflow, inertia, and wall movement. Flow separation appeared to be ``delayed'' during the vibratory cycle, leading to movement of the separation point upstream of the glottal end only after a significant divergent angle was reached, and to persist upstream into the convergent phase of the cycle.
Numerical Models of Broad-Bandwidth Nanosecond Optical Parametric Oscillators
Bowers, M.S.; Gehr. R.J.; Smith, A.V.
1998-10-22
We present three new methods for modeling broad-bandwidth, nanosecond optitcal parametric oscillators in the plane-wave approximation. Each accounts for the group-velocity differences that determine the operating linewidth of unseeded optical parametric oscillators, and each allows the signal and idler waves to develop from quantum noise. The first two methods are based on split-step integration methods in which nonlinear mixing and propagation are calculated separately on alternate steps. One method relies on Fourier transforming handle propagation, wiih mixing integrated over a the fields between t and u to Az step: the other transforms between z and k= in the propagation step, with mixing integrated over At. The third method is based on expansion of the three optical fields in terms of their respective longitudinal empty cavity modes, taking into account the cavity boundary condi- tions. Equations describing the time development of the mode amplitudes are solved to yield the time dependence of the three output fields. These plane-wave models exclude diffractive effects, but can be readily extended to include them.
Modeling oscillations and spiral waves in Dictyostelium populations.
Noorbakhsh, Javad; Schwab, David J; Sgro, Allyson E; Gregor, Thomas; Mehta, Pankaj
2015-06-01
Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales-from biochemical networks within individual cells to spatially structured cellular populations. Here we present a family of "multiscale" models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cyclic adenosine monophosphate (cAMP) used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various preprocessing modules. We use this family of models to study spatially unstructured populations of "fixed" cells by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then briefly discuss an extension of our model that includes spatial structure and show how this naturally gives rise to spiral waves. Our models exhibit a wide range of novel phenomena. including a density-dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations. PMID:26172740
Modeling oscillations and spiral waves in Dictyostelium populations
NASA Astrophysics Data System (ADS)
Noorbakhsh, Javad; Schwab, David J.; Sgro, Allyson E.; Gregor, Thomas; Mehta, Pankaj
2015-06-01
Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales—from biochemical networks within individual cells to spatially structured cellular populations. Here we present a family of "multiscale" models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cyclic adenosine monophosphate (cAMP) used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various preprocessing modules. We use this family of models to study spatially unstructured populations of "fixed" cells by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then briefly discuss an extension of our model that includes spatial structure and show how this naturally gives rise to spiral waves. Our models exhibit a wide range of novel phenomena. including a density-dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations.
Vibratory responses of synthetic, self-oscillating vocal fold models.
Murray, Preston R; Thomson, Scott L
2012-11-01
The flow-induced responses of four self-oscillating synthetic vocal fold models are compared. All models were life-sized and fabricated using flexible silicone compounds with material properties comparable to those of human vocal fold tissue. Three of the models had two layers of different stiffness to represent the body-cover grouping of vocal fold tissue. Two of the two-layer models were based on the "M5" geometry [Scherer et al., J. Acoust. Soc. Am. 109, 1616-1630 (2001)], while the third was based on magnetic resonance imaging data. The fourth model included several layers, including a thin epithelial layer, an exceedingly flexible superficial lamina propria layer, a ligament layer that included an anteriorly-posteriorly oriented fiber to restrict vertical motion, and a body layer. Measurements were performed with these models in full larynx and hemilarynx configurations. Data included onset pressure, vibration frequency, glottal flow rate, maximum glottal width, and medial surface motion, the latter two of which were acquired using high-speed imaging techniques. The fourth, multi-layer model exhibited onset pressure, frequency, and medial surface motion traits that are comparable to published human vocal fold data. Importantly, the model featured an alternating convergent-divergent glottal profile and mucosal wave-like motion, characteristics which are important markers of human vocal fold vibration. PMID:23145623
A NON-RADIAL OSCILLATION MODEL FOR PULSAR STATE SWITCHING
Rosen, R.; McLaughlin, M. A.; Thompson, S. E.
2011-02-10
Pulsars are unique astrophysical laboratories because of their clock-like timing precision, providing new ways to test general relativity and detect gravitational waves. One impediment to high-precision pulsar timing experiments is timing noise. Recently, Lyne et al. showed that the timing noise in a number of pulsars is due to quasi-periodic fluctuations in the pulsars' spin-down rates and that some of the pulsars have associated changes in pulse profile shapes. Here we show that a non-radial oscillation model based on asteroseismological theory can explain these quasi-periodic fluctuations. Application of this model to neutron stars will increase our knowledge of neutron star emission and neutron star interiors and may improve pulsar timing precision.
A new model for realistic random perturbations of stochastic oscillators
NASA Astrophysics Data System (ADS)
Dieci, Luca; Li, Wuchen; Zhou, Haomin
2016-08-01
Classical theories predict that solutions of differential equations will leave any neighborhood of a stable limit cycle, if white noise is added to the system. In reality, many engineering systems modeled by second order differential equations, like the van der Pol oscillator, show incredible robustness against noise perturbations, and the perturbed trajectories remain in the neighborhood of a stable limit cycle for all times of practical interest. In this paper, we propose a new model of noise to bridge this apparent discrepancy between theory and practice. Restricting to perturbations from within this new class of noise, we consider stochastic perturbations of second order differential systems that -in the unperturbed case- admit asymptotically stable limit cycles. We show that the perturbed solutions are globally bounded and remain in a tubular neighborhood of the underlying deterministic periodic orbit. We also define stochastic Poincaré map(s), and further derive partial differential equations for the transition density function.
Temperature dependence of universal fluctuations in the two-dimensional harmonic XY model
NASA Astrophysics Data System (ADS)
Palma, G.
2006-04-01
We compute exact analytical expressions for the skewness and kurtosis in the two-dimensional harmonic XY model. These quantities correspond to the third and fourth normalized moments of the probability density function (PDF) of the magnetization of the model. From their behavior, we conclude that they depend explicitly on the system temperature even in the thermodynamic limit, and hence the PDF itself must depend on it. Our results correct the hypothesis called universal fluctuations, they confirm and extend previous results which showed a T dependence of the PDF, including perturbative expansions within the XY model up to first order in temperature.
Reference Model 5 (RM5): Oscillating Surge Wave Energy Converter
Yu, Y. H.; Jenne, D. S.; Thresher, R.; Copping, A.; Geerlofs, S.; Hanna, L. A.
2015-01-01
This report is an addendum to SAND2013-9040: Methodology for Design and Economic Analysis of Marine Energy Conversion (MEC) Technologies. This report describes an Oscillating Water Column Wave Energy Converter (OSWEC) reference model design in a complementary manner to Reference Models 1-4 contained in the above report. A conceptual design for a taut moored oscillating surge wave energy converter was developed. The design had an annual electrical power of 108 kilowatts (kW), rated power of 360 kW, and intended deployment at water depths between 50 m and 100 m. The study includes structural analysis, power output estimation, a hydraulic power conversion chain system, and mooring designs. The results were used to estimate device capital cost and annual operation and maintenance costs. The device performance and costs were used for the economic analysis, following the methodology presented in SAND2013-9040 that included costs for designing, manufacturing, deploying, and operating commercial-scale MEC arrays up to 100 devices. The levelized cost of energy estimated for the Reference Model 5 OSWEC, presented in this report, was for a single device and arrays of 10, 50, and 100 units, and it enabled the economic analysis to account for cost reductions associated with economies of scale. The baseline commercial levelized cost of energy estimate for the Reference Model 5 device in an array comprised of 10 units is $1.44/kilowatt-hour (kWh), and the value drops to approximately $0.69/kWh for an array of 100 units.
A nonlinear dynamic model of relaxation oscillations in tokamaks
NASA Astrophysics Data System (ADS)
Thyagaraja, A.; Haas, F. A.; Harvey, D. J.
1999-06-01
Tokamaks exhibit several types of relaxation oscillations such as sawteeth, fishbones and Edge Localized Modes (ELMs) under appropriate conditions. Several authors have introduced model nonlinear dynamic systems with a small number of degrees of freedom which can illustrate the generic characteristics of such oscillations. In these models, one focuses on physically "relevant" degrees of freedom, without attempting to simulate all the myriad details of the fundamentally nonlinear tokamak phenomena. Such degrees of freedom often involve the plasma macroscopic quantities such as pressure or density and also some measure of the plasma turbulence, which is thought to control transport. In addition, "coherent" modes may be involved in the dynamics of relaxation, as well as radial electric fields, sheared flows, etc. In the present work, an extension of an earlier sawtooth model (which involved only two degrees of freedom) due to the authors is presented. The dynamical consequences of a pressure-driven "coherent" mode, which interacts with the turbulence in a specific manner, are investigated. Varying only the two parameters related to the coherent mode, the bifurcation properties of the system have been studied. These turn out to be remarkably rich and varied and qualitatively similar to the behavior found experimentally in actual tokamaks. The dynamic model presented involves only continuous nonlinearities and is the simplest known to the authors that can yield features such as sawteeth, "compound sawteeth" with partial crashes, "monster" sawteeth, metastability, intermittency, chaos, periodic and "grassy" ELMing in appropriate regions of parameter space. The results suggest that linear stability analysis of systems, while useful in elucidating instability drives, can be misleading in understanding the dynamics of nonlinear systems over time scales much longer than linear growth times and states far from stable equilibria.
Separation of harmonic sounds using multipitch analysis and linear models for the overtone series
NASA Astrophysics Data System (ADS)
Virtanen, Tuomas; Klapuri, Anssi
2002-05-01
A signal processing method for the separation of concurrent harmonic sounds is described. The method is based on a two-stage approach. First, a multiple fundamental frequency estimator is applied to find initial sound parameters which are reliable, but inaccurate and static. Second, time-varying sinusoidal parameters are estimated in an iterative algorithm. The harmonic structure is retained by keeping the frequency ratio of overtones constant over time. Overlapping harmonic components are resolved using linear models for the overtone series. In practice, the models retain the spectral envelope continuity of natural sounds. Simulation experiments were carried out using generated test signals, which were random mixtures of two to six notes from recorded natural instruments. The system is able to produce meaningful results in all polyphonies, the quality of separated sounds gradually degrading along with the polyphony. Some denoising algorithms were applied to suppress nonstationary noise component, such as drums in real-world music signals. However, the usability of the system for real musical signals is still quite limited.
Frictional-faulting model for harmonic tremor before Redoubt Volcano eruptions
Dmitrieva, Ksenia; Hotovec-Ellis, Alicia J.; Prejean, Stephanie G.; Dunham, Eric M.
2013-01-01
Seismic unrest, indicative of subsurface magma transport and pressure changes within fluid-filled cracks and conduits, often precedes volcanic eruptions. An intriguing form of volcano seismicity is harmonic tremor, that is, sustained vibrations in the range of 0.5–5 Hz. Many source processes can generate harmonic tremor. Harmonic tremor in the 2009 eruption of Redoubt Volcano, Alaska, has been linked to repeating earthquakes of magnitudes around 0.5–1.5 that occur a few kilometres beneath the vent. Before many explosions in that eruption, these small earthquakes occurred in such rapid succession—up to 30 events per second—that distinct seismic wave arrivals blurred into continuous, high-frequency tremor. Tremor abruptly ceased about 30 s before the explosions. Here we introduce a frictional-faulting model to evaluate the credibility and implications of this tremor mechanism. We find that the fault stressing rates rise to values ten orders of magnitude higher than in typical tectonic settings. At that point, inertial effects stabilize fault sliding and the earthquakes cease. Our model of the Redoubt Volcano observations implies that the onset of volcanic explosions is preceded by active deformation and extreme stressing within a localized region of the volcano conduit, at a depth of several kilometres.
2016-01-01
Molecular mechanics force fields that explicitly account for induced polarization represent the next generation of physical models for molecular dynamics simulations. Several methods exist for modeling induced polarization, and here we review the classical Drude oscillator model, in which electronic degrees of freedom are modeled by charged particles attached to the nuclei of their core atoms by harmonic springs. We describe the latest developments in Drude force field parametrization and application, primarily in the last 15 years. Emphasis is placed on the Drude-2013 polarizable force field for proteins, DNA, lipids, and carbohydrates. We discuss its parametrization protocol, development history, and recent simulations of biologically interesting systems, highlighting specific studies in which induced polarization plays a critical role in reproducing experimental observables and understanding physical behavior. As the Drude oscillator model is computationally tractable and available in a wide range of simulation packages, it is anticipated that use of these more complex physical models will lead to new and important discoveries of the physical forces driving a range of chemical and biological phenomena. PMID:26815602
Lemkul, Justin A; Huang, Jing; Roux, Benoît; MacKerell, Alexander D
2016-05-11
Molecular mechanics force fields that explicitly account for induced polarization represent the next generation of physical models for molecular dynamics simulations. Several methods exist for modeling induced polarization, and here we review the classical Drude oscillator model, in which electronic degrees of freedom are modeled by charged particles attached to the nuclei of their core atoms by harmonic springs. We describe the latest developments in Drude force field parametrization and application, primarily in the last 15 years. Emphasis is placed on the Drude-2013 polarizable force field for proteins, DNA, lipids, and carbohydrates. We discuss its parametrization protocol, development history, and recent simulations of biologically interesting systems, highlighting specific studies in which induced polarization plays a critical role in reproducing experimental observables and understanding physical behavior. As the Drude oscillator model is computationally tractable and available in a wide range of simulation packages, it is anticipated that use of these more complex physical models will lead to new and important discoveries of the physical forces driving a range of chemical and biological phenomena. PMID:26815602
Cosmological perturbations in coherent oscillating scalar field models
NASA Astrophysics Data System (ADS)
Cembranos, J. A. R.; Maroto, A. L.; Jareño, S. J. Núñez
2016-03-01
The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials V( ϕ) = λ| ϕ| n /n. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained c eff 2 = ω = ( n - 2)/( n + 2) with ω the effective equation of state. We also obtain the first order correction in k 2/ ω eff 2 , when the wavenumber k of the perturbations is much smaller than the background oscillation frequency, ω eff. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the natural ansatz for δϕ; and for sub-Hubble modes, exploiting Floquet's theorem.
Stalled Pulsing Inertial Oscillation Model for a Tornadic Cyclone
NASA Technical Reports Server (NTRS)
Costen, Robert C.
2005-01-01
A supercell storm is a tall, rotating thunderstorm that can generate hail and tornadoes. Two models exist for the development of the storm's rotation or mesocyclone - the conventional splitting-storm model, and the more recent pulsing inertial oscillation (PIO) model, in which a nonlinear pulse represents the supercell. Although data support both models and both could operate in the same supercell, neither model has satisfactorily explained the tornadic cyclone. A tornadic cyclone is an elevated vorticity concentration of Rossby number approximately 1000 that develops within the contracting mesocyclone shortly before a major tornado appears at the surface. We now show that if the internal temperature excess due to latent energy release is limited to the realistic range of -12 K to +12 K, the PIO model can stall part way through the pulse in a state of contraction and spin-up. Should this happen, the stalled-PIO model can evolve into a tornadic cyclone with a central pressure deficit that exceeds 40 mb, which is greater than the largest measured value. This simulation uses data from a major tornadic supercell that occurred over Oklahoma City, Oklahoma, USA, on May 3, 1999. The stalled-PIO mechanism also provides a strategy for human intervention to retard or reverse the development of a tornadic cyclone and its pendant tornado.
Experimental constraints on the neutrino oscillations and a simple model of three-flavor mixing
Raczka, P.A.; Szymacha, A. ); Tatur, S. )
1994-02-01
A simple model of neutrino mixing is considered which contains only one right-handed neutrino field coupled, via the mass term, to the three usual left-handed fields. This is the simplest model that allows for three-flavor neutrino oscillations. The existing experimental limits on the neutrino oscillations are used to obtain constraints on the two free-mixing parameters of the model. A specific sum rule relating the oscillation probabilities of different flavors is derived.
Periodic motions and resonances of impact oscillators
NASA Astrophysics Data System (ADS)
Dyskin, Arcady V.; Pasternak, Elena; Pelinovsky, Efim
2012-06-01
Bilinear oscillators - the oscillators whose springs have different stiffnesses in compression and tension - model a wide range of phenomena. A limiting case of bilinear oscillator with infinite stiffness in compression - the impact oscillator - is studied here. We investigate a special set of impact times - the eigenset, which corresponds to the solution of the homogeneous equation, i.e. the oscillator without the driving force. We found that this set and its subsets are stable with respect to variation of initial conditions. Furthermore, amongst all periodic sets of impact times with the period commensurate with the period of driving force, the eigenset is the only one which can support resonances, in particular the multi-'harmonic' resonances. Other resonances should produce non-periodic sets of impact times. This funding indicates that the usual simplifying assumption [e.g., S.W. Shaw, P.J. Holmes, A periodically forced piecewise linear oscillator, Journal of Sound and Vibration 90 (1983) 129-155] that the times between impacts are commensurate with the period of the driving force does not always hold. We showed that for the first sub-'harmonic resonance' - the resonance achieved on a half frequency of the main resonance - the set of impact times is asymptotically close to the eigenset. The envelope of the oscillations in this resonance increases as a square root of time, opposite to the linear increase characteristic of multi-'harmonic' resonances.
The Ohio State 1991 geopotential and sea surface topography harmonic coefficient models
NASA Technical Reports Server (NTRS)
Rapp, Richard H.; Wang, Yan Ming; Pavlis, Nikolaos K.
1991-01-01
The computation is described of a geopotential model to deg 360, a sea surface topography model to deg 10/15, and adjusted Geosat orbits for the first year of the exact repeat mission (ERM). This study started from the GEM-T2 potential coefficient model and it's error covariance matrix and Geosat orbits (for 22 ERMs) computed by Haines et al. using the GEM-T2 model. The first step followed the general procedures which use a radial orbit error theory originally developed by English. The Geosat data was processed to find corrections to the a priori geopotential model, corrections to a radial orbit error model for 76 Geosat arcs, and coefficients of a harmonic representation of the sea surface topography. The second stage of the analysis took place by doing a combination of the GEM-T2 coefficients with 30 deg gravity data derived from surface gravity data and anomalies obtained from altimeter data. The analysis has shown how a high degree spherical harmonic model can be determined combining the best aspects of two different analysis techniques. The error analysis was described that has led to the accuracy estimates for all the coefficients to deg 360. Significant work is needed to improve the modeling effort.
Quantum interference of high-order harmonics from mixed gases
NASA Astrophysics Data System (ADS)
González-Fernández, A.; Velarde, P.
2016-08-01
We present a theoretical study about the interference of the harmonics generated by a mixture of two gases, He-Ne. Our model is based on the electron quantum paths, a discrete number of electron trajectories, and continuum-bound transitions. A laser with intensity around 1014W/cm2 that interacts with a mixture of gases, He-Ne, produces an interference that is destructive at the low-order harmonics and oscillates between constructive and destructive near to cutoff. This destructive interference at high-order harmonics may be used to explore other transitions, which are currently hidden. At low-order harmonic frequencies, our numerical results are in very good agreement with experimental data. At higher-order harmonics, where there are no experimental data, comparison is with a Schrödinger solver.
High harmonic phase in molecular nitrogen
McFarland, Brian K.
2009-10-17
Electronic structure in atoms and molecules modulates the amplitude and phase of high harmonic generation (HHG). We report measurements of the high harmonic spectral amplitude and phase in N{sub 2}. The phase is measured interferometrically by beating the N{sub 2} harmonics with those of an Ar reference oscillator in a gas mixture. A rapid phase shift of 0.2{pi} is observed in the vicinity of the HHG spectral minimum, where a shift of {pi} had been presumed [J. Itatani et al., Nature 432, 867 (2004)]. We compare the phase measurements to a simulation of the HHG recombination step in N{sub 2} that is based on a simple interference model. The results of the simulation suggest that modifications beyond the simple interference model are needed to explain HHG spectra in molecules.
Coherent harmonic production using a two-section undulator FEL
Jaroszynski, D.A.; Prazeres, R.; Glotin, F.
1995-12-31
We present measurements and a theoretical analysis of a new method of generating harmonic radiation in a free-electron laser oscillator with a two section undulator in a single optical cavity. To produce coherent harmonic radiation the undulator is arranged so that the downstream undulator section resonance frequency matches a harmonic of the upstream undulator. Both the fundamental and the harmonic optical fields evolve in the same optical cavity and are coupled out with different extraction fractions using a hole in one of the cavity mirrors. We present measurements that show that the optical power at the second and third harmonic can be enhanced by more than an order of magnitude in this fundamental/harmonic configuration. We compare the production of harmonic radiation of a two sectioned fundamental/harmonic undulator with that produced from a FEL operating at its highest efficiency with a step-tapered undulator, where the bunching at the end of the first section is very large. We examine, the dependence of the harmonic power on the intracavity power by adjusting the optical cavity desynchronism, {delta}L. We also examine the evolution of the fundamental and harmonic powers as a function of cavity roundtrip number to evaluate the importance of the small signal gain at the harmonic. We compare our measurements with predictions of a multi-electron numerical model that follows the evolution of fundamental and harmonic power to saturation. This fundamental/harmonic mode, of operation of the FEL may have useful applications in the production of coherent X-ray and VUV radiation, a spectral range where high reflectivity optical cavity mirrors are difficult or impossible to manufacture.
Quantum-optical model for the dynamics of high-order-harmonic generation
NASA Astrophysics Data System (ADS)
Gombkötő, Ákos; Czirják, Attila; Varró, Sándor; Földi, Péter
2016-07-01
We investigate a two-level atom in the field of a strong laser pulse. The resulting time-dependent polarization is the source of a radiation the frequency components of which are essentially harmonics of the driving field's carrier frequency. The time evolution of this secondary radiation is analyzed in terms of the expectation values of the photon-number operators for a large number of electromagnetic modes that are initially in the vacuum state. Our method is based on a multimode version of the Jaynes-Cummings-Paul model and can be generalized to different radiating systems as well. We show that, after the exciting pulse, the final distribution of the photon numbers is close to the conventional (Fourier-transform-based) power spectrum of the secondary radiation. The details of the high-order-harmonic spectra (HHG spectra) are also analyzed; for many-cycle excitations a clear physical interpretation is given in terms of the Floquet quasienergies. A first step towards the determination of the photon statistics of the high-order-harmonic modes reveals states with slightly super-Poissonian distribution.
NASA Astrophysics Data System (ADS)
Garmier, Romain; Barriot, Jean-Pierre; Konopliv, Alexander S.; Yeomans, Donald K.
2002-04-01
The gravity field for asteroid 433 Eros has been determined in terms of ellipsoidal harmonic functions by processing the Doppler tracking data of the NEAR spacecraft while it was in orbit about the asteroid. Using the same set of NEAR spacecraft Doppler tracking data, comparative descriptions of the Eros gravity field are provided for both the ellipsoidal and the traditional spherical harmonic models. It is shown that for elongated bodies, like the asteroid Eros, the ellipsoidal harmonics model permits a better representation of the gravity signature than does the spherical harmonics model. Eros has a nearly uniform density but there are negative gravity anomalies near the ends of Eros and positive gravity anomalies near the Psyche crater and the Himeros depression.
Properties of Coupled Oscillator Model for Bidirectional Associative Memory
NASA Astrophysics Data System (ADS)
Kawaguchi, Satoshi
2016-08-01
In this study, we consider the stationary state and dynamical properties of a coupled oscillator model for bidirectional associative memory. For the stationary state, we apply the replica method to obtain self-consistent order parameter equations. The theoretical results for the storage capacity and overlap agree well with the numerical simulation. For the retrieval process, we apply statistical neurodynamics to include temporal noise correlations. For the successful retrieval process, the theoretical result obtained with the fourth-order approximation qualitatively agrees with the numerical simulation. However, for the unsuccessful retrieval process, higher-order noise correlations suppress severely; therefore, the maximum value of the overlap and the relaxation time are smaller than those of the numerical simulation. The reasons for the discrepancies between the theoretical result and numerical simulation, and the validity of our analysis are discussed.
Stable time integration suppresses unphysical oscillations in the bidomain model
NASA Astrophysics Data System (ADS)
Torabi Ziaratgahi, Saeed; Marsh, Megan; Sundnes, Joakim; Spiteri, Raymond
2014-07-01
The bidomain model is a popular model for simulating electrical activity in cardiac tissue. It is a continuum-based model consisting of non-linear ordinary differential equations (ODEs) describing spatially averaged cellular reactions and a system of partial differential equations (PDEs) describing electrodiffusion on tissue level. Because of this multi-scale, ODE/PDE structure of the model, operator-splitting methods that treat the ODEs and PDEs in separate steps are natural candidates as numerical solution methods. Second-order methods can generally be expected to be more effective than first-order methods under normal accuracy requirements. However, the simplest and the most commonly applied second-order method for the PDE step, the Crank--Nicolson (CN) method, may generate unphysical oscillations. In this paper, we investigate the performance of a two-stage, L-stable singly diagonally implicit Runge--Kutta method for solving the PDEs of the bidomain model. Numerical experiments show that the enhanced stability property of this method leads to more physically realistic numerical simulations compared to both the CN and backward Euler methods.
The Madden-Julian Oscillation in General Circulation Models
Sperber, K R; Gleckler, P J; Doutriaux, C; Groups, A M; Groups, C M; Slingo, J M; Inness, P M; Gualdi, S; Li, W
2003-10-27
A methodology is utilized to analyze in a standardized fashion the Madden-Julian Oscillation (MJO) in general circulation models. This is attained by projecting 20-100 day bandpass filtered outgoing longwave radiation (OLR) from the models onto the two leading empirical orthogonal functions (EOF's) of observed OLR that characterize the propagation of MJO convection from the Indian Ocean to the central Pacific Ocean. The resulting principal component time series are then screened to isolate boreal winters during which they exhibit a lead-lag relationship consistent with observations. This PC subset is used for linear regression to determine the ability of the models to simulate the observed spacetime variability of the MJO. The vast majority of models underestimate the amplitude of the MJO convective anomalies by a factor of two or more, and the eastward propagation of convection is less coherent than observed, typically. For a given family of models, coupling to an ocean leads to better organization of the large-scale convection. The low-level moisture convergence mechanism for eastward propagation is represented in limited cases, as is the vertical structure of the MJO.
Modelling of soldier fly halteres for gyroscopic oscillations
Parween, Rizuwana; Pratap, Rudra
2015-01-01
ABSTRACT Nature has evolved a beautiful design for small-scale vibratory rate-gyro in the form of dipteran halteres that detect body rotations via Coriolis acceleration. In most Diptera, including soldier fly, Hermetia illucens, halteres are a pair of special organs, located in the space between the thorax and the abdomen. The halteres along with their connecting joint with the fly's body constitute a mechanism that is used for muscle-actuated oscillations of the halteres along the actuation direction. These oscillations lead to bending vibrations in the sensing direction (out of the haltere's actuation plane) upon any impressed rotation due to the resulting Coriolis force. This induced vibration is sensed by the sensory organs at the base of the haltere in order to determine the rate of rotation. In this study, we evaluate the boundary conditions and the stiffness of the anesthetized halteres along the actuation and the sensing direction. We take several cross-sectional SEM (scanning electron microscope) images of the soldier fly haltere and construct its three dimensional model to get the mass properties. Based on these measurements, we estimate the natural frequency along both actuation and sensing directions, propose a finite element model of the haltere's joint mechanism, and discuss the significance of the haltere's asymmetric cross-section. The estimated natural frequency along the actuation direction is within the range of the haltere's flapping frequency. However, the natural frequency along the sensing direction is roughly double the haltere's flapping frequency that provides a large bandwidth for sensing the rate of rotation to the soldier flies. PMID:25572422
Modelling of soldier fly halteres for gyroscopic oscillations.
Parween, Rizuwana; Pratap, Rudra
2015-01-01
Nature has evolved a beautiful design for small-scale vibratory rate-gyro in the form of dipteran halteres that detect body rotations via Coriolis acceleration. In most Diptera, including soldier fly, Hermetia illucens, halteres are a pair of special organs, located in the space between the thorax and the abdomen. The halteres along with their connecting joint with the fly's body constitute a mechanism that is used for muscle-actuated oscillations of the halteres along the actuation direction. These oscillations lead to bending vibrations in the sensing direction (out of the haltere's actuation plane) upon any impressed rotation due to the resulting Coriolis force. This induced vibration is sensed by the sensory organs at the base of the haltere in order to determine the rate of rotation. In this study, we evaluate the boundary conditions and the stiffness of the anesthetized halteres along the actuation and the sensing direction. We take several cross-sectional SEM (scanning electron microscope) images of the soldier fly haltere and construct its three dimensional model to get the mass properties. Based on these measurements, we estimate the natural frequency along both actuation and sensing directions, propose a finite element model of the haltere's joint mechanism, and discuss the significance of the haltere's asymmetric cross-section. The estimated natural frequency along the actuation direction is within the range of the haltere's flapping frequency. However, the natural frequency along the sensing direction is roughly double the haltere's flapping frequency that provides a large bandwidth for sensing the rate of rotation to the soldier flies. PMID:25572422
NASA Astrophysics Data System (ADS)
Fredette, Luke; Dreyer, Jason T.; Rook, Todd E.; Singh, Rajendra
2016-06-01
The dynamic stiffness properties of automotive hydraulic bushings exhibit significant amplitude sensitivity which cannot be captured by linear time-invariant models. Quasi-linear and nonlinear models are therefore proposed with focus on the amplitude sensitivity in magnitude and loss angle spectra (up to 50 Hz). Since production bushing model parameters are unknown, dynamic stiffness tests and laboratory experiments are utilized to extract model parameters. Nonlinear compliance and resistance elements are incorporated, including their interactions in order to improve amplitude sensitive predictions. New solution approximations for the new nonlinear system equations refine the multi-term harmonic balance term method. Quasi-linear models yield excellent accuracy but cannot predict trends in amplitude sensitivity since they rely on available dynamic stiffness measurements. Nonlinear models containing both nonlinear resistance and compliance elements yield superior predictions to those of prior models (with a single nonlinearity) while also providing more physical insight. Suggestion for further work is briefly mentioned.
Oscillating hysteresis in the q -neighbor Ising model
NASA Astrophysics Data System (ADS)
JÈ©drzejewski, Arkadiusz; Chmiel, Anna; Sznajd-Weron, Katarzyna
2015-11-01
We modify the kinetic Ising model with Metropolis dynamics, allowing each spin to interact only with q spins randomly chosen from the whole system, which corresponds to the topology of a complete graph. We show that the model with q ≥3 exhibits a phase transition between ferromagnetic and paramagnetic phases at temperature T*, which linearly increases with q . Moreover, we show that for q =3 the phase transition is continuous and that it is discontinuous for larger values of q . For q >3 , the hysteresis exhibits oscillatory behavior—expanding for even values of q and shrinking for odd values of q . Due to the mean-field-like nature of the model, we are able to derive the analytical form of transition probabilities and, therefore, calculate not only the probability density function of the order parameter but also precisely determine the hysteresis and the effective potential showing stable, unstable, and metastable steady states. Our results show that a seemingly small modification of the kinetic Ising model leads not only to the switch from a continuous to a discontinuous phase transition, but also to an unexpected oscillating behavior of the hysteresis and a puzzling phenomenon for q =5 , which might be taken as evidence for the so-called mixed-order phase transition.
MAVRIC Flutter Model Transonic Limit Cycle Oscillation Test
NASA Technical Reports Server (NTRS)
Edwards, John W.; Schuster, David M.; Spain, Charles V.; Keller, Donald F.; Moses, Robert W.
2001-01-01
The Models for Aeroelastic Validation Research Involving Computation semi-span wind-tunnel model (MAVRIC-I), a business jet wing-fuselage flutter model, was tested in NASA Langley's Transonic Dynamics Tunnel with the goal of obtaining experimental data suitable for Computational Aeroelasticity code validation at transonic separation onset conditions. This research model is notable for its inexpensive construction and instrumentation installation procedures. Unsteady pressures and wing responses were obtained for three wingtip configurations of clean, tipstore, and winglet. Traditional flutter boundaries were measured over the range of M = 0.6 to 0.9 and maps of Limit Cycle Oscillation (LCO) behavior were made in the range of M = 0.85 to 0.95. Effects of dynamic pressure and angle-of-attack were measured. Testing in both R134a heavy gas and air provided unique data on Reynolds number, transition effects, and the effect of speed of sound on LCO behavior. The data set provides excellent code validation test cases for the important class of flow conditions involving shock-induced transonic flow separation onset at low wing angles, including LCO behavior.
The fundamental structure function of oscillator noise models
NASA Technical Reports Server (NTRS)
Greenhall, C. A.
1983-01-01
Continuous-time models of oscillator phase noise x(t) usually have stationary nth differences, for some n. The covariance structure of such a model can be characterized in the time domain by the structure function: D sub n (t;gamma sub 1, gamma sub 2) = E delta (n) sub gamma sub 1 x(s+t) delta(n) sub gamma sub 2 x (s). Although formulas for the special case D sub 2 (0;gamma,gamma) (the Allan variance times 2 gamma(2)) exist for power-law spectral models, certain estimation problems require a more complete knowledge of (0). Exhibited is a much simpler function of one time variable, D(t), from which (0) can easily be obtained from the spectral density by uncomplicated integrations. Believing that D(t) is the simplest function of time that holds the same information as (0), D(t) is called the fundamental structure function. D(t) is computed for several power-law spectral models. Two examples are D(t) = K/t/(3) for random walk FM, D(t) = Kt(2) 1n/t/ for flicker FM. Then, to demonstrate its use, a BASIC program is given that computes means and variances of two Allan variance estimators, one of which incorporates a method of frequency drift estimation and removal.
Oscillating hysteresis in the q-neighbor Ising model.
Jȩdrzejewski, Arkadiusz; Chmiel, Anna; Sznajd-Weron, Katarzyna
2015-11-01
We modify the kinetic Ising model with Metropolis dynamics, allowing each spin to interact only with q spins randomly chosen from the whole system, which corresponds to the topology of a complete graph. We show that the model with q≥3 exhibits a phase transition between ferromagnetic and paramagnetic phases at temperature T*, which linearly increases with q. Moreover, we show that for q=3 the phase transition is continuous and that it is discontinuous for larger values of q. For q>3, the hysteresis exhibits oscillatory behavior-expanding for even values of q and shrinking for odd values of q. Due to the mean-field-like nature of the model, we are able to derive the analytical form of transition probabilities and, therefore, calculate not only the probability density function of the order parameter but also precisely determine the hysteresis and the effective potential showing stable, unstable, and metastable steady states. Our results show that a seemingly small modification of the kinetic Ising model leads not only to the switch from a continuous to a discontinuous phase transition, but also to an unexpected oscillating behavior of the hysteresis and a puzzling phenomenon for q=5, which might be taken as evidence for the so-called mixed-order phase transition. PMID:26651645
ERIC Educational Resources Information Center
Gluck, P.; Krakower, Zeev
2010-01-01
We present a unit comprising theory, simulation and experiment for a body oscillating on a vertical spring, in which the simultaneous use of a force probe and an ultrasonic range finder enables one to explore quantitatively and understand many aspects of simple and damped harmonic motions. (Contains 14 figures.)
Forced oscillation, integer and fractional-order modeling in asthma.
Faria, Alvaro C D; Veiga, Juliana; Lopes, Agnaldo J; Melo, Pedro L
2016-05-01
The purpose of this study was to evaluate the use of fractional-order (FrOr) modeling in asthma. To this end, three FrOr models were compared with traditional parameters and an integer-order model (InOr). We investigated which model would best fit the data, the correlation with traditional lung function tests and the contribution to the diagnostic of airway obstruction. The data consisted of forced oscillation (FO) measurements obtained from healthy (n=22) and asthmatic volunteers with mild (n=22), moderate (n=19) and severe (n=19) obstructions. The first part of this study showed that a FrOr was the model that best fit the data (relative distance: FrOr=4.3±2.4; InOr=5.1±2.6%). The correlation analysis resulted in reasonable (R=0.36) to very good (R=0.77) associations between FrOr parameters and spirometry. The closest associations were observed between parameters related to peripheral airway obstruction, showing a clear relationship between the FrOr models and lung mechanics. Receiver-operator analysis showed that FrOr parameters presented a high potential to contribute to the detection of the mild obstruction in a clinical setting. The accuracy [area under the Receiver Operating Characteristic curve (AUC)] observed in these parameters (AUC=0.954) was higher than that observed in traditional FO parameters (AUC=0.732) and that obtained from the InOr model (AUC=0.861). Patients with moderate and severe obstruction were identified with high accuracy (AUC=0.972 and 0.977, respectively). In conclusion, the results obtained are in close agreement with asthma pathology, and provide evidence that FO measurement associated with FrOr models is a non-invasive, simple and radiation-free method for the detection of biomechanical abnormalities in asthma. PMID:27040828
Oguz, H Kagan; Olcum, Selim; Senlik, Muhammed N; Taş, Vahdettin; Atalar, Abdullah; Köymen, Hayrettin
2010-01-01
Finite element method (FEM) is used for transient dynamic analysis of capacitive micromachined ultrasonic transducers (CMUT) and is particularly useful when the membranes are driven in the nonlinear regime. One major disadvantage of FEM is the excessive time required for simulation. Harmonic balance (HB) analysis, on the other hand, provides an accurate estimate of the steady-state response of nonlinear circuits very quickly. It is common to use Mason's equivalent circuit to model the mechanical section of CMUT. However, it is not appropriate to terminate Mason's mechanical LC section by a rigid piston's radiation impedance, especially for an immersed CMUT. We studied the membrane behavior using a transient FEM analysis and found out that for a wide range of harmonics around the series resonance, the membrane displacement can be modeled as a clamped radiator. We considered the root mean square of the velocity distribution on the membrane surface as the circuit variable rather than the average velocity. With this definition, the kinetic energy of the membrane mass is the same as that in the model. We derived the force and current equations for a clamped radiator and implemented them using a commercial HB simulator. We observed much better agreement between FEM and the proposed equivalent model, compared with the conventional model. PMID:20178910
Rapid automated superposition of shapes and macromolecular models using spherical harmonics
Konarev, Petr V.; Petoukhov, Maxim V.; Svergun, Dmitri I.
2016-01-01
A rapid algorithm to superimpose macromolecular models in Fourier space is proposed and implemented (SUPALM). The method uses a normalized integrated cross-term of the scattering amplitudes as a proximity measure between two three-dimensional objects. The reciprocal-space algorithm allows for direct matching of heterogeneous objects including high- and low-resolution models represented by atomic coordinates, beads or dummy residue chains as well as electron microscopy density maps and inhomogeneous multi-phase models (e.g. of protein–nucleic acid complexes). Using spherical harmonics for the computation of the amplitudes, the method is up to an order of magnitude faster than the real-space algorithm implemented in SUPCOMB by Kozin & Svergun [J. Appl. Cryst. (2001 ▸), 34, 33–41]. The utility of the new method is demonstrated in a number of test cases and compared with the results of SUPCOMB. The spherical harmonics algorithm is best suited for low-resolution shape models, e.g. those provided by solution scattering experiments, but also facilitates a rapid cross-validation against structural models obtained by other methods. PMID:27275142
Hegedűs, Ferenc; Klapcsik, Kálmán
2015-11-01
In the last decade many industrial applications have emerged based on the rapidly developing ultrasonic technology such as ultrasonic pasteurization, alteration of the viscosity of food systems, and mixing immiscible liquids. The fundamental physical basis of these applications is the prevailing extreme conditions (high temperature, pressure and even shock waves) during the collapse of acoustically excited bubbles. By applying the sophisticated numerical techniques of modern bifurcation theory, the present study intends to reveal the regions in the excitation pressure amplitude-ambient temperature parameter plane where collapse-like motion of an acoustically driven gas bubble in highly viscous glycerine exists. We report evidence that below a threshold temperature the bubble model, the Keller-Miksis equation, becomes an overdamped oscillator suppressing collapse-like behaviour. In addition, we have found periodic windows interspersed with chaotic regions indicating the presence of transient chaos, which is important from application point of view if predictability is required. PMID:26186832
Using Hough harmonics to validate and assess nonlinear shallow-water models
NASA Technical Reports Server (NTRS)
Dee, Dick P.; Moraes Da Silva, Arlindo
1986-01-01
The implementation of a technique for locating programming errors in shallow-water codes, establishing the correctness of the code, and assessing the performance of the numerical model under various flow conditions is described. The right-hand side of the differential equations is modified in such a way that the exact solution of the nonlinear initial-value problem is known, so that the truncation errors of the numerical scheme can be studied in detail. The exact solution is prescribed to be any linear combination of Hough harmonics which propagate in time according to their natural frequencies.
Solar Cycle Variations and Equatorial Oscillations: Modeling Study
NASA Technical Reports Server (NTRS)
Mayr, H. G.; Mengel, J. G.; Drob, D. P.; Chan, K. L.; Porter, H. S.; Bhartia, P. K. (Technical Monitor)
2001-01-01
Solar cycle activity effects (SCAE) in the lower and middle atmosphere, reported in several studies, are difficult to explain on the basis of the small changes in solar radiation that accompany the 11-year cycle, It is therefore natural to speculate that dynamical processes may come into play to produce a leverage. Such a leverage may be provided by the Quasi-Biennial Oscillation (QBO) in the zonal circulation of the stratosphere, which has been linked to solar activity variations. Driven primarily by wave mean flow interaction, the QBO period and its amplitude are variable but are also strongly influenced by the seasonal cycle in the solar radiation. This influence extends to low altitudes referred to as "downward control". Relatively small changes in solar radiative forcing can produce small changes in the period and phase of the QBO, but this in turn can produce measurable differences in the wind field. Thus, the QBO may be an amplifier of solar activity variations and a natural conduit of these variations to lower altitudes. To test this hypothesis, we conducted experiments with a 2D (two-dimensional) version of our Numerical Spectral Model that incorporates Hines' Doppler Spread Parameterization for small-scale gravity waves (GW). Solar cycle radiance variations (SCRV) are accounted for by changing the radiative heating rate on a logarithmic scale from 0.1 % at the surface to 1 % at 50 km to 10% at 100 km. With and without SCRV, but with the same GW flux, we then conduct numerical experiments to evaluate the magnitude of the SCAE in the zonal circulation. The numerical results indicate that, under certain conditions, the SCAE is significant and can extend to lower altitudes where the SCRV is inconsequential. At 20-km the differences in the modeled wind velocities are as large as 5 m/s. For a modeled QBO period of 30 months, we find that the seasonal cycle in the solar forcing (through the Semi-annual Oscillation (SAO)) acts as a strong pacemaker to lockup the
Matter Effects on Neutrino Oscillations in Different Supernova Models
NASA Astrophysics Data System (ADS)
Xu, Jing; Hu, Li-Jun; Li, Rui-Cheng; Guo, Xin-Heng; Young, Bing-Lin
2016-04-01
In recent years, with the development of simulations about supernova explosion, we have a better understanding about the density profiles and the shock waves in supernovae than before. There might be a reverse shock wave, another sudden change of density except the forward shock wave, or even no shock wave, emerging in the supernova. Instead of using the expression of the crossing probability at the high resonance, PH, we have studied the matter effects on neutrino oscillations in different supernova models. In detail, we have calculated the survival probability of ve (Ps) and the conversion probability of vx (Pc) in the Schrödinger equation within a simplified two-flavor framework for a certain case, in which the neutrino transfers through the supernova matter from an initial flavor eigenstate located at the core of the supernova. Our calculations was based on the data of density in three different supernova models obtained from simulations. In our work, we do not steepen the density gradient around the border of the shock wave, which differs to what was done in most of the other simulations. It is found that the mass and the density distribution of the supernova do make a difference on the behavior of Ps and Pc. With the results of Ps and Pc, we can estimate the number of ve (and vx) remained in the beam after they go through the matter in the supernova. Supported by National Science Foundation of China under Grant Nos. 11175020 and 11275025
The numerical modelling of a driven nonlinear oscillator
Shew, C.
1995-11-01
The torsional oscillator in the Earth Sciences Division was developed at Lawrence Livermore National Laboratory and is the only one of its kind. It was developed to study the way rocks damp vibrations. Small rock samples are tested to determine the seismic properties of rocks, but unlike other traditional methods that propagate high frequency waves through small samples, this machine forces the sample to vibrate at low frequencies, which better models real-life properties of large masses. In this particular case, the rock sample is tested with a small crack in its middle. This forces the rock to twist against itself, causing a {open_quotes}stick-slip{close_quotes} friction, known as stiction. A numerical model that simulates the forced torsional osillations of the machine is currently being developed. The computer simulation implements the graphical language LabVIEW, and is looking at the nonlinear spring effects, the frictional forces, and the changes in amplitude and frequency of the forced vibration. Using LabVIEW allows for quick prototyping and greatly reduces the {open_quotes}time to product{close_quotes} factor. LabVIEW`s graphical environment allows scientists and engineers to use familiar terminology and icons (e.g. knobs, switches, graphs, etc.). Unlike other programming systems that use text-based languages, such as C and Basic, LabVIEW uses a graphical programming language to create programs in block diagram form.
Dynamically Scaled Glottal Flow Through Symmetrically Oscillating Vocal Fold Models
NASA Astrophysics Data System (ADS)
Halvorson, Lori; Baitinger, Andrew; Sherman, Erica; Krane, Michael; Zhang, Lucy; Wei, Timothy
2011-11-01
Experimental results derived from DPIV measurements in a scaled up dynamic human vocal fold model are presented. The 10x scale vocal fold model is a new design that incorporates key features of vocal fold oscillatory motion. This includes coupling of down/upstream rocking as well as the oscillatory open/close motions. Experiments were dynamically scaled to examine a range of frequencies, 100 - 200 Hz, corresponding to the male and female voice. By using water as the working fluid, very high resolution, both spatial and temporal resolution, was achieved. Time resolved movies of flow through symmetrically oscillating vocal folds will be presented. Both individual realizations as well as phase-averaged data will be shown. Key features, such as randomness and development time of the Coanda effect, vortex shedding, and volume flow rate data will be shown. In this talk, effects associated with paralysis of one vocal fold will be discussed. This talk provides the baseline fluid dynamics for the vocal fold paralysis study presented in Sherman, et al. Supported by the NIH.
Generalized Radiation Boundary Conditions in Gyrotron Oscillator Modeling
NASA Astrophysics Data System (ADS)
Alberti, S.; Tran, T. M.; Brunner, S.; Braunmueller, F.; Genoud, J.; Hogge, J.-Ph.; Tran, M. Q.
2015-11-01
A numerical procedure to implement a frequency-independent generalized non-reflecting radiation boundary conditions, GNRBC, based on the Laplace Transform, is described in details and tested successfully on a simple 2 frequency test problem. In the case of non-stationary regimes occurring in gyrotron oscillators, it is shown that the reflection at frequencies significantly separated from the carrier frequency can be effectively suppressed by this method. A detailed analysis shows that this numerical approach can be consistently used only for models in which there is no assumed separation of time scales between the RF field envelope time-evolution and the electron time of flight across the interaction region. The GNRBC has been implemented in a nonlinear time-dependent self-consistent monomode model, TWANGpic, in which there is no time scale separation since the RF field envelope is updated at each integration time step of the electron motion. The illustration of the effectiveness of the GNRBC is made with TWANGpic on a gyrotron for which extensive theoretical and experimental results have been performed.
A Simulation Model for Local Harmonic Motion Monitoring of Focused Ultrasound Surgery
NASA Astrophysics Data System (ADS)
Heikkilä, Janne; Curiel, Laura; Hynynen, Kullervo
2009-04-01
A computational model for local harmonic motion (LHM) imaging-based monitoring of high-intensity focused ultrasound surgery (FUS) is presented. LMH technique is based on a focused ultrasound radiation force excitation, which induces local mechanical vibrations at the focal region. These pulse-echo imaged vibrations are then used to estimate the mechanical properties of the sonication region. LHM has been proven to be feasible for FUS monitoring because changes in the material properties during the coagulation affect the measured displacements. The presented model includes separate models to simulate acoustic fields, sonication induced temperature elevation and mechanical vibrations, and pulse-echo imaging of the induced motions. These simulation models are based on Rayleigh integral, finite element, and spatial impulse response methods. Simulated temperature rise and vibration amplitudes have been compared with in vivo rabbit experiments with noninvasive MRI thermometry.
NASA Astrophysics Data System (ADS)
de Santis, A.; de Franceschi, G.; Zolesi, B.; Cander, Lj. R.
1992-09-01
The Haines et al. (1985) method of spherical cap harmonic (SCH) analysis has been applied to the critical frequency of the F2 layer observed at several European vertical incident ionospheric stations. The aim was the regional mapping and modeling of this parameter in Europe. To make it possible, a spherical cap including Europe, centered at 50 deg N, 14 deg E with the half-angle of 20 deg has been considered. The model is based on the expansion of Fourier longitudinal series and Legendre colatitudinal functions as the orthogonal basis functions over the caplike region of interest. It has been found that, for the modeling of the foF2, a SCH model with only 9 coefficients (K up to 2) well portrays its basic features.
NASA Astrophysics Data System (ADS)
Gallego, Sergi; Ortuño, Manuel; Neipp, Cristian; Márquez, Andrés; Beléndez, Augusto; Pascual, Inmaculada
2005-10-01
Several theoretical models have been proposed to predict the behavior of photopolymers as holographic recording materials. Basically these models have been applied to study thin layers (around 100 µm thick). The increasing importance of holographic memories recorded in photopolymers (thickness of >500 µm) makes it necessary to extend the ideas proposed by these models to study thick photopolymer layers. We calculate the temporal evolution of the diffraction efficiencies for thick layers using a first-harmonic diffusion model, and the results obtained are compared with the corresponding values for thin layers. Furthermore, the values of the average diffusivity of the polymer chains after the grating is formed are also obtained. In general, we find that the monomer and polymer diffusivity increases when higher values of thickness are used.
A Simulation Model for Local Harmonic Motion Monitoring of Focused Ultrasound Surgery
Heikkilae, Janne; Curiel, Laura; Hynynen, Kullervo
2009-04-14
A computational model for local harmonic motion (LHM) imaging-based monitoring of high-intensity focused ultrasound surgery (FUS) is presented. LMH technique is based on a focused ultrasound radiation force excitation, which induces local mechanical vibrations at the focal region. These pulse-echo imaged vibrations are then used to estimate the mechanical properties of the sonication region. LHM has been proven to be feasible for FUS monitoring because changes in the material properties during the coagulation affect the measured displacements. The presented model includes separate models to simulate acoustic fields, sonication induced temperature elevation and mechanical vibrations, and pulse-echo imaging of the induced motions. These simulation models are based on Rayleigh integral, finite element, and spatial impulse response methods. Simulated temperature rise and vibration amplitudes have been compared with in vivo rabbit experiments with noninvasive MRI thermometry.
Low-frequency oscillations in radiative-convective models
Hu, Qi; Randall, D.A.
1991-12-31
Although eastward propagation is usually regarded as an essential feature of the low-frequency ``Madden-Julian oscillation`` observed in the tropical atmosphere, many observations indicate that there is an important stationary or quasi-stationary component of the oscillation. Yasunari (1979), for example, investigated the stationary 30--60 day variation in upper tropospheric cloudiness in the Asian summer monsoon region. In a case study of the 30--60 day oscillation. Hsu et al. (1990) found a strong stationary oscillation of the divergence, outgoing longwave mdiadon and other fields. A recent observational study by Weickmann and Khalsa (1990) offers further evidence that the Madden-Julian oscillation has an important stationary component. In this paper, we present evidence that intraseasonal oscillations can be produced by local radiative and convective processes. This suggests that the observed propagating Madden-Julian wave is produced by interactions between these local processes and the large scale motion field, and is not essential for the existence of the observed oscillation.
Low-frequency oscillations in radiative-convective models
Hu, Qi; Randall, D.A.
1991-01-01
Although eastward propagation is usually regarded as an essential feature of the low-frequency Madden-Julian oscillation'' observed in the tropical atmosphere, many observations indicate that there is an important stationary or quasi-stationary component of the oscillation. Yasunari (1979), for example, investigated the stationary 30--60 day variation in upper tropospheric cloudiness in the Asian summer monsoon region. In a case study of the 30--60 day oscillation. Hsu et al. (1990) found a strong stationary oscillation of the divergence, outgoing longwave mdiadon and other fields. A recent observational study by Weickmann and Khalsa (1990) offers further evidence that the Madden-Julian oscillation has an important stationary component. In this paper, we present evidence that intraseasonal oscillations can be produced by local radiative and convective processes. This suggests that the observed propagating Madden-Julian wave is produced by interactions between these local processes and the large scale motion field, and is not essential for the existence of the observed oscillation.
Generative Models of Cortical Oscillations: Neurobiological Implications of the Kuramoto Model
Breakspear, Michael; Heitmann, Stewart; Daffertshofer, Andreas
2010-01-01
Understanding the fundamental mechanisms governing fluctuating oscillations in large-scale cortical circuits is a crucial prelude to a proper knowledge of their role in both adaptive and pathological cortical processes. Neuroscience research in this area has much to gain from understanding the Kuramoto model, a mathematical model that speaks to the very nature of coupled oscillating processes, and which has elucidated the core mechanisms of a range of biological and physical phenomena. In this paper, we provide a brief introduction to the Kuramoto model in its original, rather abstract, form and then focus on modifications that increase its neurobiological plausibility by incorporating topological properties of local cortical connectivity. The extended model elicits elaborate spatial patterns of synchronous oscillations that exhibit persistent dynamical instabilities reminiscent of cortical activity. We review how the Kuramoto model may be recast from an ordinary differential equation to a population level description using the nonlinear Fokker–Planck equation. We argue that such formulations are able to provide a mechanistic and unifying explanation of oscillatory phenomena in the human cortex, such as fluctuating beta oscillations, and their relationship to basic computational processes including multistability, criticality, and information capacity. PMID:21151358
NASA Astrophysics Data System (ADS)
Golovkov, Vadim P.; Zvereva, Tatiana I.; Chernova, Tatiana A.
2005-12-01
A simple method is proposed for constructing a space-time model of the main magnetic field based on the high-accuracy satellite survey data. At the first stage, we expand the CHAMP daily mean data into spherical harmonics with constant coefficients. It provides us with a series of the daily mean spherical-harmonic models (DMM) over a survey interval of several years, which are, then, expanded into the natural orthogonal components (NOC). It is shown that the NOC series converges rapidly, and that the accuracy of the space-time model over the time interval under consideration is no worse than the accuracy of the traditional models.
Analysis of chaotic oscillations induced in two coupled Wilson-Cowan models.
Maruyama, Yuya; Kakimoto, Yuta; Araki, Osamu
2014-06-01
Although it is known that two coupled Wilson-Cowan models with reciprocal connections induce aperiodic oscillations, little attention has been paid to the dynamical mechanism for such oscillations so far. In this study, we aim to elucidate the fundamental mechanism to induce the aperiodic oscillations in the coupled model. First, aperiodic oscillations observed are investigated for the case when the connections are unidirectional and when the input signal is a periodic oscillation. By the phase portrait analysis, we determine that the aperiodic oscillations are caused by periodically forced state transitions between a stable equilibrium and a stable limit cycle attractors around the saddle-node and saddle separatrix loop bifurcation points. It is revealed that the dynamical mechanism where the state crosses over the saddle-node and saddle separatrix loop bifurcations significantly contributes to the occurrence of chaotic oscillations forced by a periodic input. In addition, this mechanism can also give rise to chaotic oscillations in reciprocally connected Wilson-Cowan models. These results suggest that the dynamic attractor transition underlies chaotic behaviors in two coupled Wilson-Cowan oscillators. PMID:24789794
Wang, Chen-Wen; Zhu, Chaoyuan Lin, Sheng-Hsien; Yang, Ling; Yu, Jian-Guo
2014-08-28
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 {sup 1}A{sub g} ↔ A{sup 1}B{sub 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{sub 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.
The Z3 zonal harmonic model of Saturn's magnetic field Analyses and implications
NASA Technical Reports Server (NTRS)
Acuna, M. H.; Connerney, J. E. P.; Ness, N. F.
1983-01-01
The planetary magnetic field of Saturn has been studied by the spacecraft Pioneer 11 in 1979, Voyager 1 in 1980, and Voyager 2 in 1981. The field is found to be primarily dipolar and axially coincident with the rotation axis, but with significant quadrupole and octupole moments. The harmonic terms are g1(0) = 21535 nT, g2(0) = 1642 nT, and g3(0) = 2743 nT. This model field, Z3, in conjunction with a model for an equatorial ring current, represents very precisely the in situ magnetic-field measurements and data on charged-particle absorption by satellites and rings within 8 Saturn radii of the planet. However, this axisymmetric model fails to explain the periodic modulation of Saturn's kilometric radiation or Saturn's electrostatic discharges. This enigma of Saturn's magnetosphere remains unsolved in spite of extensive reconsideration of all available data bearing on this issue.
Square-Wave Model for a Pendulum with Oscillating Suspension
ERIC Educational Resources Information Center
Yorke, Ellen D.
1978-01-01
Demonstrates that if a sinusoidal oscillation of the point of support of a pendulum is approximated by a square wave, a matrix method may be used to discuss parametric resonance and the stability of the inverted pendulum. (Author/SL)
Low-frequency combustion oscillations in a model afterburner
Macquisten, M.A.; Dowling, A.P. )
1993-08-01
Low-frequency combustion oscillations, involving the interaction between longitudinal acoustic waves and unsteady combustion, are investigated for a model afterburner. An experimental rig, in which a confined flame is stabilized in the wake of a conical gutter, is run with inlet conditions representative of an engine afterburner. Results are presented for inlet Mach numbers in the range of 0.15--0.27, with inlet temperatures up to 630 K. Comparison is made between theory and experiment. Although the theory was developed from low Mach number data, it is found to apply equally well at these faster flow rates. The theory is able to predict the frequency of the instability and the mode shape, accurately reproducing the changes due to variations in the inlet Mach number and temperature. The effect of altering the downstream boundary condition by replacing the open end by a choked nozzle is also investigated. Such a change is found to be highly destabilizing, both experimentally and theoretically. Again, predictions from the theory are in good agreement with the observations.
Bifurcations in a mathematical model for circadian oscillations of clock genes.
Tsumoto, Kunichika; Yoshinaga, Tetsuya; Iida, Hitoshi; Kawakami, Hiroshi; Aihara, Kazuyuki
2006-03-01
Circadian oscillations with a period of about 24h are observed in nearly all living organisms as conspicuous biological rhythms. In this paper, we investigate various kinds of bifurcation phenomena produced in a circadian oscillator model of Drosophila. In Drosophila, it is known that circadian oscillations in the levels of two proteins, PER and TIM, result from the negative feedback exerted by a PER-TIM complex on the expression of the per and tim genes that code for the two proteins. For studying circadian oscillations of proteins in Drosophila, a mathematical model has been proposed. The model cannot only account for regular circadian oscillations in environmental conditions such as constant darkness, but also give rise to more complex oscillatory phenomena including chaos and birhythmicity. By calculating bifurcations using Kawakami's method, we obtain detailed bifurcation diagrams related to stable and unstable invariant sets, and identify parameter regions in which the model generates complex oscillations as well as regular circadian oscillations. Moreover, we study bifurcations observed in the model incorporating the effect on a light-dark (LD) cycle and show that the waveform of the periodic variation in the light-induced parameter has a marked influence on the global bifurcation structure or the type of dynamic behavior resulting from the forcing term of the circadian oscillator by the LD cycles. PMID:16143345
NASA Astrophysics Data System (ADS)
Kamdoum Tamba, V.; Fotsin, H. B.; Kengne, J.; Kapche Tagne, F.; Talla, P. K.
2015-07-01
This paper deals with the mathematical modelling and synchronization of a new controlled Colpitts oscillator. The new electronic oscillator is constructed by considering standard/classical Colpitts oscillator with two further elements (coupled inductors and variable resistor). An accurate mathematical model is provided. The dynamics of the new controlled Colpitts oscillator is investigated theoretically and experimentally by examining dissipativity, equilibrium point, stability, bifurcation and Lyapunov exponent. It is found that the oscillator moves from the limit cycle motion to chaos via the usual paths of period-doubling, intermittency and interior crisis routes as the control resistor R L is monitored. The electronic circuit of the oscillator is implemented, and a very good qualitative agreement is obtained between the theoretical and experimental results. Furthermore, the problem of synchronization is investigated, in order to promote chaos-based synchronization designs of this type of oscillators. Firstly, we design a coupling function for unidirectional coupling in identical and mismatched controlled Colpitts oscillators to realize a modified function projective synchronization through the open-plus-closed-loop (OPCL) method. Secondly, two different coupling configurations, namely, coupled collector nodes (C-C) and coupled emitter nodes (E-E) of controlled Colpitts oscillators, are studied. Numerical simulations and experimental results are performed to show the effectiveness and robustness of the proposed control schemes.
The stratopause semiannual oscillation in the NCAR Community Climate Model
NASA Technical Reports Server (NTRS)
Sassi, Fabrizio; Garcia, Roland R.; Boville, Byron A.
1993-01-01
The middle atmospheric version of the NCAR Community Climate Model (CCM2) has been used to study the development of the equatorial semiannual oscillation (SAO) in the stratosphere. The model domain extends from the ground to about 80 km, with a vertical resolution of 1 km. Transport of nitrous oxide (N2O) with simplified photochemistry is included in the calculation to illustrate the influence of tropical circulations on the distribution of trace species. Diagnosis of model output reveals two distinct phases in the evolution of the zonal mean state on the equator. In early December, a strong and broad easterly jet appears near the stratopause in connection with a midlatitude wave event (sudden stratospheric warming) that reverses the winter westerlies of the Northern Hemisphere throughout the upper stratosphere. When the wave forcing dies out, the radiative drive allows the westerlies to recover at midlatitudes, while easterlies persist in the tropics. The resulting strong meridional gradient of the zonal mean wind provides favorable conditions for the development of inertial instability at lower latitudes. The meridional circulation associated with the instability shapes the 'nose' of the easterly jet, reducing the extension of the unstable region. In equinoctial conditions, a jet of westerlies appears in the lower equatorial mesosphere and descends to lower altitudes; positive accelerations associated with the descending westerlies are due primarily to Kelvin waves. The descent of the westerly jet does not reproduce well the observed behavior of the SAO westerly phase, either in amplitude or in the extent of downward propagation. As a consequence, the model does not simulate the 'double peak' observed in the tropical distribution of N2O. Comparison of wave amplitudes in the model with those derived from satellite observations shows that the calculated amplitudes are larger than observed in the upper stratosphere. It follows that inadequate Kelvin wave forcing is
NASA Astrophysics Data System (ADS)
Masterton, S. M.; Gubbins, D.; Müller, D.; Williams, S.
2013-12-01
The lithospheric contribution to the geomagnetic field arises from magnetised rocks that are cooler than the Curie temperature of their constituent minerals. Inversion of the magnetic field for this magnetisation is subject to inherent non-uniqueness, as many magnetisation distributions yield no potential field outside of the lithosphere. Such distributions are termed annihilators. We use a complete set of orthogonal vector spherical harmonics that separate the part of the magnetisation responsible for the magnetic field observed above the Earth's surface from the annihilators. A similar set of vector harmonics has been developed in Cartesian geometry suitable for small scale, industrial applications. In an attempt to quantify the significance of the annihilators, we first construct a global model of vertically integrated magnetisation (VIM) by combining a model of remanent magnetisation for the oceans with a previous model of induced magnetisation for the whole Earth. Remanence is computed by assigning magnetisations to the oceanic lithosphere acquired at the location and time of formation. The magnetising field is assumed to be an axial dipole that switches polarity with the reversal time scale. The magnetisation evolves with time by decay of thermal remanence and acquisition of chemical remanence. Remanence directions are calculated by implementing finite rotations of the original geomagnetic field direction with respect to an absolute reference frame. We then represent our estimated VIM in terms of vector spherical harmonics, to allow us to evaluate its relative contributions to a potential field that is observable outside of the lithosphere and to fields (both potential and non-potential) that are not observable. This analysis shows that our model of magnetisation is dominated by a part of the magnetisation that produces a potential field restricted to Earth's sub-lithospheric interior; it therefore contributes significantly to the huge null space in the
NASA Technical Reports Server (NTRS)
Marcus, S. L.; Ghil, M.; Dickey, J. O.
1994-01-01
Variations in atmospheric angular momentum (AAM) are examined in a three-year simulation of the large-scale atmosphere with perpetual January forcing. The simulation is performed with a version of the University of California at Los Angeles (UCLA) general circulation model that contains no tropical Madden-Julian Oscillation (MJO). In addition, the results of three shorter experiments with no topography are analyzed. The three-year standard topography run contains no significant intraseasonal AAM periodicity in the tropics, consistent with the lack of the MJO, but produces a robust, 42-day AAM oscillation in the Northern Hemisphere (NH) extratropics. The model tropics undergoes a barotropic, zonally symmetric oscillation, driven by an exchange of mass with the NH extratropics. No intraseasonal periodicity is found in the average tropical latent heating field, indicating that the model oscillation is dynamically rather than thermodynamically driven. The no-mountain runs fail to produce an intraseasonal AAM oscillation, consistent with a topographic origin for the NH extratropical oscillation in the standard model. The spatial patterns of the oscillation in the 500-mb height field, and the relationship of the extratropical oscillation to intraseasonal variations in the tropics, will be discussed in Part 2 of this study.
NASA Astrophysics Data System (ADS)
Nakai, Hiromi; Ishikawa, Atsushi
2014-11-01
We propose a novel quantum chemical method, called the harmonic solvation model (HSM), for calculating thermochemical parameters in the condensed phase, particularly in the liquid phase. The HSM represents translational and rotational motions of a solute as vibrations interacting with a cavity wall of solvent molecules. As examples, the HSM and the ideal-gas model (IGM) were used for the standard formation reaction of liquid water, combustion reactions of liquid formic acid, methanol, and ethanol, vapor-liquid equilibration of water and ethanol, and dissolution of gaseous CO2 in water. The numerical results confirmed the reliability and applicability of the HSM. In particular, the temperature dependence of the Gibbs energy of liquid molecules was accurately reproduced by the HSM; for example, the boiling point of water was reasonably determined using the HSM, whereas the conventional IGM treatment failed to obtain a crossing of the two Gibbs energy curves for gaseous and liquid water.
Nakai, Hiromi; Ishikawa, Atsushi
2014-11-07
We propose a novel quantum chemical method, called the harmonic solvation model (HSM), for calculating thermochemical parameters in the condensed phase, particularly in the liquid phase. The HSM represents translational and rotational motions of a solute as vibrations interacting with a cavity wall of solvent molecules. As examples, the HSM and the ideal-gas model (IGM) were used for the standard formation reaction of liquid water, combustion reactions of liquid formic acid, methanol, and ethanol, vapor–liquid equilibration of water and ethanol, and dissolution of gaseous CO{sub 2} in water. The numerical results confirmed the reliability and applicability of the HSM. In particular, the temperature dependence of the Gibbs energy of liquid molecules was accurately reproduced by the HSM; for example, the boiling point of water was reasonably determined using the HSM, whereas the conventional IGM treatment failed to obtain a crossing of the two Gibbs energy curves for gaseous and liquid water.
A Review of Flood Loss Models as Basis for Harmonization and Benchmarking
Kreibich, Heidi; Franco, Guillermo; Marechal, David
2016-01-01
presents an approach for a quantitative comparison of disparate models via the reduction to the joint input variables of all models. Harmonization of models for benchmarking and comparison requires profound insight into the model structures, mechanisms and underlying assumptions. Possibilities and challenges are discussed that exist in model harmonization and the application of the inventory in a benchmarking framework. PMID:27454604
Menouar, Salah; Maamache, Mustapha; Choi, Jeong Ryeol
2010-08-15
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.
Globally coupled noisy oscillators with inhomogeneous periodic forcing
NASA Astrophysics Data System (ADS)
Gabbay, Michael; Larsen, Michael L.; Tsimring, Lev S.
2004-12-01
We study the collective properties of an array of nonlinear noisy oscillators driven by nonidentical periodic signals. We consider the case of a globally coupled array of harmonically forced, weakly nonlinear oscillators where there is a constant difference between the phases of the forcing signals applied to adjacent oscillators. This system is a prototypical model of a nonlinear phased array receiver. We derive analytical results for the array output in the limit of a large number of oscillators for the noise-free and noisy cases. Numerical simulations show good agreement with the theoretical analysis.
Deep-UV 236.5 nm laser by fourth-harmonic generation of a single-crystal fiber Nd:YAG oscillator.
Deyra, Loïc; Martial, Igor; Didierjean, Julien; Balembois, François; Georges, Patrick
2014-04-15
We demonstrate a deep-UV laser at 236.5 nm based on extracavity fourth-harmonic generation of a Q-switched Nd:YAG single-crystal fiber laser at 946 nm. We first compare two nonlinear crystals available for second-harmonic generation: LBO and BiBO. The best results at 473 nm are obtained with a BiBO crystal, with an average output power of 3.4 W at 20 kHz, corresponding to a second-harmonic generation efficiency of 38%. This blue laser is frequency-converted to 236.5 nm in a BBO crystal with an overall fourth-harmonic generation yield of 6.5%, corresponding to an average output power of 600 mW at 20 kHz. This represents an order of magnitude increase in average power and energy compared to previously reported pulsed lasers at 236.5 nm. This work opens the possibility of LIDAR detection of dangerous compounds for military or civilian applications. PMID:24978960
Modeling the lateral pedestrian force on a rigid floor by a self-sustained oscillator
NASA Astrophysics Data System (ADS)
Erlicher, Silvano; Trovato, Andrea; Argoul, Pierre
2010-07-01
The main goal of this paper is the definition of a nonlinear single-degree-of-freedom oscillator able to accurately predict the lateral walking force of a pedestrian. The force exerted on the floor corresponds to its restoring force. The rigid floor case is analyzed, leading to an autonomous oscillator. Even though such an oscillator is a simplified representation of the human body, it should be able to reproduce two experimentally observed phenomena: (i) the time-history of lateral force is an approximately periodic signal; (ii) the walking motion is self-sustained, in the sense that the pedestrian/oscillator produces by itself the energy needed to sustain its motion. This implies that such an oscillator must be self-sustained. In addition, the self-sustained character entails that the autonomous oscillation has a natural amplitude and frequency, representing the natural walking amplitude and frequency of the pedestrian. An original model is proposed by modifying the so-called hybrid Van der Pol/Rayleigh oscillator, already used for applications in the field of robotics. A dynamic analysis of this oscillator is then performed through an energetic approach and a perturbation technique in order to get the stable limit cycle. The model parameters are finally identified from the experimental force signals, resulting from a test campaign on a population of 12 pedestrians: the agreement between model and experimental results is very good.
Testing Spontaneous Wave-Function Collapse Models on Classical Mechanical Oscillators
NASA Astrophysics Data System (ADS)
Diósi, Lajos
2015-02-01
We show that the heating effect of spontaneous wave-function collapse models implies an experimentally significant increment Δ Tsp of equilibrium temperature in a mechanical oscillator. The obtained new form Δ Tsp is linear in the oscillator's relaxation time τ and independent of the mass. The oscillator can be in a classical thermal state, also the effect Δ Tsp is classical for a wide range of frequencies and quality factors. We note that the test of Δ Tsp does not necessitate quantum state monitoring just tomography. In both the gravity-related and the continuous spontaneous localization models the strong-effect edge of their parameter range can be challenged in existing experiments on classical oscillators. For the continuous spontaneous localization theory, the conjectured highest collapse rate parameter values become immediately constrained by evidences from current experiments on extreme slow-ring-down oscillators.
Testing spontaneous wave-function collapse models on classical mechanical oscillators.
Diósi, Lajos
2015-02-01
We show that the heating effect of spontaneous wave-function collapse models implies an experimentally significant increment ΔT(sp) of equilibrium temperature in a mechanical oscillator. The obtained new form ΔT(sp) is linear in the oscillator's relaxation time τ and independent of the mass. The oscillator can be in a classical thermal state, also the effect ΔT(sp) is classical for a wide range of frequencies and quality factors. We note that the test of ΔT(sp) does not necessitate quantum state monitoring just tomography. In both the gravity-related and the continuous spontaneous localization models the strong-effect edge of their parameter range can be challenged in existing experiments on classical oscillators. For the continuous spontaneous localization theory, the conjectured highest collapse rate parameter values become immediately constrained by evidences from current experiments on extreme slow-ring-down oscillators. PMID:25699424
Human brain networks function in connectome-specific harmonic waves
Atasoy, Selen; Donnelly, Isaac; Pearson, Joel
2016-01-01
A key characteristic of human brain activity is coherent, spatially distributed oscillations forming behaviour-dependent brain networks. However, a fundamental principle underlying these networks remains unknown. Here we report that functional networks of the human brain are predicted by harmonic patterns, ubiquitous throughout nature, steered by the anatomy of the human cerebral cortex, the human connectome. We introduce a new technique extending the Fourier basis to the human connectome. In this new frequency-specific representation of cortical activity, that we call ‘connectome harmonics', oscillatory networks of the human brain at rest match harmonic wave patterns of certain frequencies. We demonstrate a neural mechanism behind the self-organization of connectome harmonics with a continuous neural field model of excitatory–inhibitory interactions on the connectome. Remarkably, the critical relation between the neural field patterns and the delicate excitation–inhibition balance fits the neurophysiological changes observed during the loss and recovery of consciousness. PMID:26792267
Neutrino Oscillations, the Higgs Boson, and the Private Higgs Model
NASA Astrophysics Data System (ADS)
BenTov, Jonathan
"CESR, PEP, PETRA, ISABELLE, p-bar p colliders, LEP, the tevatron, and ep machines are at various levels of design or construction. They will study the properties of b-matter, see weak intermediaries, and perhaps find the t-quark and the Higgs boson. Never before was there such a bestiary waiting to be discovered; and what surprises will be found!" - S. L. Glashow ("The Future of Elementary Particle Physics," Quarks and Leptons, NATO Advanced Study Institutes Series Volume 61, 1980, pp 687-713) The situation in 1980 was clearly different from the present situation in 2013, in which we face the very real possibilty that no new degrees of freedom will ever again be within reach of a collider. In an intriguing twist of fate, this very fact results in a sharp paradox for fundamental physics: the Higgs mass should be MP/m h ˜ 1017 times larger than it actually is, and the vacuum energy density of the universe should be (M P/A)4 ˜ (1031)4 times larger than it actually is, and apparently nature refuses to give us any more clues as to why. These together are what I would call the main problem of 21st century physics: despite all of the predictive success of particle physics so far, we must find a way to suitably modify the rules of quantum field theory, lest we accept the unproductive defeatist attitude that our universe is simply fine-tuned. In the meantime, there is much interesting work to be done in more "traditional" particle physics: we have learned that neutrinos actually have tiny but nonzero masses, which is clear and unambiguous evidence for physics beyond the Standard Model. I will allocate the first third of this document to phenomena related to neutrino oscillations. In particular, I would like to argue that some of the apparent differences between neutrino mixing and quark mixing are to an extent illusory, and actually many aspects of the two sectors can be understood in a coherent framework for extending the Standard Model. The remaining two-thirds of this
Investigating Magnetic Oscillations.
ERIC Educational Resources Information Center
Brueningsen, Christopher A.
1993-01-01
Studies magnetic oscillation using an air track. Ceramic magnets are attached to the cart and also are used as dampeners in place of the springs. The resulting oscillations are fairly sinusoidal and is a good example of simple harmonic motion. (MVL)
NASA Astrophysics Data System (ADS)
Ndem Ikot, Akpan; Akpan, Ita O.; Abbey, T. M.; Hassanabadi, Hassan
2016-05-01
We propose improved ring shaped like potential of the form, V(r, θ) = V(r) + (ħ2/2Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2 and its exact solutions are presented via the Nikiforov–Uvarov method. The angle dependent part V(θ) = (ħ2 / 2 Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2, which is reported for the first time embodied the novel angle dependent (NAD) potential and harmonic novel angle dependent potential (HNAD) as special cases. We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials.
Modeling helicopter near-horizon harmonic noise due to transient maneuvers
NASA Astrophysics Data System (ADS)
Sickenberger, Richard D.
A new first principles model has been developed to estimate the external harmonic noise radiation for a helicopter performing transient maneuvers in the longitudinal plane. This model, which simulates the longitudinal fuselage dynamics, main rotor blade flapping, and far field acoustics, was validated using in-flight measurements and recordings from ground microphones during a full-scale flight test featuring a Bell 206B-3 helicopter. The flight test was specifically designed to study transient maneuvers. The validated model demonstrated that the flapping of the main rotor blades does not significantly affect the acoustics radiated by the helicopter during maneuvering flight. Furthermore, the model also demonstrated that Quasi-Static Acoustic Mapping (Q-SAM) methods can be used to reliably predict the noise radiated during transient maneuvers. The model was also used to identify and quantify the contributions of main rotor thickness noise, low frequency loading noise, and blade-vortex interaction (BVI) noise during maneuvering flight for the Bell 206B-3 helicopter. Pull-up and push-over maneuvers from pure longitudinal cyclic and pure collective control inputs were investigated. The contribution of thickness noise and low frequency loading noise during maneuvering flight was found to depend on the orientation of the tip-path plane relative to the observer. The contribution of impulsive BVI noise during maneuvering flight was found to depend on the inflow through the main rotor and the orientation of the tip-path plane relative to the observer.
A southern Africa harmonic spline core field model derived from CHAMP satellite data
NASA Astrophysics Data System (ADS)
Nahayo, E.; Kotzé, P. B.; McCreadie, H.
2015-02-01
The monitoring of the Earth's magnetic field time variation requires a continuous recording of geomagnetic data with a good spatial coverage over the area of study. In southern Africa, ground recording stations are limited and the use of satellite data is needed for the studies where high spatial resolution data is required. We show the fast time variation of the geomagnetic field in the southern Africa region by deriving an harmonic spline model from CHAMP satellite measurements recorded between 2001 and 2010. The derived core field model, the Southern Africa Regional Model (SARM), is compared with the global model GRIMM-2 and the ground based data recorded at Hermanus magnetic observatory (HER) in South Africa and Tsumeb magnetic observatory (TSU) in Namibia where the focus is mainly on the long term variation of the geomagnetic field. The results of this study suggest that the regional model derived from the satellite data alone can be used to study the small scale features of the time variation of the geomagnetic field where ground data is not available. In addition, these results also support the earlier findings of the occurrence of a 2007 magnetic jerk and rapid secular variation fluctuations of 2003 and 2004 in the region.
Local harmonic motion monitoring of focused ultrasound surgery--a simulation model.
Heikkilä, Janne; Curiel, Laura; Hynynen, Kullervo
2010-01-01
In this paper, a computational model for localized harmonic motion (LHM) imaging-based monitoring of high-intensity focused ultrasound surgery (FUS) is presented. The LHM technique is based on a focused, time-varying ultrasound radiation force excitation, which induces local oscillatory motions at the focal region. These vibrations are tracked, using pulse-echo imaging, and then, used to estimate the mechanical properties of the sonication region. LHM is feasible for FUS monitoring because changes in the material properties during the coagulation process affect the measured displacements. The presented model includes separate models to simulate acoustic sonication fields, sonication-induced temperature elevation and mechanical motion, and pulse-echo imaging of the induced motions. These 3-D simulation models are based on Rayleigh-Sommerfield integral, finite element, and spatial impulse response methods. Simulated-tissue temperature elevation and mechanical motion were compared with previously published in vivo measurements. Finally, the simulation model was used to simulate coagulation and LHM monitoring, as would occur with multiple, neighbouring sonication locations covering a large tumor. PMID:19822463
Li, Yu-Sheng; Oldendick, James E; Chang, Wei
2013-01-01
Pinhole collimators are widely used for SPECT imaging of small organs and animals. There also has been renewed interest in using pinhole arrays for clinical cardiac SPECT imaging to achieve high sensitivity and complete data sampling. Overall sensitivity of a pinhole array is critical in determining a system’s performance. Conventionally, a point source model has been used to evaluate the sensitivity and optimize the system design. This model is simple but far from realistic. This work addresses the use of more realistic source models to assess the sensitivity performance of pinhole collimation. We have derived an analytical formula for pinhole collimation sensitivity with a general source distribution model using spherical harmonics. As special cases of this general model, we provided the pinhole sensitivity formulae for line, disk and sphere sources. These results show that the point source model is just the zeroth-order approximation of the other source models. The point source model overestimates or underestimates the sensitivity relative to the more realistic model. The sphere source model yields the same sensitivity as a point source located at the center of the sphere when attenuation is not taken into account. In the presence of attenuation, the average path length of emitted gamma-rays is 3/4 of the radius of the sphere source. The calculated sensitivities based on these formulae show good agreement with separate Monte Carlo simulations in simple cases. The general and special sensitivity formulae derived here can be useful for the design and optimization of SPECT systems that utilize pinhole collimators. PMID:20400812
Fluctuations in a coupled-oscillator model of the cardiovascular system
NASA Astrophysics Data System (ADS)
González, Jorge A.; Suárez-Vargas, Jose J.; Stefanovska, Aneta; McClintock, Peter V. E.
2007-06-01
We present a model of the cardiovascular system (CVS) based on a system of coupled oscillators. Using this approach we can describe several complex physiological phenomena that can have a range of applications. For instance, heart rate variability (HRV), can have a new deterministic explanation. The intrinsic dynamics of the HRV is controlled by deterministic couplings between the physiological oscillators in our model and without the need to introduce external noise as is commonly done. This new result provides potential applications not only for physiological systems but also for the design of very precise electronic generators where the frequency stability is crucial. Another important phenomenon is that of oscillation death. We show that in our CVS model the mechanism leading to the quenching of the oscillations can be controlled, not only by the coupling parameter, but by a more general scheme. In fact, we propose that a change in the relative current state of the cardiovascular oscillators can lead to a cease of the oscillations without actually changing the strength of the coupling among them. We performed real experiments using electronic oscillators and show them to match the theoretical and numerical predictions. We discuss the relevance of the studied phenomena to real cardiovascular systems regimes, including the explanation of certain pathologies, and the possible applications in medical practice.
Face transformation with harmonic models by the finite-volume method with delaunay triangulation.
Li, Zi-Cai; Chiang, John Y; Suen, Ching Y
2010-12-01
To carry out face transformation, this paper presents new numerical algorithms, which consist of two parts, namely, the harmonic models for changes of face characteristics and the splitting techniques for grayness transition. The main method in this paper is a combination of the finite-volume method (FVM) with Delaunay triangulation to solve the Laplace equations in the harmonic transformation of face images. The advantages of the FVM with Delaunay triangulation are given as follows: 1) easy to formulate the linear algebraic equations; 2) good in retaining the pertinent geometric and physical need; and 3) less central processing unit time needed. Numerical and graphical experiments have been conducted for the face transformation from a female (woman) to a male (man), and vice versa. The computed sequential errors are O(N⁻³/²), where N² is the division number of a pixel into subpixels. These computed errors coincide with the analysis on the splitting-shooting method (SSM) with piecewise constant interpolation in the previous paper of Li and Bai. In computation, the average absolute errors of restored pixel grayness can be smaller than 2 out of 256 grayness levels. The FVM is as simple as the finite-difference method (FDM) and as flexible as the finite-element method (FEM). Hence, the FVM is particularly useful when dealing with large face images with a huge number of pixels in shape distortion. The numerical transformation of face images in this paper can be used not only in pattern recognition but also in resampling, image morphing, and computer animation. PMID:20363682
A New Physical Model for Pulsars as Gravitational Shielding and Oscillating Neutron Stars
NASA Astrophysics Data System (ADS)
Zhang, Tianxi
2014-06-01
Pulsars are fast rotating neutron stars that synchronously emit periodic Dirac delta shape pulses of radio-frequency radiation and Lorentzian shape oscillations of X-rays. The acceleration of particles near the magnetic poles, which derivate from the rotating axis produces coherent beams of radio emissions that are viewed as pulses of radiation whenever the magnetic poles sweep the viewers. However, the conventional lighthouse model of pulsars is only conceptual. The physical mechanism through which particles are accelerated to produce coherent beams of radio emissions is still poorly understood. The process for periodically oscillating X-rays to emit from hot spots at the inner edge of accretion disks of pulsars is also remained as an unsolved mystery. Recently, a new physical model of pulsars is proposed by the author to quantitatively interpret the emission characteristics of pulsars, in accordance with his well-developed five-dimensional fully covariant Kaluza-Klein gravitational shielding theory and the physics of thermal and accelerating charged particle radiation. The results indicate that with the significant gravitational shielding by scalar field a neutron star nonlinearly oscillates and produces synchronous periodically Dirac delta shape pulse-like radio-frequency radiation (emitted by the oscillating or accelerating charged particles) as well as periodically Lorentzian shape oscillating X-rays (as the thermal radiation of neutron stars that temperature varies due to the oscillation). This physical model of pulsars as gravitational shielding and oscillating neutron stars broadens our understanding of neutron stars and develops an innovative mechanism to disclose the mystery of pulsars. In this presentation, I will show the results obtained from the quantitative studies of this new physical model of pulsars for the oscillations of neutron stars and the powers of radio pulse-like emissions and oscillating X-rays.
Model-driven harmonic parameterization of the cortical surface: HIP-HOP.
Auzias, G; Lefèvre, J; Le Troter, A; Fischer, C; Perrot, M; Régis, J; Coulon, O
2013-05-01
In the context of inter subject brain surface matching, we present a parameterization of the cortical surface constrained by a model of cortical organization. The parameterization is defined via an harmonic mapping of each hemisphere surface to a rectangular planar domain that integrates a representation of the model. As opposed to previous landmark-based registration methods we do not match folds between individuals but instead optimize the fit between cortical sulci and specific iso-coordinate axis in the model. This strategy overcomes some limitation to sulcus-based registration techniques such as topological variability in sulcal landmarks across subjects. Experiments on 62 subjects with manually traced sulci are presented and compared with the result of the Freesurfer software. The evaluation involves a measure of dispersion of sulci with both angular and area distortions. We show that the model-based strategy can lead to a natural, efficient and very fast (less than 5 min per hemisphere) method for defining inter subjects correspondences. We discuss how this approach also reduces the problems inherent to anatomically defined landmarks and open the way to the investigation of cortical organization through the notion of orientation and alignment of structures across the cortex. PMID:23358957
NASA Astrophysics Data System (ADS)
Searle, G. F. C.
2014-05-01
1. Elementary theory of harmonic motion; 2. Experimental work in harmonic motion; Experiment 1. Determination of g by a simple pendulum; Experiment 2. Harmonic motion of a body suspended by a spring; Experiment 3. Harmonic motion of a rigid body suspended by a torsion wire; Experiment 4. Study of a system with variable moment of inertia; Experiment 5. Dynamical determination of ratio of couple to twist for a torsion wire; Experiment 6. Comparison of the moments of inertia of two bodies; Experiment 7. Experiment with a pair of inertia bars; Experiment 8. Determination of the moment of inertia of a rigid pendulum; Experiment 9. Experiment on a pendulum with variable moment of inertia; Experiment 10. Determination of g by a rigid pendulum; Experiment 11. Pendulum on a yielding support; Experiment 12. Determination of the radius of curvature of a concave mirror by the oscillations of a sphere rolling in it; Experiment 13. Determination of g by the oscillations of a rod rolling on a cylinder; Experiment 14. Study of a vibrating system with two degrees of freedom; Note 1. On the vibration of a body suspended from a light spring; Note 2. Periodic time of a pendulum vibrating through a finite arc; Note 3. Periodic time for finite motion; Note 4. Periodic times of a pendulum with two degrees of freedom.
Harmonically excited orbital variations
Morgan, T.
1985-08-06
Rephrasing the equations of motion for orbital maneuvers in terms of Lagrangian generalized coordinates instead of Newtonian rectangular cartesian coordinates can make certain harmonic terms in the orbital angular momentum vector more readily apparent. In this formulation the equations of motion adopt the form of a damped harmonic oscillator when torques are applied to the orbit in a variationally prescribed manner. The frequencies of the oscillator equation are in some ways unexpected but can nonetheless be exploited through resonant forcing functions to achieve large secular variations in the orbital elements. Two cases are discussed using a circular orbit as the control case: (1) large changes in orbital inclination achieved by harmonic excitation rather than one impulsive velocity change, and (2) periodic and secular changes to the longitude of the ascending node using both stable and unstable excitation strategies. The implications of these equations are also discussed for both artificial satellites and natural satellites. For the former, two utilitarian orbits are suggested, each exploiting a form of harmonic excitation. 5 refs.
Probing wave function collapse models with a classically driven mechanical oscillator
NASA Astrophysics Data System (ADS)
Ho, Melvyn; Lafont, Ambroise; Sangouard, Nicolas; Sekatski, Pavel
2016-03-01
We show that the interaction of a pulsed laser light with a mechanical oscillator through the radiation pressure results in an opto-mechanical entangled state in which the photon number is correlated with the oscillator position. Interestingly, the mechanical oscillator can be delocalized over a large range of positions when driven by an intense laser light. This provides a simple yet sensitive method to probe hypothetical post-quantum theories including an explicit wave function collapse model, like the Diosi & Penrose model. We propose an entanglement witness to reveal the quantum nature of this opto-mechanical state as well as an optical technique to record the decoherence of the mechanical oscillator. We also report on a detailed feasibility study giving the experimental challenges that need to be overcome in order to confirm or rule out predictions from explicit wave function collapse models.
NASA Astrophysics Data System (ADS)
Bagchi, Bijan; Marquette, Ian
2015-08-01
We derive a one-step extension of the well known Swanson oscillator that describes a specific type of pseudo-Hermitian quadratic Hamiltonian connected to an extended harmonic oscillator model. Our analysis is based on the use of the techniques of supersymmetric quantum mechanics and addresses various representations of the ladder operators starting from a seed solution of the harmonic oscillator expressed in terms of a pseudo-Hermite polynomial. The role of the resulting chain of Hamiltonians related to similarity transformation is then exploited. In the second part we write down a two dimensional generalization of the Swanson Hamiltonian and establish superintegrability of such a system.
Modeling of Soft Poroelastic Tissue in Time-Harmonic MR Elastography
Perriñez, Phillip R.; Kennedy, Francis E.; Van Houten, Elijah E. W.; Weaver, John B.; Paulsen, Keith D.
2010-01-01
Elastography is an emerging imaging technique that focuses on assessing the resistance to deformation of soft biological tissues in vivo. Magnetic resonance elastography (MRE) uses measured displacement fields resulting from low-amplitude, low-frequency (10 Hz–1 kHz) time-harmonic vibration to recover images of the elastic property distribution of tissues including breast, liver, muscle, prostate, and brain. While many soft tissues display complex time-dependent behavior not described by linear elasticity, the models most commonly employed in MRE parameter reconstructions are based on elastic assumptions. Further, elasticity models fail to include the interstitial fluid phase present in vivo. Alternative continuum models, such as consolidation theory, are able to represent tissue and other materials comprising two distinct phases, generally consisting of a porous elastic solid and penetrating fluid. MRE reconstructions of simulated elastic and poroelastic phantoms were performed to investigate the limitations of current-elasticity-based methods in producing accurate elastic parameter estimates in poroelastic media. The results indicate that linearly elastic reconstructions of fluid-saturated porous media at amplitudes and frequencies relevant to steady-state MRE can yield misleading effective property distributions resulting from the complex interaction between their solid and fluid phases. PMID:19272864
Application of the spherical harmonic gravity model in high precision inertial navigation systems
NASA Astrophysics Data System (ADS)
Wang, Jing; Yang, Gongliu; Li, Xiangyun; Zhou, Xiao
2016-09-01
The spherical harmonic gravity model (SHM) may, in general, be considered as a suitable alternative to the normal gravity model (NGM), because it represents the Earth’s gravitational field more accurately. However, the high-resolution SHM has never been used in current inertial navigation systems (INSs) due to its extremely complex expression. In this paper, the feasibility and accuracy of a truncated SHM are discussed for application in a real-time free-INS with a precision demand better than 0.8 nm h‑1. In particular, the time and space complexity are analyzed mathematically to verify the feasibility of the SHM. Also, a test on a typical navigation computer shows a storable range of cut-off degrees. To further evaluate the appropriate degree and accuracy of the truncated SHM, analyses of covariance and truncation error are proposed. Finally, a SHM of degree 12 is demonstrated to be the appropriate model for routine INSs in the precision range of 0.4–0.75 nm h‑1. Flight simulations and road tests show its outstanding performance over the traditional NGM.
Is the Langevin phase equation an efficient model for oscillating neurons?
NASA Astrophysics Data System (ADS)
Ota, Keisuke; Tsunoda, Takamasa; Omori, Toshiaki; Watanabe, Shigeo; Miyakawa, Hiroyoshi; Okada, Masato; Aonishi, Toru
2009-12-01
The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.
Numerical Verification of an Analytical Model for Phase Noise in MEMS Oscillators.
Agrawal, D K; Bizzarri, F; Brambilla, A; Seshia, A A
2016-08-01
A new analytical formulation for phase noise in MEMS oscillators was recently presented encompassing the role of essential nonlinearities in the electrical and mechanical domains. In this paper, we validate the effectiveness of the proposed analytical formulation with respect to the unified theory developed by Demir et al. describing phase noise in oscillators. In particular, it is shown that, over a range of the second-order mechanical nonlinear stiffness of the MEMS resonator, both models exhibit an excellent match in the phase diffusion coefficient calculation for a square-wave MEMS oscillator. PMID:27295660
NASA Astrophysics Data System (ADS)
Brill, K. A.; Waite, G. P.
2012-12-01
Tremor signals at volcanoes are typically attributed to fluid movement within the system. Characteristics of harmonic tremor (i.e. duration, frequency content, polarization) can convey detailed information about source processes from which they emanate, but decoding these signals poses great challenges due to the complexity of volcanic environments. We recorded instances of harmonic tremor at both Santiaguito and Fuego volcanoes Guatemala, Central America. The instances of harmonic tremor occur both independent from and contemporaneous with explosions, and last anywhere from 30 seconds to tens of minutes. The signals have fundamental frequencies between 0.3 and 2.5 Hz, with as many as 20 overtones, and exhibit spectral gliding of up to 0.75 Hz over the course of an event, changing as quickly as 0.1 Hz/second. Field observations; video recordings; and time-lapse, ultraviolet, and thermal imagery; collected simultaneously with acoustic and seismic recordings allow us to constrain source locations and processes beyond what would otherwise be possible just acoustic and seismic recordings. We propose that the harmonic tremor signals are generated by nonlinear excitation of fracture walls as gas vents out of the systems. Additionally, we investigate the complex wavefield generated by harmonic tremor and the heterogeneous volcanic media. Particle motions at both volcanoes are typically elliptical, but vary dramatically over time as the fundamental frequency glides up and down (see figure). In addition, the particle motions of harmonics often have different polarities from each other and the fundamental frequency. Through finite difference modeling, we isolate the effects of near-field terms, topography, and source mechanism to explore each of these factors' contribution to the unexpected behavior.
NASA Technical Reports Server (NTRS)
Espinosa, Ismael; Gonzalez, Hortensia; Quiza, Jorge; Gonazalez, J. Jesus; Arroyo, Ruben; Lara, Ritaluz
1995-01-01
Oscillation of electrical activity has been found in many nervous systems, from invertebrates to vertebrates including man. There exists experimental evidence of very simple circuits with the capability of oscillation. Neurons with intrinsic oscillation have been found and also neural circuits where oscillation is a property of the network. These two types of oscillations coexist in many instances. It is nowadays hypothesized that behind synchronization and oscillation there is a system of coupled oscillators responsible for activities that range from locomotion and feature binding in vision to control of sleep and circadian rhythms. The huge knowledge that has been acquired on oscillators from the times of Lord Rayleigh has made the simulation of neural oscillators a very active endeavor. This has been enhanced with more recent physiological findings about small neural circuits by means of intracellular and extracellular recordings as well as imaging methods. The future of this interdisciplinary field looks very promising; some researchers are going into quantum mechanics with the idea of trying to provide a quantum description of the brain. In this work we describe some simulations using neuron models by means of which we form simple neural networks that have the capability of oscillation. We analyze the oscillatory activity with root locus method, cross-correlation histograms, and phase planes. In the more complicated neural network models there is the possibility of chaotic oscillatory activity and we study that by means of Lyapunov exponents. The companion paper shows an example of that kind.
Scaling, cluster dynamics and complex oscillations in a multispecies Lattice Lotka-Volterra Model
NASA Astrophysics Data System (ADS)
Shabunin, A. V.; Efimov, A.; Tsekouras, G. A.; Provata, A.
2005-03-01
The cluster formation in the cyclic (4+1)-Lattice Lotka-Volterra Model is studied by Kinetic Monte Carlo simulations on a square lattice support. At the Mean Field level this model demonstrates conservative four-dimensional oscillations which, depending on the parameters, can be chaotic or quasi-periodic. When the system is realized on a square lattice substrate the various species organize in domains (clusters) with fractal boundaries and this is consistent with dissipative dynamics. For small lattice sizes, the entire lattice oscillates in phase and the size distribution of the clusters follows a pure power law distribution. When the system size is large many independently oscillating regions are formed and as a result the cluster size distribution in addition to the power law, acquires a exponential decay dependence. This combination of power law and exponential decay of distributions and correlations is indicative, in this case, of mixing and superposition of regions oscillating asynchronously.
Harmonization of future needs for dermal exposure assessment and modeling: a workshop report.
Marquart, H; Maidment, S; McClaflin, J L; Fehrenbacher, M C
2001-02-01
Dermal exposure assessment and modeling is still in early phases of development. This article presents the results of a workshop organized to harmonize the future needs in this field. Methods for dermal exposure assessment either assess the mass of contaminant that is transferred to the skin, or the transfer of contaminant through the skin. Models for dermal exposure are either knowledge-based or deterministic. Any method or model should be transparent, validated, and open to further development. Some (partly) validated and standardized methods are available for measuring or modeling permeation of the skin or of personal protective equipment (PPE). Further validation and standardization is necessary. More research is needed on permeation of dusts and aerosols and more realistic tests should be developed and used for PPE. Several methods have been developed to measure contamination of surfaces or skin, but they are not validated or standardized. A number of non-validated models exist to assess dermal exposure. A clear need exists for more studies of dermal exposure, regarding measurement methods, models and actual exposure levels. A running four-year European study will greatly expand the knowledge in this field. Simple tools to assess and control the risks of dermal exposure in small and medium sized enterprises are also needed. Increasing the general knowledge of practitioners (e.g., safety professionals, occupational hygienists and physicians) in the field of dermal exposure is a first requirement. Available data, for example, on the permeation of PPE, should be made more readily available, using modern information technology. When information on dermal exposure is gathered and stored, the core information needs are partly the same as those for inhalation exposure. Some elements of process and activity, substance and product or worker, specific for dermal exposure, have been suggested by the workshop. PMID:11217714
A Resonantly Excited Disk-Oscillation Model of High-Frequency QPOs of Microquasars
NASA Astrophysics Data System (ADS)
Kato, Shoji
2012-12-01
A possible model of twin high-frequency QPOs (HF QPOs) of microquasars is examined. The disk is assumed to have global magnetic fields and to be deformed with a two-armed pattern. In this deformed disk, a set of a two-armed (m = 2) vertical p-mode oscillation and an axisymmetric (m = 0) g-mode oscillation is considered. They resonantly interact through the disk deformation when their frequencies are the same. This resonant interaction amplifies the set of the above oscillations in the case where these two oscillations have wave energies of opposite signs. These oscillations are assumed to be excited most efficiently in the case where the radial group velocities of these two waves vanish at the same place. The above set of oscillations is not unique, depending on the node number n, of oscillations in the vertical direction. We consider that the basic two sets of oscillations correspond to the twin QPOs. The frequencies of these oscillations depend on the disk parameters, such as the strength of the magnetic fields. For observational mass ranges of GRS 1915+ 105, GRO J1655-40, XTE J1550-564, and HEAO H1743-322, the spins of these sources are estimated. High spins of these sources can be described if the disks have weak poloidal magnetic fields as well as toroidal magnetic fields of moderate strength. In this model the 3:2 frequency ratio of high-frequency QPOs is not related to their excitation, but occurs by chance.
Brigham, John C.; Aquino, Wilkins; Aguilo, Miguel A.; Diamessis, Peter J.
2010-01-01
An approach for efficient and accurate finite element analysis of harmonically excited soft solids using high-order spectral finite elements is presented and evaluated. The Helmholtz-type equations used to model such systems suffer from additional numerical error known as pollution when excitation frequency becomes high relative to stiffness (i.e. high wave number), which is the case, for example, for soft tissues subject to ultrasound excitations. The use of high-order polynomial elements allows for a reduction in this pollution error, but requires additional consideration to counteract Runge's phenomenon and/or poor linear system conditioning, which has led to the use of spectral element approaches. This work examines in detail the computational benefits and practical applicability of high-order spectral elements for such problems. The spectral elements examined are tensor product elements (i.e. quad or brick elements) of high-order Lagrangian polynomials with non-uniformly distributed Gauss-Lobatto-Legendre nodal points. A shear plane wave example is presented to show the dependence of the accuracy and computational expense of high-order elements on wave number. Then, a convergence study for a viscoelastic acoustic-structure interaction finite element model of an actual ultrasound driven vibroacoustic experiment is shown. The number of degrees of freedom required for a given accuracy level was found to consistently decrease with increasing element order. However, the computationally optimal element order was found to strongly depend on the wave number. PMID:21461402
Brigham, John C; Aquino, Wilkins; Aguilo, Miguel A; Diamessis, Peter J
2011-01-15
An approach for efficient and accurate finite element analysis of harmonically excited soft solids using high-order spectral finite elements is presented and evaluated. The Helmholtz-type equations used to model such systems suffer from additional numerical error known as pollution when excitation frequency becomes high relative to stiffness (i.e. high wave number), which is the case, for example, for soft tissues subject to ultrasound excitations. The use of high-order polynomial elements allows for a reduction in this pollution error, but requires additional consideration to counteract Runge's phenomenon and/or poor linear system conditioning, which has led to the use of spectral element approaches. This work examines in detail the computational benefits and practical applicability of high-order spectral elements for such problems. The spectral elements examined are tensor product elements (i.e. quad or brick elements) of high-order Lagrangian polynomials with non-uniformly distributed Gauss-Lobatto-Legendre nodal points. A shear plane wave example is presented to show the dependence of the accuracy and computational expense of high-order elements on wave number. Then, a convergence study for a viscoelastic acoustic-structure interaction finite element model of an actual ultrasound driven vibroacoustic experiment is shown. The number of degrees of freedom required for a given accuracy level was found to consistently decrease with increasing element order. However, the computationally optimal element order was found to strongly depend on the wave number. PMID:21461402
Phase-locking regions in a forced model of slow insulin and glucose oscillations
NASA Astrophysics Data System (ADS)
Sturis, Jeppe; Knudsen, Carsten; O'Meara, Niall M.; Thomsen, Jesper S.; Mosekilde, Erik; Van Cauter, Eve; Polonsky, Kenneth S.
1995-03-01
We present a detailed numerical investigation of the phase-locking regions in a forced model of slow oscillations in human insulin secretion and blood glucose concentration. The bifurcation structures of period 2π and 4π tongues are mapped out and found to be qualitatively identical to those of several other periodically forced self-oscillating systems operating across a Hopf-bifurcation point. The numerical analyses are supplemented by clinical experiments.
Analysis of Types of Oscillations in Goodwin's Model of Business Cycle
NASA Astrophysics Data System (ADS)
Antonova, A. O.; Reznik, S. N.; Todorov, M. D.
2010-11-01
Types of solutions of the Goodwin business cycle model with the fixed investment time lag have been numerically studied. It is shown that the long-periodic Goodwin's oscillations are excited by the independent investment A in case A exceeds a threshold. If A falls below the threshold, then there are only sawtooth oscillations with a period equal to the investment time lag. Near the threshold, the time behavior of the income is irregular.
Properties of finite difference models of non-linear conservative oscillators
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1988-01-01
Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.
NASA Technical Reports Server (NTRS)
Miller, R. H.
1991-01-01
Long-lived oscillations that act like normal modes are described. The total kinetic energy is found to vary with time by amounts far in excess of the fluctuations expected from the virial theorem, and the variation shows periodic patterns that suggest oscillations. Experimental results indicate that oscillation amplitudes depend on the nature of the model. It is noted that it is difficult to answer questions about likely amplitudes in real galaxies with any confidence at the present time.
Stuttering Min oscillations within E. coli bacteria: a stochastic polymerization model
NASA Astrophysics Data System (ADS)
Sengupta, Supratim; Derr, Julien; Sain, Anirban; Rutenberg, Andrew D.
2012-10-01
We have developed a 3D off-lattice stochastic polymerization model to study the subcellular oscillation of Min proteins in the bacteria Escherichia coli, and used it to investigate the experimental phenomenon of Min oscillation stuttering. Stuttering was affected by the rate of immediate rebinding of MinE released from depolymerizing filament tips (processivity), protection of depolymerizing filament tips from MinD binding and fragmentation of MinD filaments due to MinE. Processivity, protection and fragmentation each reduce stuttering, speed oscillations and MinD filament lengths. Neither processivity nor tip protection were, on their own, sufficient to produce fast stutter-free oscillations. While filament fragmentation could, on its own, lead to fast oscillations with infrequent stuttering; high levels of fragmentation degraded oscillations. The infrequent stuttering observed in standard Min oscillations is consistent with short filaments of MinD, while we expect that mutants that exhibit higher stuttering frequencies will exhibit longer MinD filaments. Increased stuttering rate may be a useful diagnostic to find observable MinD polymerization under experimental conditions.
Intraseasonal Oscillations over South America: A Study with a Regional Climate Model
NASA Technical Reports Server (NTRS)
Chen, Baode; Chao, Winston
2003-01-01
The National Center for Atmospheric Research (NCAR) regional climate model version 2 (RegCM2) is used to investigate the observed characteristics of intraseasonal oscillations over South America. Our study is mainly concentrated on an intraseaonal mode, which is observed to account for a large portion of the intraseasonal variation, to have a standing feature and to be independent of the MJO. The NCEPDOE AMIP-II reanalysis is utilized to provide initial and lateral boundary conditions for the RegCM2 based upon the OOZ, 062, 122 and 182 data.Our results indicate that the intraseasonal oscillation still exists with time- averaged lateral boundary condition, which prevents the MJO and other outside disturbances from entering the model's domain, suggesting a locally forced oscillation responsible for ths intraseasonal mode independent of the MJO. Further experiments show that the annual and daily variabilities and a radiative-convective interaction are not essential to the locally forced intraseasonal oscillation. The intraseasonal oscillations over Amazon in our model essentially result from interactions among atmospheric continental- scale circulation, surface radiation, surface sensible and latent heat fluxes, and cumulus convection. The wavelet analyses of various surface energy fluxes and surface energy budget also verify that the primary cause of intraseasonal oscillation is the interaction of land surface processes with the atmosphere.
Davis, R.; Fishman, D.; Frank, E. D.; Wigmosta, M. S.; Aden, A.; Coleman, A. M.; Pienkos, P. T.; Skaggs, R. J.; Venteris, E. R.; Wang, M. Q.
2012-06-01
The U.S. Department of Energy's Biomass Program has begun an initiative to obtain consistent quantitative metrics for algal biofuel production to establish an 'integrated baseline' by harmonizing and combining the Program's national resource assessment (RA), techno-economic analysis (TEA), and life-cycle analysis (LCA) models. The baseline attempts to represent a plausible near-term production scenario with freshwater microalgae growth, extraction of lipids, and conversion via hydroprocessing to produce a renewable diesel (RD) blendstock. Differences in the prior TEA and LCA models were reconciled (harmonized) and the RA model was used to prioritize and select the most favorable consortium of sites that supports production of 5 billion gallons per year of RD. Aligning the TEA and LCA models produced slightly higher costs and emissions compared to the pre-harmonized results. However, after then applying the productivities predicted by the RA model (13 g/m2/d on annual average vs. 25 g/m2/d in the original models), the integrated baseline resulted in markedly higher costs and emissions. The relationship between performance (cost and emissions) and either productivity or lipid fraction was found to be non-linear, and important implications on the TEA and LCA results were observed after introducing seasonal variability from the RA model. Increasing productivity and lipid fraction alone was insufficient to achieve cost and emission targets; however, combined with lower energy, less expensive alternative technology scenarios, emissions and costs were substantially reduced.
Nguyen, Hoai; Neiman, Alexander B.
2010-01-01
We study statistical properties, response dynamics, and information transmission in a Hodgkin-Huxley–type neuron system, modeling peripheral electroreceptors in paddlefish. In addition to sodium and potassium currents, the neuron model includes fast calcium and slow afterhyperpolarization (AHP) potassium currents. The synaptic transmission from sensory epithelium is modeled by a Poission process with a rate modulated by narrow-band noise, mimicking stochastic epithelial oscillations observed experimentally. We study how the interplay of parameters of AHP current and synaptic noise affects the statistics of spontaneous dynamics and response properties of the system. In particular, we confirm predictions made earlier with perfect integrate and fire and phase neuron models that epithelial oscillations enhance stimulus–response coherence and thus information transmission in electroreceptor system. In addition, we consider a strong stimulus regime and show that coherent epithelial oscillations may reduce variability of electroreceptor responses to time-varying stimuli. PMID:20975925
Bansal, Dipanshu; Aref, Amjad; Dargush, Gary; Delaire, Olivier A.
2016-07-20
Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally-derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. In this study, we illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound FeSi over a wide range of temperature. Our results agreemore » well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.« less
Bansal, Dipanshu; Aref, Amjad; Dargush, Gary; Delaire, Olivier
2016-09-28
Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally-derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. We illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound [Formula: see text] over a wide range of temperature. Results agree well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials. PMID:27438881
NASA Astrophysics Data System (ADS)
Bansal, Dipanshu; Aref, Amjad; Dargush, Gary; Delaire, Olivier
2016-09-01
Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally-derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. We illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound \\text{FeSi} over a wide range of temperature. Results agree well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.
Two-oscillator Kantowski-Sachs model of the Schwarzschild black hole interior
NASA Astrophysics Data System (ADS)
Djordjevic, Goran S.; Nesic, Ljubisa; Radovancevic, Darko
2016-08-01
In this paper the interior of the Schwarzschild black hole, which is presented as a vacuum, homogeneous and anisotropic Kantowski-Sachs minisuperspace cosmological model, is considered. Lagrangian of the model is reduced by a suitable coordinate transformation to Lagrangian of two decoupled oscillators with the same frequencies and with zero energy in total (an oscillator-ghost-oscillator system). The model is presented in a classical, a p-adic and a noncommutative case. Then, within the standard quantum approach Wheeler-DeWitt equation and its general solutions, i.e. a wave function of the model is written, and then an adelic wave function is constructed. Finally, thermodynamics of the model is studied by using the Feynman-Hibbs procedure.
Peach, Gillian; Whittingham, Ian B.; Beams, Timothy J.
2004-09-01
We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two highly efficient computational methods for determining the bound state energies and eigenfunctions of such systems. The perturbed harmonic oscillator problem is characterized by a long asymptotic region beyond the effective range of the interatomic potential. The first method, which is based on quantum defect theory and is an adaptation of a technique developed by one of the authors (G.P.) for highly excited states in a modified Coulomb potential, is very efficient for integrating through this outer region. The second method is a direct numerical solution of the radial Schroedinger equation using a discrete variable representation of the kinetic energy operator and a scaled radial coordinate grid. The methods are applied to the case of trapped spin-polarized metastable helium atoms. The calculated eigenvalues agree very closely for the two methods, and with the eigenvalues computed using the generalized self-consistent method.
A single ion anharmonic mechanical oscillator with nonlinear dissipation
NASA Astrophysics Data System (ADS)
Akerman, Nitzan; Kotler, Shlomi; Glickman, Yinnon; Keselman, Anna; Dallal, Yehonatan; Ozeri, Roee
2010-03-01
A driven, damped, nearly harmonic oscillator with a small cubic term in the force, is known as the Duffing oscillator. The Duffing oscillator shows various interesting features of non-linear response such as bistability and hysteresis. Several features of the Duffing instability have been recently measured using superconducting qubits and nano-mechanical resonators. Linear Paul traps can be well approximated as harmonic but have a small an-harmonicity due to their deviation from an ideal quadruple geometry. We study the steady state motion of a single trapped Sr^+ ion, subject to a near-resonance drive and dissipation in a linear Paul trap with a small anharmonicity. The driving force is applied by an oscillating voltage on the trap end-caps. Dissipation is the result of laser Doppler cooling. We measure both the amplitude and phase of the driven oscillations and find a good agreement with the Duffing oscillator model. When the cooling laser is close to resonance the standard Duffing model has to be extended to account for non-linearity in the dissipative force. Both the linear and the nonlinear terms of the dissipative force for various cooling laser detunings are determined by the line-shape of the - cooling transition and the cooling laser intensity and can therefore be conveniently controlled.