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.)
Harmonic Oscillator Model for Radin's Markov-Chain Experiments
NASA Astrophysics Data System (ADS)
Sheehan, D. P.; Wright, J. H.
2006-10-01
The conscious observer stands as a central figure in the measurement problem of quantum mechanics. Recent experiments by Radin involving linear Markov chains driven by random number generators illuminate the role and temporal dynamics of observers interacting with quantum mechanically labile systems. In this paper a Lagrangian interpretation of these experiments indicates that the evolution of Markov chain probabilities can be modeled as damped harmonic oscillators. The results are best interpreted in terms of symmetric equicausal determinism rather than strict retrocausation, as posited by Radin. Based on the present analysis, suggestions are made for more advanced experiments.
Harmonic Oscillator Model for Radin's Markov-Chain Experiments
Sheehan, D. P.; Wright, J. H.
2006-10-16
The conscious observer stands as a central figure in the measurement problem of quantum mechanics. Recent experiments by Radin involving linear Markov chains driven by random number generators illuminate the role and temporal dynamics of observers interacting with quantum mechanically labile systems. In this paper a Lagrangian interpretation of these experiments indicates that the evolution of Markov chain probabilities can be modeled as damped harmonic oscillators. The results are best interpreted in terms of symmetric equicausal determinism rather than strict retrocausation, as posited by Radin. Based on the present analysis, suggestions are made for more advanced experiments.
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…
Time-dependent Hartree approximation and time-dependent harmonic oscillator model
NASA Astrophysics Data System (ADS)
Blaizot, J. P.; Schulz, H.
1982-03-01
We present an analytically soluble model for studying nuclear collective motion within the framework of the time-dependent Hartree (TDH) approximation. The model reduces the TDH equations to the Schrödinger equation of a time-dependent harmonic oscillator. Using canonical transformations and coherent states we derive a few properties of the time-dependent harmonic oscillator which are relevant for applications. We analyse the role of the normal modes in the time evolution of a system governed by TDH equations. We show how these modes couple together due to the anharmonic terms generated by the non-linearity of the theory.
NASA Astrophysics Data System (ADS)
Deymier, P. A.; Runge, K.; Vasseur, J. O.
2016-12-01
We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.
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.
Damped harmonic oscillator model for analyzing the dynamic characteristics of STM system
NASA Astrophysics Data System (ADS)
Liu, A. P.; Yao, X. X.; Wang, X.; Yang, D. X.; Zhang, X. M.
2015-09-01
Recognizing and distinguishing the dynamic characteristics of scanning tunneling microscopy (STM) system is fatal for studying STM image. In this paper, a method for analyzing system’s characteristics by using a damped harmonic oscillator model is presented. The model is driven by random force and all of its properties are described by damping and periodic. For the general solution of such harmonic oscillator’s Langevin equation is deduced and the auto-correlation function (ACF) is obtained for fitting curve. It is shown that damping and periodic property of the two curves have a good agreement by comparing the fitting curve with the auto-correlation curve of time series dates which are acquired by STM. It could be concluded that the damped harmonic oscillator model and auto-correlation method are feasible for analyzing the dynamic characteristics of STM system.
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.
Synchronous Discrete Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Antippa, Adel F.; Dubois, Daniel M.
2008-10-01
We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2π in phase space, is an integral multiple N of the discrete time step Δt. It is fully synchronous when N is even. It is pseudo-synchronous when T/Δt is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is "blue shifted" relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval Δt. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.
NASA Astrophysics Data System (ADS)
Hamerly, Ryan; Marandi, Alireza; Jankowski, Marc; Fejer, M. M.; Yamamoto, Yoshihisa; Mabuchi, Hideo
2016-12-01
We develop reduced models that describe half-harmonic generation in a synchronously pumped optical parametric oscillator above threshold, where nonlinearity, dispersion, and group-velocity mismatch are all relevant. These models are based on (1) an eigenmode expansion for low pump powers, (2) a simultonlike sech-pulse ansatz for intermediate powers, and (3) dispersionless box-shaped pulses for high powers. Analytic formulas for pulse compression, degenerate vs nondegenerate operation, and stability are derived and compared to numerical and experimental results.
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.
Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator
NASA Astrophysics Data System (ADS)
Mahdifar, A.; Roknizadeh, R.; Naderi, M. H.
2006-06-01
In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using the nonlinear coherent states approach. For this purpose, we study two-dimensional harmonic oscillators on the flat surface and on a sphere by applying the Higgs model. With the use of their algebras, we show that the two-dimensional oscillator algebra on a surface can be considered as a deformed one-dimensional oscillator algebra where the effect of the curvature of the surface appears as a deformation function. We also show that the curvature of the physical space plays the role of deformation parameter. Then we construct the associated coherent states on the flat surface and on a sphere and compare their quantum statistical properties, including quadrature squeezing and antibunching effect.
Markovian evolution of strongly coupled harmonic oscillators
NASA Astrophysics Data System (ADS)
Joshi, Chaitanya; Öhberg, Patrik; Cresser, James D.; Andersson, Erika
2014-12-01
We investigate how to model Markovian evolution of coupled harmonic oscillators, each of them interacting with a local environment. When the coupling between the oscillators is weak, dissipation may be modeled using local Lindblad terms for each of the oscillators in the master equation, as is commonly done. When the coupling between oscillators is strong, this model may become invalid. We derive a master equation for two coupled harmonic oscillators that are subject to individual heat baths modeled by a collection of harmonic oscillators and show that this master equation in general contains nonlocal Lindblad terms. We compare the resulting time evolution with that obtained for dissipation through local Lindblad terms for each individual oscillator and show that the evolution is different in the two cases. In particular, the two descriptions give different predictions for the steady state and for the entanglement between strongly coupled oscillators. This shows that when describing strongly coupled harmonic oscillators, one must take great care in how dissipation is modeled and that a description using local Lindblad terms may fail. This may be particularly relevant when attempting to generate entangled states of strongly coupled quantum systems.
A time-discrete harmonic oscillator model of human car-following
NASA Astrophysics Data System (ADS)
Wagner, P.
2011-12-01
A time-discrete stochastic harmonic oscillator is presented as a model of human car-following behaviour. This describes especially the non-continuous control of a human driver - acceleration changes from time to time at so called action-points and is kept constant in between. Analytical results can be derived which allow to classify the different types of motion possible within this approach. These results show that with weaker control by the human, unstable behaviour of the oscillator becomes more likely. This is in line with common understanding about the causes of accidents. Finally, since even the stochastic behaviour of this model is in parts analytically tractable, the width of the speed-difference and distance fluctuations can be expressed as function of the model's parameter. This allows a fresh view on empirical car-following data and the identification of parameters from real data in the context of the theory presented here.
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).
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.
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.
Covariant harmonic oscillators: 1973 revisited
NASA Technical Reports Server (NTRS)
Noz, M. E.
1993-01-01
Using the relativistic harmonic oscillator, a physical basis is given to the phenomenological wave function of Yukawa which is covariant and normalizable. It is shown that this wave function can be interpreted in terms of the unitary irreducible representations of the Poincare group. The transformation properties of these covariant wave functions are also demonstrated.
Application of Elliott's SU(3) model to the triaxially deformed harmonic oscillators
NASA Astrophysics Data System (ADS)
Sugawara-Tanabe, Kazuko
2011-05-01
We have introduced new bosons corresponding to the integral ratio of three frequencies for a harmonic oscillator potential, by means of a non-linear transformation which realizes the SU(3) group as a dynamical symmetry group, and which leaves the anisotropic harmonic oscillator Hamiltonian invariant. The classification of the single-particle levels based on this covering group predicts magic numbers depending on the deformation parameters δ and γ. The special cases with tan γ = 1/√3 (γ = 30°) and √3 /5(γ˜19°) are discussed.
Application of Elliott's SU(3) model to the triaxially deformed harmonic oscillators
Sugawara-Tanabe, Kazuko
2011-05-06
We have introduced new bosons corresponding to the integral ratio of three frequencies for a harmonic oscillator potential, by means of a non-linear transformation which realizes the SU(3) group as a dynamical symmetry group, and which leaves the anisotropic harmonic oscillator Hamiltonian invariant. The classification of the single-particle levels based on this covering group predicts magic numbers depending on the deformation parameters {delta} and {gamma}. The special cases with tan {gamma} = 1/{radical}(3)({gamma} = 30 deg.) and {radical}(3)/5({gamma}{approx}19 deg.) are discussed.
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.
Thomas, Gareth E; Bass, Stephen F; Grainger, Roy G; Lambert, Alyn
2005-03-01
A new method for the retrieval of the spectral refractive indices of micrometer-sized particles from infrared aerosol extinction spectra has been developed. With this method we use a classical damped harmonic-oscillator model of molecular absorption in conjunction with Mie scattering to model extinction spectra, which we then fit to the measurements using a numerical optimal estimation algorithm. The main advantage of this method over the more traditional Kramers-Kronig approach is that it allows the full complex refractive-index spectra, along with the parameters of the particle size distribution, to be retrieved from a single extinction spectrum. The retrieval scheme has been extensively characterized and has been found to provide refractive indices with a maximum uncertainty of approximately 10% (with a minimum of approximately 0.1%). Comparison of refractive indices calculated from measurements of a ternary solution of HNO3, H2SO4, and H2O with those published in J. Phys. Chem. A 104, 783 (2000) show similar differences as found by other authors.
Isar, A.; Sandulescu, A. ); Scheid, W. )
1990-05-01
In the frame of the Lindblad theory of open quantum systems, the spherical harmonic oscillator with opening operators linear in the coordinates and the momenta of the considered system is analyzed. Explicit expressions for the damping of the energy, angular momentum and its projection, including the coupling of the harmonic oscillator due to the environment, are obtained.
Relation of squeezed states between damped harmonic and simple harmonic oscillators
NASA Technical Reports Server (NTRS)
Um, Chung-In; Yeon, Kyu-Hwang; George, Thomas F.; Pandey, Lakshmi N.
1993-01-01
The minimum uncertainty and other relations are evaluated in the framework of the coherent states of the damped harmonic oscillator. It is shown that the coherent states of the damped harmonic oscillator are the squeezed coherent states of the simple harmonic oscillator. The unitary operator is also constructed, and this connects coherent states with damped harmonic and simple harmonic oscillators.
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.
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…
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.
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.
Finite quantum kinematics of the harmonic oscillator
Shiri-Garakani, Mohsen; Finkelstein, David Ritz
2006-03-15
Arbitrarily small changes in the commutation relations suffice to transform the usual singular quantum theories into regular quantum theories. This process is an extension of canonical quantization that we call general quantization. Here we apply general quantization to the time-independent linear harmonic oscillator. The unstable Heisenberg group becomes the stable group SO(3). This freezes out the zero-point energy of very soft or very hard oscillators, like those responsible for the infrared or ultraviolet divergencies of usual field theories, without much changing the medium oscillators. It produces pronounced violations of equipartition and of the usual uncertainty relations for soft or hard oscillators, and interactions between the previously uncoupled excitation quanta of the oscillator, weakly attractive for medium quanta, strongly repulsive for soft or hard quanta.
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
Quantum kicked harmonic oscillator in contact with a heat bath
NASA Astrophysics Data System (ADS)
Prado Reynoso, M. Á.; López Vázquez, P. C.; Gorin, T.
2017-02-01
We consider the quantum harmonic oscillator in contact with a finite-temperature bath, modeled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system in different dynamical regimes between classical integrability and chaos, on the one hand, and ballistic or diffusive energy absorption, on the other. We then investigate the influence of the heat bath on the oscillator in each case. Phase-space techniques allow us to simulate the evolution of the system efficiently. In this way, we calculate high-resolution Wigner functions at long times, where the system approaches a quasistationary cyclic evolution. Thereby, we perform an accurate study of the thermodynamic properties of a nonintegrable, quantum chaotic system in contact with a heat bath at finite temperature. In particular, we find that the heat transfer between harmonic oscillator and heat bath is governed by Fourier's law.
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).
NASA Astrophysics Data System (ADS)
Mandal, Swapan
2017-03-01
The classical harmonic oscillator with time dependent mass and frequency is investigated to obtain a closed form exact analytical solution. It is found that the closed form analytical solutions are indeed possible if the time dependent mass of the oscillator is inversely proportional to the time dependent frequency. The scaled wronskian obtained from the linearly independent solutions of the equation of motion of the classical oscillator is used to obtain the solution corresponding to its quantum mechanical counterpart. The analytical solution of the present oscillator is used to obtain the squeezing effects of the input coherent light. In addition to the possibilities of getting the squeezed states, the present solution will be of use for investigating various quantum statistical properties of the radiation fields. As an example, we investigate the antibunching of the input thermal (chaotic) light coupled to the oscillator. Therefore, the appearance of the photon antibunching does not warrant the squeezing and vice-versa. The exact solution is obtained at the cost of the stringent condition where the product of time dependent mass and frequency of the oscillator is time invariant.
Brownian motion with adhesion: harmonic oscillator with fluctuating mass.
Gitterman, M; Klyatskin, V I
2010-05-01
In contrast to the cases usually studied of a harmonic oscillator subject to a random force (Brownian motion) or having random frequency or random damping, we consider a random mass which corresponds to an oscillator for which the particles of the surrounding medium adhere to it for some (random) time after the collision, thereby changing the oscillator mass. This model, which describes Brownian motion with adhesion, can be useful for the analysis of chemical and biological solutions as well as nanotechnological devices. We consider dichotomous noise and its limiting case, white noise.
Harmonic oscillator interaction with squeezed radiation
NASA Technical Reports Server (NTRS)
Dodonov, V. V.; Nikonov, D. E.
1993-01-01
Although the problem of electromagnetic radiation by a quantum harmonic oscillator is considered in textbooks on quantum mechanics, some of its aspects have remained unclear until now. By this, we mean that usually the initial quantum states of both the oscillator and the field are assumed to be characterized by a definite energy level of the oscillator and definite occupation numbers of the field modes. In connection with growing interest in squeezed states, it would be interesting to analyze the general case when the initial states of both subsystems are arbitrary superpositions of energy eigenstates. This problem was considered in other work, where the power of the spontaneous emission was calculated in the case of an arbitrary oscillator's initial state, but the field was initially in a vacuum state. In the present article, we calculate the rate of the oscillator average energy, squeezing, and correlation parameter change under the influence of an arbitrary external radiation field. Some other problems relating to the interaction between quantum particles (atoms) or oscillators where the electromagnetic radiation is an arbitrary (in particular squeezed) state were investigated.
Finite quantum theory of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Shiri-Garakani, Mohsen
We apply the Segal process of group simplification to the linear harmonic oscillator. The result is a finite quantum theory with three quantum constants h, h', h″ instead of the usual one. We compare the classical (CLHO), quantum (QLHO), and finite (FLHO) linear harmonic oscillators and their canonical or unitary groups. The FLHO is isomorphic to a dipole rotator with N = l(l + 1) ˜ 1/(h ' h″) states and Hamiltonian H = A(Lx)2 + B(Ly)2, and the physically interesting case has N ≫ 1. The position and momentum variables are quantized with uniform finite spectra. For fixed quantum constants and large N ≫ 1 there are three broad classes of FLHO: soft, medium, and hard, with B/A ≪ 1, B/A ˜ 1, and B/A ≫ 1 respectively. The field oscillators responsible for infra-red and ultraviolet divergences are soft and hard respectively. Medium oscillators have B/A ˜ 1 and approximate the QLHO. They have ˜ N low-lying states with nearly the same zero-point energy and level spacing as the QLHO, and nearly obeying the Heisenberg uncertainty principle and the equipartition principle. The corresponding rotators are nearly polarized along the z axis with Lz ˜ +/-l. The soft and hard FLHO's have infinitesimal 0-point energy and grossly violate equipartition and the Heisenberg uncertainty principle. They do not resemble the QLHO at all. Their low-lying energy states correspond to rotators with Lx ˜ 0 or Ly ˜ 0 instead of Lz ˜ +/-l. Soft oscillators have frozen momentum, because their maximum potential energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to excite one quantum of position.
Equity prices as a simple harmonic oscillator with noise
NASA Astrophysics Data System (ADS)
Ataullah, Ali; Tippett, Mark
2007-08-01
The centred return on the London Stock Exchange's FTSE All Share Index is modelled as a simple harmonic oscillator with noise over the period from 1 January, 1994 until 30 June 2006. Our empirical results are compatible with the hypothesis that there is a period in the FTSE All Share Index of between two and two and one half years. This means the centred return will on average continue to increase for about a year after reaching the minimum in its oscillatory cycle; alternatively, it will continue on average to decline for about a year after reaching a maximum. Our analysis also shows that there is potential to exploit the harmonic nature of the returns process to earn abnormal profits. Extending our analysis to the low energy states of a quantum harmonic oscillator is also suggested.
Observations of Harmonic Oscillations and ELM Magnetic Precursors in NSTX
NASA Astrophysics Data System (ADS)
Kelly, F.; Fredrickson, E.; Bell, R.; Tritz, K.; Maingi, R.; Takahashi, H.
2010-11-01
Recent experiments in the National Spherical Torus Experiment (NSTX) demonstrated the progressive suppression of edge localized modes (ELMs) with increasing lithium deposition. Sufficient lithium suppressed ELMs and made the occurrence of low-frequency, low-n harmonics more frequent. Signatures of these harmonic oscillations with a significant edge component were observed in both the high-n Mirnov magnetic and soft X-ray diagnostics of NSTX. Two distinct sets of harmonic oscillations can be observed during some ELM-free periods. The harmonic oscillations are consistent with modes localized in the edge with the frequency of the n = 1 harmonic near the rotation frequency of the edge plasma. NSTX magnetic diagnostics also observe distinctive signatures of ELMs. Transient n = 1 and n = 2 mode bursts and occasional higher n modes with frequency in the 30 to 90 kHz range occurred simultaneous with the increase in fast Da signal. These bursts of n = 1 and n = 2 modes resemble a model simulation of ELMs by T. Evans in which a bifurcation of magnetic topology is driven by nonlinear feedback amplification of thermoelectric currents from linear peeling-ballooning modes.
Random reverse-cyclic matrices and screened harmonic oscillator
NASA Astrophysics Data System (ADS)
Srivastava, Shashi C. L.; Jain, Sudhir R.
2012-04-01
We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an N-body exactly solvable model. We refer to this well-known model potential as a screened harmonic oscillator. The connection enables us to obtain all the correlations among the particle positions moving in a screened harmonic potential. The density of nontrivial eigenvalues of this ensemble is found to be of the Wigner form and admits a hole at the origin, in contrast to the semicircle law of the Gaussian orthogonal ensemble of random matrices. The spacing distributions assume different forms ranging from Gaussian-like to Wigner.
Chou, Chung-Hsien; Yu, Ting; Hu, B L
2008-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to N, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations, and dissipation of mesoscopic objects toward the construction of a theoretical framework for macroscopic quantum phenomena.
Classical and revival time periods of confined harmonic oscillator
NASA Astrophysics Data System (ADS)
Ghosh, P.; Ghosh, S.; Bera, N.
2015-02-01
We have used perturbation theory to compute energy eigenvalues, classical and the revival time periods for a one-dimensional harmonic oscillator confined in a box. First we have considered a simple harmonic oscillator as the unperturbed problem and boundary as perturbation. In next case, free particle in a box is considered as unperturbed problem that has been perturbed by a parabolic potential. We have used Fourier Grid Hamiltonian method to estimate classical and revival time period for the confined harmonic oscillator, which crosses smoothly from free particle in a box to a simple harmonic oscillator.
Lin, J. Y. Y.; Aczel, Adam A; Abernathy, Douglas L; Nagler, Stephen E; Buyers, W. J. L.; Granroth, Garrett E
2014-01-01
Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of- flight chopper spectrometers [A.A. Aczel et al, Nature Communications 3, 1124 (2012)]. These modes are well described by 3D isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for the nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states (PDOS), and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T-dependence of the scattering from these modes is strongly influenced by the uranium lattice.
NASA Astrophysics Data System (ADS)
Lin, J. Y. Y.; Aczel, A. A.; Abernathy, D. L.; Nagler, S. E.; Buyers, W. J. L.; Granroth, G. E.
2014-04-01
Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of-flight chopper spectrometers [A. A. Aczel et al., Nat. Commun. 3, 1124 (2012), 10.1038/ncomms2117]. These modes are well described by three-dimensional isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states, and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature-dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T dependence of the scattering from these modes is strongly influenced by the uranium lattice.
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
Binder, S.; Ekström, Jan A.; Hagen, Gaute; ...
2016-04-25
In this paper, we develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leadingmore » order. Finally, many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.« less
Effective field theory in the harmonic oscillator basis
Binder, S.; Ekström, Jan A.; Hagen, Gaute; Papenbrock, Thomas F.; Wendt, Kyle A.
2016-04-25
In this paper, we develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Finally, many-body coupled-cluster calculations of nuclei up to ^{132}Sn converge fast for the ground-state energies and radii in feasible model spaces.
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.
A possible generalization of the harmonic oscillator potential
NASA Technical Reports Server (NTRS)
Levai, Geza
1995-01-01
A four-parameter potential is analyzed, which contains the three-dimensional harmonic oscillator as a special case. This potential is exactly solvable and retains several characteristics of the harmonic oscillator, and also of the Coulomb problem. The possibility of similar generalizations of other potentials is also pointed out.
Coherent states for the relativistic harmonic oscillator
NASA Technical Reports Server (NTRS)
Aldaya, Victor; Guerrero, J.
1995-01-01
Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.
A Look at Damped Harmonic Oscillators through the Phase Plane
ERIC Educational Resources Information Center
Daneshbod, Yousef; Latulippe, Joe
2011-01-01
Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the…
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.
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.
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
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…
On quantum harmonic oscillator being subjected to absolute potential state
NASA Astrophysics Data System (ADS)
Nityayogananda, Swami
2017-01-01
In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. In this paper, assuming a boundary condition that the product of momentum and position, or the product of energy density and position remains constant in the QHO, it is established that a particle subjected to increasing frequencies becomes gradually subtler to transform into a very high dormant potential energy. This very high dormant potential energy is referred to as `like-potential' energy in this paper. In the process a new wave function is generated. This new function, which corresponds to new sets of particles, has scope to raise the quantum oscillator energy (QOE) up to infinity. It is proposed to show that this high energy does not get cancelled but remains dormant. Further, it is proposed that the displacement about the equilibrium goes to zero when the vibration of the oscillator stops and then the QOE becomes infinity - this needs further research. The more the QOE, the greater will be the degree of dormancy. A simple mathematical model has been derived here to discuss the possibilities that are involved in the QHO under the above-mentioned boundary conditions.
Observations of ELM Magnetic Precursors and Harmonic Oscillations in NSTX
NASA Astrophysics Data System (ADS)
Kelly, F.; Frederickson, E.; Bell, R.; Tritz, K.; Takahashi, H.; Maingi, R.; NSTX Collaboration
2011-10-01
Recent experiments on NSTX have shown n=1 dominant and n=2 mode ELM magnetic precursors with mode frequency in the 30 to 90 kHz range. The growing magnetic oscillations measured with the NSTX high-n Mirnov diagnostic occurred simultaneous with the onset of the increase in fast D α signal. These bursts of dominantly n=1, some n=2 and fewer higher modes resemble the predictions of a model simulation of ELMs by T. Evans in which a feedback amplification mechanism causes explosive growth of the separatrix topology driven by thermoelectric currents in flux tubes connecting the divertor plates. The n=1 mode remained dominant as wall recycling was reduced with lithium conditioning and n=3 RMP was applied, suggesting the trigger mechanism remained the same. Sufficient lithium suppressed ELMs and made the occurrence of low-frequency, low-n Harmonics Oscillations (HOs) more frequent. The HOs are consistent with modes localized in the edge with the frequency of the n = 1 harmonic near the rotation frequency of the edge plasma. Work supported in part by US DOE contract no. DE-AC02-09CH11466.
Chiral potential renormalized in harmonic-oscillator space
NASA Astrophysics Data System (ADS)
Yang, C.-J.
2016-12-01
We renormalize the chiral effective field theory potential in harmonic-oscillator (HO) model space. The low energy constants (LECs) are utilized to absorb not just the ultraviolet part of the physics due to the cutoff, but also the infrared part due to the truncation of model space. We use the inverse J -matrix method to reproduce the nucleon-nucleon scattering phase shifts in the given model space. We demonstrate that by including the NLO correction, the nucleon-nucleon scattering in the continuum could be well reproduced in the truncated HO trap space up to laboratory energy Tlab=100 MeV with number of HO basis nmax as small as 10. A perturbative power counting starts at subleading order is adopted in this work, and how to extract the perturbative contribution is demonstrated. This work serves as the input to perform ab initio calculations.
Nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator
Enjieu Kadji, H. G.; Nana Nbendjo, B. R.; Chabi Orou, J. B.; Talla, P. K.
2008-03-15
This paper considers nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator. These plasma oscillations are described by a nonlinear differential equation of the form xe+{epsilon}(1+x{sup 2})x+x+{kappa}x{sup 2}+{delta}x{sup 3}=F cos {omega}t. The amplitudes of the forced harmonic, superharmonic, and subharmonic oscillatory states are obtained using the harmonic balance technique and the multiple time scales method. Admissible values of the amplitude of the external strength are derived. Bifurcation sequences displayed by the model for each type of oscillatory states are performed numerically through the fourth-order Runge-Kutta scheme.
Hamiltonian of mean force and a damped harmonic oscillator in an anisotropic medium
NASA Astrophysics Data System (ADS)
Jafari, Marjan; Kheirandish, Fardin
2017-01-01
The quantum dynamics of a damped harmonic oscillator is investigated in the presence of an anisotropic heat bath. The medium is modeled by a continuum of three dimensional harmonic oscillators and anisotropic coupling is treated by introducing tensor coupling functions. Starting from a classical Lagrangian, the total system is quantized in the framework of the canonical quantization. Following the Fano technique, the Hamiltonian of the system is diagonalized in terms of creation and annihilation operators that are linear combinations of the basic dynamical variables. Using the diagonalized Hamiltonian, the mean force internal energy, free energy and entropy of the damped oscillator are calculated.
Violation of smooth observable macroscopic realism in a harmonic oscillator.
Leshem, Amir; Gat, Omri
2009-08-14
We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. We demonstrate a breakdown of dynamical realism in a wide parameter range that is maximized in a scaling limit of extreme squeezing, where it is based on measurements of smooth observables, implying that macroscopic realism is not valid in the harmonic oscillator. We propose an indirect experimental test of these predictions with entangled photons by demonstrating that local realism in a composite system implies dynamical realism in a subsystem.
The Acoustic Simple Harmonic Oscillator: Experimental Verification and Applications
NASA Astrophysics Data System (ADS)
Matteson, Sam
2009-04-01
In his famous volume, The Sensations of Tone, published in 1877, Hermann Helmholtz introduced a resonator that was central to his investigations of acoustics. This talk revisits the device that Helmholtz described and examines it as a manifestation of an acoustic simple harmonic oscillator (SHO). The presentation demonstrates that an enclosed volume which communicates with the outside world via a narrow tube exhibits a single strong frequency response in analogy to a mechanical SHO, along with weaker resonances of the air in the short pipe that comprises the ``neck.'' The investigations, furthermore, report results of a straightforward experiment that confirms the SHO model (with damping) and that is very accessible to undergraduate students using inexpensive equipment and internet-obtainable freeware. The current work also extends the analysis to include applications of the Helmholtz Resonator to several folk instruments, namely, the ocarina, whistling, and the ``bottle band.''
Ecological optimization of an irreversible harmonic oscillators Carnot heat engine
NASA Astrophysics Data System (ADS)
Liu, Xiaowei; Chen, Lingen; Wu, Feng; Sun, Fengrui
2009-12-01
A model of an irreversible quantum Carnot heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting harmonic oscillators is established in this paper. Based on the quantum master equation and semi-group approach, equations of some important performance parameters, such as power output, efficiency, exergy loss rate and ecological function for the irreversible quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. Effects of internal irreversibility and heat leakage on the ecological performance are discussed. A performance comparison of the quantum heat engine under maximum ecological function and maximum power conditions is also performed.
Caligiuri, Luigi Maxmilian
2015-01-01
The question regarding the potential biological and adverse health effects of non-ionizing electromagnetic fields on living organisms is of primary importance in biophysics and medicine. Despite the several experimental evidences showing such occurrence in a wide frequency range from extremely low frequency to microwaves, a definitive theoretical model able to explain a possible mechanism of interaction between electromagnetic fields and living matter, especially in the case of weak and very weak intensities, is still missing. In this paper it has been suggested a possible mechanism of interaction involving the resonant absorption of electromagnetic radiation by microtubules. To this aim these have been modeled as non-dissipative forced harmonic oscillators characterized by two coupled "macroscopic" degrees of freedom, respectively describing longitudinal and transversal vibrations induced by the electromagnetic field. We have shown that the proposed model, although at a preliminary stage, is able to explain the ability of even weak electromagnetic radiating electromagnetic fields to transfer high quantities of energy to living systems by means of a resonant mechanism, so capable to easily damage microtubules structure.
Entanglement prethermalization in an interaction quench between two harmonic oscillators
NASA Astrophysics Data System (ADS)
Ikeda, Tatsuhiko N.; Mori, Takashi; Kaminishi, Eriko; Ueda, Masahito
2017-02-01
Entanglement prethermalization (EP) refers to a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble exactly describes the total system if we take into account nonlocal conserved quantities that act nontrivially on both subsystems. In the presence of a symmetry-breaking perturbation, the relaxation dynamics of the system exhibits a quasi-stationary EP plateau and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.
Entanglement prethermalization in an interaction quench between two harmonic oscillators.
Ikeda, Tatsuhiko N; Mori, Takashi; Kaminishi, Eriko; Ueda, Masahito
2017-02-01
Entanglement prethermalization (EP) refers to a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble exactly describes the total system if we take into account nonlocal conserved quantities that act nontrivially on both subsystems. In the presence of a symmetry-breaking perturbation, the relaxation dynamics of the system exhibits a quasi-stationary EP plateau and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.
Symmetry algebra of a generalized anisotropic harmonic oscillator
NASA Technical Reports Server (NTRS)
Castanos, O.; Lopez-Pena, R.
1993-01-01
It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.
The One-Dimensional Damped Forced Harmonic Oscillator Revisited
ERIC Educational Resources Information Center
Flores-Hidalgo, G.; Barone, F. A.
2011-01-01
In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.
Nonsingular parametric oscillators Darboux-related to the classical harmonic oscillator
NASA Astrophysics Data System (ADS)
Rosu, H. C.; Cornejo-Pérez, O.; Chen, P.
2012-12-01
Interesting nonsingular parametric oscillators which are Darboux-related to the classical harmonic oscillator and have periodic dissipative/gain features are identified through a modified factorization method. The same method is applied to the upside-down (hyperbolic) “oscillator” for which the obtained Darboux partners show transient underdamped features.
Harmonic and anharmonic oscillations investigated by using a microcomputer-based Atwood's machine
NASA Astrophysics Data System (ADS)
Pecori, Barbara; Torzo, Giacomo; Sconza, Andrea
1999-03-01
We describe how the Atwood's machine, interfaced to a personal computer through a rotary encoder, is suited for investigating harmonic and anharmonic oscillations, exploiting the buoyancy force acting on a body immersed in water. We report experimental studies of oscillators produced by driving forces of the type F=-kxn with n=1,2,3, and F=-k sgn(x). Finally we suggest how this apparatus can be used for showing to the students a macroscopic model of interatomic forces.
Quantum harmonic oscillator: an elementary derivation of the energy spectrum
NASA Astrophysics Data System (ADS)
Borghi, Riccardo
2017-03-01
An elementary treatment of the quantum harmonic oscillator is proposed. No previous knowledge of linear differential equation theory or Fourier analysis are required, but rather only a few basics of elementary calculus. The pivotal role in our analysis is played by the sole particle localization constraint, which implies square integrability of stationary-state wavefunctions. The oscillator ground-state characterization is then achieved in a way that could be grasped, in principle, even by first-year undergraduates. A very elementary approach to build up and to characterize all higher-level energy eigenstates completes our analysis.
Pisot q-coherent states quantization of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Gazeau, J. P.; del Olmo, M. A.
2013-03-01
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories.
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.
Equilibrium and stationary nonequilibrium states in a chain of colliding harmonic oscillators
Sano
2000-02-01
Equilibrium and nonequilibrium properties of a chain of colliding harmonic oscillators (ding-dong model) are investigated. Our chain is modeled as harmonically bounded particles that can only interact with neighboring particles by hard-core interaction. Between the collisions, particles are just independent harmonic oscillators. We are especially interested in the stationary nonequilibrium state of the ding-dong model coupled with two stochastic heat reservoirs (not thermostated) at the ends, whose temperature is different. We check the Gallavotti-Cohen fluctuation theorem [G. Gallavoti and E. G. D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)] and also the Evans-Searles identity [D. Evans and D. Searles, Phys. Rev. E. 50, 1994 (1994)] numerically. It is verified that the former theorem is satisfied for this system, although the system is not a thermostated system.
An analogue of the Berry phase for simple harmonic oscillators
NASA Astrophysics Data System (ADS)
Suslov, S. K.
2013-03-01
We evaluate a variant of Berry's phase for a ‘missing’ family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables (in a natural way). Instead, it is obtained by the action of the maximal kinematical invariance group on the standard solutions. A simple closed formula for the phase (in terms of elementary functions) is found here by integration with the help of a computer algebra system.
Coherent and squeezed states for the 3D harmonic oscillator
NASA Astrophysics Data System (ADS)
Mazouz, Amel; Bentaiba, Mustapha; Mahieddine, Ali
2017-01-01
A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.
High gain amplifiers: Power oscillations and harmonic generation
Dattoli, G.; Ottaviani, P. L.; Pagnutti, S.
2007-08-01
We discuss the power oscillations in saturated high gain free electron laser amplifiers and show that the relevant period can be written in terms of the gain length. We use simple arguments following from the solution of the pendulum equation in terms of Jacobi elliptic functions. Nontrivial effects due to nonlinear harmonic generation and inhomogeneous broadening are discussed too, as well as the saturated dynamics of short pulses.
Collision-induced squeezing in a harmonic oscillator
NASA Technical Reports Server (NTRS)
Lee, Hai-Woong
1993-01-01
The concept of squeezing has so far been applied mainly to light, as is evidenced by the number of research works on the subject of squeezed light. Since, in quantum mechanics, both light and the simple harmonic oscillator are described within the same mathematical framework, there is of course no difficulty in applying the concept to the simple harmonic oscillator as well. In fact, the theoretical development of squeezed states and squeezed light owes much to the physical insights that one obtains as the analogy between light and the harmonic oscillator is exploited. The example presented shows clearly that two states with different phases in general have different degrees of squeezing, even if they have the same state distribution. This means that, even if one considers collision processes that produce the same state distribution, the degree of squeezing obtained during and after the collisions can be quite different, depending on how the phases phi(sub n) of the probability amplitudes develop in time as the collisions proceed. It is therefore evident that, for a detailed study of collision-induced squeezing, further study on the time development of the phases in collisions and its relation to collision parameters such as potential energy surfaces and collision energy is needed.
Teaching from a Microgravity Environment: Harmonic Oscillator and Pendulum
NASA Astrophysics Data System (ADS)
Benge, Raymond; Young, Charlotte; Davis, Shirley; Worley, Alan; Smith, Linda; Gell, Amber
2009-04-01
This presentation reports on an educational experiment flown in January 2009 as part of NASA's Microgravity University program. The experiment flown was an investigation into the properties of harmonic oscillators in reduced gravity. Harmonic oscillators are studied in every introductory physics class. The equation for the period of a harmonic oscillator does not include the acceleration due to gravity, so the period should be independent of gravity. However, the equation for the period of a pendulum does include the acceleration due to gravity, so the period of a pendulum should appear longer under reduced gravity (such as lunar or Martian gravity) and shorter under hyper-gravity. These environments can be simulated aboard an aircraft. Video of the experiments being performed aboard the aircraft is to be used in introductory physics classes. Students will be able to record information from watching the experiment performed aboard the aircraft in a similar manner to how they collect data in the laboratory. They can then determine if the experiment matches theory. Video and an experimental procedure are being prepared based upon this flight, and these materials will be available for download by faculty anywhere with access to the internet who wish to use the experiment in their own classrooms.
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.
Pure Gaussian states from quantum harmonic oscillator chains with a single local dissipative process
NASA Astrophysics Data System (ADS)
Ma, Shan; Woolley, Matthew J.; Petersen, Ian R.; Yamamoto, Naoki
2017-03-01
We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of (2\\aleph +1) quantum harmonic oscillators where the central oscillator of the chain is coupled to a single reservoir. We then completely parametrize the class of (2\\aleph +1) -mode pure Gaussian states that can be prepared by this type of quantum harmonic oscillator chain. This parametrization allows us to determine the steady-state entanglement properties of such quantum harmonic oscillator chains.
Avoiding dissipation in a system of three quantum harmonic oscillators
NASA Astrophysics Data System (ADS)
Manzano, Gonzalo; Galve, Fernando; Zambrini, Roberta
2013-03-01
We analyze the symmetries in an open quantum system composed by three coupled and detuned harmonic oscillators in the presence of a common heat bath. It is shown analytically how to engineer the couplings and frequencies of the system so as to have several degrees of freedom unaffected by decoherence, irrespective of the specific spectral density or initial state of the bath. This partial thermalization allows observing asymptotic entanglement at moderate temperatures, even in the nonresonant case. This latter feature cannot be seen in the simpler situation of only two oscillators, highlighting the richer structural variety of the three-body case. When departing from the strict conditions for partial thermalization, a hierarchical structure of dissipation rates for the normal modes is observed, leading to a long transient where quantum correlations such as the quantum discord are largely preserved, as well as to synchronous dynamics of the oscillators quadratures.
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...
Morales, J.; Ovando, G.; Pena, J. J.
2010-12-23
One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.
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.
Harmonic Oscillations in Homeostatic Controllers: Dynamics of the p53 Regulatory System
Jolma, Ingunn W.; Ni, Xiao Yu; Rensing, Ludger; Ruoff, Peter
2010-01-01
Abstract Homeostatic mechanisms are essential for the protection and adaptation of organisms in a changing and challenging environment. Previously, we have described molecular mechanisms that lead to robust homeostasis/adaptation under inflow or outflow perturbations. Here we report that harmonic oscillations occur in models of such homeostatic controllers and that a close relationship exists between the control of the p53/Mdm2 system and that of a homeostatic inflow controller. This homeostatic control model of the p53 system provides an explanation why large fluctuations in the amplitude of p53/Mdm2 oscillations may arise as part of the homeostatic regulation of p53 by Mdm2 under DNA-damaging conditions. In the presence of DNA damage p53 is upregulated, but is subject to a tight control by Mdm2 and other factors to avoid a premature apoptotic response of the cell at low DNA damage levels. One of the regulatory steps is the Mdm2-mediated degradation of p53 by the proteasome. Oscillations in the p53/Mdm2 system are considered to be part of a mechanism by which a cell decides between cell cycle arrest/DNA repair and apoptosis. In the homeostatic inflow control model, harmonic oscillations in p53/Mdm2 levels arise when the binding strength of p53 to degradation complexes increases. Due to the harmonic character of the oscillations rapid fluctuating noise can lead, as experimentally observed, to large variations in the amplitude of the oscillation but not in their period, a behavior which has been difficult to simulate by deterministic limit-cycle models. In conclusion, the oscillatory response of homeostatic controllers may provide new insights into the origin and role of oscillations observed in homeostatically controlled molecular networks. PMID:20197027
Elementary derivation of the quantum propagator for the harmonic oscillator
NASA Astrophysics Data System (ADS)
Shao, Jiushu
2016-10-01
Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.
Analysis of transonic flow about harmonically oscillating airfoils and wings
NASA Technical Reports Server (NTRS)
Weatherill, W. H.; Ehlers, F. E.
1980-01-01
A finite difference method for analyzing the unsteady transonic flow about harmonically oscillating wings is discussed. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting partial differential equations for small disturbances. Initial solutions were obtained using relaxation procedures, but the solution range proved to be limited in terms of Mach number and reduced frequency. Recent two-dimensional results are presented which have been obtained with direct solution procedures in which the difference equations are solved 'all at once' and these provide reasonable correlation for practical values of Mach number and reduced frequency.
Generalized Energy Equipartition in Harmonic Oscillators Driven by Active Baths
NASA Astrophysics Data System (ADS)
Maggi, Claudio; Paoluzzi, Matteo; Pellicciotta, Nicola; Lepore, Alessia; Angelani, Luca; Di Leonardo, Roberto
2014-12-01
We study experimentally and numerically the dynamics of colloidal beads confined by a harmonic potential in a bath of swimming E. coli bacteria. The resulting dynamics is well approximated by a Langevin equation for an overdamped oscillator driven by the combination of a white thermal noise and an exponentially correlated active noise. This scenario leads to a simple generalization of the equipartition theorem resulting in the coexistence of two different effective temperatures that govern dynamics along the flat and the curved directions in the potential landscape.
A method of solving simple harmonic oscillator Schroedinger equation
NASA Technical Reports Server (NTRS)
Maury, Juan Carlos F.
1995-01-01
A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.
Paal, Eugen; Virkepu, Jueri
2009-05-15
Operadic Lax representations for the harmonic oscillator are used to construct the dynamical deformations of three-dimensional (3D) real Lie algebras in the Bianchi classification. It is shown that the energy conservation of the harmonic oscillator is related to the Jacobi identities of the dynamically deformed algebras. Based on this observation, it is proved that the dynamical deformations of 3D real Lie algebras in the Bianchi classification over the harmonic oscillator are Lie algebras.
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
NASA Astrophysics Data System (ADS)
Chou, Chia-Chun
2016-10-01
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton-Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Heat and work fluctuations for a harmonic oscillator.
Sabhapandit, Sanjib
2012-02-01
The formalism of Kundu et al. [J. Stat. Mech. P03007 (2011)], for computing the large deviations of heat flow in harmonic systems, is applied to the case of single Brownian particle in a harmonic trap and coupled to two heat baths at different temperatures. The large-τ form of the moment generating function
1-GHz harmonically pumped femtosecond optical parametric oscillator frequency comb.
Balskus, K; Leitch, S M; Zhang, Z; McCracken, R A; Reid, D T
2015-01-26
We present the first example of a femtosecond optical parametric oscillator frequency comb harmonically-pumped by a 333-MHz Ti:sapphire laser to achieve a stabilized signal comb at 1-GHz mode spacing in the 1.1-1.6-µm wavelength band. Simultaneous locking of the comb carrier-envelope-offset and repetition frequencies is achieved with uncertainties over 1 s of 0.27 Hz and 5 mHz respectively, which are comparable with those of 0.27 Hz and 1.5 mHz achieved for 333-MHz fundamental pumping. The phase-noise power-spectral density of the CEO frequency integrated from 1 Hz-64 kHz was 2.8 rad for the harmonic comb, 1.0 rad greater than for fundamental pumping. The results show that harmonic operation does not substantially compromise the frequency-stability of the comb, which is shown to be limited only by the Rb atomic frequency reference used.
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
2016-01-01
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies. PMID:27886252
NASA Astrophysics Data System (ADS)
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
2016-11-01
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies.
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
2016-11-25
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies.
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.
Exact solution of a quantum forced time-dependent harmonic oscillator
NASA Technical Reports Server (NTRS)
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
1992-01-01
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
ERIC Educational Resources Information Center
Earl, Boyd L.
2008-01-01
A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…
Phase-space treatment of the driven quantum harmonic oscillator
NASA Astrophysics Data System (ADS)
Campos, Diógenes
2017-03-01
A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the standard position and momentum wave functions, together with expressions for the ηth derivatives with respect to q and p, respectively. Afterwards, general formulae for momentum, position and energy expectation values are obtained, and the Ehrenfest theorem is verified. Subsequently, general expressions for the cross-Wigner functions are deduced. Finally, a specific example is considered to numerically and graphically illustrate some results.
A Perturbation of the Dunkl Harmonic Oscillator on the Line
NASA Astrophysics Data System (ADS)
Álvarez López, Jesús A.; Calaza, Manuel
2015-07-01
Let J_σ be the Dunkl harmonic oscillator on R (σ>-1/2). For 00, it is proved that, if σ>u-1/2, then the operator U=J_σ+ξ|x|^{-2u}, with appropriate domain, is essentially self-adjoint in L^2({R},|x|^{2σ} dx), the Schwartz space S is a core of overline U^{1/2}, and overline U has a discrete spectrum, which is estimated in terms of the spectrum of overline{J_σ}. A generalization J_{σ,τ} of J_σ is also considered by taking different parameters σ and τ on even and odd functions. Then extensions of the above result are proved for J_{σ,τ}, where the perturbation has an additional term involving, either the factor x^{-1} on odd functions, or the factor x on even functions. Versions of these results on R_+ are derived.
Excitation with quantum light. I. Exciting a harmonic oscillator
NASA Astrophysics Data System (ADS)
Carreño, J. C. López; Laussy, F. P.
2016-12-01
We present a two-part study of the excitation of an optical target by quantum light. In this first part, we introduce the problematic and address the first case of interest, that of exciting the quantum harmonic oscillator, corresponding to, e.g., a single-mode passive cavity or a noninteracting bosonic field. We introduce a mapping of the Hilbert space that allows to chart usefully the accessible regions. We then consider the quantum excitation from single-photon sources in the form of a two-level system under various regimes of (classical) pumping: incoherent, coherent, and in the Mollow triplet regime. We close this first part with an overview of the material to be covered in the subsequent work.
Quantum Harmonic Oscillator Subjected to Quantum Vacuum Fluctuations
Gevorkyan, A. S.; Burdik, C.; Oganesyan, K. B.
2010-05-04
Spontaneous transitions between bound states of an atomic system, 'Lamb Shift' of energy level, as well as many other phenomena in real nonrelativistic quantum systems are connected with the influence of quantum vacuum fluctuations which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system 'quantum harmonic oscillator (QHO)+ environment' is described in terms of complex probabilistic processes (CPP) which satisfies a stochastic differential equation (SDE) of Langevin-Schroedinger (L-Sch) type. On the basis of orthogonal CPP, the method of stochastic density matrix (SDM) is developed. The energy spectrum of QHO and a possibility of infringement of detailed balance of transitions between quantum levels including spontaneous decay of <
Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Singh, Manu Pratap; Rajput, B. S.
2016-10-01
Realization of qudit quantum computation has been presented in terms of number operator and phase operators associated with one-dimensional harmonic oscillator and it has been demonstrated that the representations of generalized Pauli group, viewed in harmonic oscillator operators, allow the qudits to be explicitly encoded in such systems. The non-Hermitian quantum phase operators contained in decomposition of the annihilation and creation operators associated with harmonic oscillator have been analysed in terms of semi unitary transformations (SUT) and it has been shown that the non-vanishing analytic index for harmonic oscillator leads to an alternative class of quantum anomalies. Choosing unitary transformation and the Hermitian phase operator free from quantum anomalies, the truncated annihilation and creation operators have been obtained for harmonic oscillator and it has been demonstrated that any attempt of removal of quantum anomalies leads to absence of minimum uncertainty.
Double Fourier Harmonic Balance Method for Nonlinear Oscillators by Means of Bessel Series
2014-10-16
Double Fourier harmonic balance method for nonlinear oscillators by means of Bessel series T.C. Lipscombe∗1 and C.E. Mungan†2 1Catholic University of... harmonic balance method consists in expanding the displacement of an oscillator as a Fourier cosine series in time. A key modification is proposed here, in...than the exact value. Even better, the predicted frequency for the V-ramp case turns out to be exact. Keywords: Fourier expansion, harmonic balance
Feinberg-Horodecki states of a time-dependent mass distribution harmonic oscillator
NASA Astrophysics Data System (ADS)
Eshghi, M.; Sever, R.; Ikhdair, S. M.
2016-07-01
The solution of the Feinberg-Horodecki (FH) equation for a time-dependent mass (TDM) harmonic oscillator quantum system is studied. A certain interaction is applied to a mass m(t) to provide a particular spectrum of stationary energies. The related spectrum of the harmonic oscillator potential V(t) acting on the TDM m(t) oscillators is found. We apply the time version of the asymptotic iteration method (AIM) to calculate analytical expressions of the TDM stationary state energies and their wave functions. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the time-dependent mass reduces to m0.
Damping of a harmonic oscillator in a squeezed vacuum without rotating-wave approximation
NASA Astrophysics Data System (ADS)
Hassan, S. S.; Joshi, A.; Frege, O. M.; Emam, W.
2007-09-01
A single harmonic oscillator interacting with a broadband squeezed reservoir is analyzed within the framework of master equation without invoking the rotating-wave approximation. The dynamical evolution and photon statistics of the system are investigated by studying mean photon number and second order intensity-intensity correlation function, respectively, under resonance condition which show transient oscillations at twice the harmonic oscillator frequency. The transient fluorescent spectrum reveals asymmetric features. Inclusion of vacuum and field-dependent frequency shifts affects the thermal equilibrium value of the average photon number of the harmonic oscillator.
Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.
Li, Haifeng; Shao, Jiushu; Wang, Shikuan
2011-11-01
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.
NASA Astrophysics Data System (ADS)
Laguna, Humberto; Sagar, Robin
2013-03-01
The confined quantum harmonic oscillator (CHO) is an intermediate model which lies between the particle-in-a-box (PIAB), where the free particle is confined, and the quantum harmonic oscillator (HO) where the particle is not confined but is under the influence of a harmonic potential. Position and momentum space densities, and phase-space Wigner functions, are obtained for this system and analyzed using tools from information theory. Shannon entropies are used to gain insights into the localization of the particle in position, momentum and phase-space. The statistical correlation between the position and momentum of the particle is examined using the Wigner function and its mutual information. The analysis is performed as a function of the quantum number and of the box length, and the calculated quantities are compared to those of the PIAB and HO models. Our interests lie in determining similarities or differences among the different models and if there are regimes where the behavior of the CHO model more closely resembles either that of the PIAB or HO model. Departamento de Quimica
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…
On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on ℝ
NASA Astrophysics Data System (ADS)
Alvarez-Nodarse, R.; Atakishiyeva, M. K.; Atakishiyev, N. M.
2005-11-01
We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics based on a q-extension of the classical Hermite polynomials H n ( x) recently introduced by us in R. Alvarez-Nodarse et al.: Boletin de la Sociedad Matematica Mexicana (3) 8 (2002) 127. The wave functions in this q-model of the quantum harmonic oscillator possess the continuous orthogonality property on the whole real line ℝ with respect to a positive weight function. A detailed description of the corresponding q-system is carried out.
Edge Event-Triggered Synchronization in Networks of Coupled Harmonic Oscillators.
Wei, Bo; Xiao, Feng; Dai, Ming-Zhe
2016-08-30
The synchronization problems of networks of coupled harmonic oscillators are addressed by the edge event-triggered approach in this paper. The network dynamics with respect to edge states are presented and a new edge event-triggered control protocol is designed. Combined with the periodic event-detecting and edge event-triggered approach, sufficient conditions that guarantee the synchronization of coupled harmonic oscillators are presented. Two event-detecting rules are given to achieve the synchronization of coupled harmonic oscillators with low resource consumption. Finally, simulations are conducted to illustrate the effectiveness of the edge event-triggered control algorithm.
Data harmonization and model performance
NASA Astrophysics Data System (ADS)
The Joint Committee on Urban Storm Drainage of the International Association for Hydraulic Research (IAHR) and International Association on Water Pollution Research and Control (IAWPRC) was formed in 1982. The current committee members are (no more than two from a country): B. C. Yen, Chairman (USA); P. Harremoes, Vice Chairman (Denmark); R. K. Price, Secretary (UK); P. J. Colyer (UK), M. Desbordes (France), W. C. Huber (USA), K. Krauth (FRG), A. Sjoberg (Sweden), and T. Sueishi (Japan).The IAHR/IAWPRC Joint Committee is forming a Task Group on Data Harmonization and Model Performance. One objective is to promote international urban drainage data harmonization for easy data and information exchange. Another objective is to publicize available models and data internationally. Comments and suggestions concerning the formation and charge of the Task Group are welcome and should be sent to: B. C. Yen, Dept. of Civil Engineering, Univ. of Illinois, 208 N. Romine St., Urbana, IL 61801.
Calorimetric measurement of work for a driven harmonic oscillator
NASA Astrophysics Data System (ADS)
Sampaio, Rui; Suomela, Samu; Ala-Nissila, Tapio
2016-12-01
A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.
Calorimetric measurement of work for a driven harmonic oscillator.
Sampaio, Rui; Suomela, Samu; Ala-Nissila, Tapio
2016-12-01
A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.
Resonant behavior of a harmonic oscillator with fluctuating mass driven by a Mittag-Leffler noise
NASA Astrophysics Data System (ADS)
Zhong, Suchuan; Yang, Jianqiang; Zhang, Lu; Ma, Hong; Luo, Maokang
2017-02-01
The resonant behavior of a generalized Langevin equation (GLE) in the presence of a Mittag-Leffler noise is studied analytically in this paper. Considering that a GLE with a Mittag-Leffler friction kernel is very useful for modeling anomalous diffusion processes with long-memory and long-range dependence, and the surrounding molecules do not only collide with the Brownian particle but also adhere to the Brownian particle for random time. Thus, we consider the Brownian particle with fluctuating mass, and the fluctuations of the mass are modelled as a dichotomous noise. Applying the stochastic averaging method, we obtain the exact expression of the output amplitude gain of the system. By studying the impact of the driving frequency and the noise parameters, we find the non-monotonic behaviors of the output amplitude gain. The results indicate that the bona fide SR, the wide sense SR and the conventional SR phenomena occur in the proposed harmonic oscillator with fluctuating mass driven by Mittag-Leffler noise. It is found that when we consider the output amplitude gain versus the driving frequency, the phenomena of stochastic multi-resonance (SMR) with two, three and four peaks are observed, and the quadruple-peaks SR phenomenon had never been observed in previous literature. Besides, when we investigate the dependence of output amplitude gain on the memory exponent, the inverse stochastic resonance (ISR) phenomenon takes place, in contrast to the well-known phenomenon of stochastic resonance. Furthermore, we compare the corresponding ordinary harmonic oscillator without memory to our generalized model, and found that the properties of long-memory and long-range dependence endows our generalized model with more abundant dynamic behaviors than the ordinary harmonic oscillator without memory.
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…
NASA Technical Reports Server (NTRS)
Yeon, Kyu-Hwang; Um, Chung-In; George, Thomas F.; Pandey, Lakshmi N.
1993-01-01
Starting with evaluations of propagator and wave function for the damped harmonic oscillator with time-dependent frequency, exact coherent states are constructed. These coherent states satisfy the properties which coherent states should generally have.
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.
Sonic horizon formation for oscillating Bose-Einstein condensates in isotropic harmonic potential
Wang, Ying; Zhou, Yu; Zhou, Shuyu
2016-01-01
We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study. PMID:27922129
Sonic horizon formation for oscillating Bose-Einstein condensates in isotropic harmonic potential.
Wang, Ying; Zhou, Yu; Zhou, Shuyu
2016-12-06
We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study.
Amplitude and phase representation of quantum invariants for the time-dependent harmonic oscillator
Fernandez Guasti, M.; Moya-Cessa, H.
2003-06-01
The correspondence between classical and quantum invariants is established. The Ermakov-Lewis quantum invariant of the time-dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase operators. In doing so, Turski's phase operator as well as Susskind-Glogower operators are generalized to the time-dependent harmonic-oscillator case. A quantum derivation of the Manley-Rowe relations is shown as an example.
Brownian motion of a harmonic oscillator in a noninertial reference frame.
Jiménez-Aquino, J I; Romero-Bastida, M
2013-08-01
The Brownian motion of a charged harmonic oscillator in the presence of additional force fields, such as a constant magnetic field and arbitrary time-dependent electric and mechanical forces, is studied in a rotational reference frame under uniform motion. By assuming an isotropic surrounding medium (a scalar friction constant), we solve explicitly the Smoluchowski equation associated with the Langevin equation for the charged harmonic oscillator and calculate the mean square displacements along and orthogonal to the rotation axis.
Discrete Excitation Spectrum of a Classical Harmonic Oscillator in Zero-Point Radiation
NASA Astrophysics Data System (ADS)
Huang, Wayne Cheng-Wei; Batelaan, Herman
2015-03-01
We report that upon excitation by a single pulse, a classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation exhibits a discrete harmonic spectrum in agreement with that of its quantum counterpart. This result is interesting in view of the fact that the vacuum field is needed in the classical calculation to obtain the agreement.
Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators.
Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong
2016-03-10
Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO.
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.}
Experimental demonstration of a technique for generation of arbitrary harmonic oscillator states.
NASA Astrophysics Data System (ADS)
Ben-Kish, A.; Demarco, B.; Rowe, M.; Meyer, V.; Britton, J.; Itano, W. M.; Jelenković, B. M.; Langer, C.; Leibfried, D.; Rosenband, T.; Wineland, D. J.
2002-05-01
Synthesizing arbitrary quantum states is at the heart of such diverse fields as quantum computation and reaction control in chemistry. For harmonic oscillator states, particular interactions (in general, non-linear) can be used to generate special states such as squeezed states. However, it is usually intractable to realize the interactions required to create arbitrary states. Law and Eberly [1] have devised a technique for arbitrary harmonic oscillator state generation that couples the oscillator to a two-level atomic or spin system and applies a sequence of operations that use simple interactions. We demonstrate the general features of this technique on the harmonic motion of a single trapped ^9Be^+ ion and extend it to the generation of arbitrary spin-oscillator states [2]. [1] C. K. Law and J. H. Eberly, Phys. Rev. Lett. 76, 1055 (1996). [2] B. Kneer and C. K. Law, Phys. Rev. A 57, 2096 (1998).
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.
Nonlinear harmonic generation in finite amplitude black hole oscillations
NASA Astrophysics Data System (ADS)
Papadopoulos, Philippos
2002-04-01
The nonlinear generation of harmonics in gravitational perturbations of black holes is explored using numerical relativity based on an ingoing light-cone framework. Localized, finite, perturbations of an isolated black hole are parametrized by amplitude and angular harmonic form. The response of the black hole spacetime is monitored and its harmonic content analyzed to identify the strength of the nonlinear generation of harmonics as a function of the initial data amplitude. It is found that overwhelmingly the black hole responds at the harmonic mode perturbed, even for spacetimes with 10% of the black hole mass radiated. The coefficients for down and up scattering in harmonic space are computed for a range of couplings. Down scattering, leading to smoothing out of angular structure, is found to be equally as or more efficient than the up scatterings that would lead to increased rippling. The details of this nonlinear balance may form the quantitative mechanism by which black holes avoid fission even for arbitrary strong distortions.
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.
Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Plyushchay, Mikhail S.
2016-11-01
Ladder operators for the simplest version of a rationally extended quantum harmonic oscillator (REQHO) are constructed by applying a Darboux transformation to the quantum harmonic oscillator system. It is shown that the physical spectrum of the REQHO carries a direct sum of a trivial and an infinite-dimensional irreducible representation of the polynomially deformed bosonized osp (1 |2 ) superalgebra. In correspondence with this the ground state of the system is isolated from other physical states but can be reached by ladder operators via nonphysical energy eigenstates, which belong to either an infinite chain of similar eigenstates or to the chains with generalized Jordan states. We show that the discrete chains of the states generated by ladder operators and associated with physical energy levels include six basic generalized Jordan states, in comparison with the two basic Jordan states entering in analogous discrete chains for the quantum harmonic oscillator.
Entanglement in a continuously measured two-level system coupled to a harmonic oscillator
Hernandez-Concepcion, E.; Alonso, D.; Brouard, S.
2009-05-15
The dynamics of a two-level system (TLS) coupled to a harmonic oscillator (HO) is studied under the combined effect of a thermal bath acting on the HO and of a detector continuously measuring one of the components of the spinlike TLS. The analysis focuses on the dynamics of the 'relative entropy of entanglement' (REE) in the one-energy-excitation manifold of the reduced TLS+HO system. For this model system, a stationary state is shown to be reached for which the relative entropy of entanglement is in general nonzero, even though, under certain approximations, the separate effects of bath and detector would be to remove any trace of this resource from the system. Analytical as well as numerical results are obtained for the REE as a function of the different parameters involved in the model definition.
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
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)
Marengo, Edwin A.; Khodja, Mohamed R.
2006-09-01
The nonrelativistic Larmor radiation formula, giving the power radiated by an accelerated charged point particle, is generalized for a spatially extended particle in the context of the classical charged harmonic oscillator. The particle is modeled as a spherically symmetric rigid charge distribution that possesses both translational and spinning degrees of freedom. The power spectrum obtained exhibits a structure that depends on the form factor of the particle, but reduces, in the limit of an infinitesimally small particle and for the charge distributions considered, to Larmor’s familiar result. It is found that for finite-duration small-enough accelerations as well as perpetual uniform accelerations the power spectrum of the spatially extended particle reduces to that of a point particle. It is also found that when the acceleration is violent or the size parameter of the particle is very large compared to the wavelength of the emitted radiation the power spectrum is highly suppressed. Possible applications are discussed.
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.
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.
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
Quantum optics. Quantum harmonic oscillator state synthesis by reservoir engineering.
Kienzler, D; Lo, H-Y; Keitch, B; de Clercq, L; Leupold, F; Lindenfelser, F; Marinelli, M; Negnevitsky, V; Home, J P
2015-01-02
The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to generate squeezed, coherent, and displaced-squeezed states as steady states in the presence of noise. We verify the created state by generating two-state correlated spin-motion Rabi oscillations, resulting in high-contrast measurements. For both cooling and measurement, we use spin-oscillator couplings that provide transitions between oscillator states in an engineered Fock state basis. Our approach should facilitate studies of entanglement, quantum computation, and open-system quantum simulations in a wide range of physical systems.
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.
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.
Constructing quantum logic gates using q-deformed harmonic oscillator algebras
NASA Astrophysics Data System (ADS)
Altintas, Azmi Ali; Ozaydin, Fatih; Yesilyurt, Can; Bugu, Sinan; Arik, Metin
2014-04-01
We study two-level q-deformed angular momentum states, and using q-deformed harmonic oscillators, we provide a framework for constructing qubits and quantum gates. We also present the construction of some basic one-qubit and two-qubit quantum logic gates.
Generalized uncertainty principle corrections to the simple harmonic oscillator in phase space
NASA Astrophysics Data System (ADS)
Das, Saurya; Robbins, Matthew P. G.; Walton, Mark A.
2016-01-01
We compute Wigner functions for the harmonic oscillator including corrections from generalized uncertainty principles (GUPs), and study the corresponding marginal probability densities and other properties. We show that the GUP corrections to the Wigner functions can be significant, and comment on their potential measurability in the laboratory.
Convergence for Fourier Series Solutions of the Forced Harmonic Oscillator II
ERIC Educational Resources Information Center
Fay, Temple H.
2002-01-01
This paper compliments two recent articles by the author in this journal concerning solving the forced harmonic oscillator equation when the forcing is periodic. The idea is to replace the forcing function by its Fourier series and solve the differential equation term-by-term. Herein the convergence of such series solutions is investigated when…
Note on the Time-Dependent Damped and Forced Harmonic Oscillator.
ERIC Educational Resources Information Center
Leach, P. G. L.
1978-01-01
A Hamiltonian for the time-dependent damped and forced harmonic oscillator is derived. A simple time-dependent linear canonical transformation transforms the Hamiltonian to one whose solution is readily obtained. The wave function for the corresponding quantum mechanical problem is given. (Author/GA)
Harmonic mode competition in a terahertz gyrotron backward-wave oscillator
Kao, S. H.; Chiu, C. C.; Chang, P. C.; Wu, K. L.; Chu, K. R.
2012-10-15
Electron cyclotron maser interactions at terahertz (THz) frequencies require a high-order-mode structure to reduce the wall loss to a tolerable level. To generate THz radiation, it is also essential to employ cyclotron harmonic resonances to reduce the required magnetic field strength to a value within the capability of the superconducting magnets. However, much weaker harmonic interactions in a high-order-mode structure lead to serious mode competition problems. The current paper addresses harmonic mode competition in the gyrotron backward wave oscillator (gyro-BWO). We begin with a comparative study of the mode formation and oscillation thresholds in the gyro-BWO and gyromonotron. Differences in linear features result in far fewer 'windows' for harmonic operation of the gyro-BWO. Nonlinear consequences of these differences are examined in particle simulations of the multimode competition processes in the gyro-BWO, which shed light on the competition criteria between modes of different as well as the same cyclotron harmonic numbers. The viability of a harmonic gyro-BWO is assessed on the basis of the results obtained.
NASA Astrophysics Data System (ADS)
Vignat, C.; Lamberti, P. W.
2009-10-01
Recently, Cariñena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.
Time-Variant Least Squares Harmonic Modeling
2003-01-01
SNR situations. We show applicability to high accuracy speech pitch and heart sound beat epoch estimation. 1. INTRODUCTION Harmonic modeling...techniques have been successfully used for low bit-rate speech coding; however their performance degrades at low SNR . The LSH model is capable of...producing more accurate and robust harmonic analysis, even at very low SNR ; however, as will be shown, its performance degrades significantly with rapid
Entangling Qubits in a One-Dimensional Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Owen, Edmund; Dean, Matthew; Barnes, Crispin
2012-02-01
We present a method for generating entanglement between qubits associated with a pair of particles interacting in a one-dimensional harmonic potential. By considering the effect of the interaction on the energy spectrum of the system, we show that, under certain approximations, a ``power-of-SWAP" operation is performed on the initial two-qubit quantum state without requiring any time-dependent control. Initialization errors and deviations from our approximation are shown to have a negligible effect on the final state. Using a GPU-accelerated iteration scheme to find numerical solutions to the two-particle time-dependent Schr"odinger equation, we demonstrate that it is possible to generate maximally entangled Bell states between the two qubits with high fidelity for a range of possible interaction potentials.
Non-Heisenberg states of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Dechoum, K.; França, H. M.
1995-11-01
The effects of the vacuum electromagnetic fluctuations and the radiation reaction fields on the time development of a simple microscopic system are identified using a new mathematical method. This is done by studying a charged mechanical oscillator (frequency Ω 0) within the realm of stochastic electrodynamics, where the vacuum plays the role of an energy reservoir. According to our approach, which may be regarded as a simple mathematical exercise, we show how the oscillator Liouville equation is transformed into a Schrödinger-like stochastic equation with a free parameter h' with dimensions of action. The role of the physical Planck's constant h is introduced only through the zero-point vacuum electromagnetic fields. The perturbative and the exact solutions of the stochastic Schrödinger-like equation are presented for h'>0. The exact solutions for which h'
A two phase harmonic model for left ventricular function.
Dubi, Shay; Dubi, Chen; Dubi, Yonatan
2007-11-01
A minimal model for mechanical motion of the left ventricle is proposed. The model assumes the left ventricle to be a harmonic oscillator with two distinct phases, simulating the systolic and diastolic phases, at which both the amplitude and the elastic constant of the oscillator are different. Taking into account the pressure within the left ventricle, the model shows qualitative agreement with functional parameters of the left ventricle. The model allows for a natural explanation of heart failure with preserved systolic left ventricular function, also termed diastolic heart failure. Specifically, the rise in left ventricular filling pressures following increased left-ventricular wall stiffness is attributed to a mechanism aimed at preserving heart rate and cardiac output.
Whitfield, Troy W; Martyna, Glenn J
2007-02-21
In the effort to develop atomistic models capable of accurately describing nanoscale systems with complex interfaces, it has become clear that simple treatments with rigid charge distributions and dispersion coefficients selected to generate bulk properties are insufficient to predict important physical properties. The quantum Drude oscillator model, a system of one-electron pseudoatoms whose "pseudoelectrons" are harmonically bound to their respective "pseudonuclei," is capable of treating many-body polarization and dispersion interactions in molecular systems on an equal footing due to the ability of the pseudoatoms to mimic the long-range interactions that characterize real materials. Using imaginary time path integration, the Drude oscillator model can, in principle, be solved in computer operation counts that scale linearly with the number of atoms in the system. In practice, however, standard expressions for the energy and pressure, including the commonly used virial estimator, have extremely large variances that require untenably long simulation times to generate converged averages. In this paper, low-variance estimators for the internal energy are derived, in which the large zero-point energy of the oscillators does not contribute to the variance. The new estimators are applicable to any system of harmonic oscillators coupled to one another (or to the environment) via an arbitrary set of anharmonic interactions. The variance of the new estimators is found to be much smaller than standard estimators in three example problems, a one-dimensional anharmonic oscillator and quantum Drude models of the xenon dimer and solid (fcc) xenon, respectively, yielding 2-3 orders of magnitude improvement in computational efficiency.
Manipulating Fock states of a harmonic oscillator while preserving its linearity
NASA Astrophysics Data System (ADS)
Juliusson, K.; Bernon, S.; Zhou, X.; Schmitt, V.; le Sueur, H.; Bertet, P.; Vion, D.; Mirrahimi, M.; Rouchon, P.; Esteve, D.
2016-12-01
We present a scheme for controlling the quantum state of a harmonic oscillator by coupling it to an anharmonic multilevel system (MLS) with first- to second-excited-state transition on resonance with the oscillator. In this scheme, which we call ef-resonant, the spurious oscillator Kerr nonlinearity inherited from the MLS is very small, while its Fock states can still be selectively addressed via an MLS transition at a frequency that depends on the number of photons. We implement this concept in a circuit-QED setup with a microwave three-dimensional cavity (the oscillator, with frequency 6.4 GHz and quality factor QO=2 ×106 ) embedding a frequency tunable transmon qubit (the MLS). We characterize the system spectroscopically and demonstrate selective addressing of Fock states and a Kerr nonlinearity below 350 Hz. At times much longer than the transmon coherence times, a nonlinear cavity response with driving power is also observed and explained.
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.
Harmonically pumped femtosecond optical parametric oscillator with multi-gigahertz repetition rate.
Tian, Wenlong; Wang, Zhaohua; Zhu, Jiangfeng; Wei, Zhiyi
2016-12-26
We report a multi-gigahertz (GHz) repetition-rate femtosecond MgO:PPLN optical parametric oscillator (OPO) harmonically pumped by a 75.6 MHz Kerr-lens mode-locked Yb:KGW laser. By fractionally increasing the OPO cavity length, we obtained OPO operation up to the 493rd harmonic of the pump laser repetition rate, corresponding to a repetition rate as high as 37.3 GHz. Using a 1.5% output coupler, we are able to extract signal pulses with up to 260 mW average power at the 102nd harmonic (7.7 GHz) and 90 mW at the 493rd harmonic (37.3 GHz) under 2 W pump power. The measured relative standard deviations of the fundamental and the 102nd harmonic signal power were recorded to be 0.5% and 2.1%, respectively. The signal pulse durations at different harmonics were measured in the range of 160-230 fs.
Coherent states for nonlinear harmonic oscillator and some of its properties
Amir, Naila E-mail: naila.amir@sns.nust.edu.pk; Iqbal, Shahid E-mail: siqbal@sns.nust.edu.pk
2015-06-15
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
Study of the harmonic oscillation on EAST by an eight-channel Doppler Backscattering (DBS) system
NASA Astrophysics Data System (ADS)
Zhou, C.; Liu, A. D.; Wang, M. Y.; Hu, J. Q.; Zhang, J.; Li, H.; Lan, T.; Xie, J. L.; Liu, W. D.; Yu, C. X.; Doyle, E. J.; University of California, Los Angeles Collaboration; University of Science; Technology of China Team
2016-10-01
The eight-channel DBS system has been installed for turbulence measurements in such plasmas. The frequency range is 55 to 75 GHz, covering the entire H-mode pedestal, with a turbulence wavenumber range of 4-12/cm. A harmonic oscillation has been observed by DBS on EAST during ELMy-free H mode. The fundamental frequency of the coherent oscillation is 12-20 kHz and 2nd-8th harmonic are observed, and the radial coverage is from the edge to rho 0.85. Work supported by the Natural Science Foundation of China (NSFC) under 11475173, 11505184, National Magnetic Confinement Fusion Energy Development Program of China under 2013GB106002 and 2014GB109002, and DOE Grants DE- SC0010424 and DE-SC0010469.
Transformations of the perturbed two-body problem to unperturbed harmonic oscillators
NASA Technical Reports Server (NTRS)
Szebehely, V.; Bond, V.
1983-01-01
Singular, nonlinear, and Liapunov unstable equations are made regular and linear through transformations that change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients, so that the stable solution may be immediately written in terms of the new variables. The use of arbitrary and special functions for the transformations allows the systematic discussion of previously introduced and novel anomalies. For the case of the unperturbed two-body problem, it is proved that if transformations are power functions of the radial variable, only the eccentric and the true anomalies (with the corresponding transformations of the radial variable) will result in harmonic oscillators. The present method significantly reduces computation requirements in autonomous space operations.
Bound States Energies of a Harmonic Oscillator Perturbed by Point Interactions
NASA Astrophysics Data System (ADS)
Ferkous, N.; Boudjedaa, T.
2017-03-01
We determine explicitly the exact transcendental bound states energies equation for a one-dimensional harmonic oscillator perturbed by a single and a double point interactions via Green’s function techniques using both momentum and position space representations. The even and odd solutions of the problem are discussed. The corresponding limiting cases are recovered. For the harmonic oscillator with a point interaction in more than one dimension, divergent series appear. We use to remove this divergence an exponential regulator and we obtain a transcendental equation for the energy bound states. The results obtained here are consistent with other investigations using different methods. Supported by the Algerian Ministry of Higher Education and Scientific Research under the CNEPRU project No. D01720140001
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.
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.
Parallel-path biquad active-RC oscillator with enhanced harmonic rejection
NASA Astrophysics Data System (ADS)
Vosper, J. V.; Heima, M.; Cryan, R. A.
1995-04-01
A biquad active-RC oscillator is described and a linear analysis given which shows that harmonics injected within the feedback loop are multiplied by a factor which is inversely proportional to the effective open-loop Q-factor Q(sub 0). Experimental results show that distortion is low at high Q(sub 0) values even when saturated operation of the main gain-producing opamp is allowed.
Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise
NASA Astrophysics Data System (ADS)
Jara, Milton; Komorowski, Tomasz; Olla, Stefano
2015-10-01
We consider a one dimensional infinite chain of harmonic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to the solution of the fractional diffusion equation . For a pinned system we prove that its energy evolves diffusively, generalizing some results of Basile and Olla (J. Stat. Phys. 155(6):1126-1142, 2014).
Dynamics of SU(1,1) coherent states for the damped harmonic oscillator
Choi, Jeong Ryeol; Yeon, Kyu Hwang
2009-05-15
Gerry, Ma, and Vrscay [Phys. Rev. A 39, 668 (1989)] studied the time evolution of SU(1,1) coherent states for the damped harmonic oscillator by introducing the Kanai-Caldirola Hamiltonian. The purposes of this Brief Report are to demonstrate that there are somewhat serious errors on their results and to correct them. Most of the figures given in their work are reproduced with correction in order to facilitate our explanation of results.
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.
Brownian motion of a classical harmonic oscillator in a magnetic field.
Jiménez-Aquino, J I; Velasco, R M; Uribe, F J
2008-05-01
In this paper, the stochastic diffusion process of a charged classical harmonic oscillator in a constant magnetic field is exactly described through the analytical solution of the associated Langevin equation. Due to the presence of the magnetic field, stochastic diffusion takes place across and along the magnetic field. Along the magnetic field, the Brownian motion is exactly the same as that of the ordinary one-dimensional classical harmonic oscillator, which was very well described in Chandrasekhar's celebrated paper [Rev. Mod. Phys. 15, 1 (1943)]. Across the magnetic field, the stochastic process takes place on a plane, perpendicular to the magnetic field. For internally Gaussian white noise, this planar-diffusion process is exactly described through the first two moments of the positions and velocities and their corresponding cross correlations. In the absence of the magnetic field, our analytical results are the same as those calculated by Chandrasekhar for the ordinary harmonic oscillator. The stochastic planar diffusion is also well characterized in the overdamped approximation, through the solutions of the Langevin equation.
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.
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.
Are There Signatures of Harmonic Oscillator Shells Far from Stability? First Spectroscopy of 110Zr
NASA Astrophysics Data System (ADS)
Paul, N.; Corsi, A.; Obertelli, A.; Doornenbal, P.; Authelet, G.; Baba, H.; Bally, B.; Bender, M.; Calvet, D.; Château, F.; Chen, S.; Delaroche, J.-P.; Delbart, A.; Gheller, J.-M.; Giganon, A.; Gillibert, A.; Girod, M.; Heenen, P.-H.; Lapoux, V.; Libert, J.; Motobayashi, T.; Niikura, M.; Otsuka, T.; Rodríguez, T. R.; Roussé, J.-Y.; Sakurai, H.; Santamaria, C.; Shimizu, N.; Steppenbeck, D.; Taniuchi, R.; Togashi, T.; Tsunoda, Y.; Uesaka, T.; Ando, T.; Arici, T.; Blazhev, A.; Browne, F.; Bruce, A. M.; Carroll, R.; Chung, L. X.; Cortés, M. L.; Dewald, M.; Ding, B.; Flavigny, F.; Franchoo, S.; Górska, M.; Gottardo, A.; Jungclaus, A.; Lee, J.; Lettmann, M.; Linh, B. D.; Liu, J.; Liu, Z.; Lizarazo, C.; Momiyama, S.; Moschner, K.; Nagamine, S.; Nakatsuka, N.; Nita, C.; Nobs, C. R.; Olivier, L.; Patel, Z.; Podolyák, Zs.; Rudigier, M.; Saito, T.; Shand, C.; Söderström, P.-A.; Stefan, I.; Orlandi, R.; Vaquero, V.; Werner, V.; Wimmer, K.; Xu, Z.
2017-01-01
The first measurement of the low-lying states of the neutron-rich 110Zr and 112Mo was performed via in-beam γ -ray spectroscopy after one proton removal on hydrogen at ˜200 MeV /nucleon . The 21+ excitation energies were found at 185(11) keV in 110Zr, and 235(7) keV in 112Mo, while the R42=E (41+)/E (21+) ratios are 3.1(2), close to the rigid rotor value, and 2.7(1), respectively. These results are compared to modern energy density functional based configuration mixing models using Gogny and Skyrme effective interactions. We conclude that first levels of 110Zr exhibit a rotational behavior, in agreement with previous observations of lighter zirconium isotopes as well as with the most advanced Monte Carlo shell model predictions. The data, therefore, do not support a harmonic oscillator shell stabilization scenario at Z =40 and N =70 . The present data also invalidate predictions for a tetrahedral ground state symmetry in 110Zr.
Fidler, Andrew F; Engel, Gregory S
2013-10-03
We present a theory for a bath model in which we approximate the adiabatic nuclear potential surfaces on the ground and excited electronic states by displaced harmonic oscillators that differ in curvature. Calculations of the linear and third-order optical response functions employ an effective short-time approximation coupled with the cumulant expansion. In general, all orders of correlation contribute to the optical response, indicating that the solvation process cannot be described as Gaussian within the model. Calculations of the linear absorption and fluorescence spectra resulting from the theory reveal a stronger temperature dependence of the Stokes shift along with a general asymmetry between absorption and fluorescence line shapes, resulting purely from the difference in the phonon side band. We discuss strategies for controlling spectral tuning and energy-transfer dynamics through the manipulation of the excited-state and ground-state curvature. Calculations of the nonlinear response also provide insights into the dynamics of the system-bath interactions and reveal that multidimensional spectroscopies are sensitive to a difference in curvature between the ground- and excited-state adiabatic surfaces. This extension allows for the elucidation of short-time dynamics of dephasing that are accessible in nonlinear spectroscopic methods.
Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges
NASA Astrophysics Data System (ADS)
Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, W. M.; Tobias, B. J.; Yan, Z.
2016-07-01
In the quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHOs) play an important role in avoiding transient edge localized mode (ELM) power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n ⩽ 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended magentoohydrodynamics (MHD) code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-Imaging and microwave imaging reflectometer (MIR) diagnostics, as well as the kink/peeling mode properties found by the ideal MHD code ELITE. Numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by rotation and/or rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that EHOs can be destabilized in principle with rotation in either direction. The modeling results are consistent with observations of EHO, support the proposed theory of the EHO as a low-n kink/peeling mode destabilized by edge E × B rotational shear, and improve our understanding and confidence in creating and sustaining QH-mode in present and future devices.
Rotational Shear Effects on Edge Harmonic Oscillations in DIII-D Quiescent H-mode Discharges
NASA Astrophysics Data System (ADS)
Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, Wm.; Tobias, B. J.; Yan, Z.
2015-11-01
In quiescent H-mode (QH) regime, the edge harmonic oscillations (EHO) play an important role in avoiding the transient ELM power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n <= 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended MHD code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-I and MIR diagnostics, as well as the kink/peeling mode properties of the ideal MHD code ELITE. The numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by the toroidal rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that the low-n EHO can be destabilized in principle with rotation in both directions. These modeling results are consistent with experimental observations of the EHO and support the proposed theory of the EHO as a rotational shear driven kink/peeling mode.
Paul, N; Corsi, A; Obertelli, A; Doornenbal, P; Authelet, G; Baba, H; Bally, B; Bender, M; Calvet, D; Château, F; Chen, S; Delaroche, J-P; Delbart, A; Gheller, J-M; Giganon, A; Gillibert, A; Girod, M; Heenen, P-H; Lapoux, V; Libert, J; Motobayashi, T; Niikura, M; Otsuka, T; Rodríguez, T R; Roussé, J-Y; Sakurai, H; Santamaria, C; Shimizu, N; Steppenbeck, D; Taniuchi, R; Togashi, T; Tsunoda, Y; Uesaka, T; Ando, T; Arici, T; Blazhev, A; Browne, F; Bruce, A M; Carroll, R; Chung, L X; Cortés, M L; Dewald, M; Ding, B; Flavigny, F; Franchoo, S; Górska, M; Gottardo, A; Jungclaus, A; Lee, J; Lettmann, M; Linh, B D; Liu, J; Liu, Z; Lizarazo, C; Momiyama, S; Moschner, K; Nagamine, S; Nakatsuka, N; Nita, C; Nobs, C R; Olivier, L; Patel, Z; Podolyák, Zs; Rudigier, M; Saito, T; Shand, C; Söderström, P-A; Stefan, I; Orlandi, R; Vaquero, V; Werner, V; Wimmer, K; Xu, Z
2017-01-20
The first measurement of the low-lying states of the neutron-rich ^{110}Zr and ^{112}Mo was performed via in-beam γ-ray spectroscopy after one proton removal on hydrogen at ∼200 MeV/nucleon. The 2_{1}^{+} excitation energies were found at 185(11) keV in ^{110}Zr, and 235(7) keV in ^{112}Mo, while the R_{42}=E(4_{1}^{+})/E(2_{1}^{+}) ratios are 3.1(2), close to the rigid rotor value, and 2.7(1), respectively. These results are compared to modern energy density functional based configuration mixing models using Gogny and Skyrme effective interactions. We conclude that first levels of ^{110}Zr exhibit a rotational behavior, in agreement with previous observations of lighter zirconium isotopes as well as with the most advanced Monte Carlo shell model predictions. The data, therefore, do not support a harmonic oscillator shell stabilization scenario at Z=40 and N=70. The present data also invalidate predictions for a tetrahedral ground state symmetry in ^{110}Zr.
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…
Form of the effective interaction in harmonic-oscillator-based effective theory
NASA Astrophysics Data System (ADS)
Haxton, W. C.
2008-03-01
I explore the form of the effective interaction in harmonic-oscillator-based effective theory (HOBET) in leading order (LO) through next-to-next-to-next-to-leading order (NLO3). Because the included space in a HOBET (as in the shell model) is defined by the oscillator energy, both long-distance (low-momentum) and short-distance (high-momentum) degrees of freedom reside in the high-energy excluded space. A HOBET effective interaction is developed in which a short-range contact-gradient expansion, free of operator mixing and corresponding to a systematic expansion in nodal quantum numbers, is combined with an exact summation of the relative kinetic energy. By this means the very strong coupling of the included (P) and excluded (Q) spaces by the kinetic energy is removed. One finds a simple and rather surprising result, that the interplay of QT and QV is governed by a single parameter κ, the ratio of an observable, the binding energy |E|, to a parameter in the effective theory, the oscillator energy ℏω. Once the functional dependence on κ is identified, the remaining order-by-order subtraction of the short-range physics residing in Q becomes systematic and rapidly converging. Numerical calculations are used to demonstrate how well the resulting expansion reproduces the running of Heff from high scales to a typical shell-model scale of 8ℏω. At NLO3 various global properties of Heff are reproduced to a typical accuracy of 0.01%, or about 1 keV, at 8ℏω. Channel-by-channel variations in convergence rates are similar to those found in effective field theory approaches. The state dependence of the effective interaction has been a troubling problem in nuclear physics and is embodied in the energy dependence of Heff(|E|) in the Bloch-Horowitz formalism. It is shown that almost all of this state dependence is also extracted in the procedures followed here, isolated in the analytic dependence of Heff on κ. Thus there exists a simple, Hermitian Heff that can be use
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators.
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
2016-07-01
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators
NASA Astrophysics Data System (ADS)
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
2016-07-01
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.
The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
NASA Astrophysics Data System (ADS)
Quintela, T. S.; Fabris, J. C.; Nogueira, J. A.
2016-12-01
In this work, we explicitly solve the problem of the harmonic oscillator in the classical limit of a minimal-length scenario. We show that (i) the motion equation of the oscillator is not linear anymore because the presence of a minimal length introduces an anarmonic term and (ii) its motion is described by a Jacobi sine elliptic function. Therefore, the motion is periodic with the same amplitude and with the new period depending on the minimal length. This result (the change in the period of oscillation) is very important since it enables us to find in a quite simple way the most relevant effect of the presence of a minimal length and consequently traces of the Planck-scale physics. We show applications of our results in spectroscopy and gravity.
NASA Astrophysics Data System (ADS)
Stepšys, A.; Mickevicius, S.; Germanas, D.; Kalinauskas, R. K.
2014-11-01
This new version of the HOTB program for calculation of the three and four particle harmonic oscillator transformation brackets provides some enhancements and corrections to the earlier version (Germanas et al., 2010) [1]. In particular, new version allows calculations of harmonic oscillator transformation brackets be performed in parallel using MPI parallel communication standard. Moreover, higher precision of intermediate calculations using GNU Quadruple Precision and arbitrary precision library FMLib [2] is done. A package of Fortran code is presented. Calculation time of large matrices can be significantly reduced using effective parallel code. Use of Higher Precision methods in intermediate calculations increases the stability of algorithms and extends the validity of used algorithms for larger input values. Catalogue identifier: AEFQ_v4_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFQ_v4_0.html Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 Number of lines in programs, including test data, etc.: 1711 Number of bytes in distributed programs, including test data, etc.: 11667 Distribution format: tar.gz Program language used: FORTRAN 90 with MPI extensions for parallelism Computer: Any computer with FORTRAN 90 compiler Operating system: Windows, Linux, FreeBSD, True64 Unix Has the code been vectorized of parallelized?: Yes, parallelism using MPI extensions. Number of CPUs used: up to 999 RAM(per CPU core): Depending on allocated binomial and trinomial matrices and use of precision; at least 500 MB Catalogue identifier of previous version: AEFQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181, Issue 2, (2010) 420-425 Does the new version supersede the previous version? Yes Nature of problem: Calculation of matrices of three-particle harmonic oscillator brackets (3HOB) and four-particle harmonic oscillator brackets (4HOB) in a more
Use of videos for students to see the effect of changing gravity on harmonic oscillators
NASA Astrophysics Data System (ADS)
Benge, Raymond; Young, Charlotte; Worley, Alan; Davis, Shirley; Smith, Linda; Gell, Amber
2010-03-01
In introductory physics classes, students are introduced to harmonic oscillators such as masses on springs and the simple pendulum. In derivation of the equations describing these systems, the term ``g'' for the acceleration due to gravity cancels in the equation for the period of a mass oscillating on a spring, but it remains in the equation for the period of a pendulum. Frequently there is a homework problem asking how the system described would behave on the Moon, Mars, etc. Students have to have faith in the equations. In January, 2009, a team of community college faculty flew an experiment aboard an aircraft in conjunction with NASA's Microgravity University program. The experiment flown was a study in harmonic oscillator and pendulum behavior under various gravity situations. The aircraft simulated zero gravity, Martian, Lunar, and hypergravity conditions. The experiments were video recorded for students to study the behavior of the systems in varying gravity conditions. These videos are now available on the internet for anyone to use in introductory physics classes.
NASA Astrophysics Data System (ADS)
Afshar, Davood; Motamedinasab, Amin; Anbaraki, Azam; Jafarpour, Mojtaba
2016-02-01
In this paper, we have constructed even and odd superpositions of supercoherent states, similar to the standard even and odd coherent states of the harmonic oscillator. Then, their nonclassical properties, that is, squeezing and entanglement have been studied. We have observed that even supercoherent states show squeezing behavior for some values of parameters involved, while odd supercoherent states do not show squeezing at all. Also sub-Poissonian statistics have been observed for some ranges of the parameters in both states. We have also shown that these states may be considered as logical qubits which reduce to the Bell states at a limit, with concurrence equal to 1.
Step potential problem and harmonic oscillator problem in the minimum length quantum mechanics
NASA Astrophysics Data System (ADS)
Park, Soyeon; Woo, Byeong Hyo; Jung, Min; Jang, Eun Ji; Chung, Won Sang
2015-05-01
In this paper, we use the quasi-position representation of the minimum length quantum mechanics (MLQM) to study the effects of minimum length uncertainty principle (MLUP) on the quantum mechanical system up to a first-order in β. We introduce the probability density and the probability flux to discuss two problems such as particle in a box and step potential problem. For the step potential, we compute the transmission coefficient and the reflection coefficient and compare them with those of the ordinary quantum mechanics. We also discuss the harmonic oscillator problem in MLQM.
Comment on 'Wave functions of a time-dependent harmonic oscillator in a static magnetic field'
Maamache, M.; Bounames, A.; Ferkous, N.
2006-01-15
We show that the procedure used by Ferreira et al. [Phys. Rev. A 66, 024103 (2002)] is not correct for the following reasons: (i) the invariant I(t) they derived does not satisfy the Liouville-Von Neuman equation. (ii) They found that the eigenvalues of I(t) are time dependent which should not be the case according to the Lewis-Riesenfeld theory. We give a correct procedure to find the solution of the system they considered, i.e., the Schroedinger equation for a two-dimensional harmonic oscillator with time-dependent mass and frequency in the presence of a static magnetic field.
NASA Astrophysics Data System (ADS)
Guo, Feng; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Li, Heng
2016-10-01
Stochastic resonance in a fractional harmonic oscillator with random mass and signal-modulated noise is investigated. Applying linear system theory and the characteristics of the noises, the analysis expression of the mean output-amplitude-gain (OAG) is obtained. It is shown that the OAG varies non-monotonically with the increase of the intensity of the multiplicative dichotomous noise, with the increase of the frequency of the driving force, as well as with the increase of the system frequency. In addition, the OAG is a non-monotonic function of the system friction coefficient, as a function of the viscous damping coefficient, as a function of the fractional exponent.
Harmonic oscillators and resonance series generated by a periodic unstable classical orbit
NASA Technical Reports Server (NTRS)
Kazansky, A. K.; Ostrovsky, Valentin N.
1995-01-01
The presence of an unstable periodic classical orbit allows one to introduce the decay time as a purely classical magnitude: inverse of the Lyapunov index which characterizes the orbit instability. The Uncertainty Relation gives the corresponding resonance width which is proportional to the Planck constant. The more elaborate analysis is based on the parabolic equation method where the problem is effectively reduced to the multidimensional harmonic oscillator with the time-dependent frequency. The resonances form series in the complex energy plane which is equidistant in the direction perpendicular to the real axis. The applications of the general approach to various problems in atomic physics are briefly exposed.
NASA Astrophysics Data System (ADS)
Kurt, Arzu; Eryigit, Resul
2015-12-01
The master equation for a charged harmonic oscillator coupled to an electromagnetic reservoir is investigated up to fourth order in the interaction strength by using Krylov averaging method. The interaction is in the velocity-coupling form and includes a diamagnetic term. Exact analytical expressions for the second-, the third-, and the fourth-order contributions to mass renormalization, decay constant, normal and anomalous diffusion coefficients are obtained for the blackbody type environment. It is found that, generally, the third- and the fourth-order contributions have opposite signs when their magnitudes are comparable to that of the second-order one.
Pyragas, Viktoras; Pyragas, Kestutis
2015-08-01
In a recent paper [Phys. Rev. E 91, 012920 (2015)] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.
NASA Astrophysics Data System (ADS)
Pyragas, Viktoras; Pyragas, Kestutis
2015-08-01
In a recent paper [Phys. Rev. E 91, 012920 (2015), 10.1103/PhysRevE.91.012920] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.
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.
NASA Astrophysics Data System (ADS)
Guseinov, I. I.; Mamedov, B. A.
2017-04-01
In this paper, the physical nature of quantum usual and self-friction (SF) harmonic oscillators is presented. The procedure for studying these harmonic oscillators is identical; therefore, we can benefit from the theory of the usual harmonic oscillator. To study the SF harmonic oscillator, using analytical formulae for the L^{{(pl^{ * } )}}-SF Laguerre polynomials (L^{{(pl^{ * } )}}-SFLPs) and L^{{(α^{*} )}}-modified SFLPs (L^{{(α^{*} )}}-MSFLPs) in standard convention, the V^{{(pl^{ * } )}}-SF potentials (V^{{(pl^{ * } )}}-SFPs), V^{{(α^{*} )}}-modified SFPs (V^{{(α^{*} )}}-MSFPs), F^{{(pl^{ * } )}}-SF forces (F^{{(pl^{ * } )}}-SFFs) and F^{{(α^{*} )}}-modified SFFs (F^{{(α^{*} )}}-MSFFs) are investigated, where pl^{ * } = 2l + 2 - α^{*} and α^{*} is the integer (α^{*} = α, - ∞ < α ≤ 2) or non-integer (α^{*} ≠ α, - ∞ < α < 3) SF quantum number. We note that the potentials (V^{{(pl^{ * } )}}-SFPs and V^{{(α^{*} )}}-MSFPs), and forces (F^{{(pl^{ * } )}}-SFFs and F^{{(α^{*} )}}-MSFFs), respectively, are independent functions. It is shown that the numerical values of these independent functions are the same, i.e., V_{num}^{{(pl^{ * } )}} = V_{num}^{{(α^{*} )}} and F_{num}^{{(pl^{ * } )}} = F_{num}^{{(α^{*} )}}. The dependence of the SF harmonic oscillator as a function of the distance is analyzed. The presented relationships are valid for arbitrary values of parameters.
NASA Astrophysics Data System (ADS)
Wang, Zhiguo; Liang, Zhenguo
2017-04-01
In this paper we prove an infinite dimensional KAM theorem, in which the assumptions on the derivatives of the perturbation in [24] are weakened from polynomial decay to logarithmic decay. As a consequence, we can apply it to 1D quantum harmonic oscillators and prove the reducibility of the linear harmonic oscillator, T=-\\frac{{{\\text{d}}2}}{\\text{d}{{x}2}}+{{x}2} , on {{L}2}≤ft({R}\\right) perturbed by the quasi-periodic in the time potential V(x,ω t;ω ) with logarithmic decay. This proves the pure-point nature of the spectrum of the Floquet operator K, where K:=‑i∑k=1nωk∂∂θk‑d2dx2+x2+εV(x,θω) is defined on {{L}2}≤ft({R}\\right)\\otimes {{L}2}≤ft({{{T}}n}\\right) , and the potential V(x,θ ;ω ) has logarithmic decay as well as its gradient in ω.
A generalized harmonic balance method for forced non-linear oscillations: the subharmonic cases
NASA Astrophysics Data System (ADS)
Wu, J. J.
1992-12-01
This paper summarizes and extends results in two previous papers, published in conference proceedings, on a variant of the generalized harmonic balance method (GHB) and its application to obtain subharmonic solutions of forced non-linear oscillation problems. This method was introduced as an alternative to the method of multiple scales, and it essentially consists of two parts. First, the part of the multiple scales method used to reduce the problem to a set of differential equations is used to express the solution as a sum of terms of various harmonics with unknown, time dependent coefficients. Second, the form of solution so obtained is substituted into the original equation and the coefficients of each harmonic are set to zero. Key equations of approximations for a subharmonic case are derived for the cases of both "small" damping and excitations, and "Large" damping and excitations, which are shown to be identical, in the intended order of approximation, to those obtained by Nayfeh using the method of multiple scales. Detailed numerical formulations, including the derivation of the initial conditions, are presented, as well as some numerical results for the frequency-response relations and the time evolution of various harmonic components. Excellent agreement is demonstrated between results by GHB and by integrating the original differential equation directly. The improved efficiency in obtaining numerical solutions using GHB as compared with integrating the original differential equation is demonstrated also. For the case of large damping and excitations and for non-trivial solutions, it is noted that there exists a threshold value of the force beyond which no subharmonic excitations are possible.
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.
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…
Song, Yongli; Zhang, Tonghua; Tadé, Moses O
2008-12-01
We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov-Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved.
Alternative descriptions of wave and particle aspects of the harmonic oscillator
NASA Technical Reports Server (NTRS)
Schuch, Dieter
1993-01-01
The dynamical properties of the wave and particle aspects of the harmonic oscillator can be studied with the help of the time-dependent Schroedinger equation (SE). Especially the time-dependence of maximum and width of Gaussian wave packet solutions allow to show the evolution and connections of those two complementary aspects. The investigation of the relations between the equations describing wave and particle aspects leads to an alternative description of the considered systems. This can be achieved by means of a Newtonian equation for a complex variable in connection with a conservation law for a nonclassical angular momentum-type quantity. With the help of this complex variable, it is also possible to develop a Hamiltonian formalism for the wave aspect contained in the SE, which allows to describe the dynamics of the position and momentum uncertainties. In this case the Hamiltonian function is equivalent to the difference between the mean value of the Hamiltonian operator and the classical Hamiltonian function.
NASA Astrophysics Data System (ADS)
Gaiko, Nick V.; van Horssen, Wim T.
2016-11-01
In this paper, the free transverse vibrations of a vertically moving string with a harmonically time-varying length are studied. The string length variations are assumed to be small. By using the multiple-timescales perturbation method in conjunction with a Fourier series approach, we determine the resonance frequencies and derive the non-secularity conditions in the form of an infinite dimensional system of coupled ordinary differential equations. This system describes the long time behavior of the amplitudes of the oscillations. Then, the eigenvalues of the obtained system are studied by the Galerkin truncation method, and applicability of this method is discussed. Apart from this, the dynamic stability of the solution is investigated by an energy analysis. Additionally, resonance detuning is considered.
LETTER TO THE EDITOR: Exact energy distribution function in a time-dependent harmonic oscillator
NASA Astrophysics Data System (ADS)
Robnik, Marko; Romanovski, Valery G.; Stöckmann, Hans-Jürgen
2006-09-01
Following a recent work by Robnik and Romanovski (2006 J. Phys. A: Math. Gen. 39 L35, 2006 Open Syst. Inf. Dyn. 13 197-222), we derive an explicit formula for the universal distribution function of the final energies in a time-dependent 1D harmonic oscillator, whose functional form does not depend on the details of the frequency ω(t) and is closely related to the conservation of the adiabatic invariant. The normalized distribution function is P(x) = \\pi^{-1} (2\\mu^2 - x^2)^{-\\frac{1}{2}} , where x=E_1- \\skew3\\bar{E}_1 ; E1 is the final energy, \\skew3\\bar{E}_1 is its average value and µ2 is the variance of E1. \\skew3\\bar{E}_1 and µ2 can be calculated exactly using the WKB approach to all orders.
Rodriguez-Gallardo, M.; Arias, J. M.; Gomez-Camacho, J.; Moro, A. M.; Johnson, R. C.; Tostevin, J. A.; Thompson, I. J.
2008-06-15
The scattering of a weakly bound three-body system by a target is discussed. A transformed harmonic oscillator basis is used to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum of the projectile. The continuum-discretized coupled-channels framework is used for the scattering calculations. The formalism is applied to different reactions, {sup 6}He+{sup 12}C at 229.8 MeV, {sup 6}He+{sup 64}Zn at 10 and 13.6 MeV, and {sup 6}He+{sup 208}Pb at 22 MeV, induced by the Borromean nucleus {sup 6}He. Both the Coulomb and nuclear interactions with a target are taken into account.
Moro, A. M.; Arias, J. M.; Gomez-Camacho, J.; Perez-Bernal, F.
2009-11-15
A new method for continuum discretization in continuum-discretized coupled-channels calculations is proposed. The method is based on an analytic local-scale transformation of the harmonic-oscillator wave functions proposed for other purposes in a recent work [Karatagladis et al., Phys. Rev. C 71, 064601 (2005)]. The new approach is compared with the standard method of continuum discretization in terms of energy bins for the reactions d+{sup 58}Ni at 80 MeV, {sup 6}Li+{sup 40}Ca at 156 MeV, and {sup 6}He+{sup 208}Pb at 22 MeV and 240 MeV/nucleon. In all cases very good agreement between both approaches is found.
The quantum fidelity for the time-periodic singular harmonic oscillator
NASA Astrophysics Data System (ADS)
Combescure, Monique
2006-03-01
In this paper we perform an exact study of "quantum fidelity" (also called Loschmidt echo) for the time-periodic quantum harmonic oscillator of the following Hamiltonian: Ĥg(t)≔(P2/2)+f(t)(Q2/2)+(g2/Q2), when compared with the quantum evolution induced by Ĥ0(t) (g=0), in the case where f is a T-periodic function and g a real constant. The reference (initial) state is taken to be an arbitrary "generalized coherent state" in the sense of Perelomov. We show that, starting with a quadratic decrease in time in the neighborhood of t =0, this quantum fidelity may recur to its initial value 1 at an infinite sequence of times tk. We discuss the result when the classical motion induced by Hamiltonian Ĥ0(t) is assumed to be stable versus unstable.
NASA Astrophysics Data System (ADS)
Xiong, Huai; Kong, Xianren; Li, Haiqin; Yang, Zhenguo
2017-01-01
This paper considers dynamics of bilinear hysteretic systems, which are widely used for vibration control and vibration absorption such as magneto-rheological damper, metal-rubber. The method of incremental harmonic balance (IHB) technique that hysteresis is considered in the corrective term is improved in order to determine periodic solutions of bilinear hysteretic systems. The improved continuation method called two points tracing algorithm which is stable to the turning point makes the calculation more efficient for tracing amplitude-frequency response. Precise Hsu's method for analysing the stability of periodic solutions is introduced. The effects of different parameters of bilinear hysteretic oscillator on the response are discussed numerically. Some numerical simulations of considered bilinear hysteretic systems, including a single DOF and a 2DOF system, are effectively obtained by the modified IHB method and the results compare very well with the 4-oder Runge-Kutta method.
Fourth-order master equation for a charged harmonic oscillator coupled to an electromagnetic field
NASA Astrophysics Data System (ADS)
Kurt, Arzu; Eryigit, Resul
Using Krylov averaging method, we have derived a fourth-order master equation for a charged harmonic oscillator weakly coupled to an electromagnetic field. Interaction is assumed to be of velocity coupling type which also takes into account the diagmagnetic term. Exact analytical expressions have been obtained for the second, the third and the fourth-order corrections to the diffusion and the drift terms of the master equation. We examined the validity range of the second order master equation in terms of the coupling constant and the bath cutoff frequency and found that for the most values of those parameters, the contribution from the third and the fourth order terms have opposite signs and cancel each other. Inclusion of the third and the fourth-order terms is found to not change the structure of the master equation. Bolu, Turkey.
Modelling harmonic generation measurements in solids.
Best, S R; Croxford, A J; Neild, S A
2014-02-01
Harmonic generation measurements typically make use of the plane wave result when extracting values for the nonlinearity parameter, β, from experimental measurements. This approach, however, ignores the effects of diffraction, attenuation, and receiver integration which are common features in a typical experiment. Our aim is to determine the importance of these effects when making measurements of β over different sample dimensions, or using different input frequencies. We describe a three-dimensional numerical model designed to accurately predict the results of a typical experiment, based on a quasi-linear assumption. An experiment is designed to measure the axial variation of the fundamental and second harmonic amplitude components in an ultrasonic beam, and the results are compared with those predicted by the model. The absolute β values are then extracted from the experimental data using both the simulation and the standard plane wave result. A difference is observed between the values returned by the two methods, which varies with axial range and input frequency.
Spherical harmonic stacking for the singlets of Earth's normal modes of free oscillation
NASA Astrophysics Data System (ADS)
Chao, Benjamin F.; Ding, Hao
2014-08-01
We extend the spherical harmonic stacking (SHS) method of Buland et al. (1979) for the radial (vertical) component in the seismogram to the transverse (horizontal) components of the displacement field. Taking advantage of the orthogonality of the spherical harmonic functions (scalar and vectorial), SHS isolates and accentuates the signals of individual singlets of the Earth's normal modes of free oscillation. We apply the SHS on the broadband Incorporated Research Institutions for Seismology (IRIS) seismograms from up to 97 IRIS seismic stations for the 2004 Sumatra-Andaman earthquake, in experiments targeted to spheroidal as well as toroidal modes—2S1, 0S3, 2S2, 3S1, 1S3, 0T2, and 0T3. We report the complete resolution of the singlet frequencies of these multiplets, some for the first time, and estimate the singlets' complex frequencies using the frequency domain autoregressive method of Chao and Gilbert (1980). The latter contain useful information to be used in inversions for the 3-D structure of the Earth's interior.
NASA Technical Reports Server (NTRS)
Ehlers, F. E.; Weatherill, W. H.; Yip, E. L.
1984-01-01
A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.
NASA Astrophysics Data System (ADS)
Tong, Zhengrong; Wang, Zhiyong; En, De; Chen, Caihe; Li, Xuejiao; Xie, Xiaofang
2008-03-01
A kind of photo-electronic integrated acceleration seismic detecting technology, which is novel and precise based on waveguide M-Z interference, is presented. It provieds modern geologic prospect with a novel detection technology. The principle of the photo-electronic integrated acceleration seismic geophone is introduced in this paper. The core of the photo-electronic integrated acceleration is the silicon harmonic oscillator, which is supported by four silicon beams and integrated on the signal beam of the M-Z interferometer. When the seismic mass is subjected to a normal acceleration a z, the acceleration a z, will result in an inertial force F z, causing the mass to move up or down like the piston, until the counter force of the beam suspension equals this inertial force. The principle of the harmonic oscillator is briefly introduced, the factors influencing the anisotropic etching quality of the harmonic oscillator are analyzed in detail. In experiment, the fabrication technology was studied and improved. The high quality harmonic oscillator has been successfully fabricated. It has been applied in the integrated optical chip of "the theory and experiment research of photoelectric integrated acceleration seismic geophone technology".
Cari, C. Suparmi, A.
2014-09-30
Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.
Non-Sticking Oscillation Formulae for Coulomb Friction Under Harmonic Loading
NASA Astrophysics Data System (ADS)
HONG, H.-K.; LIU, C.-S.
2001-07-01
In this paper, a new estimate for periodic non-sticking (i.e., zero stop per cycle) solutions is presented for the steady state responses of the Coulomb friction oscillator subjected to harmonic loading. Compared with the Den Hartog (1931 Transactions of the American Society of Mechanical Engineers53, 107-115 [1]) estimate, the new estimate leads to the same formulae for the maximum displacement and its time lag, but only the new estimate offers the closed-form formulae for the maximum velocity and its time lag. More importantly, a simple formula is derived for estimating the minimum driving force amplitude needed to prevent an oscillating object from sticking to the friction surface on which it slides. The validity of the assumptions made for the new estimate and the accuracy of the formulae developed are confirmed by comparing with the exact solutions (Hong and Liu 2000 Journal of Sound and Vibration229, 1171-1192 [2]). It is also found that there exists the best driving force amplitude for maximum dissipation efficiency.
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.
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.
Generalized su(1,1) coherent states for pseudo harmonic oscillator and their nonclassical properties
NASA Astrophysics Data System (ADS)
Mojaveri, B.; Dehghani, A.
2013-08-01
In this paper we define a non-unitary displacement operator, which by acting on the vacuum state of the pseudo harmonic oscillator (PHO), generates new class of generalized coherent states (GCSs). An interesting feature of this approach is that, contrary to the Klauder-Perelomov and Barut-Girardello approaches, it does not require the existence of dynamical symmetries associated with the system under consideration. These states admit a resolution of the identity through positive definite measures on the complex plane. We have shown that the realization of these states for different values of the deformation parameters leads to the well-known Klauder-Perelomov and Barut-Girardello CSs associated with the su(1,1) Lie algebra. This is why we call them the generalized su(1,1) CSs for the PHO. Finally, study of some statistical characters such as squeezing, anti-bunching effect and sub-Poissonian statistics reveals that the constructed GCSs have indeed nonclassical features.
NASA Technical Reports Server (NTRS)
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
NASA Astrophysics Data System (ADS)
Davis, Brian Thompson
1998-07-01
An isotropic three-dimensional non-relativistic charged harmonic oscillator immersed in the stochastic zero point field, an applied classical radiation field, and a constant uniform magnetic field is treated. The method followed is that of previous work [1, 2, 3, 4] with no static magnetic field present. Starting from a non-runaway classical stochastic motion equation, an appropriate conjugate momentum is derived. The classical position/conjugate momentum phase space distribution, a product of Dirac delta distributions, is ensemble averaged. The Liouville equation for this ensemble averaged phase space distribution, along with a separate independent equation that the distribution must satisfy, are derived in dipole approximation. The Weyl transformed Liouville, equation is used to derive a stochastic Schroedinger equation valid to first order in the Larmor frequency. The stochastic equation is the same as the quantum one to this order, except for the presence of radiation reaction vector potentials that produce spontaneous emission without quantization of the applied radiation field. The ensemble averaged Weyl transformed phase space distribution is also shown to be separable into a product of Schroedinger eigenfunctions, in general. Electric dipole spectra and transition probabilities for spontaneous emission and resonant absorption are calculated using the stochastic Schroedinger equation and its exact solutions. The results are compared to the corresponding predictions of quantum electrodynamics and found to be in agreement.
Xu, L; Chan, H-Y; Alam, S-U; Richardson, D J; Shepherd, D P
2015-07-15
We demonstrate the generation of high-energy, mid-IR, picosecond pulses in a high-harmonic-cavity optical parametric oscillator (OPO) that has a relatively compact cavity with a length that is a small fraction of that required to match the pump repetition rate. The OPO, based on an MgO-doped periodically poled LiNbO3 crystal, is pumped by a fiber master-oscillator-power-amplifier system employing direct amplification and delivering 11-μJ, 150-ps pulses at 1035 nm. For a 1.554-m-long OPO cavity, resonating near-infrared signal pulses with a repetition rate that is the 193rd harmonic of the 1-MHz pump are demonstrated. The mid-infrared idler output pulses, tunable from 2300 nm to 3500 nm, are generated at a 1-MHz repetition rate and have energies as high as 1.5 μJ.
NASA Astrophysics Data System (ADS)
Chen, Y. F.; Tung, J. C.; Tuan, P. H.; Yu, Y. T.; Liang, H. C.; Huang, K. F.
2017-01-01
A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.
Chen, Y F; Tung, J C; Tuan, P H; Yu, Y T; Liang, H C; Huang, K F
2017-01-01
A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.
NASA Astrophysics Data System (ADS)
Lo, C. F.
2014-02-01
Recently Zhang (2013 J. Phys. A: Math. Theor. 46 455302) proposed an analytical approach to solve the time-independent Schrödinger equation for the single-mode and two-mode squeezed harmonic oscillators in the Bargmann space of entire functions. In this comment we show that the eigenfunctions of these two systems exist in closed form and are expressed in terms of the Hermite polynomials. Moreover, since both oscillators exhibit the SU(1,1) dynamical symmetry, the eigenvalue problem can be tackled in a unified manner. In the Hilbert space of analytic functions of a complex variable in the unit disc, the energy eigenvalue equations involve first-order ordinary differential equations only, so we can easily solve these equations to obtain simple closed-form solutions.
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)
Hwang, Myung-Joong; Choi, Mahn-Soo
2010-08-15
The nonclassical behavior of a two-level system coupled to a harmonic oscillator is investigated in the ultrastrong coupling regime. We revisit the variational solution of the ground state and find that the existing solutions do not account accurately for nonclassical effects such as squeezing. We suggest a trial wave function and demonstrate that it has an excellent accuracy for the quantum correlation effects as well as for the energy.
A quantum anharmonic oscillator model for the stock market
NASA Astrophysics Data System (ADS)
Gao, Tingting; Chen, Yu
2017-02-01
A financially interpretable quantum model is proposed to study the probability distributions of the stock price return. The dynamics of a quantum particle is considered an analog of the motion of stock price. Then the probability distributions of price return can be computed from the wave functions that evolve according to Schrodinger equation. Instead of a harmonic oscillator in previous studies, a quantum anharmonic oscillator is applied to the stock in liquid market. The leptokurtic distributions of price return can be reproduced by our quantum model with the introduction of mixed-state and multi-potential. The trend following dominant market, in which the price return follows a bimodal distribution, is discussed as a specific case of the illiquid market.
Gasulla, Ivana; Sancho, Juan; Capmany, José; Lloret, Juan; Sales, Salvador
2010-12-06
We theoretically and experimentally evaluate the propagation, generation and amplification of signal, harmonic and intermodulation distortion terms inside a Semiconductor Optical Amplifier (SOA) under Coherent Population Oscillation (CPO) regime. For that purpose, we present a general optical field model, valid for any arbitrarily-spaced radiofrequency tones, which is necessary to correctly describe the operation of CPO based slow light Microwave Photonic phase shifters which comprise an electrooptic modulator and a SOA followed by an optical filter and supplements another recently published for true time delay operation based on the propagation of optical intensities. The phase shifter performance has been evaluated in terms of the nonlinear distortion up to 3rd order, for a modulating signal constituted of two tones, in function of the electrooptic modulator input RF power and the SOA input optical power, obtaining a very good agreement between theoretical and experimental results. A complete theoretical spectral analysis is also presented which shows that under small signal operation conditions, the 3rd order intermodulation products at 2Ω1 + Ω2 and 2Ω2 + Ω1 experience a power dip/phase transition characteristic of the fundamental tones phase shifting operation.
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…
Scaling of Harmonic Oscillator Eigenfunctions and Their Nodal Sets Around the Caustic
NASA Astrophysics Data System (ADS)
Hanin, Boris; Zelditch, Steve; Zhou, Peng
2017-03-01
We study the scaling asymptotics of the eigenspace projection kernels Π_{hbar, E}(x,y) of the isotropic Harmonic Oscillator {hat{H}_{hbar} = - hbar^2 Δ +|x|^2} of eigenvalue {E = hbar(N + d/2)} in the semi-classical limit {hbar to 0} . The principal result is an explicit formula for the scaling asymptotics of Π_{hbar, E}(x,y) for x, y in a {hbar^{2/3}} neighborhood of the caustic C_E as {hbar → 0.} The scaling asymptotics are applied to the distribution of nodal sets of Gaussian random eigenfunctions around the caustic as {hbar to 0} . In previous work we proved that the density of zeros of Gaussian random eigenfunctions of {hat{H}_{hbar}} have different orders in the Planck constant {hbar} in the allowed and forbidden regions: In the allowed region the density is of order {hbar^{-1}} while it is {hbar^{-1/2}} in the forbidden region. Our main result on nodal sets is that the density of zeros is of order {hbar^{-2/3}} in an {hbar^{2/3}} -tube around the caustic. This tube radius is the `critical radius'. For annuli of larger inner and outer radii {hbar^{α}} with {0 < α < 2/3} we obtain density results that interpolate between this critical radius result and our prior ones in the allowed and forbidden region. We also show that the Hausdorff ( d-2)-dimensional measure of the intersection of the nodal set with the caustic is of order {hbar^{- 2/3}}.
NASA Astrophysics Data System (ADS)
Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.
1995-08-01
The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.
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…
An octahedron model for oscillating, bouncing drops
NASA Astrophysics Data System (ADS)
Blanchette, Francois
2016-11-01
We present a model for oscillating and bouncing liquid drops. The model uses 6 point masses distributed as the vertices of an octahedron, connected by linear springs. We derive the physically relevant choice of parameters and use this model to study drops bouncing on solid surfaces, as well as drops bouncing on a nearly inviscid liquid surfaces. The surfaces may be stationary of subject to forced oscillations.
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.
Mathematical Modeling of an Oscillating Droplet
NASA Technical Reports Server (NTRS)
Berry, S.; Hyers, R. W.; Racz, L. M.; Abedian, B.; Rose, M. Franklin (Technical Monitor)
2000-01-01
Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is performed by electromagnetic levitation. The natural oscillation frequency of the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k-epsilon turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity.
The q-DEFORMED SCHRÖDINGER Equation of the Harmonic Oscillator on the Quantum Euclidean Space
NASA Astrophysics Data System (ADS)
Carow-Watamura, Ursula; Watamura, Satoshi
We consider the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidean space. The creation and annihilation operators are found, which systematically produce all energy levels and eigenfunctions of the Schrödinger equation. In order to get the q series representation of the eigenfunction, we also give an alternative way to solve the Schrödinger equation which is based on the q analysis. We represent the Schrödinger equation by the q difference equation and solve it by using q polynomials and q exponential functions.
NASA Technical Reports Server (NTRS)
Isar, Aurelian
1995-01-01
The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.
NASA Astrophysics Data System (ADS)
Gautam, Kumar; Chauhan, Garv; Rawat, Tarun Kumar; Parthasarathy, Harish; Sharma, Navneet
2015-09-01
This paper presents the design of a given quantum unitary gate by perturbing a three-dimensional (3-D) quantum harmonic oscillator with a time-varying but spatially constant electromagnetic field. The idea is based on expressing the radiation- perturbed Hamiltonian as the sum of the unperturbed Hamiltonian and O( e) and perturbations and then solving the Schrödinger equation to obtain the evolution operator at time T up to , and this is a linear-quadratic function of the perturbing electromagnetic field values over the time interval [0, T]. Setting the variational derivative of the error energy with respect to the electromagnetic field values with an average electromagnetic field energy constraint leads to the optimal electromagnetic field solution, a linear integral equation. The reliability of such a gate design procedure in the presence of heat bath coupling is analysed, and finally, an example illustrating how atoms and molecules can be approximated using oscillators is presented.
NASA Astrophysics Data System (ADS)
Xu, Shi-Min; Xu, Xing-Lei; Li, Hong-Qi
2008-06-01
The intermediate representation (namely intermediate coordinate-momentum representation) | x> λ, ν are introduced and employed to research the expression of the operator tauhat{p}+σhat{x} in intermediate representation | x> λ, ν . The systematic Hamilton operator hat{H} of 3D cross coupling quantum harmonic oscillator was diagonalized by virtue of quadratic form theory. The quantity of λ, ν, τand σ were figured out. The dynamic problems of 3D cross coupling quantum harmonic oscillator are researched by virtue of intermediate representation. The energy eigen-value and eigenwave function of 3D cross coupling quantum harmonic oscillator were obtained in intermediate representation. The importance of intermediate representation was discussed. The results show that the Radon transformation of Wigner operator is just the projectional operator | x> λ, ν λ, ν < x|, and the Radon transformation of Wigner function is just a margin distribution.
Decoherence of a quantum harmonic oscillator monitored by a Bose-Einstein condensate
Brouard, S.; Alonso, D.; Sokolovski, D.
2011-07-15
We investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double-well potential. It is demonstrated that the oscillator may experience various degrees of decoherence depending on the variable being measured and the state in which the BEC is prepared. These range from a ''coherent'' regime in which only the variances of the oscillator position and momentum are affected by measurement, to a slow (power-law) or rapid (Gaussian) decoherence of the mean values themselves.
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…
Physical models for the source of Lascar's harmonic tremor
NASA Astrophysics Data System (ADS)
Hellweg, M.
2000-08-01
Over an 18 h interval in April 1994, the tremor at Lascar volcano, Chile, was characterized by a spectrum with narrow peaks at a fundamental freqency of about 0.63 Hz and more than 25 overtones at exact integer multiples. This harmonic tremor was recorded at four three-component, high-dynamic range stations during the deployment of the Proyecto de Investigación Sismológica de la Cordillera Occidental 94 (PISCO'94). Usually this tremor's source is modeled as the resonance of a fluid-filled crack or organ pipe-like structure in the volcano. The resonance of a real, physical structure, however, can produce neither as many overtones nor such exact multiples as those observed in the harmonic tremor at Lascar. Harmonics also occur in a spectrum if the source signal is repetitive but nonsinusoidal. Fluid dynamics offers at least three realistic source models for harmonic tremor which produce repetitive, nonsinusoidal waveforms: the release of gas through a very small outlet (the soda bottle model), slug flow in a narrow conduit, and von Kármán vortices produced at obstacles. These models represent different flow regimes, each with its own characteristic range of Reynolds numbers. For each model the fundamental frequency of the tremor is related to the Reynolds number for the flow. Combining the Reynolds numbers for each model with typical kinematic viscosities for the possible fluids present in a volcano—magma, water, steam, air or some combination, at appropriate temperatures and pressures—provides limits on such physical parameters of the volcano as the dimensions of the flow conduit and the flow velocity of the fluid generating the tremor. If any single one of these three models is actually the process in the volcano which generates harmonic tremor, then the tremor is caused by movements of water or gases in the hydrothermal system near the volcano's surface.
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)
Carow-Watamura, U.; Watamura, S.
With the aim to construct a dynamical model with quantum group symmetry, the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidian space is investigated. After reviewing the differential calculus on the q-Euclidian space, the q-analog of the creation-annihilation operator is constructed. It is shown that it produces systematically all eigenfunctions of the Schrödinger equation and eigenvalues. We also present an alternative way to solve the Schrödinger equation which is based on the q-analysis. We represent the Schrödinger equation by the q-difference equation and solve it by using q-polynomials and q-exponential functions. The problem of the involution corresponding to the reality condition is discussed.
On su{sub q}(1,1)-models of quantum oscillator
Atakishiyev, M. N.; Atakishiyev, N. M.; Klimyk, A. U.
2006-09-15
Models of the quantum oscillator, based on the discrete series representations of the quantum algebra su{sub q}(1,1), are constructed. The position and momentum operators in these models are twisted generators J{sub 2} and J{sub 1} for such su{sub q}(1,1)-representations, respectively. As in the case of the standard harmonic oscillator in quantum mechanics, the position and momentum operators here have continuous simple spectra. These spectra cover a finite interval on the real line, which depends on a value of q. Eigenfunctions of these operators are explicitly found. It is shown that the Macfarlane-Biedenharn q-oscillator is a limit case of the oscillators under discussion. The q=1 limit case, in which spectra of the position and momentum operators cover the whole real line, is also considered in detail.
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.
Mathematical modelling for nanotube bundle oscillators
NASA Astrophysics Data System (ADS)
Thamwattana, Ngamta; Cox, Barry J.; Hill, James M.
2009-07-01
This paper investigates the mechanics of a gigahertz oscillator comprising a nanotube oscillating within the centre of a uniform concentric ring or bundle of nanotubes. The study is also extended to the oscillation of a fullerene inside a nanotube bundle. In particular, certain fullerene-nanotube bundle oscillators are studied, namely C60-carbon nanotube bundle, C60-boron nitride nanotube bundle, B36N36-carbon nanotube bundle and B36N36-boron nitride nanotube bundle. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the fullerene and the nanotube bundle oscillators. While previous studies in this area have been undertaken through molecular dynamics simulations, this paper emphasizes the use of applied mathematical modelling techniques which provides considerable insight into the underlying mechanisms. The paper presents a synopsis of the major results derived in detail by the present authors in [1, 2].
NASA Astrophysics Data System (ADS)
Alejo-Molina, Adalberto; Hingerl, Kurt; Hardhienata, Hendradi
2015-04-01
We report for the first time a comprehensive study of the fourth rank tensor describing third harmonic generation (THG) and electric field induced second harmonic (EFISH) in centrosymmetric material from two different viewpoints: Group Theory (GT) and the Simplified Bond Hyperpolarizability Model (SBHM). We show that the fourth rank tensor related to THG and direct current (DC) EFISH can be reduced to two independent elements whereas SBHM always gives only one, reproducing perfectly well EFISH experimental results in Metal Oxyde Semiconductor (MOS). We argue that it is possible to reduce the fourth rank tensor describing EFISH to a third rank tensor and further deliver a classical explanation of EFISH regarding symmetry breaking where the term containing $r^3$ in the potential immediately leads to second harmonic generation (SHG).
Bright multi-keV harmonic generation from relativistically oscillating plasma surfaces.
Dromey, B; Kar, S; Bellei, C; Carroll, D C; Clarke, R J; Green, J S; Kneip, S; Markey, K; Nagel, S R; Simpson, P T; Willingale, L; McKenna, P; Neely, D; Najmudin, Z; Krushelnick, K; Norreys, P A; Zepf, M
2007-08-24
The first evidence of x-ray harmonic radiation extending to 3.3 A, 3.8 keV (order n>3200) from petawatt class laser-solid interactions is presented, exhibiting relativistic limit efficiency scaling (eta approximately n{-2.5}-n{-3}) at multi-keV energies. This scaling holds up to a maximum order, n{RO} approximately 8{1/2}gamma;{3}, where gamma is the relativistic Lorentz factor, above which the first evidence of an intensity dependent efficiency rollover is observed. The coherent nature of the generated harmonics is demonstrated by the highly directional beamed emission, which for photon energy hnu>1 keV is found to be into a cone angle approximately 4 degrees , significantly less than that of the incident laser cone (20 degrees ).
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.
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.
NASA Astrophysics Data System (ADS)
Liu, Q. H.; Zhuo, H.
The Perelomov and the Barut-Girardello SU(1, 1) coherent states for harmonic oscillator in one-dimensional half space are constructed. Results show that the uncertainty products ΔxΔp for these two coherent states are bound from below √ {9/4-6/π } that is the uncertainty for the ground state, and the mean values for position x and momentum p in classical limit go over to their classical quantities respectively. In classical limit, the uncertainty given by Perelomov coherent does not vanish, and the Barut-Girardello coherent state reveals a node structure when positioning closest to the boundary x = 0 which has not been observed in coherent states for other systems.
Oscillation frequencies of solar models
Cox, A.N.; Guzik, J.A.; Kidman, R.B.
1988-01-01
Two solar models have been constructed, one with no diffusion of the atomic nuclei, and another including diffusive element separation. The opacity at the bottom of the convection zone was increased 15--20 percent (within its theoretical uncertainty) to obtain a few microhertz agreement with observed p-mode frequencies. Original helium mass fractions were 0.291 and 0.289 for the no-diffusion and diffusion models, respectively. The diffusion model evolved to a surface Y = 0.256 at the solar age, and the original Z value of 0.0200 decreased to 0.0179. Agreement of l = 0 and 2 p-mode frequency separations with those observed is good. The g-mode nonadiabatic solutions do not have equal period spacing until high radial order. The lowest order modes are more visible if they all have the same kinetic energy. High central temperatures, produce over 9 SNUs from the B and 1.5 SNUs from the Be reactions. Models with iron condensed-out below the convection zone, and with WIMPs cooling the central regions to reduce the SNUs, agree less well with p-mode frequency separations. 53 refs., 6 figs., 4 tabs.
A three-phase converter model for harmonic analysis of HVDC systems
Xu, W.; Drakos, J.E.; Mansour, Y.; Chang, A. )
1994-07-01
An equivalent circuit model is presented to model bridge converters for three-phase HVDC harmonic power flow analysis. The validity and accuracy of the model are verified by comparing simulation results against field test results. The model is interfaced with a multiphase harmonic load flow program to investigate the generation of non-characteristic harmonics from HVDC links and the flow of HVDC harmonics in a real system.
NASA Astrophysics Data System (ADS)
De Rosis, Alessandro
2014-12-01
In this paper, a rigid thickless lamina is immersed in a quiescent viscous fluid and it undergoes transverse finite amplitude harmonic oscillations near a solid surface. The surrounding flow physics is computed through the lattice Boltzmann method. In order to account for the presence of the lamina in the lattice fluid background, the Immersed Boundary method is adopted. Several scenarios are investigated by varying the distance between the initial position of the lamina and the solid wall. For a given lamina-solid surface distance, the effect of the Reynolds number is investigated, together with the influence of the Keulegan-Carpenter number. Findings in terms of drag coefficient show that the force exerted by the encompassing fluid upon the lamina is remarkably influenced by the distance from the solid surface, especially for low values of the Reynolds number. Moreover, such results are confirmed by the computation of the hydrodynamic function. In fact, it highlights that the added mass effect and the non-linear damping experienced by the oscillating lamina grow as the above mentioned distance and the Reynolds number reduce.
1988-08-15
could. The criterion for the validity of semiclassical calculation is that, for given initial oscillator and incident energies, the ;% possible...This is an expression of the correspondence principle. As is well known, suitable semiclassical calculations may give rather accurate results even when...follows: I "> - Ikot> + Co +’ VKT >, (6) where ;o,> is the normalized eigen function of Ho and Go is the Green s function, defined by ’,.4 G lim (7) -oE-Ho
Improved harmonic mean estimator for phylogenetic model evidence.
Arima, Serena; Tardella, Luca
2012-04-01
Bayesian phylogenetic methods are generating noticeable enthusiasm in the field of molecular systematics. Many phylogenetic models are often at stake, and different approaches are used to compare them within a Bayesian framework. The Bayes factor, defined as the ratio of the marginal likelihoods of two competing models, plays a key role in Bayesian model selection. We focus on an alternative estimator of the marginal likelihood whose computation is still a challenging problem. Several computational solutions have been proposed, none of which can be considered outperforming the others simultaneously in terms of simplicity of implementation, computational burden and precision of the estimates. Practitioners and researchers, often led by available software, have privileged so far the simplicity of the harmonic mean (HM) estimator. However, it is known that the resulting estimates of the Bayesian evidence in favor of one model are biased and often inaccurate, up to having an infinite variance so that the reliability of the corresponding conclusions is doubtful. We consider possible improvements of the generalized harmonic mean (GHM) idea that recycle Markov Chain Monte Carlo (MCMC) simulations from the posterior, share the computational simplicity of the original HM estimator, but, unlike it, overcome the infinite variance issue. We show reliability and comparative performance of the improved harmonic mean estimators comparing them to approximation techniques relying on improved variants of the thermodynamic integration.
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.
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.
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.
Modeling flexible flapping wings oscillating at resonance
NASA Astrophysics Data System (ADS)
Alexeev, Alexander; Masoud, Hassan
2010-03-01
Using a hybrid approach for fluid-structure interactions that integrates the lattice Boltzmann and lattice spring models, we study the three-dimensional aerodynamics of flexible flapping wings at hovering. The wings are a pair of flat elastic plates tilted from the horizontal and driven to oscillate according to the sinusoidal law. Our simulations reveal that resonance oscillations of flexible wings dramatically increase aerodynamic lift at low Reynolds number. Comparing to otherwise identical rigid wings, flexible wings at resonance generate up to two orders of magnitude greater lift. Within the resonance band, we identify two operation regimes leading to the maximum lift and the maximum efficiency, respectively. The maximum lift occurs when the wing tip and root move with a phase lag of 90 degrees, whereas the maximum efficiency occurs at the frequency where the wing tip and root oscillate in counterphase. Our results suggest that the resonance regimes would be optimal for the design of microscale flying machines using flexible flapping wings driven by simple kinematic strokes.
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.
A representation of Jacchia's thermospheric models in spherical harmonic functions
NASA Technical Reports Server (NTRS)
Blum, P.; Harris, I.
1974-01-01
The Jacchia models are represented in terms of spherical harmonic functions. This representation has the advantage of ease of comparison with other global theoretical and empirical models that use this mathematical form. Furthermore, it is analytic, continuous, and has continuous derivatives all over the globe. The representation of the exospheric temperatures shows clearly the amplitudes of the various periodic terms and uses relatively few constants. An example of a similar representation for the total mass density at a particular height and level of solar activity is given as well.
Modeling Very Oscillating Signals. Application to Image Processing
Aubert, Gilles Aujol, Jean-Francois
2005-03-15
This article is a companion paper of a previous work where we have developed the numerical analysis of a variational model first introduced by Rudin et al. and revisited by Meyer for removing the noise and capturing textures in an image. The basic idea in this model is to decompose an image f into two components (u + v) and then to search for (u,v) as a minimizer of an energy functional. The first component u belongs to BV and contains geometrical information, while the second one v is sought in a space G which contains signals with large oscillations, i.e. noise and textures. In Meyer carried out his study in the whole R{sup 2} and his approach is rather built on harmonic analysis tools. We place ourselves in the case of a bounded set{omega} of R{sup 2} which is the proper setting for image processing and our approach is based upon functional analysis arguments. We define in this context the space G, give some of its properties, and then study in this continuous setting the energy functional which allows us to recover the components u and v. We present some numerical experiments to show the relevance of the model for image decomposition and for image denoising.
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.
Low-noise sub-harmonic injection locked multiloop ring oscillator
NASA Astrophysics Data System (ADS)
Weilin, Xu; Di, Wu; Xueming, Wei; Baolin, Wei; Jihai, Duan; Fadi, Gui
2016-09-01
A three-stage differential voltage-controlled ring oscillator is presented for wide-tuning and low-phase noise requirement of clock and data recovery circuit in ultra wideband (UWB) wireless body area network. To improve the performance of phase noise of delay cell with coarse and fine frequency tuning, injection locked technology together with pseudo differential architecture are adopted. In addition, a multiloop is employed for frequency boosting. Two RVCOs, the standard RVCO without the IL block and the proposed IL RVCO, were fabricated in SMIC 0.18 μm 1P6M Salicide CMOS process. The proposed IL RVCO exhibits a measured phase noise of -112.37 dBc/Hz at 1 MHz offset from the center frequency of 1 GHz, while dissipating a current of 8 mA excluding the buffer from a 1.8-V supply voltage. It shows a 16.07 dB phase noise improvement at 1 MHz offset compared to the standard topology. Project supported by the National Natural Science Foundation of China (No. 61264001), the Guangxi Natural Science Foundation (Nos. 2013GXNSFAA019333, 2015GXNSFAA139301, 2014GXNSFAA118386), the Graduate Education Innovation Program of GUET (No. GDYCSZ201457), the Project of Guangxi Education Department (No. LD14066B) and the High-Level-Innovation Team and Outstanding Scholar Project of Guangxi Higher Education Institutes.
Nicu, Valentin Paul
2016-08-03
Motivated by the renewed interest in the coupled oscillator (CO) model for VCD, in this work a generalised coupled oscillator (GCO) expression is derived by introducing the concept of a coupled oscillator origin. Unlike the standard CO expression, the GCO expression is exact within the harmonic approximation. Using two illustrative example molecules, the theoretical concepts introduced here are demonstrated by performing a GCO decomposition of the rotational strengths computed using DFT. This analysis shows that: (1) the contributions to the rotational strengths that are normally neglected in the standard CO model can be comparable to or larger than the CO contribution, and (2) the GCO mechanism introduced here can affect the VCD intensities of all types of modes in symmetric and asymmetric molecules.
Braun, J; Buntkowsky, G; Bernarding, J; Tolxdorff, T; Sack, I
2001-06-01
New methods for simulating and analyzing Magnetic Resonance Elastography (MRE) images are introduced. To simulate a two-dimensional shear wave pattern, the wave equation is solved for a field of coupled harmonic oscillators with spatially varying coupling and damping coefficients in the presence of an external force. The spatial distribution of the coupling and the damping constants are derived from an MR image of the investigated object. To validate the simulation as well as to derive the elasticity modules from experimental MRE images, the wave patterns are analyzed using a Local Frequency Estimation (LFE) algorithm based on Gauss filter functions with variable bandwidths. The algorithms are tested using an Agar gel phantom with spatially varying elasticity constants. Simulated wave patterns and LFE results show a high agreement with experimental data. Furthermore, brain images with estimated elasticities for gray and white matter as well as for exemplary tumor tissue are used to simulate experimental MRE data. The calculations show that already small distributions of pathologically changed brain tissue should be detectable by MRE even within the limit of relatively low shear wave excitation frequency around 0.2 kHz.
Jakas, M. M.; Perez de la Rosa, F. J.; Custidiano, E. R.
2003-09-01
The accuracy of Bohr's and more recent analytical calculations of the electronic stopping of heavy charges by a classical harmonic oscillator is analyzed. According to results in this paper, for |{xi}|{>=}100 ({xi} being the Bohr stopping parameter) the present simulations agree with previous theoretical calculations, whereas for smaller |{xi}| values, discrepancies are evident. In fact, for |{xi}|<100 the stopping cross section seems to be sensitive to the sign of the ion charge. The so-called Barkas effect is unambiguously observed and positively charged projectiles appear to have a larger stopping compared to that of negative ones at the same {xi}. Bohr's calculations, however, seem to reproduce the stopping of negative charges relatively well, but those of positive ions are consequently underestimated. By giving the electron an initial velocity, the so-called inner-shell effect on the stopping can be readily studied. The present simulations show that previous analytical predictions of this effect do not account for the present results.
NASA Astrophysics Data System (ADS)
Ivanovich Aptekarev, Alexander; Nikolaevich Tulyakov, Dmitry; Valero Toranzo, Irene; Sanchez Dehesa, Jesús
2016-03-01
The Rényi entropies Rp [ ρ ], p> 0, ≠ 1 of the highly-excited quantum states of the D-dimensional isotropic harmonic oscillator are analytically determined by use of the strong asymptotics of the orthogonal polynomials which control the wavefunctions of these states, the Laguerre polynomials. This Rydberg energetic region is where the transition from classical to quantum correspondence takes place. We first realize that these entropies are closely connected to the entropic moments of the quantum-mechanical probability ρn(r) density of the Rydberg wavefunctions Ψn,l, { μ }(r); so, to the ℒp-norms of the associated Laguerre polynomials. Then, we determine the asymptotics n → ∞ of these norms by use of modern techniques of approximation theory based on the strong Laguerre asymptotics. Finally, we determine the dominant term of the Rényi entropies of the Rydberg states explicitly in terms of the hyperquantum numbers (n,l), the parameter order p and the universe dimensionality D for all possible cases D ≥ 1. We find that (a) the Rényi entropy power decreases monotonically as the order p is increasing and (b) the disequilibrium (closely related to the second order Rényi entropy), which quantifies the separation of the electron distribution from equiprobability, has a quasi-Gaussian behavior in terms of D.
NASA Astrophysics Data System (ADS)
Aptekarev, Alexander Ivanovich; Tulyakov, Dmitry Nikolaevich; Toranzo, Irene Valero; Dehesa, Jesús Sanchez
2016-03-01
The Rényi entropies R p [ ρ ], p> 0, ≠ 1 of the highly-excited quantum states of the D-dimensional isotropic harmonic oscillator are analytically determined by use of the strong asymptotics of the orthogonal polynomials which control the wavefunctions of these states, the Laguerre polynomials. This Rydberg energetic region is where the transition from classical to quantum correspondence takes place. We first realize that these entropies are closely connected to the entropic moments of the quantum-mechanical probability ρ n (r) density of the Rydberg wavefunctions Ψ n,l, { μ }(r); so, to the ℒ p -norms of the associated Laguerre polynomials. Then, we determine the asymptotics n → ∞ of these norms by use of modern techniques of approximation theory based on the strong Laguerre asymptotics. Finally, we determine the dominant term of the Rényi entropies of the Rydberg states explicitly in terms of the hyperquantum numbers (n,l), the parameter order p and the universe dimensionality D for all possible cases D ≥ 1. We find that (a) the Rényi entropy power decreases monotonically as the order p is increasing and (b) the disequilibrium (closely related to the second order Rényi entropy), which quantifies the separation of the electron distribution from equiprobability, has a quasi-Gaussian behavior in terms of D.
NASA Astrophysics Data System (ADS)
Liu, Yongfang; Zhao, Yu; Chen, Guanrong
2016-11-01
This paper studies the distributed consensus and containment problems for a group of harmonic oscillators with a directed communication topology. First, for consensus without a leader, a class of distributed consensus protocols is designed by using motion planning and Pontryagin's principle. The proposed protocol only requires relative information measurements at the sampling instants, without requiring information exchange over the sampled interval. By using stability theory and the properties of stochastic matrices, it is proved that the distributed consensus problem can be solved in the motion planning framework. Second, for the case with multiple leaders, a class of distributed containment protocols is developed for followers such that their positions and velocities can ultimately converge to the convex hull formed by those of the leaders. Compared with the existing consensus algorithms, a remarkable advantage of the proposed sampled-data-based protocols is that the sampling periods, communication topologies and control gains are all decoupled and can be separately designed, which relaxes many restrictions in controllers design. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.
Liu, Yongfang; Zhao, Yu; Chen, Guanrong
2016-11-01
This paper studies the distributed consensus and containment problems for a group of harmonic oscillators with a directed communication topology. First, for consensus without a leader, a class of distributed consensus protocols is designed by using motion planning and Pontryagin's principle. The proposed protocol only requires relative information measurements at the sampling instants, without requiring information exchange over the sampled interval. By using stability theory and the properties of stochastic matrices, it is proved that the distributed consensus problem can be solved in the motion planning framework. Second, for the case with multiple leaders, a class of distributed containment protocols is developed for followers such that their positions and velocities can ultimately converge to the convex hull formed by those of the leaders. Compared with the existing consensus algorithms, a remarkable advantage of the proposed sampled-data-based protocols is that the sampling periods, communication topologies and control gains are all decoupled and can be separately designed, which relaxes many restrictions in controllers design. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.
NASA Technical Reports Server (NTRS)
Weatherill, W. H.; Ehlers, F. E.; Yip, E.; Sebastian, J. D.
1980-01-01
Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.
Statistical model of clutter suppression in tissue harmonic imaging.
Yan, Xiang; Hamilton, Mark F
2011-03-01
A statistical model is developed for the suppression of clutter in tissue harmonic imaging (THI). Tissue heterogeneity is modeled as a random phase screen that is characterized by its correlation length and variance. With the autocorrelation function taken to be Gaussian and for small variance, statistical solutions are derived for the mean intensities at the fundamental and second-harmonic frequencies in the field of a focused sound beam that propagates through the phase screen. The statistical solutions are verified by comparison with ensemble averaging of direct numerical simulations. The model demonstrates that THI reduces the aberration clutter appearing in the focal region regardless of the depth of the aberrating layer, with suppression of the clutter most effective when the layer is close to the source. The model is also applied to the reverberation clutter that is transmitted forward along the axis of the beam. As with aberration clutter, suppression of such reverberation clutter by THI is most pronounced when the tissue heterogeneity is located close to the source.
Noguera, Norman; Rózga, Krzysztof
2015-07-15
In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case of a slightly more general potential than the one for harmonic oscillator.
NASA Astrophysics Data System (ADS)
Graham Hoover, William; Clinton Sprott, Julien; Griswold Hoover, Carol
2016-10-01
We describe the application of adaptive (variable time step) integrators to stiff differential equations encountered in many applications. Linear harmonic oscillators subject to nonlinear thermal constraints can exhibit either stiff or smooth dynamics. Two closely related examples, Nosé's dynamics and Nosé-Hoover dynamics, are both based on Hamiltonian mechanics and generate microstates consistent with Gibbs' canonical ensemble. Nosé's dynamics is stiff and can present severe numerical difficulties. Nosé-Hoover dynamics, although it follows exactly the same trajectory, is smooth and relatively trouble-free. We emphasize the power of adaptive integrators to resolve stiff problems such as the Nosé dynamics for the harmonic oscillator. The solutions also illustrate the power of computer graphics to enrich numerical solutions.
Spherical Harmonics Functions Modelling of Meteorological Parameters in PWV Estimation
NASA Astrophysics Data System (ADS)
Deniz, Ilke; Mekik, Cetin; Gurbuz, Gokhan
2016-08-01
Aim of this study is to derive temperature, pressure and humidity observations using spherical harmonics modelling and to interpolate for the derivation of precipitable water vapor (PWV) of TUSAGA-Active stations in the test area encompassing 38.0°-42.0° northern latitudes and 28.0°-34.0° eastern longitudes of Turkey. In conclusion, the meteorological parameters computed by using GNSS observations for the study area have been modelled with a precision of ±1.74 K in temperature, ±0.95 hPa in pressure and ±14.88 % in humidity. Considering studies on the interpolation of meteorological parameters, the precision of temperature and pressure models provide adequate solutions. This study funded by the Scientific and Technological Research Council of Turkey (TUBITAK) (The Estimation of Atmospheric Water Vapour with GPS Project, Project No: 112Y350).
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.
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.
Memcapacitor model and its application in chaotic oscillator with memristor
NASA Astrophysics Data System (ADS)
Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching
2017-01-01
Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.
Memcapacitor model and its application in chaotic oscillator with memristor.
Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching
2017-01-01
Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.
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.
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.
Farner, Snorre; Vergez, Christophe; Kergomard, Jean; Lizée, Aude
2006-03-01
The harmonic balance method (HBM) was originally developed for finding periodic solutions of electronical and mechanical systems under a periodic force, but has been adapted to self-sustained musical instruments. Unlike time-domain methods, this frequency-domain method does not capture transients and so is not adapted for sound synthesis. However, its independence of time makes it very useful for studying any periodic solution, whether stable or unstable, without care of particular initial conditions in time. A computer program for solving general problems involving nonlinearly coupled exciter and resonator, HARMBAL, has been developed based on the HBM. The method as well as convergence improvements and continuation facilities are thoroughly presented and discussed in the present paper. Applications of the method are demonstrated, especially on problems with severe difficulties of convergence: the Helmholtz motion (square signals) of single-reed instruments when no losses are taken into account, the reed being modeled as a simple spring.
An electric-field representation of the harmonic XY model
NASA Astrophysics Data System (ADS)
Faulkner, Michael F.; Bramwell, Steven T.; Holdsworth, Peter C. W.
2017-03-01
The two-dimensional harmonic XY (HXY) model is a spin model in which the classical spins interact via a piecewise parabolic potential. We argue that the HXY model should be regarded as the canonical classical lattice spin model of phase fluctuations in two-dimensional condensates, as it is the simplest model that guarantees the modular symmetry of the experimental systems. Here we formulate a lattice electric-field representation of the HXY model and contrast this with an analogous representation of the Villain model and the two-dimensional Coulomb gas with a purely rotational auxiliary field. We find that the HXY model is a spin-model analogue of a lattice electric-field model of the Coulomb gas with an auxiliary field, but with a temperature-dependent vacuum (electric) permittivity that encodes the coupling of the spin vortices to their background spin-wave medium. The spin vortices map to the Coulomb charges, while the spin-wave fluctuations correspond to auxiliary-field fluctuations. The coupling explains the striking differences in the high-temperature asymptotes of the specific heats of the HXY model and the Coulomb gas with an auxiliary field. Our results elucidate the propagation of effective long-range interactions throughout the HXY model (whose interactions are purely local) by the lattice electric fields. They also imply that global spin-twist excitations (topological-sector fluctuations) generated by local spin dynamics are ergodically excluded in the low-temperature phase. We discuss the relevance of these results to condensate physics.
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.
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.
A three-pulse model of d. c. side harmonic flow in HVDC systems
Shore, N.L.; Andersson, G.; Canelhas, A.P.; Asplund, G.
1989-07-01
A new model for analysis of d.c. side harmonics in HVDC systems is proposed. The model includes the stray capacitances of converter transformers and bushings and represents the 12-pulse converter as four three-pulse harmonic voltage sources. The appearance of ground mode triplen harmonics of troublesome magnitude in pole and electrode lines, as noted in recent site measurements, is explained, as is the increase in magnitude of the characteristic 12-pulse harmonics. The consequences for d.c. filter design and the specification of telephone interference criteria are also discussed.
Finite element modeling of the higher harmonic controlled OH-6A helicopter airframe
NASA Technical Reports Server (NTRS)
Ferg, Douglas; Toossi, Mostafa
1990-01-01
An MSC/NASTRAN finite element model of the higher harmonic control configured OH-6A helicopter fuselage was developed. This finite element model was verified by performing various model checkouts and correlation with results from a ground vibration test.
TDH solution of the Suzuki model of nuclear monopole oscillation
NASA Astrophysics Data System (ADS)
Skalski, J.
1987-09-01
The exact time-dependent Hartree solution of the schematic model describing nuclear monopole oscillation — the Suzuki model — is presented. The energies of vibrational states are quantized according to the gauge-invariant periodic quantization prescription.
Ingold, Kirk A; Marandi, Alireza; Digonnet, Michel J F; Byer, Robert L
2015-09-15
We demonstrate a femtosecond fiber-feedback optical parametric oscillator (OPO) at degeneracy. The OPO cavity comprises an 80-cm-long fiber composed of a combination of normal and anomalous dispersion sections that provide a net intracavity group delay dispersion close to zero. By using a mode-locked, Yb-doped fiber laser as the pump, we achieved half-harmonic generation of 250-MHz, 1.2-nJ nearly transform-limited 97-fs pulses centered at 2090 nm with a total conversion efficiency of 36%.
NASA Astrophysics Data System (ADS)
Sobhani, Hadi; Hassanabadi, Hassan
2016-08-01
This paper contains study of Bohr Hamiltonian considering time-dependent form of two important and famous nuclear potentials and harmonic oscillator. Dependence on time in interactions is considered in general form. In order to investigate this system, a powerful mathematical method has been employed, so-called Lewis-Riesenfeld dynamical invariant method. Appropriate dynamical invariant for considered system has been constructed. Then its eigen functions and the wave function are derived. At the end, we discussed about physical meaning of the results.
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.
Third Harmonic Mechanism in Complex Plasmonic Fano Structures.
Metzger, Bernd; Schumacher, Thorsten; Hentschel, Mario; Lippitz, Markus; Giessen, Harald
2014-06-18
We perform third harmonic spectroscopy of dolmen-type nanostructures, which exhibit plasmonic Fano resonances in the near-infrared. Strong third harmonic emission is predominantly radiated close to the low energy peak of the Fano resonance. Furthermore, we find that the third harmonic polarization of the subradiant mode interferes destructively and diminishes the nonlinear signal in the far-field. By comparing the experimental third harmonic spectra with finite element simulations and an anharmonic oscillator model, we find strong indications that the source of the third harmonic is the optical nonlinearity of the bare gold enhanced by the resonant plasmonic polarization.
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.
Transonic limit cycle oscillation analysis using reduced order aerodynamic models
NASA Astrophysics Data System (ADS)
Dowell, E. H.; Thomas, J. P.; Hall, K. C.
2004-01-01
Limit cycle oscillations have been observed in flight operations of modern aircraft, wind tunnel experiments and mathematical models. Both fluid and structural nonlinearities are thought to contribute to these phenomena. With recent advances in reduced order aerodynamic modeling, it is now feasible to analyze limit cycle oscillations that may occur in transonic flow including the effects of structural and fluid nonlinearities. In this paper an airfoil with control surface freeplay (a common structural nonlinearity) is used to investigate transonic flutter and limit cycle oscillations. The reduced order aerodynamic model used in this paper assumes the shock motion is small and in proportion to the structural motions.
Emergence of coherent oscillations in stochastic models for circadian rhythms
NASA Astrophysics Data System (ADS)
Gonze, Didier; Halloy, José; Goldbeter, Albert
2004-10-01
Most living organisms have developed the capability of generating autonomously sustained oscillations with a period close to 24 h. The mechanism responsible for these circadian rhythms relies on the negative regulation exerted by a protein on the expression of its own gene. Deterministic models for circadian rhythms account for the occurrence of autonomous oscillations of the limit cycle type, for their entrainment by light-dark cycles, and for their phase shifting by light pulses. Such models, however, do not take into consideration the molecular fluctuations which arise when the number of molecules involved in the regulatory mechanism is low. Here we resort to a stochastic description of a core model for circadian rhythms to study the emergence of coherent oscillations in gene expression in the presence of molecular noise. We show that despite the “bar code” pattern of gene activation, robust circadian oscillations can be observed. Simulations of the deterministic, fully developed version of the circadian model indicate, however, that sustained oscillations only emerge above a critical value of the rate constants characterizing the reversible binding of repressor to the gene, while below this value the system evolves towards an excitable steady state. This explains why, depending on whether or not the critical value of these rate constants is exceeded, stochastic simulations of the model produce coherent oscillations or very noisy oscillations with a highly variable period.
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
NASA Astrophysics Data System (ADS)
Wang, Chen-Wen; Yang, Ling; Zhu, Chaoyuan; Yu, Jian-Guo; Lin, Sheng-Hsien
2014-08-01
Damped harmonic oscillators are utilized to calculate Franck-Condon factors within displaced harmonic oscillator approximation. This is practically done by scaling unperturbed Hessian matrix that represents local modes of force constants for molecule in gaseous phase, and then by diagonalizing perturbed Hessian matrix it results in direct modification of Huang-Rhys factors which represent normal modes of solute molecule perturbed by solvent environment. Scaling parameters are empirically introduced for simulating absorption and fluorescence spectra of an isolated solute molecule in solution. The present method is especially useful for simulating vibronic spectra of polycyclic aromatic hydrocarbon molecules in which hydrogen atom vibrations in solution can be scaled equally, namely the same scaling factor being applied to all hydrogen atoms in polycyclic aromatic hydrocarbons. The present method is demonstrated in simulating solvent enhanced X 1Ag ↔ A1B1u absorption and fluorescence spectra of perylene (medium-sized polycyclic aromatic hydrocarbon) in benzene solution. It is found that one of six active normal modes v10 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.
Excitable Oscillators as Models for Central Pattern Generators
NASA Astrophysics Data System (ADS)
Taylor, David; Holmes, Philip; Cohen, Avis H.
Chains of coupled oscillators have been used to model the central pattern generator for locomotion in lamprey1,2,3, as well as electrical waves in the mammalian small intestine4. In this paper we examine a variation on the equations for the coupled oscillators used in a number of these papers. In particular, we investigate the effect of modeling the uncoupled oscillators as excitable. The motivation behind this is that it may provide some insight into the electrical activity of the lamprey spinal cord with brainstem attached5
Synchronized oscillations in a mathematical model of segmentation in zebrafish
NASA Astrophysics Data System (ADS)
Liao, Kang-Ling; Shih, Chih-Wen; Tseng, Jui-Pin
2012-04-01
Somitogenesis is a process for the development of somites which are transient, segmental structures that lie along the anterior-posterior axis of vertebrate embryos. The pattern of somites is governed by the segmentation clock and its timing is controlled by the clock genes which undergo synchronous oscillation over adjacent cells in the posterior presomitic mesoderm (PSM). In this paper, we analyze a mathematical model which depicts the kinetics of the zebrafish segmentation clock genes subject to direct autorepression by their own products under time delay, and cell-to-cell interaction through Delta-Notch signalling. Our goal is to elucidate how synchronous oscillations are generated for the cells in the posterior PSM, and how oscillations are arrested for the cells in the anterior PSM. For this system of delayed equations, an iteration technique is employed to derive the global convergence to the synchronous equilibrium, which corresponds to the oscillation-arrested. By applying the delay Hopf bifurcation theory and the center manifold theorem, we derive the criteria for the existence of stable synchronous oscillations for the cells at the tail bud of the PSM. Our analysis provides the basic parameter ranges and delay magnitudes for stable synchronous, asynchronous oscillation and oscillation-arrested. We exhibit how synchronous oscillations are affected by the degradation rates and delays. Extended from the analytic theory, further numerical findings linked to the segmentation process are presented.
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.
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.
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.
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
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.
NASA Astrophysics Data System (ADS)
Tay, Buang Ann
The eigenvalue problem of Kossakowski-Linblad's kinetic equation associated with the reduced density matrix of a harmonic oscillator interacting with a thermal bath in equilibrium is solved. The solution gives rise to a complete orthogonal eigenbasis endowed with Hilbert space structure that has a weighted norm. We find that the eigenfunctions at finite temperature can be obtained from the eigenfunction at zero temperature through a hyperbolic rotation on the position variables. This transformation enables the extension of the simple harmonic oscillator density matrix to that of a finite temperature. We further investigate the decay of these extended states under our dissipative kinetic equation. Furthermore, the Hilbert space structure enables the proof of a H -theorem in this system. We apply the eigenbasis expansion of an initial state to analyze decoherence as well as coherence processes. We find that coherence process occurs at a longer time scale compared to decoherence process. The time scales of both processes are estimated with the eigenbasis expansion. In the same way we analyze the evolution of the coherent state. We show that in addition to the ordinary decay time, we found another time scale which is defined by the time when the motion of the peak of the coherent state become comparative to the width of the coherent state. In contrast to the ordinary decay time this new relaxation time depends on the initial value of the momentum of the oscillator. We also find that our eigenbasis is applicable to a class of non-linear interactions, with a slight extension of the form of transport coefficients due to the non-linear interactions.
Rico, J.J.; Acha, E.; Miller, T.J.E.
1996-07-01
The main objective of this paper is to report on a newly developed three phase Thyristor Controlled Reactor (TCR) model which is based on the use of harmonic switching vectors and discrete convolutions. This model is amenable to direct frequency domain operations and provides a fast and reliable means for assessing 6- and 12-pulse TCR plant performance at harmonic frequencies. The use of alternate time domain and frequency domain representations is avoided as well as the use of FFTs. In this approach, each single phase unit of the TCR is modelled as a voltage-dependent harmonic Norton equivalent where all the harmonics and cross-couplings between harmonics are explicitly shown. This model is suitable for direct incorporation into the harmonic domain frame of reference where all the busbars, phases, harmonics and cross-couplings between harmonics are combined together for a unified iterative solution through a Newton-Raphson technique exhibiting quadratic convergence.
Testing solar models with global solar oscillations in the 5-minute band
NASA Technical Reports Server (NTRS)
Ulrich, R. K.; Rhodes, E. J., Jr.
1983-01-01
Frequencies of solar oscillation for normal modes described by spherical harmonics with l-values between 0 and 4 are computed. The method of computation is discussed and some of the theoretical uncertainties are examined. It is shown that the standard solar model has eigenfrequencies which do not agree with the frequencies observed for the low l-modes to within the estimated accuracy of either the observed or theoretical frequencies. Four non-standard models are considered: (1) the interior Z abundance is lower than the surface abundance; (2) the interior Z abundance is higher than the surface abundance; (3) the interior Z abundance is altered by mixing; and (4) a large primordial magnetic field remains in the solar core. The effect of all these models on the solar neutrino flux is considered, with the result that the high-Z model is rejected. The conclusions of Bahcall and Ulrich (1971) that a primordial magnetic field increases the neutrino flux are disputed.
Bierbach, Jana; Yeung, Mark; Eckner, Erich; ...
2015-05-01
Surface high-harmonic generation in the relativistic regime is demonstrated as a source of extreme ultra-violet (XUV) pulses with extended operation time. Relativistic high-harmonic generation is driven by a frequency-doubled high-power Ti:Sapphire laser focused to a peak intensity of 3·1019 W/cm2 onto spooling tapes. We demonstrate continuous operation over up to one hour runtime at a repetition rate of 1 Hz. Harmonic spectra ranging from 20 eV to 70 eV (62 nm to 18 nm) were consecutively recorded by an XUV spectrometer. An average XUV pulse energy in the µJ range is measured. With the presented setup, relativistic surface high-harmonic generationmore » becomes a powerful source of coherent XUV pulses that might enable applications in, e.g. attosecond laser physics and the seeding of free-electron lasers, when the laser issues causing 80-% pulse energy fluctuations are overcome.« less
Ikuma, Takeshi; Kunduk, Melda; McWhorter, Andrew J
2012-09-01
High-speed videoendoscopy (HSV) enables the observation and measurement of vibratory behaviors of vocal folds by capturing the laryngeal imagery at high frame rates. The frame rates of commercially available HSVs, however, are still limited to carry out sample-based time-domain objective analyses. To mitigate the resulting lack of temporal resolution, existing studies have employed sum-of-harmonics parametric models to evaluate temporal vocal-fold behaviors. This paper focuses on the other weakness of HSV: its inherent susceptibility to temporal aliasing. Aliasing occurs when there are substantial harmonics above the Nyquist frequency of the HSV camera, and video cameras offer very little means to filter out these harmonics. Although the aliasing effect in HSV data minimally affects many of the laryngeal objective parameter measurements, some parameters, such as harmonics-to-noise ratio and derivative-based parameters, are sensitive to the aliased content. The use of a parametric model with a careful selection of the number of harmonics enables classification of the aliased harmonics as a part of the harmonic signal. Glottal area waveform examples are included to illustrate the modeling capability for cases of normal and disordered vocal folds.
Oscillation characteristics of endodontic files: numerical model and its validation.
Verhaagen, Bram; Lea, Simon C; de Bruin, Gerrit J; van der Sluis, Luc W M; Walmsley, A Damien; Versluis, Michel
2012-11-01
During a root canal treatment, an antimicrobial fluid is injected into the root canal to eradicate all bacteria from the root canal system. Agitation of the fluid using an ultrasonically vibrating miniature file results in a significant improvement in the cleaning efficacy over conventional syringe irrigation. Numerical analysis of the oscillation characteristics of the file, modeled as a tapered, driven rod, shows a sinusoidal wave pattern with an increase in amplitude and decrease in wavelength toward the free end of the file. Measurements of the file oscillation with a scanning laser vibrometer show good agreement with the numerical simulation. The numerical model of endodontic file oscillation has the potential for predicting the oscillation pattern and fracture likeliness of various file types and the acoustic streaming they induce during passive ultrasonic irrigation.
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.
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.
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.
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.
Analysis of harmonic spline gravity models for Venus and Mars
NASA Technical Reports Server (NTRS)
Bowin, Carl
1986-01-01
Methodology utilizing harmonic splines for determining the true gravity field from Line-Of-Sight (LOS) acceleration data from planetary spacecraft missions was tested. As is well known, the LOS data incorporate errors in the zero reference level that appear to be inherent in the processing procedure used to obtain the LOS vectors. The proposed method offers a solution to this problem. The harmonic spline program was converted from the VAX 11/780 to the Ridge 32C computer. The problem with the matrix inversion routine that improved inversion of the data matrices used in the Optimum Estimate program for global Earth studies was solved. The problem of obtaining a successful matrix inversion for a single rev supplemented by data for the two adjacent revs still remains.
NASA Astrophysics Data System (ADS)
Ayvaz, Muzaffer; Demiralp, Metin
2011-09-01
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.
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.
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.
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…
NASA Astrophysics Data System (ADS)
Truong, D. D.; Fonck, R. J.; McKee, G. R.; Yan, Z.; Grierson, B. A.
2016-10-01
The UF-CHERS (Ultra Fast CHarge Exchange Recombination Spectroscopy) diagnostic at DIII-D measures local, long-wavelength ion temperature and toroidal velocity fluctuations at turbulence-relevant spatiotemporal scales from emission of the CVI n=8 ->7 transition. During Quiescent H-mode (QH-mode) plasmas, which offer ELM-free improved confinement, UF-CHERS measurements observed coherent, low frequency (fo 10kHz) pedestal oscillations in Ti and vtor at the Edge Harmonic Oscillation (EHO) frequency while several modes between 35-75 kHz are suppressed when the EHO appears. Although broadband ion temperature and density fluctuations were reduced by the EHO, the toroidal rotation showed increased fluctuation amplitude. Investigating ion temperature and toroidal fluctuations associated with the EHO may provide insights into the saturated instability driving the EHO. Supported by DOE Grants DE-FG02-08ER54999, DE-FC02-04ER54698, and NSF GRFP Grant DGE-1256259.
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.
Nonequilibrium simulations of model ionomers in an oscillating electric field
Ting, Christina L.; Sorensen-Unruh, Karen E.; Stevens, Mark J.; ...
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.
2016-07-25
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 understood by comparison with relevant time scales in the systems, obtained from independent calculations.
Nonequilibrium simulations of model ionomers in an oscillating electric field
NASA Astrophysics Data System (ADS)
Ting, Christina L.; Sorensen-Unruh, Karen E.; Stevens, Mark J.; Frischknecht, Amalie L.
2016-07-01
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.
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.
Kurihara, Eru; Hay, Todd A.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.
2011-01-01
Interaction between acoustically driven or laser-generated bubbles causes the bubble surfaces to deform. Dynamical equations describing the motion of two translating, nominally spherical bubbles undergoing small shape oscillations in a viscous liquid are derived using Lagrangian mechanics. Deformation of the bubble surfaces is taken into account by including quadrupole and octupole perturbations in the spherical-harmonic expansion of the boundary conditions on the bubbles. Quadratic terms in the quadrupole and octupole amplitudes are retained, and surface tension and shear viscosity are included in a consistent manner. A set of eight coupled second-order ordinary differential equations is obtained. Simulation results, obtained by numerical integration of the model equations, exhibit qualitative agreement with experimental observations by predicting the formation of liquid jets. Simulations also suggest that bubble-bubble interactions act to enhance surface mode instability. PMID:22088009
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).
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.
Homodyne detection of short-range Doppler radar using a forced oscillator model
Kittipute, Kunanon; Saratayon, Peerayudh; Srisook, Suthasin; Wardkein, Paramote
2017-01-01
This article presents the homodyne detection in a self-oscillation system, which represented by a short-range radar (SRR) circuit, that is analysed using a multi-time forced oscillator (MTFO) model. The MTFO model is based on a forced oscillation perspective with the signal and system theory, a second-order differential equation, and the multiple time variable technique. This model can also apply to analyse the homodyne phenomenon in a difference kind of the oscillation system under same method such as the self-oscillation system, and the natural oscillation system with external forced. In a free oscillation system, which forced by the external source is represented by a pendulum with an oscillating support experiment, and a modified Colpitts oscillator circuit in the UHF band with input as a Doppler signal is a representative of self-oscillation system. The MTFO model is verified with the experimental result, which well in line with the theoretical analysis. PMID:28252000
Homodyne detection of short-range Doppler radar using a forced oscillator model
NASA Astrophysics Data System (ADS)
Kittipute, Kunanon; Saratayon, Peerayudh; Srisook, Suthasin; Wardkein, Paramote
2017-03-01
This article presents the homodyne detection in a self-oscillation system, which represented by a short-range radar (SRR) circuit, that is analysed using a multi-time forced oscillator (MTFO) model. The MTFO model is based on a forced oscillation perspective with the signal and system theory, a second-order differential equation, and the multiple time variable technique. This model can also apply to analyse the homodyne phenomenon in a difference kind of the oscillation system under same method such as the self-oscillation system, and the natural oscillation system with external forced. In a free oscillation system, which forced by the external source is represented by a pendulum with an oscillating support experiment, and a modified Colpitts oscillator circuit in the UHF band with input as a Doppler signal is a representative of self-oscillation system. The MTFO model is verified with the experimental result, which well in line with the theoretical analysis.
Nonlinear oscillations in a muscle pacemaker cell model
NASA Astrophysics Data System (ADS)
González-Miranda, J. M.
2017-02-01
This article presents a numerical simulation study of the nonlinear oscillations displayed by the Morris-Lecar model [Biophys. J. 35 (1981) 193] for the oscillations experimentally observed in the transmembrane potential of a muscle fiber subject to an external electrical stimulus. We consider the model in the case when there is no external stimulation, aiming to establish the ability of the model to display biophysically reasonable pacemaker dynamics. We obtain 2D bifurcation diagrams showing that indeed the model presents oscillatory dynamics, displaying the two main types of action potentials that are observed in muscle fibers. The results obtained are shown to be structurally stable; that is, robust against changes in the values of system parameters. Moreover, it is demonstrated how the model is appropriate to analyze the action potentials observed in terms of the transmembrane currents creating them.
Method of Harmonic Balance in Full-Scale-Model Tests of Electrical Devices
NASA Astrophysics Data System (ADS)
Gorbatenko, N. I.; Lankin, A. M.; Lankin, M. V.
2017-01-01
Methods for determining the weber-ampere characteristics of electrical devices, one of which is based on solution of direct problem of harmonic balance and the other on solution of inverse problem of harmonic balance by the method of full-scale-model tests, are suggested. The mathematical model of the device is constructed using the describing function and simplex optimization methods. The presented results of experimental applications of the method show its efficiency. The advantage of the method is the possibility of application for nondestructive inspection of electrical devices in the processes of their production and operation.
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.
Multivariable Harmonic Balance for Central Pattern Generators.
Iwasaki, Tetsuya
2008-12-01
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.
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.
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.
NASA Astrophysics Data System (ADS)
Jia, Ji; Shangguan, Zhichun; Li, Haihong; Wu, Ye; Liu, Weiqing; Xiao, Jinghua; Kurths, Jürgen
2016-11-01
Upside-down bottles containing water which are common in our daily life exhibit rich vibration dynamics. Rich dynamic regimes are observed in bottle oscillators by directly measuring the pressure difference between inside and outside of a bottle with the aid of pressure sensors. We observe experimentally that an asymmetrical oscillation process between the outflow of water and the inflow of air is formed in a single bottle oscillator and, in addition, a kind of 2:1 frequency synchronization occurs in a coupled system of two non-identical bottle oscillators. The peak values of the oscillation of pressure differences between inside and outside of the bottle decease as the height of the liquid surface steps down, while the oscillation period increases gradually. The theoretical model of the oscillator is amended to understand the regimes in the experiment by introducing time-dependent parameters related to the asymmetrical oscillation processes. Our numerical results based on the model fit well with the experimental ones.
Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.; Kunold, A.
2015-11-15
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. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a
Extracting harmonic signal from a chaotic background with local linear model
NASA Astrophysics Data System (ADS)
Li, Chenlong; Su, Liyun
2017-02-01
In this paper, the problems of blind detection and estimation of harmonic signal in strong chaotic background are analyzed, and new methods by using local linear (LL) model are put forward. The LL model has been exhaustively researched and successfully applied for fitting and forecasting chaotic signal in many chaotic fields. We enlarge the modeling capacity substantially. Firstly, we can predict the short-term chaotic signal and obtain the fitting error based on the LL model. Then we detect the frequencies from the fitting error by periodogram, a property on the fitting error is proposed which has not been addressed before, and this property ensures that the detected frequencies are similar to that of harmonic signal. Secondly, we establish a two-layer LL model to estimate the determinate harmonic signal in strong chaotic background. To estimate this simply and effectively, we develop an efficient backfitting algorithm to select and optimize the parameters that are hard to be exhaustively searched for. In the method, based on sensitivity to initial value of chaos motion, the minimum fitting error criterion is used as the objective function to get the estimation of the parameters of the two-layer LL model. Simulation shows that the two-layer LL model and its estimation technique have appreciable flexibility to model the determinate harmonic signal in different chaotic backgrounds (Lorenz, Henon and Mackey-Glass (M-G) equations). Specifically, the harmonic signal can be extracted well with low SNR and the developed background algorithm satisfies the condition of convergence in repeated 3-5 times.
Unsteady Boundary Layer Due to an Oscillating Free Stream vs. an Oscillating Model.
1982-06-25
dimensional stagnation point flow generated by an infinite flat plate. A uniform flow, U., approaching a plane wall which oscillates with velocity, VP...for certain in-plane oscillations equivalent surface stress distributions are produced. One example of equivalent transverse oscillations is the two
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.
NASA Astrophysics Data System (ADS)
Mirzaeva, G.; Goodwin, G. C.
2015-07-01
Inverters play a central role in modern society including renewable energy integration and motor drives. Due to the inherent switched nature of the inverter waveforms harmonic distortion is an issue. Additionally, the switching patterns are perturbed by unavoidable switching delays. Amongst those, nonlinear and load-dependent switching delays (known as inverter 'dead-time delays') are the most difficult to compensate. In this paper, we propose a new approach to delay compensation and harmonic suppression in inverter voltage. The proposed approach is based on variable prediction horizon nonlinear model predictive control.
Novel harmonic regularization approach for variable selection in Cox's proportional hazards model.
Chu, Ge-Jin; Liang, Yong; Wang, Jia-Xuan
2014-01-01
Variable selection is an important issue in regression and a number of variable selection methods have been proposed involving nonconvex penalty functions. In this paper, we investigate a novel harmonic regularization method, which can approximate nonconvex Lq (1/2 < q < 1) regularizations, to select key risk factors in the Cox's proportional hazards model using microarray gene expression data. The harmonic regularization method can be efficiently solved using our proposed direct path seeking approach, which can produce solutions that closely approximate those for the convex loss function and the nonconvex regularization. Simulation results based on the artificial datasets and four real microarray gene expression datasets, such as real diffuse large B-cell lymphoma (DCBCL), the lung cancer, and the AML datasets, show that the harmonic regularization method can be more accurate for variable selection than existing Lasso series methods.
Dickmander, D.L.; Peterson, K.J.
1989-04-01
The harmonic analysis of the dc-side of an HVDC line transmission requires realistic models of the converters, the dc line, and other relevant equipment. These models must include all important paths for harmonic current, and appropriate sources of harmonic voltage generation. The classical converter modeling technique has been demonstrated to be insufficient in field measurements and analysis of the harmonic spectra found on recent HVDC line transmission. For this reason, a new model of the converter bridge which takes into account the major stray capacitances in the converter (the three-pulse model) has been developed, and is described in detail elsewhere. This paper presents comparisons between the classical and three-pulse calculations for the Intermountain Power Project (IPP) HVDC transmission. The calculation results from the three-pulse model agree favorably with the harmonics found in field measurements.
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
Harmonic balance optimization of terahertz Schottky diode multipliers using an advanced device model
NASA Technical Reports Server (NTRS)
Schlecht, E. T.; Chattopadhyay, G.; Maestrini, A.; Pukala, D.; Gill, J.; Mehdi, I.
2002-01-01
Substantial proress has been made recently in the advancement of solid state terahertz sources using chains of Schottky diode frequency multipliers. We have developed a harmonic balance simulator and corresponding diode model that incorporates many other factors participating in the diode behavior.
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).
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.
Issues in consumer exposure modeling: towards harmonization on a global scale.
Kephalopoulos, Stylianos; Bruinen de Bruin, Yuri; Arvanitis, Athanasios; Hakkinen, Pertti; Jantunen, Matti
2007-12-01
Understanding where and how chemicals are used throughout their life cycle is becoming increasingly important. In 2003, within the context of REACH and GPSD legislation, the European Commission started developing a European and global infrastructure of exposure methods and tools. The infrastructure aims (1) to link modeling tools and exposure-related data and scenarios in a single framework so that harmonized exposure assessment procedures can be developed for consumer products in the EU and (2) to make this framework flexible enough to allow global application. A number of issues are raised by a global infrastructure of consumer exposure modeling that answers to multi-legislative mandates. These include transparency, consistency, usability, and defensibility of the models, including the relevant degree of complexity for priority setting versus assessment. As part of the initiative to set up a harmonized global infrastructure on consumer exposure assessment, these issues were presented, discussed, and further developed in a series of European Commission-sponsored workshops organized in October 2004 and June 2005 as part of the "Harmonization of Consumer Exposure Models on a Global Scale" project. The project focused on development, harmonization, and validation of consumer exposure modeling approaches. The workshops included experts from the EU, USA, Japan, and Canada. The conclusions and recommendations made on the basis of this work are described. To help achieve harmonization of approaches, the European Commission's Joint Research Centre is proposing a framework (1) to compare information on elements of chemical risk assessment to understand exposure regulations in different countries, (2) to save time and expense by sharing information and models, and (3) to promote credible science through better communication among organizations and by peer review of assessments and assessment procedures.
Modelling of global boundary effects on harmonic motion imaging of soft tissues.
Zhao, Xiaodong; Pelegri, Assimina A
2014-01-01
Biomechanical imaging techniques have been developed for soft tissue characterisation and detection of breast tumours. Harmonic motion imaging (HMI) uses a focused ultrasound technology to generate a harmonic radiation force in a localised region inside a soft tissue. The resulting dynamic response is used to map the local distribution of the mechanical properties of the tissue. In this study, a finite element (FE) model is developed to investigate the effect of global boundary conditions on the dynamic response of a soft tissue during HMI. The direct-solution steady-state dynamic analysis procedure is used to compute the harmonic displacement amplitude in FE simulations. The model is parameterised in terms of boundary conditions and viscoelastic properties, and the corresponding raster-scan displacement amplitudes are captured to examine its response. The effect of the model's global dimensions on the harmonic response is also investigated. It is observed that the dynamic response of soft tissue with high viscosity is independent of the global boundary conditions for regions remote to the boundary; thus, it can be subjected to local analysis to estimate the underlying mechanical properties. However, the dynamic response is sensitive to global boundary conditions for tissue with low viscosity or regions located near to the boundary.
Development of a canine model for recurrent laryngeal injury by harmonic scalpel.
Lee, Kyu-Eun; Jee, Hyeon-Gun; Kim, Hoon-Yub; Park, Won-Seo; Park, Sung-Hye; Youn, Yeo-Kyu
2012-12-01
Various energy devices had been used in thyroid surgery. Aim of study is to develop canine model for recurrent laryngeal nerve injury by harmonic scalpel and to evaluate feasibility of using this model for evaluating the safety use of harmonic scalpel during thyroid surgery. Nine dogs were divided into 3 groups according to distance between harmonic scalpel application and recurrent laryngeal nerve; group 1 (1 mm), 2 (2 mm), and 3 (3 mm). Vocal cord function was assessed pre- and postoperatively using video laryngoscopy. Harmonic scalpel was applied adjacent to left recurrent laryngeal nerve and, two weeks later, right recurrent laryngeal nerve at assigned distances. Recurrent laryngeal nerves were evaluated for subacute and acute morphologic changes. Laryngoscopy demonstrated 3 abnormal vocal cords in group 1, 1 in group 2, and no in group 3 (P=0.020). Subacute histologic changes were observed in nerves with abnormal function. Acute histologic changes were observed 5/8 (62.5%) in group 1, 1/7 (14.3%) in group 2, and not in group 3. We developed canine model for recurrent laryngeal injury. The functional outcomes matched with the histologic changes. These warrant further study to determine the safety margin for energy device in vicinity of recurrent laryngeal nerve.
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...
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
Ferrohydrodynamic modeling of magnetic nanoparticle harmonic spectra for magnetic particle imaging
Dhavalikar, Rohan; Maldonado-Camargo, Lorena; Garraud, Nicolas; Rinaldi, Carlos
2015-01-01
Magnetic Particle Imaging (MPI) is an emerging imaging technique that uses magnetic nanoparticles as tracers. In order to analyze the quality of nanoparticles developed for MPI, a Magnetic Particle Spectrometer (MPS) is often employed. In this paper, we describe results for predictions of the nanoparticle harmonic spectra obtained in a MPS using three models: the first uses the Langevin function, which does not take into account finite magnetic relaxation; the second model uses the magnetization equation by Shliomis (Sh), which takes into account finite magnetic relaxation using a constant characteristic time scale; and the third model uses the magnetization equation derived by Martsenyuk, Raikher, and Shliomis (MRSh), which takes into account the effect of magnetic field magnitude on the magnetic relaxation time. We make comparisons between these models and with experiments in order to illustrate the effects of field-dependent relaxation in the MPS. The models results suggest that finite relaxation results in a significant drop in signal intensity (magnitude of individual harmonics) and in faster spectral decay. Interestingly, when field dependence of the magnetic relaxation time was taken into account, through the MRSh model, the simulations predict a significant improvement in the performance of the nanoparticles, as compared to the performance predicted by the Sh equation. The comparison between the predictions from models and experimental measurements showed excellent qualitative as well as quantitative agreement up to the 19th harmonic using the Sh and MRSh equations, highlighting the potential of ferrohydrodynamic modeling in MPI. PMID:26576063
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.
Oscillations in a size-structured prey-predator model.
Bhattacharya, Souvik; Martcheva, Maia
2010-11-01
This article introduces a predator-prey model with the prey structured by body size, based on reports in the literature that predation rates are prey-size specific. The model is built on the foundation of the one-species physiologically structured models studied earlier. Three types of equilibria are found: extinction, multiple prey-only equilibria and possibly multiple predator-prey coexistence equilibria. The stabilities of the equilibria are investigated. Comparison is made with the underlying ODE Lotka-Volterra model. It turns out that the ODE model can exhibit sustain oscillations if there is an Allee effect in the net reproduction rate, that is the net reproduction rate grows for some range of the prey's population size. In contrast, it is shown that the structured PDE model can exhibit sustain oscillations even if the net reproductive rate is strictly declining with prey population size. We find that predation, even size-non-specific linear predation can destabilize a stable prey-only equilibrium, if reproduction is size specific and limited to individuals of large enough size. Furthermore, we show that size-specific predation can also destabilize the predator-prey equilibrium in the PDE model. We surmise that size-specific predation allows for temporary prey escape which is responsible for destabilization in the predator-prey dynamics.
Development of QTc prolongation model incorporating circadian rhythm using harmonic model.
Back, Hyun-moon; Lee, Jong-Hwa; Yun, Hwi-yeol; Kwon, Kwang-il
2015-05-01
1. QT prolongation is one of the major safety tests used in the development of a new drug. The ICH guidelines for the evaluation of QT prolongation recommend the use of the in vitro hERG assay and the in vivo telemetry test. However, QT intervals change under normal conditions due to circadian rhythm and can affect the results of the tests. In this study, we developed a PK/PD model to describe the QT interval after the administration of astemizole allowing for the normal changes by circadian rhythm. 2. The typical PK parameters of absorption rate constant (ka), volume of distribution (Vc and Vm), metabolism (km), and elimination rate constant (kel and kel-m) were 0.49 h(-1), 4950 L, 20 L, 0.0127 h(-1), 0.0095 h(-1), and 0.95 h(-1), respectively. The final PK/PD model was the biophase model with the modified harmonic model. The typical PK/PD parameters, base QTc interval (QT0), amplitude (T1, T3), period of QTc interval changing (T2, T4), and EC50 were 233 ms, 3.31, 1.5, -9.24 h, 1.85 h, and 0.81 ng/ml, respectively. 3. The PK/PD model to explain the changes of the QT interval that allows normal changes in the circadian rhythm after the administration of astemizole was developed successfully. This final model can be applied to the development of a human model.
The zonal harmonic model of polarity transitions: A test using successive reversals
NASA Astrophysics Data System (ADS)
Theyer, F.; Herrero-Bervera, E.; Hsu, V.; Hammond, S. R.
1985-02-01
A recently developed zonal model for the last geomagnetic field reversal, which describes time- and latitude-dependent transitional behavior of intensity and inclination in terms of dominance of low-order field harmonics, was tested using a latitudinal and chronological succession of transition records. The primary data were derived from a high-resolution study of five Matuyama to Brunhes deep-sea cores collected along a 40° meridional band in the north-central Pacific. The transitions analyzed were the onsets and terminations of the Olduvai and Jaramaillo events and the Matuyama-Brunhes boundary. Supplementary data, published by previous workers, included a Jaramillo onset record from the southern Indian Ocean and a transition recorded in the Triassic Chugwater Formation of North America. In a general sense, the measured inclination and intensity records indicate the Jaramillo transitions and the last reversal to be remarkably similar to each other and to differ from the Olduvais. Crosscorrelation of the measured data sets with synthetic zonal harmonic records for the core latitudes indicates that the zonal harmonic model does predict the behavior of Matuyama-Brunhes reversal in the northern hemisphere. For the older reversals, however, the present model requires substantial modification. This is particularly so in the case of the Jaramillo onset: although two inclination and intensity records of this transition from northern and southern hemisphere sediments strongly resemble each other, the current model produces a synthetic record for one hemisphere that is incompatible with that hemisphere's measured data. Further, to model zonally the Olduvai reversals (for which a wide latitudinal northern hemisphere sampling was available), a substantially different ratio of low-order multipole components from that of the standard model is required, and the modeled solution was unsatisfactory at very low latitude. A modified zonal harmonic approach, which introduces a
Spherical harmonic modelling to ultra-high degree of Bouguer and isostatic anomalies
NASA Astrophysics Data System (ADS)
Balmino, G.; Vales, N.; Bonvalot, S.; Briais, A.
2012-07-01
The availability of high-resolution global digital elevation data sets has raised a growing interest in the feasibility of obtaining their spherical harmonic representation at matching resolution, and from there in the modelling of induced gravity perturbations. We have therefore estimated spherical Bouguer and Airy isostatic anomalies whose spherical harmonic models are derived from the Earth's topography harmonic expansion. These spherical anomalies differ from the classical planar ones and may be used in the context of new applications. We succeeded in meeting a number of challenges to build spherical harmonic models with no theoretical limitation on the resolution. A specific algorithm was developed to enable the computation of associated Legendre functions to any degree and order. It was successfully tested up to degree 32,400. All analyses and syntheses were performed, in 64 bits arithmetic and with semi-empirical control of the significant terms to prevent from calculus underflows and overflows, according to IEEE limitations, also in preserving the speed of a specific regular grid processing scheme. Finally, the continuation from the reference ellipsoid's surface to the Earth's surface was performed by high-order Taylor expansion with all grids of required partial derivatives being computed in parallel. The main application was the production of a 1' × 1' equiangular global Bouguer anomaly grid which was computed by spherical harmonic analysis of the Earth's topography-bathymetry ETOPO1 data set up to degree and order 10,800, taking into account the precise boundaries and densities of major lakes and inner seas, with their own altitude, polar caps with bedrock information, and land areas below sea level. The harmonic coefficients for each entity were derived by analyzing the corresponding ETOPO1 part, and free surface data when required, at one arc minute resolution. The following approximations were made: the land, ocean and ice cap gravity spherical
Modeling, simulation, and control of cavity flow oscillations
NASA Astrophysics Data System (ADS)
Rowley, Clarence W.
2002-09-01
This thesis involves the modeling of self-sustained oscillations in the flow past a rectangular cavity. The emphasis is on developing low-dimensional models that are suitable for analysis using tools from dynamical systems and control theory. Two-dimensional direct numerical simulations are performed, and indicate the presence of a "wake mode," which has been observed previously in experiments, but which is much less well understood than the "shear-layer mode" usually observed. We characterize the flow in both shear-layer mode and wake mode, and provide a criterion for predicting the onset of wake mode, as a function of the various geometrical and flow-related parameters. We focus on the modeling of shear-layer mode, and employ two distinct modeling approaches: first, we use the method of Proper Orthogonal Decomposition (POD) and Galerkin projection to reduce the Navier-Stokes equations to a low-dimensional system of ordinary differential equations (ODEs). We extend the method to compressible flows, using approximations that are valid for cold flows at moderate Mach number. In a compressible flow, both the kinematic and thermodynamic variables contribute to the total energy, and an inner product is introduced which respects this, and allows one to use vector-valued POD modes for the Galerkin projection, We obtain models in the form of ODEs with between 2 and 60 states, and compare models based on scalar-valued and vector-valued POD modes. All of the models work well for short times (a few periods of oscillation), but the models based on scalar-valued modes deviate for longer times, while in general the models based on vector-valued modes retain qualitatively correct dynamical behavior. In the second modeling approach, we model the underlying physical mechanisms separately (shear-layer amplification, acoustic scattering, acoustic propagation), and obtain linear models that are suitable for control design and analysis. We design a controller which stabilizes the
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
Effects of asymmetrical damping on a 2 DOF quarter-car model under harmonic excitation
NASA Astrophysics Data System (ADS)
Silveira, M.; Wahi, P.; Fernandes, J. C. M.
2017-02-01
The objective of this work is to study the dynamical behavior of vehicle suspension systems employing asymmetrical viscous damping, with a focus on improving passenger comfort. Previous studies have shown that the use of asymmetrical dampers in these types of systems can be advantageous with regard to comfort of the passengers. The modeling and the behavior of a quarter-car model with asymmetrical viscous damping under harmonic excitation is presented. The response is obtained with an analytical approximation via the method of Harmonic Balance. The choice of the asymmetry ratio diminishes the effects that the uneven road causes on the displacement and acceleration of the sprung mass. Although current systems usually adopt larger damping during the expansion phase, it is shown in this work that, for lower frequencies, smaller damping in this phase results in better comfort.
Generalized double-gradient model of flapping oscillations: Oblique waves
NASA Astrophysics Data System (ADS)
Korovinskiy, D. B.; Kiehas, S. A.
2016-09-01
The double-gradient model of flapping oscillations is generalized for oblique plane waves, propagating in the equatorial plane. It is found that longitudinal propagation (ky = 0) is prohibited, while transversal (kx = 0) or nearly transversal waves should possess a maximum frequency, diminishing with the reduction of | k y / k x | ratio. It turns out that the sausage mode may propagate in a narrow range of directions only, | k y / k x | ≫ 1 . A simple analytical expression for the dispersion relation of the kink mode, valid in most part of wave numbers range, | k y / k x | < 9 , is derived.
Reduction of the Gibbs Oscillation in Spectral Model Simulations.
NASA Astrophysics Data System (ADS)
Navapra, A.; Stern, W. F.; Miyakoda, K.
1994-08-01
Spectral atmospheric general circulation models (GCMS) have been used for many years for the simulation and prediction of the atmospheric circulation, and their value has been widely recognized. Over the years, however, some deficiencies have been noticed. One of the major drawbacks is the inability of the spectral spherical harmonies transform to represent discontinuous features, resulting in Gibbs oscillations. In particular, precipitation and cloud fields present annoying ripple patterns, which may obscure true drought episodes in climate runs. Other fields, such as the surface winds along the Andes, are also plagued by the fictitious oscillations. On the other hand, it is not certain to what extent the large-scale flow may be affected. An attempt is made in this paper to alleviate this problem by changing the spectral representation of the fields in the GCM. The technique is to apply various filters to reduce the Gibbs oscillations. Lanczos and Cesaro filters are tested for both one and two dimensions. In addition, for two-dimensional applications an isotropic filter is tested. This filter is based on the Cesaro summation principle with a constraint on the total wavenumber. At the end, two-dimensional physical space filters are proposed that can retain high-mountain peak values. Two applications of these filters are presented.In the first application the method is applied to the orography field by filtering out sharp gradients or discontinuities. The numerical results with this method show some improvement in the cloud and precipitation fields, along with some improvement of the surface wind pattern, resulting in an overall better simulation.In the second application, a Gibbs reduction technique is applied to the condensation process. In this paper the moist-adiabatic adjustment scheme is used for the cumulus parameterization, in addition to large-scale condensation. Numerical results with this method to reduce Gibbs oscillations due to condensation show some
Zhan, Meng; Liu, Shuai; He, Zhiwei
2013-01-01
The structure-dynamics-function has become one of central problems in modern sciences, and it is a great challenge to unveil the organization rules for different dynamical processes on networks. In this work, we study the vibration spectra of the classical mass spring model with different masses on complex networks, and pay our attention to how the mass spatial configuration influences the second-smallest vibrational frequency () and the largest one (). For random networks, we find that becomes maximal and becomes minimal if the node degrees are point-to-point-positively correlated with the masses. In these cases, we call it point-to-point matching. Moreover, becomes minimal under the condition that the heaviest mass is placed on the lowest-degree vertex, and is maximal as long as the lightest mass is placed on the highest-degree vertex, and in both cases all other masses can be arbitrarily settled. Correspondingly, we call it single-point matching. These findings indicate that the matchings between the node dynamics (parameter) and the node position rule the global systems dynamics, and sometimes only one node is enough to control the collective behaviors of the whole system. Therefore, the matching rules might be the common organization rules for collective behaviors on networks. PMID:24386088
Zhan, Meng; Liu, Shuai; He, Zhiwei
2013-01-01
The structure-dynamics-function has become one of central problems in modern sciences, and it is a great challenge to unveil the organization rules for different dynamical processes on networks. In this work, we study the vibration spectra of the classical mass spring model with different masses on complex networks, and pay our attention to how the mass spatial configuration influences the second-smallest vibrational frequency (ω2) and the largest one (ωN). For random networks, we find that ω2 becomes maximal and ωN becomes minimal if the node degrees are point-to-point-positively correlated with the masses. In these cases, we call it point-to-point matching. Moreover, ω2 becomes minimal under the condition that the heaviest mass is placed on the lowest-degree vertex, and ωN is maximal as long as the lightest mass is placed on the highest-degree vertex, and in both cases all other masses can be arbitrarily settled. Correspondingly, we call it single-point matching. These findings indicate that the matchings between the node dynamics (parameter) and the node position rule the global systems dynamics, and sometimes only one node is enough to control the collective behaviors of the whole system. Therefore, the matching rules might be the common organization rules for collective behaviors on networks.
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).
Simple membrane-based model of the Min oscillator
NASA Astrophysics Data System (ADS)
Petrášek, Zdeněk; Schwille, Petra
2015-04-01
Min proteins in E. coli bacteria organize into a dynamic pattern oscillating between the two cell poles. This process identifies the middle of the cell and enables symmetric cell division. In an experimental model system consisting of a flat membrane with effectively infinite supply of proteins and energy source, the Min proteins assemble into travelling waves. Here we propose a simple one-dimensional model of the Min dynamics that, unlike the existing models, reproduces the sharp decrease of Min concentration when the majority of protein detaches from the membrane, and even the narrow MinE maximum immediately preceding the detachment. The proposed model thus provides a possible mechanism for the formation of the MinE ring known from cells. The model is restricted to one dimension, with protein interactions described by chemical kinetics allowing at most bimolecular reactions, and explicitly considering only three, membrane-bound, species. The bulk solution above the membrane is approximated as being well-mixed, with constant concentrations of all species. Unlike other models, our proposal does not require autocatalytic binding of MinD to the membrane. Instead, it is assumed that two MinE molecules are necessary to induce the dissociation of the MinD dimer and its subsequent detachment from the membrane. We investigate which reaction schemes lead to unstable homogeneous steady states and limit cycle oscillations, and how diffusion affects their stability. The suggested model qualitatively describes the shape of the Min waves observed on flat membranes, and agrees with the experimental dependence of the wave period on the MinE concentration. These results highlight the importance of MinE presence on the membrane without being bound to MinD, and of the reactions of Min proteins on the membrane.
Synchronized Cycles: An allosteric model of the cyanobacterial circadian oscillator
NASA Astrophysics Data System (ADS)
Lubensky, David; van Zon, J. S.; Altena, P.; Ten Wolde, P. R.
2007-03-01
In a remarkable experiment, Nakajima et al. [Science, 2005] showed that the 3 cyanobacterial clock proteins KaiA, KaiB, and KaiC are sufficient to generate circadian phosphorylation of KaiC in vitro. This system is thus a rare example of a functioning biochemical circuit that can be reconstituted in the test tube. Theoretically, it presents the further challenge that the only reactions driven out of equilibrium are those associated with KaiC phosphorylation and dephosphorylation. Here, we present a model of the Kai system. At its heart is the assumption, motivated by classical models of allostery, that each KaiC hexamer to tends to be phosphorylated in a cyclic manner. For macroscopic oscillations to be possible, however, the cycles of the different hexamers must be synchronized. We propose a novel synchronisation mechanism that allows us to reproduce a wide range of published data, including temperature compensation of the oscillation period, and to make nontrivial predictions about the effects of varying the concentrations of the Kai proteins.
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.
Predictability and numerical modelling of the North Atlantic Oscillation
NASA Astrophysics Data System (ADS)
Bojariu, Roxana; Gimeno, Luis
2003-10-01
The North Atlantic Oscillation (NAO) is the dominant pattern of atmospheric circulation variability in the extratropical Northern Hemisphere and it is a major controlling factor in basic meteorological variables such as surface wind, temperature and precipitation which have large socioeconomic impacts on energy, agriculture, industry, traffic and human health throughout the whole of Europe and eastern North America. Because of this dominant impact on the weather and climate of the wealthiest areas of the planet, there is a growing interest in quantifying the possible limits of predictability of the phenomenon and the ability of the climate numerical models of simulating it. This paper reviews recent work on predictability and methods of numerical modelling of the North Atlantic Oscillation used to simulate the phenomenon. Atmospheric models with no orography or land-sea contrasts are able to capture the main feature of the NAO; however, to capture any interannual or interdecadal variability of the NAO, atmospheric general circulation models (AGCM) with seasonally varying sea surface temperature (SSTs) forcing are required. Still, no model reproduces the recent observed upward trend in the NAO index, suggesting that either the models are deficient or external forcing such as man-made effects are responsible for this feature. Predictive patterns have been identified in the Atlantic SSTs preceding specific phases of the NAO by up to 6 months, in the atmospheric temperatures anomalies in the previous November, in the Eurasian snow cover and in the sea-ice extent over Arctic. The use of simulations based on ensemble prediction to estimate potential predictability shows the possibility of capturing the upward trend of the NAO and suggests that multiannual to multidecadal variations in the NAO are more predictable than interannual fluctuations.
Theory of harmonic dissipation in disordered solids
NASA Astrophysics Data System (ADS)
Damart, T.; Tanguy, A.; Rodney, D.
2017-02-01
Mechanical spectroscopy, i.e., cyclic deformations at varying frequencies, is used theoretically and numerically to compute dissipation in model glasses. From a normal mode analysis, we show that in the high-frequency terahertz regime where dissipation is harmonic, the quality factor (or loss angle) can be expressed analytically. This expression is validated through nonequilibrium molecular dynamics simulations applied to a model of amorphous silica (SiO2). Dissipation is shown to arise from nonaffine relaxations triggered by the applied strain through the excitation of vibrational eigenmodes that act as damped harmonic oscillators. We discuss an asymmetry vector field, which encodes the information about the structural origin of dissipation computed by mechanical spectroscopy. In the particular case of silica, we find that the motion of oxygen atoms, which induce a deformation of the Si-O-Si bonds, is the main contributor to harmonic energy dissipation.
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.
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.
Analytic simulation of higher harmonic control using a new aeroelastic model
NASA Technical Reports Server (NTRS)
Friedmann, P. P.; Robinson, L. H.
1989-01-01
This paper describes a higher harmonic control (HHC) study of a four bladed hingeless rotor using a coupled flap-lag-torsional aeroelastic stability and response analysis which incorporates finite-state, time-domain aerodynamics. The rotor trim condition is determined using a coupled trim-aeroelastic analysis. Deterministic and cautious controllers based on local and global HHC models are implemented with different combinations of input parameters identified using a Kalman filter. The effects of unsteady versus quasisteady aerodynamic modeling on HHC simulations are investigated, including the effectiveness of the local and global HHC models and the advantages of different identification schemes.
Temperature dependence of universal fluctuations in the two-dimensional harmonic XY model.
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.
Yu, Xiaozhi; Ren, Jindong; Zhang, Qian; Liu, Qun; Liu, Honghao
2017-04-01
Reach envelopes are very useful for the design and layout of controls. In building reach envelopes, one of the key problems is to represent the reach limits accurately and conveniently. Spherical harmonics are proved to be accurate and convenient method for fitting of the reach capability envelopes. However, extensive study are required on what components of spherical harmonics are needed in fitting the envelope surfaces. For applications in the vehicle industry, an inevitable issue is to construct reach limit surfaces with consideration of the seating positions of the drivers, and it is desirable to use population envelopes rather than individual envelopes. However, it is relatively inconvenient to acquire reach envelopes via a test considering the seating positions of the drivers. In addition, the acquired envelopes are usually unsuitable for use with other vehicle models because they are dependent on the current cab packaging parameters. Therefore, it is of great significance to construct reach envelopes for real vehicle conditions based on individual capability data considering seating positions. Moreover, traditional reach envelopes provide little information regarding the assessment of reach difficulty. The application of reach envelopes will improve design quality by providing difficulty-rating information about reach operations. In this paper, using the laboratory data of seated reach with consideration of the subjective difficulty ratings, the method of modeling reach envelopes is studied based on spherical harmonics. The surface fitting using spherical harmonics is conducted for circumstances both with and without seat adjustments. For use with adjustable seat, the seating position model is introduced to re-locate the test data. The surface fitting is conducted for both population and individual reach envelopes, as well as for boundary envelopes. Comparison of the envelopes of adjustable seat and the SAE J287 control reach envelope shows that the latter
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.
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.
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
Can inflationary models of cosmic perturbations evade the secondary oscillation test?
Lewin, Alex; Albrecht, Andreas
2001-07-15
We consider the consequences of an observed cosmic microwave background (CMB) temperature anisotropy spectrum containing no secondary oscillations. While such a spectrum is generally considered to be a robust signature of active structure formation, we show that such a spectrum can be produced by (very unusual) inflationary models or other passive evolution models. However, we show that for all these passive models the characteristic oscillations would show up in other observable spectra. Our work shows that when CMB polarization and matter power spectra are taken into account secondary oscillations are indeed a signature of even these very exotic passive models. We construct a measure of the observability of secondary oscillations in a given experiment, and show that even with foregrounds both the MAP and Planck satellites should be able to distinguish between models with and without oscillations. Thus we conclude that inflationary and other passive models cannot evade the secondary oscillation test.
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.
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.
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.
Temporal structure of neuronal population oscillations with empirical model decomposition
NASA Astrophysics Data System (ADS)
Li, Xiaoli
2006-08-01
Frequency analysis of neuronal oscillation is very important for understanding the neural information processing and mechanism of disorder in the brain. This Letter addresses a new method to analyze the neuronal population oscillations with empirical mode decomposition (EMD). Following EMD of neuronal oscillation, a series of intrinsic mode functions (IMFs) are obtained, then Hilbert transform of IMFs can be used to extract the instantaneous time frequency structure of neuronal oscillation. The method is applied to analyze the neuronal oscillation in the hippocampus of epileptic rats in vivo, the results show the neuronal oscillations have different descriptions during the pre-ictal, seizure onset and ictal periods of the epileptic EEG at the different frequency band. This new method is very helpful to provide a view for the temporal structure of neural oscillation.
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.
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.
Quantum Monte Carlo method for the Bose-Hubbard model with harmonic confining potential.
Kato, Yasuyuki; Kawashima, Naoki
2009-02-01
We study the Bose-Hubbard model with an external harmonic field, which is effective for modeling a cold atomic Bose gas trapped in an optical lattice. We modify the directed-loop algorithm to simulate large systems efficiently. As a demonstration we carry out the simulation of a system consisting of 1. 8 x 10{5} particles on a 64{3} lattice. These numbers are comparable to those in the pioneering experimental work by Greiner [Nature (London) 415, 39 (2002)]. Furthermore, we observe coherence between two superfluid spheres separated by a Mott insulator region in a "wedding-cake" structure.
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.)
Modeling Jupiter's Quasi Quadrennial Oscillation (QQO) with Wave Drag Parameterizations
NASA Astrophysics Data System (ADS)
Cosentino, Rick; Morales-Juberias, Raul; Greathouse, Thomas K.; Orton, Glenn S.
2016-10-01
The QQO in Jupiter's atmosphere was first discovered after 7.8 micron infrared observations spanning the 1980's and 1990's detected a temperature oscillation near 10 hPa (Orton et al. 1991, Science 252, 537, Leovy et. al. 1991, Nature 354, 380, Friedson 1999, Icarus 137, 34). New observations using the Texas Echelon cross-dispersed Echelle Spectrograph (TEXES), mounted on the NASA Infrared Telescope facility (IRTF), have been used to characterize a complete cycle of the QQO between January 2012 and January 2016 (Greathouse et al. 2016, DPS) . These new observations not only show the thermal oscillation at 10 hPa, but they also show that the QQO extends upwards in Jupiter's atmosphere to pressures as high as 0.4 hPa. We incorporated three different wave-drag parameterizations into the EPIC General Circulation Model (Dowling et al. 1998, Icarus 132, 221) to simulate the observed Jovian QQO temperature signatures as a function of latitude, pressure and time using results from the TEXES datasets as new constraints. Each parameterization produces unique results and offers insight into the spectra of waves that likely exist in Jupiter's atmosphere to force the QQO. High-frequency gravity waves produced from convection are extremely difficult to directly observe but likely contribute a significant portion to the QQO momentum budget. We use different models to simulate the effects of waves such as these, to indirectly explore their spectrum in Jupiter's atmosphere by varying their properties. The model temperature outputs show strong correlations to equatorial and mid-latitude temperature fields retrieved from the TEXES datasets at different epochs. Our results suggest the QQO phenomenon could be more than one alternating zonal jet that descends over time in response to Jovian atmospheric forcing (e.g. gravity waves from convection).Research funding provided by the NRAO Grote Reber Pre-Doctoral Fellowship. Computing resources include the NMT PELICAN cluster and the CISL
Backus Effect on a Perpendicular Errors in Harmonic Models of Real vs. Synthetic Data
NASA Technical Reports Server (NTRS)
Voorhies, C. V.; Santana, J.; Sabaka, T.
1999-01-01
Measurements of geomagnetic scalar intensity on a thin spherical shell alone are not enough to separate internal from external source fields; moreover, such scalar data are not enough for accurate modeling of the vector field from internal sources because of unmodeled fields and small data errors. Spherical harmonic models of the geomagnetic potential fitted to scalar data alone therefore suffer from well-understood Backus effect and perpendicular errors. Curiously, errors in some models of simulated 'data' are very much less than those in models of real data. We analyze select Magsat vector and scalar measurements separately to illustrate Backus effect and perpendicular errors in models of real scalar data. By using a model to synthesize 'data' at the observation points, and by adding various types of 'noise', we illustrate such errors in models of synthetic 'data'. Perpendicular errors prove quite sensitive to the maximum degree in the spherical harmonic expansion of the potential field model fitted to the scalar data. Small errors in models of synthetic 'data' are found to be an artifact of matched truncation levels. For example, consider scalar synthetic 'data' computed from a degree 14 model. A degree 14 model fitted to such synthetic 'data' yields negligible error, but amplifies 4 nT (rmss) added noise into a 60 nT error (rmss); however, a degree 12 model fitted to the noisy 'data' suffers a 492 nT error (rmms through degree 12). Geomagnetic measurements remain unaware of model truncation, so the small errors indicated by some simulations cannot be realized in practice. Errors in models fitted to scalar data alone approach 1000 nT (rmss) and several thousand nT (maximum).
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.
Oscillations and chaos in neural networks: an exactly solvable model.
Wang, L P; Pichler, E E; Ross, J
1990-01-01
We consider a randomly diluted higher-order network with noise, consisting of McCulloch-Pitts neurons that interact by Hebbian-type connections. For this model, exact dynamical equations are derived and solved for both parallel and random sequential updating algorithms. For parallel dynamics, we find a rich spectrum of different behaviors including static retrieving and oscillatory and chaotic phenomena in different parts of the parameter space. The bifurcation parameters include first- and second-order neuronal interaction coefficients and a rescaled noise level, which represents the combined effects of the random synaptic dilution, interference between stored patterns, and additional background noise. We show that a marked difference in terms of the occurrence of oscillations or chaos exists between neural networks with parallel and random sequential dynamics. Images PMID:2251287
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.
Modeling Intracellular Oscillations and Polarity Transition in Fission Yeast
NASA Astrophysics Data System (ADS)
Drake, Tyler; Das, Maitreyi; Verde, Fulvia; Vavylonis, Dimitrios
2011-03-01
Fission yeast, a pill-shaped model organism, restricts growth to its tips. These cells maintain an asymmetric growth state, growing at only one tip, until they meet length and cell-cycle requirements. With these met, they grow at both. The mechanism of this transition, new-end take-off (NETO), remains unclear. We find that NETO occurs due to long-range competition for fast-diffusing signaling protein Cdc42 between the old and new tips. From experimental results, we suppose that symmetric tips compete for Cdc42, which triggers growth. We describe a symmetric growth model based on competition between tips. This model restricts short cells to monopolar states while allowing longer cells to be bipolar. Autocatalytic Cdc42 recruiting at both cells tips leads to broken symmetry, and the recruiting cuts off as tip Cdc42 levels saturate. Non-linear differential equations describe the model, with stable attractors indicating valid distributions. Linear stability analysis and numerical methods identify stable fixed points over a twofold increase in cell length. The model reproduces qualitative behavior of the organism. We show that observed pole-to-pole Cdc42 oscillations may facilitate the polarity transition and discuss their relationship to the Min system in E. Coli.
Modelling of soldier fly halteres for gyroscopic oscillations.
Parween, Rizuwana; Pratap, Rudra
2015-01-08
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.
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
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.
'Glocal' robustness analysis and model discrimination for circadian oscillators.
Hafner, Marc; Koeppl, Heinz; Hasler, Martin; Wagner, Andreas
2009-10-01
To characterize the behavior and robustness of cellular circuits with many unknown parameters is a major challenge for systems biology. Its difficulty rises exponentially with the number of circuit components. We here propose a novel analysis method to meet this challenge. Our method identifies the region of a high-dimensional parameter space where a circuit displays an experimentally observed behavior. It does so via a Monte Carlo approach guided by principal component analysis, in order to allow efficient sampling of this space. This 'global' analysis is then supplemented by a 'local' analysis, in which circuit robustness is determined for each of the thousands of parameter sets sampled in the global analysis. We apply this method to two prominent, recent models of the cyanobacterial circadian oscillator, an autocatalytic model, and a model centered on consecutive phosphorylation at two sites of the KaiC protein, a key circadian regulator. For these models, we find that the two-sites architecture is much more robust than the autocatalytic one, both globally and locally, based on five different quantifiers of robustness, including robustness to parameter perturbations and to molecular noise. Our 'glocal' combination of global and local analyses can also identify key causes of high or low robustness. In doing so, our approach helps to unravel the architectural origin of robust circuit behavior. Complementarily, identifying fragile aspects of system behavior can aid in designing perturbation experiments that may discriminate between competing mechanisms and different parameter sets.
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.
Modelling of Spherical Gas Bubble Oscillations and Sonoluminescence
NASA Technical Reports Server (NTRS)
Prosperetti, A.; Hao, Y.
1999-01-01
The discovery of single-bubble sonoluminescence has led to a renewed interest in the forced radial oscillations of gas bubbles. Many of the more recent studies devoted to this topic have used several simplifications in the modelling, and in particular in accounting for liquid compressibility and thermal processes in the bubble. In this paper the significance of these simplifications is explored by contrasting the results of Lohse and co-workers with those of a more detailed model. It is found that, even though there may be little apparent difference between the radius-versus time behaviour of the bubble as predicted by the two models, quantities such as the spherical stability boundary and the threshold for rectified diffusion are affected in a quantitatively significant way. These effects are a manifestation of the subtle dependence upon dissipative processes of the phase of radial motion with respect to the driving sound field. The parameter space region, where according to the theory of Lohse and co-workers, sonoluminescence should be observable, is recalculated with the new model and is found to be enlarged with respect to the earlier estimate. The dependence of this parameter region on sound frequency is also illustrated.
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.
Biases of the wintertime Arctic Oscillation in CMIP5 models
NASA Astrophysics Data System (ADS)
Gong, Hainan; Wang, Lin; Chen, Wen; Chen, Xiaolong; Nath, Debashis
2017-01-01
Distinct biases are found in the pattern and teleconnections of the Arctic Oscillation (AO) in 32 climate models that participate the Coupled Model Intercomparison Project Phase 5 (CMIP5). Compared with observations, the Pacific (Atlantic) center of AO is excessively strong (weak) in most of the 32 CMIP5 models, and the AO-related surface air temperature anomalies are generally weak over the Eurasian continent and North America. These biases are closely tied to the excessively strong linkage, which is marginal in observations, between AO and the North Pacific mode (NPM)—the leading variability of the North Pacific sea level pressure. It implies that the AO in CMIP5 models may be compounded with some regional mode over the North Pacific. Accordingly, a bias-correction method was proposed via correcting the AO index (AOI) to improve the diagnostic estimates of the AO teleconnections. The results suggest that the biases in the pattern and teleconnections of AO can be significantly reduced when the NPM variability is linearly removed from the AOI.
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.
Model for coherence transfer in a backward optical parametric oscillator
NASA Astrophysics Data System (ADS)
Montes, Carlos; Aschieri, Pierre; Picozzi, Antonio
2011-09-01
The mirrorless backward optical parametric oscillator (BOPO), where the signal and idler waves are propagating in opposite directions, will establish a distributed feedback mechanism and thus optical parametric oscillation without the need to apply mirrors or external feedback to the cavity. It has been recently demonstrated experimentally by exploiting the periodic poling technique in second-order nonlinear crystals, that the sub-micrometer structured medium achieves an efficient quasi-phase-matching of the three wave interaction in the backward configuration. A remarkable property of such BOPO is the high degree of coherence of the backward wave component, whose spectrum may be several order of magnitudes narrower than that of the pump, due to the convectioninduced phase-locking mechanism. Experimentally and numerically proved the transfer of coherent phase modulations from the pump wave to the parametrically down-converted waves, we show here that this is also possible for a broad bandwidth spectrally incoherent pump. In order to accurately describe the nonlinear counter-propagation dynamics of the three dispersive waves, we have developed for the first time to our knowledge a new numerical scheme which combines the method of the trajectories usually employed to solve the three-wave interaction and the intraband group velocity dispersion effect is performed in the spectral domain with the help of the Fast Fourier Transform (FFT) technique. The model accurately conserves the number of photons and the Manley-Rowe invariants. This allowed us to predict various configurations of MOPOs in which, thanks to the convection-induced phase-locking mechanism, a highly coherent backward wave is spontaneously generated from a highly incoherent pump wave.
Decay of oscillating universes
NASA Astrophysics Data System (ADS)
Mithani, Audrey Todhunter
2016-08-01
It has been suggested by Ellis et al that the universe could be eternal in the past, without beginning. In their model, the "emergent universe'' exists forever in the past, in an "eternal'' phase before inflation begins. We will show that in general, such an "eternal'' phase is not possible, because of an instability due to quantum tunneling. One candidate model, the "simple harmonic universe'' has been shown by Graham et al to be perturbatively stable; we find that it is unstable with respect to quantum tunneling. We also investigate the stability of a distinct oscillating model in loop quantum cosmology with respect to small perturbations and to quantum collapse. We find that the model has perturbatively stable and unstable solutions, with both types of solutions occupying significant regions of the parameter space. All solutions are unstable with respect to collapse by quantum tunneling to zero size. In addition, we investigate the effect of vacuum corrections, due to the trace anomaly and the Casimir effect, on the stability of an oscillating universe with respect to decay by tunneling to the singularity. We find that these corrections do not generally stabilize an oscillating universe. Finally, we determine the decay rate of the oscillating universe. Although the wave function of the universe lacks explicit time dependence in canonical quantum cosmology, time evolution may be present implicitly through the semiclassical superspace variables, which themselves depend on time in classical dynamics. Here, we apply this approach to the simple harmonic universe, by extending the model to include a massless, minimally coupled scalar field φ which has little effect on the dynamics but can play the role of a "clock''.
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.
Snyder, Gregory R; Chowdhury, Azhad U; Simpson, Garth J
2014-06-19
A simple model is presented for interpreting the presence of substantial second harmonic generation (SHG) activity from assemblies of centrosymmetric molecular building blocks. Using butadiene as a computationally tractable centrosymmetric model system, time-dependent Hartree-Fock calculations of the nonlinear polarizability of butadiene dimer were well-described through exciton coupling arguments based on the electronic structure of the monomer and the relative orientation between the monomers within the dimer. Experimental studies of the centrosymmetric molecule 2,6-di-tert-butylanthraquinone suggest the formation of a combination of SHG-active and SHG-inactive crystal forms. The structure for the centrosymmetric form is known, serving as a negative control for the model, while the presence of an additional SHG-active metastable form is consistent with predictions of the model for alternative molecular packing configurations.
Noise effect on the dynamics and synchronization of saline oscillator's model
NASA Astrophysics Data System (ADS)
Fokou Kenfack, W.; Siewe Siewe, M.; Kofane, T. C.
2017-02-01
The effects of noisy flows on the dynamics and synchronization of the saline oscillator's model are studied. To this aim, we first of all take the noisy perturbations into account in our recent mathematical model of coupled saline oscillators in the form of an additive noise. We next study, through numerical simulations, the effects of the noisy perturbations on the relaxation oscillations and the bifurcation of the oscillatory mode of a sole oscillator. Lastly, the effects of noise on the synchronization of the oscillatory behaviors observed in several coupled cups are investigated through numerical simulations. We find that noises of low intensity synchronize with the internal periodicity of the system and have as effect the shortening of the relaxation time of oscillations. Also, we show that noise has as major effect, to overcome the region of "dead" dynamical behavior. Accounting for noise is useful to reproduce some of the experimental findings in the sense that noises break the identity of coupled identical oscillators.
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
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.
NASA Astrophysics Data System (ADS)
Dobaczewski, J.; Olbratowski, P.
2005-05-01
We describe the new version (v2.08k) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. Similarly as in the previous version (v2.08i), all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. In the new version, three minor errors have been corrected. New Version Program SummaryTitle of program: HFODD; version: 2.08k Catalogue number: ADVA Catalogue number of previous version: ADTO (Comput. Phys. Comm. 158 (2004) 158) Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Does the new version supersede the previous one: yes Computers on which this or another recent version has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems under which the program has been tested: UNIX, LINUX, Windows-2000 Programming language used: Fortran Memory required to execute with typical data: 10M words No. of bits in a word: 64 No. of lines in distributed program, including test data, etc.: 52 631 No. of bytes in distributed program, including test data, etc.: 266 885 Distribution format:tar.gz Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero
Time-dependent QED model for high-order harmonic generation in ultrashort intense laser pulses
NASA Astrophysics Data System (ADS)
Hu, Huayu; Yuan, Jianmin
2008-12-01
To advance the QED approach and exploit more details of the high-order harmonic generation (HHG) of atoms and molecules in intense ultrashort laser fields, a QED model for HHG is developed in a time-dependent framework and a multimode-laser setup. By introduction of the classical-field-dressed quantized Volkov states, an analytical expression to calculate HHG for hydrogenlike atoms and ions in an ultrashort intense laser pulse is obtained. This formula provides a simple intuitive interpretation of the mechanism in which the electron is first ionized to the classical-field-dressed quantized Volkov states, and then falls back to the ground state to emit the harmonic photon. Calculations using this formalism demonstrate a good agreement with recent semiclassical computations. The limiting of the existing QED models, which are successful in providing alternative perspectives on the HHG beyond semiclassical treatments, to the time-independent framework and the single-mode laser have been removed to take into account the laser pulse’s length and its shape. Possible extensive applications of this QED approach as well as its potential usefulness for research in various interesting fields are also discussed. The long-wavelength approximation and strong-field approximation are involved in the development of the formalism.
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.
The doublet majoron model and solar neutrino oscillations
NASA Astrophysics Data System (ADS)
Bertolini, S.; Santamaria, A.
1988-12-01
We present a minimal extension of the standard electroweak theory which, as a consequence of the spontaneous breaking of lepton number and the radiative origin of the neutrino mass, offers a natural framework for the solution of the solar neutrino problem through matter-enhanced neutrino oscillations (Mikheyev-Smirnov-Wolfenstein mechanism). Indeed, we show that the presently available astrophysical bounds on the lepton-breaking vacuum expectation value naturally lead to neutrino masses in the required regime. The fact that the Majoron belongs to an SU(2)L doublet and not a triplet has relevant phenomenological implications. In particular, the scalar contribution to the Z0 width is four times smaller than in the triplet model and equivalent to 1/2 a neutrino-antineutrino mode. Relevant effects related to the presence of two physical singly charged scalars, both at the quantum and tree level, are studied. As a result we find that the model is tightly constrained by present data. In particular, for a wide range of parameters, the decay μ --> eγ is within two orders of magnitude from the present experimental limit. Also at Department de Física Teòrica, Universitat de València and IFIC, Universitat de València-CSIC, Spain.
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.
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
NASA Astrophysics Data System (ADS)
Gómez-Polo, C.; Vázquez, M.; Knobel, M.
2001-01-01
A method to investigate the giant magnetoimpedance effect based on Fourier analysis is introduced. The study is carried out on a FeCoSiB amorphous wire with vanishing magnetostriction subjected to joule heating (current annealing) treatment that induces an enhancement of circumferential magnetic anisotropy and modifies the magnetoimpedance response of the samples. Experimental results are interpreted within the framework of the classical electrodynamical model, where the circumferential permeability plays the dominant role in the field dependence of the complex impedance of the sample. A rotational magnetization model is employed to determine the circular magnetization process, and a mean value of the circumferential permeability is obtained through the harmonic components obtained through Fourier analysis of the time derivative of the circular magnetization. This simple model is able to reproduce the observed experimental behavior, i.e., evolution of the field dependence of the complex impedance with annealing and the asymmetrical field dependence under a dc biased electrical current.
NASA Astrophysics Data System (ADS)
Schneider, M.; Johnson, T.; Dumont, R.; Eriksson, J.; Eriksson, L.-G.; Giacomelli, L.; Girardo, J.-B.; Hellsten, T.; Khilkevitch, E.; Kiptily, V. G.; Koskela, T.; Mantsinen, M.; Nocente, M.; Salewski, M.; Sharapov, S. E.; Shevelev, A. E.; Contributors, JET
2016-11-01
Recent JET experiments have been dedicated to the studies of fusion reactions between deuterium (D) and Helium-3 (3He) ions using neutral beam injection (NBI) in synergy with third harmonic ion cyclotron radio-frequency heating (ICRH) of the beam. This scenario generates a fast ion deuterium tail enhancing DD and D3He fusion reactions. Modelling and measuring the fast deuterium tail accurately is essential for quantifying the fusion products. This paper presents the modelling of the D distribution function resulting from the NBI+ICRF heating scheme, reinforced by a comparison with dedicated JET fast ion diagnostics, showing an overall good agreement. Finally, a sawtooth activity for these experiments has been observed and interpreted using SPOT/RFOF simulations in the framework of Porcelli’s theoretical model, where NBI+ICRH accelerated ions are found to have a strong stabilizing effect, leading to monster sawteeth.
NASA Astrophysics Data System (ADS)
Scafetta, N.
2012-12-01
We show that the Schwabe frequency band of the Zurich sunspot record since 1749 is made of three major cycles that are closely related to the spring tidal period of Jupiter and Saturn (~9.93 year), to the tidal sidereal period of Jupiter (about 11.86 years) and to a central cycle that may be associated to a quasi-11-year solar dynamo cycle. The central harmonic is approximately synchronized to the average of the two planetary frequencies. A harmonic model based on the above two planetary tidal frequencies and on the exact dates of Jupiter and Saturn planetary tidal phases, plus a theoretically deduced 10.87-year central cycle reveals major beat periods occurring at about 115, 61 and 130 years, plus a quasi-millennial large beat cycle around 983 years. Equivalent synchronized cycles are found in cosmogenic solar proxy records used to reconstruct solar activity and in proxy climate records throughout the Holocene (last 12,000 years) up to now. The quasi-secular beat oscillations hindcast reasonably well the known prolonged periods of low solar activity during the last millennium such as the Oort, Wolf, Sporer, Maunder and Dalton minima, as well as the 17 115-year long oscillations found in a detailed temperature reconstruction of the Northern Hemisphere covering the last 2000 years. The millennial three-frequency beat cycle hindcasts equivalent solar and climate cycles for 12,000 years. Finally, the harmonic model herein proposed reconstructs the prolonged solar minima around 1900-1920 and 1960-1980, the secular solar maxima around 1870-1890, 1940-1950 and 1995-2005, and a secular upward trending during the 20th century. The latter modulated trending agrees well with some solar proxy model, with the ACRIM TSI satellite composite and with the global surface temperature modulation since 1850. The model forecasts a new prolonged solar minimum during 2020-2045, which is produced by the minima of both the 61 and 115-year reconstructed cycles. Finally, the model predicts
Synthesizing Virtual Oscillators to Control Islanded Inverters
Johnson, Brian B.; Sinha, Mohit; Ainsworth, Nathan G.; Dorfler, Florian; Dhople, Sairaj V.
2016-08-01
Virtual oscillator control (VOC) is a decentralized control strategy for islanded microgrids where inverters are regulated to emulate the dynamics of weakly nonlinear oscillators. Compared to droop control, which is only well defined in sinusoidal steady state, VOC is a time-domain controller that enables interconnected inverters to stabilize arbitrary initial conditions to a synchronized sinusoidal limit cycle. However, the nonlinear oscillators that are elemental to VOC cannot be designed with conventional linear-control design methods. We address this challenge by applying averaging- and perturbation-based nonlinear analysis methods to extract the sinusoidal steady-state and harmonic behavior of such oscillators. The averaged models reveal conclusive links between real- and reactive-power outputs and the terminal-voltage dynamics. Similarly, the perturbation methods aid in quantifying higher order harmonics. The resultant models are then leveraged to formulate a design procedure for VOC such that the inverter satisfies standard ac performance specifications related to voltage regulation, frequency regulation, dynamic response, and harmonic content. Experimental results for a single-phase 750 VA, 120 V laboratory prototype demonstrate the validity of the design approach. They also demonstrate that droop laws are, in fact, embedded within the equilibria of the nonlinear-oscillator dynamics. This establishes the backward compatibility of VOC in that, while acting on time-domain waveforms, it subsumes droop control in sinusoidal steady state.
NASA Astrophysics Data System (ADS)
She, M.; Jiang, L. P.
2014-12-01
In this paper, an oscillating dark energy model is presented in an isotropic but inhomogeneous plane symmetric space-time by considering a time periodic varying deceleration parameter. We find three different types of new solutions which describe different scenarios of oscillating universe. The first two solutions show an oscillating universe with singularities. For the third one, the universe is singularity-free during the whole evolution. Moreover, the Hubble parameter oscillates and keeps positive which explores an interesting possibility to unify the early inflation and late time acceleration of the universe.
Quantitative characterization of spurious numerical oscillations in 48 CMIP5 models
NASA Astrophysics Data System (ADS)
Geil, Kerrie L.; Zeng, Xubin
2015-06-01
Spurious numerical oscillations (SNOs) (e.g., Gibbs oscillations) can appear as unrealistic spatial waves near discontinuities or sharp gradients in global model fields (e.g., orography) and have been a known problem in global models for decades. Multiple methods of oscillation reduction exist; consequently, the oscillations are presumed small in modern climate models and hence are rarely addressed in recent literature. Here we use two metrics to quantify SNOs in 13 variables from 48 Coupled Model Intercomparison Project Phase 5 models along a Pacific ocean transect near the Andes. Results show that 48% of nonspectral models and 95% of spectral models have at least one variable with SNO amplitude as large as, or greater than, atmospheric interannual variability. The impact of SNOs on climate simulations should be thoroughly evaluated and further efforts to substantially reduce SNOs in climate models are urgently needed.
Pulsed Bessel-Gauss beams: a depleted wave model for type II second-harmonic generation.
Sabaeian, Mohammad; Motazedian, Alireza; Mohammad Rezaee, Mostafa; Jalil-Abadi, Fatemeh Sedaghat
2014-11-10
In this work, a three-dimensional and time-dependent nonlinear wave model to describe the generation of pulsed Bessel-Gauss second-harmonic waves (SHWs) is presented. Three coupled equations, two for ordinary and extraordinary fundamental waves and one for extraordinary SHWs, describing type II second-harmonic generation (SHG) in a KTiOPO_{4} (KTP) crystal were solved by considering the depletion of fundamental waves (FWs). The results examined the validity of nondepleted wave approximation against the energy of pulses, beam spot size, and interaction length. It was shown that for pulses with spot sizes of ω_{f}=80 μm and energy of 0.8j, the nonlinear interaction was accomplished over a distance of ∼5 mm. Therefore, for KTP crystals with lengths longer than 5 mm, the nondepleted wave approximation can no longer be valid. To be valid, the crystal must be shorter than the interaction length, i.e., 5 mm.
A mechanical model to compute elastic modulus of tissues for harmonic motion imaging.
Shan, Baoxiang; Pelegri, Assimina A; Maleke, Caroline; Konofagou, Elisa E
2008-07-19
Numerous experimental and computational methods have been developed to estimate tissue elasticity. The existing testing techniques are generally classified into in vitro, invasive in vivo and non-invasive in vivo. For each experimental method, a computational scheme is accordingly proposed to calculate mechanical properties of soft biological tissues. Harmonic motion imaging (HMI) is a new technique that performs radio frequency (RF) signal tracking to estimate the localized oscillatory motion resulting from a radiation force produced by focused ultrasound. A mechanical model and computational scheme based on the superposition principle are developed in this paper to estimate the Young's modulus of a tissue mimicking phantom and bovine liver in vitro tissue from the harmonic displacement measured by HMI. The simulation results are verified by two groups of measurement data, and good agreement is shown in each comparison. Furthermore, an inverse function is observed to correlate the elastic modulus of uniform phantoms with amplitude of displacement measured in HMI. The computational scheme is also implemented to estimate 3D elastic modulus of bovine liver in vitro.
Harmonic motion microwave Doppler imaging: a simulation study using a simple breast model.
Top, Can Bariş; Gençer, Nevzat G
2014-02-01
A hybrid method for tissue imaging using dielectric and elastic properties is proposed and investigated with simple bi-layered breast model. In this method, local harmonic motion is generated in the tissue using a focused ultrasound probe. A narrow-band microwave signal is transmitted to the tissue. The Doppler component of the scattered signal, which depends on the dielectric and elastic properties of the vibrating region, is sensed. A plane-wave spectrum technique is used together with reciprocity theorem for calculating the response of a vibrating electrically small spherical tumor in breast tissue. The effects of operating frequency, antenna alignment and distance, and tumor depth on the received signal are presented. The effect of harmonic motion frequency on the vibration amplitude and displacement distribution is investigated with mechanical simulations using the finite element method. The safety of the method is analyzed in terms of microwave and ultrasound exposure of the breast tissue. The results show that the method has a potential in detecting tumors inside fibro-glandular breast tissue.
Modelling of quasi-periodic oscillations with wave packets
NASA Astrophysics Data System (ADS)
Alpar, M. A.; Yilmaz, A.
1997-08-01
Model dispersion relations are introduced to explore power spectra of the normal-branch (NB) and horizontal-branch (HB) quasi-periodic oscillations (QPOs; for reviews see Van der Klis (1989)[ARA&A, 27, 517], (1992) [Proc. of NATO ASI X-Ray Binaries and Recycled Pulsars, eds. E.P.J. Van den Heuvel & S.A. Rappaport, Kluwer, Dordrecht], (1995)[Proc. of NATO ASI The Lives of the Neutron Stars, eds. M.A. Alpar, Ümit Kiziloğlu, & J. van Paradijs, Kluwer, Dordrecht]) of low mass X-ray binaries (LMXBs) in terms of wave packets and to illustrate the presence of frequency bands around the Kepler and beat frequencies. For the NB QPOs wave packets of sound waves in a thick middle disk state, with frequencies determined by the rotation frequency, have wavelengths comparable to the size of the middle disk. For Z-sources on the HB, the wave packets result from disturbances in the inner disk induced by the neutron star magnetic field which rotates at the beat frequency with respect to the inner disk. For both the NB and the HB QPOs, we construct simple model dispersion relations, and show that the QPO peaks in the observed power spectra correspond to reasonable wavelengths and system parameters. The kilohertz QPOs, which were discovered after the original version of this paper was submitted, are also discussed as a possible realization of the Kepler and beat frequency bands. Problems of integrating the kHz and HB QPOs in a disk model are briefly noted. It is tentatively suggested that supersonic and wave propagation regions of the inner disk have complementary functions for the origin of kHz and HB QPOs respectively.
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 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.
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.
Anisotropic Finite Element Modeling Based on a Harmonic Field for Patient-Specific Sclera
Zheng, Wanqiu; Zou, Beiji
2017-01-01
Purpose. This study examined the influence of anisotropic material for human sclera. Method. First, the individual geometry of patient-specific sclera was reproduced from a laser scan. Then, high quality finite element modeling of individual sclera was performed using a convenient automatic hexahedral mesh generator based on harmonic field and integrated with anisotropic material assignment function. Finally, comparison experiments were designed to investigate the effects of anisotropy on finite element modeling of sclera biomechanics. Results. The experimental results show that the presented approach can generate high quality anisotropic hexahedral mesh for patient-specific sclera. Conclusion. The anisotropy shows significant differences for stresses and strain distribution and careful consideration should be given to its use in biomechanical FE studies. PMID:28271067
Human brain networks function in connectome-specific harmonic waves.
Atasoy, Selen; Donnelly, Isaac; Pearson, Joel
2016-01-21
A key characteristic of human brain activity is coherent, spatially distributed oscillations forming behaviour-dependent brain networks. However, a fundamental principle underlying these networks remains unknown. Here we report that functional networks of the human brain are predicted by harmonic patterns, ubiquitous throughout nature, steered by the anatomy of the human cerebral cortex, the human connectome. We introduce a new technique extending the Fourier basis to the human connectome. In this new frequency-specific representation of cortical activity, that we call 'connectome harmonics', oscillatory networks of the human brain at rest match harmonic wave patterns of certain frequencies. We demonstrate a neural mechanism behind the self-organization of connectome harmonics with a continuous neural field model of excitatory-inhibitory interactions on the connectome. Remarkably, the critical relation between the neural field patterns and the delicate excitation-inhibition balance fits the neurophysiological changes observed during the loss and recovery of consciousness.
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
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
A Review of Flood Loss Models as Basis for Harmonization and Benchmarking.
Gerl, Tina; Kreibich, Heidi; Franco, Guillermo; Marechal, David; Schröter, Kai
2016-01-01
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.
Three-layer model for the surface second-harmonic generation yield including multiple reflections
NASA Astrophysics Data System (ADS)
Anderson, Sean M.; Mendoza, Bernardo S.
2016-09-01
We present the three-layer model to calculate the surface second-harmonic generation (SSHG) yield. This model considers that the surface is represented by three regions or layers. The first layer is the vacuum region with a dielectric function ɛv(ω ) =1 from where the fundamental electric field impinges on the material. The second layer is a thin layer (ℓ ) of thickness d characterized by a dielectric function ɛℓ(ω ) , and it is in this layer where the SSHG takes place. The third layer is the bulk region denoted by b and characterized by ɛb(ω ) . Both the vacuum and bulk layers are semi-infinite. The model includes the multiple reflections of both the fundamental and the second-harmonic (SH) fields that take place at the thin layer ℓ . We obtain explicit expressions for the SSHG yield for the commonly used s and p polarizations of the incoming 1 ω and outgoing 2 ω electric fields, where no assumptions for the symmetry of the surface are made. These symmetry assumptions ultimately determine which components of the surface nonlinear second-order susceptibility tensor χ (-2 ω ;ω ,ω ) are different from zero, and thus contribute to the SSHG yield. Then, we particularize the results for the most commonly investigated surfaces, the (001), (110), and (111) crystallographic faces, taking their symmetries into account. We use the three-layer model and compare it against the experimental results of a Si(111)(1 ×1 ):H surface, as a test case, and use it to predict the SSHG yield of a Si(001)(2 ×1 ) surface.
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.
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.
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
Alcocer-Sosa, Mauricio; Gutiérrez, David
2016-06-25
We present a forward modeling solution in the form of an array response kernel for magnetoencephalography. We consider the case when the brain's anatomy is approximated by an ellipsoid and an equivalent current dipole model is used to approximate brain sources. The proposed solution includes the contributions up to the third-order ellipsoidal harmonic terms; hence, we compare this new approximation against the previously available one that only considered up to second-order harmonics. We evaluated the proposed solution when used in the inverse problem of estimating physiologically feasible visual evoked responses from magnetoencephalography data. Our results showed that the contribution of the third-order harmonic terms provides a more realistic representation of the magnetic fields (closer to those generated with a numerical approximation based on the boundary element method) and, subsecuently, the estimated equivalent current dipoles are a better fit to those observed in practice (e.g., in visual evoked potentials). Copyright © 2016 John Wiley & Sons, Ltd.
Heat death and oscillation in model universes containing interacting matter and radiation
NASA Astrophysics Data System (ADS)
Landsberg, P. T.; Reeves, G. A.
1982-11-01
Continuum and continuum-particle models for both oscillating and ever-expanding model universes are considered, with the consequences of various interactions between the components being traced and the connection with the irreversibility of oscillating models noted. It is for the first time shown that the relativistic equations allow the energy of an oscillating model universe to decrease by the end of a cycle, as is illustrated by a hypothetical model in which the matter temperature initially exceeds the radiation temperature. In addition, a novel continuum-particle model is introduced which is suitable for a study of universes with oscillation, or infinite expansion, and includes He formation and the effect of the Thomson interaction between matter and radiation.
NASA Astrophysics Data System (ADS)
Boerner, Paul; Zandonadi, Germana; Eberle, Gregory; Wegener, Konrad
2015-03-01
Ablation threshold experiments on various materials are carried out using a picosecond laser generating second harmonic radiation in air at atmospheric pressure. Various materials are investigated which vary according to their different electronic band gap structure and include: silicon, fine grain polycrystalline diamond, copper, steel and tungsten carbide. Through the use of scanning electron microscopy and 3D confocal microscopy, the crater depth and diameter are determined and a correlation is found. The ablation thresholds are given for the aforementioned materials and compared with recent literature results. Picosecond laser-material interactions are modelled using the two-temperature model, simulated and compared with experimental results for metallic materials. An extension of the two-temperature model to semiconducting and insulating materials is discussed. This alternative model uses multiple rate equations to describe the transient free electron density. Additionally, a set of coupled ordinary differential equations describes the processes of multiphoton excitation, inverse bremsstrahlung, and collisional excitation. The resulting electron density distribution can be used as an input for an electron density dependent twotemperature model. This multiple rate equation model is a generic and fast model, which provides important information like ablation threshold, ablation depth and optical properties.
Jang, Yunho; Jeong, Jay I; Kim, Moon K
2006-07-01
UMass Morph Server (UMMS) has been developed for the broad impact on the study of molecular dynamics (MD). The elastic network model (ENM) of a given macromolecule has been proven as a useful tool for analyzing thermal behaviors locally and predicting folding pathways globally. UMMS utilizes coarse-grained ENMs at various levels. These simplifications remarkably save computation time compared with all-atom MD simulations so that one can bring down massive computational problems from a supercomputer to a PC. To improve computational efficiency and physical reality of ENMs, the symmetry-constrained, rigid-cluster, hybrid and chemical-bond ENMs have been developed and implemented at UMMS. One can request both harmonic normal mode analysis of a single macromolecule and anharmonic pathway generation between two conformations of a same molecule using elastic network interpolation at http://biomechanics.ecs.umass.edu/umms.html.
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)
Application of Fibonacci oscillators in the Debye model
NASA Astrophysics Data System (ADS)
Marinho, André A. A.; Brito, F. A.; Chesman, C.
2014-12-01
In this paper we study the thermodynamics of a crystalline solid by applying q-deformed algebra of Fibonacci oscillators through the generalized Fibonacci sequence of two real and independent deformation parameters q1 and q2. We find a (q1, q2)-deformed Hamiltonian and consequently the q-deformed thermodynamic quantities. The results led us to interpret the deformation parameters acting as disturbance or impurities factors modifying the characteristics of a crystal structure. More specifically, we found the possibility of adjusting the Fibonacci oscillators to describe the change of thermal conductivity of a given element as one inserts impurites.
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.
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.
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.
Li, Yu-Sheng; Oldendick, James E; Chang, Wei
2010-05-07
Pinhole collimators are widely used for single photon emission computed tomography (SPECT) imaging of small organs and animals. There has also 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.
Comment on "Continuum model of vortex oscillations in rotating superfluids"
NASA Astrophysics Data System (ADS)
Tsakadze, J. S.; Tsakadze, S. J.; Sonin, E. B.
1980-04-01
Recent experiments as well as theoretical calculations show that the theory of vortex oscillations in rotating superfluids in the case of the slowest modes (Tkachenko modes) in finite containers must take into account vortex pinning at the container bottom except for the case of very long containers.
Pavlides, Alex; Hogan, S. John; Bogacz, Rafal
2015-01-01
In Parkinson’s disease, an increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with difficulty in movement initiation. An important role in the generation of these oscillations is thought to be played by the motor cortex and by a network composed of the subthalamic nucleus (STN) and the external segment of globus pallidus (GPe). Several alternative models have been proposed to describe the mechanisms for generation of the Parkinsonian beta oscillations. However, a recent experimental study of Tachibana and colleagues yielded results which are challenging for all published computational models of beta generation. That study investigated how the presence of beta oscillations in a primate model of Parkinson’s disease is affected by blocking different connections of the STN-GPe circuit. Due to a large number of experimental conditions, the study provides strong constraints that any mechanistic model of beta generation should satisfy. In this paper we present two models consistent with the data of Tachibana et al. The first model assumes that Parkinsonian beta oscillation are generated in the cortex and the STN-GPe circuits resonates at this frequency. The second model additionally assumes that the feedback from STN-GPe circuit to cortex is important for maintaining the oscillations in the network. Predictions are made about experimental evidence that is required to differentiate between the two models, both of which are able to reproduce firing rates, oscillation frequency and effects of lesions carried out by Tachibana and colleagues. Furthermore, an analysis of the models reveals how the amplitude and frequency of the generated oscillations depend on parameters. PMID:26683341
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
Pulse-transmission Oscillators: Autonomous Boolean Models and the Yeast Cell Cycle
NASA Astrophysics Data System (ADS)
Sevim, Volkan; Gong, Xinwei; Socolar, Joshua
2010-03-01
Models of oscillatory gene expression typically involve a constitutively expressed or positively autoregulated gene which is repressed by a negative feedback loop. In Boolean representations of such systems, which include the repressilator and relaxation oscillators, dynamical stability stems from the impossibility of satisfying all of the Boolean rules at once. We consider a different class of networks, in which oscillations are due to the transmission of a pulse of gene activation around a ring. Using autonomous Boolean modeling methods, we show how the circulating pulse can be stabilized by decoration of the ring with certain feedback and feed-forward motifs. We then discuss the relation of these models to ODE models of transcriptional networks, emphasizing the role of explicit time delays. Finally, we show that a network recently proposed as a generator of cell cycle oscillations in yeast contains the motifs required to support stable transmission oscillations.
Kersemans, Mathias; Martens, Arvid; Van Den Abeele, Koen; Degrieck, Joris; Pyl, Lincy; Zastavnik, Filip; Sol, Hugo; Van Paepegem, Wim
2015-04-01
Conventionally, the ultrasonic polar scan (UPS) records the amplitude or time-of-flight in transmission using short ultrasonic pulses for a wide range of incidence angles, resulting in a fingerprint of the critical bulk wave angles of the material at the insonified spot. Here, we investigate the use of quasi-harmonic ultrasound (bursts) in a polar scan experiment, both experimentally and numerically. It is shown that the nature of the fingerprint drastically changes, and reveals the positions of the leaky Lamb angles. To compare with experiments, both plane wave and bounded beam simulations have been performed based on the recursive stiffness matrix method. Whereas the plane wave computations yield a pure Lamb wave angle fingerprint, this is no longer valid for the more realistic case of a bounded beam. The experimental recordings are fully supported by the bounded beam simulations. To complement the traditional amplitude measurement, experimental and numerical investigations have been performed to record, predict and analyze the phase of the transmitted ultrasonic beam. This results in the conceptual introduction of the 'phase polar scan', exposing even more intriguing and detailed patterns. In fact, the combination of the amplitude and the phase polar scan provides the complete knowledge about the complex transmission coefficient for every possible angle of incidence. This comprehensive information will be very valuable for inverse modeling of the local elasticity tensor based on a single UPS experiment. Finally, the UPS method has been applied for the detection of an artificial delamination. Compared to the pulsed UPS, the quasi-harmonic UPS (both the amplitude and phase recording) shows a superior sensitivity to the presence of a delamination.
NASA Astrophysics Data System (ADS)
Scafetta, Nicola
2012-05-01
The Schwabe frequency band of the Zurich sunspot record since 1749 is found to be made of three major cycles with periods of about 9.98, 10.9 and 11.86 years. The side frequencies appear to be closely related to the spring tidal period of Jupiter and Saturn (range between 9.5 and 10.5 years, and median 9.93 years) and to the tidal sidereal period of Jupiter (about 11.86 years). The central cycle may be associated to a quasi-11-year solar dynamo cycle that appears to be approximately synchronized to the average of the two planetary frequencies. A simplified harmonic constituent model based on the above two planetary tidal frequencies and on the exact dates of Jupiter and Saturn planetary tidal phases, plus a theoretically deduced 10.87-year central cycle reveals complex quasi-periodic interference/beat patterns. The major beat periods occur at about 115, 61 and 130 years, plus a quasi-millennial large beat cycle around 983 years. We show that equivalent synchronized cycles are found in cosmogenic records used to reconstruct solar activity and in proxy climate records throughout the Holocene (last 12,000 years) up to now. The quasi-secular beat oscillations hindcast reasonably well the known prolonged periods of low solar activity during the last millennium such as the Oort, Wolf, Spörer, Maunder and Dalton minima, as well as the 17 115-year long oscillations found in a detailed temperature reconstruction of the Northern Hemisphere covering the last 2000 years. The millennial three-frequency beat cycle hindcasts equivalent solar and climate cycles for 12,000 years. Finally, the harmonic model herein proposed reconstructs the prolonged solar minima that occurred during 1900-1920 and 1960-1980 and the secular solar maxima around 1870-1890, 1940-1950 and 1995-2005 and a secular upward trending during the 20th century: this modulated trending agrees well with some solar proxy model, with the ACRIM TSI satellite composite and with the global surface temperature
Modelling the tsunami free oscillations in the Marquesas (French Polynesia)
NASA Astrophysics Data System (ADS)
Allgeyer, S.; Hébert, H.; Madariaga, R.
2013-06-01
The tsunami resonance inside basins (closed or semi-enclosed) depends on the period of the incident waves, reflection and energy dissipation, characteristics of the boundary and the geometry of the basin. When waves continuously enter the basin, they cause abnormal water level fluctuations and produced damage if their periods are close to the periods of free oscillation of the basin. These resonant oscillations inside harbours, bays, or other semi-enclosed or closed basins can have a direct influence on the management of harbours, shipping and coastal uses. So, it is important to determine these free oscillations. These resonant characteristics have been observed in the Marquesas, an archipelago prone to tsunami amplification, during the last three tsunamis (Samoa 2009, Maule 2010, Tohoku 2011). These events were recorded by the two tide gauges located in the Marquesas. In this archipelago, there are two monitored bays : the first one is located in Hiva Oa Island (Tahauku Bay) and the second in Nuku Hiva Island (Taihoae Bay). For all these tsunamis, more than 3 d of water tidal resonance were recorded. In this work, we make a free oscillation analysis of the Marquesas Archipelago using real tide gauge data, simulated tsunami data and theoretical computations. During the last century, this archipelago was hit by several trans-Pacific tsunamis. It is interesting to note that, following different tsunami reports the bays responded differently depending on the earthquake source region. For example, Tahauku and Atuona, two bays in Hiva Oa Island only 1 km apart, have different responses depending on the tsunami, as it was observed in 1946 (Aleutian earthquake) and 1960 (Chile earthquake). For this reason, we study the azimuthal dependence of the excitation of the free oscillation modes, and we show that some azimuths enhance tsunami amplification.
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.
Potassium Model for Slow (2-3 Hz) In Vivo Neocortical Paroxysmal Oscillations
Bazhenov, M.; Timofeev, I.; Steriade, M.; Sejnowski, T. J.
2010-01-01
In slow neocortical paroxysmal oscillations, the de- and hyperpolarizing envelopes in neocortical neurons are large compared with slow sleep oscillations. Increased local synchrony of membrane potential oscillations during seizure is reflected in larger electroencephalographic oscillations and the appearance of spike- or polyspike-wave complex recruitment at 2- to 3-Hz frequencies. The oscillatory mechanisms underlying this paroxysmal activity were investigated in computational models of cortical networks. The extracellular K+ concentration ([K+]o) was continuously computed based on neuronal K+ currents and K+ pumps as well as glial buffering. An increase of [K+]o triggered a transition from normal awake-like oscillations to 2- to 3-Hz seizure-like activity. In this mode, the cells fired periodic bursts and nearby neurons oscillated highly synchronously; in some cells depolarization led to spike inactivation lasting 50–100 ms. A [K+]o increase, sufficient to produce oscillations could result from excessive firing (e.g., induced by external stimulation) or inability of K+ regulatory system (e.g., when glial buffering was blocked). A combination of currents including high-threshold Ca2+, persistent Na+ and hyperpolarization-activated depolarizing (Ih) currents was sufficient to maintain 2- to 3-Hz activity. In a network model that included lateral K+ diffusion between cells, increase of [K+]o in a small region was generally sufficient to maintain paroxysmal oscillations in the whole network. Slow changes of [K+]o modulated the frequency of bursting and, in some case, led to fast oscillations in the 10- to 15-Hz frequency range, similar to the fast runs observed during seizures in vivo. These results suggest that modifications of the intrinsic currents mediated by increase of [K+]o can explain the range of neocortical paroxysmal oscillations in vivo. PMID:15056684
A flux-controlled model of meminductor and its application in chaotic oscillator
NASA Astrophysics Data System (ADS)
Wang, Guang-Yi; Jin, Pei-Pei; Wang, Xiao-Wei; Shen, Yi-Ran; Yuan, Fang; Wang, Xiao-Yuan
2016-09-01
A meminductor is a new type of memory device developed from the memristor. We present a mathematical model of a flux-controlled meminductor and its equivalent circuit model for exploring the properties of the meminductor in a nonlinear circuit. We explore the response characteristics of the meminductor under the exciting signals of sinusoidal, square, and triangular waves by using theoretical analysis and experimental tests, and design a meminductor-based oscillator based on the model. Theoretical analysis and experiments show that the meminductor-based oscillator possesses complex bifurcation behaviors and can generate periodic and chaotic oscillations. A special phenomenon called the co-existent oscillation that can generate multiple oscillations (such as chaotic, periodic oscillations as well as stable equilibrium) with the same parameters and different initial conditions occurs. We also design an analog circuit to realize the meminductor-based oscillator, and the circuit experiment results are in accordance with the theory analysis. 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).
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.
Interacting oscillations in neural control of breathing: modeling and qualitative analysis
Bacak, Bartholomew J.; Molkov, Yaroslav I.; Shevtsova, Natalia A.; Smith, Jeffrey C.; Rybak, Ilya A.
2012-01-01
In mammalian respiration, late-expiratory (late-E, or pre-inspiratory) oscillations emerge in abdominal motor output with increasing metabolic demands (e.g., during hypercapnia, hypoxia, etc.). These oscillations originate in the retrotrapezoid nucleus/parafacial respiratory group (RTN/pFRG) and couple with the respiratory oscillations generated by the interacting neural populations of the Bötzinger (BötC) and pre-Bötzinger (pre-BötC) complexes, representing the kernel of the respiratory central pattern generator. Recently, we analyzed experimental data on the generation of late-E oscillations and proposed a large-scale computational model that simulates the possible interactions between the BötC/pre-BötC and RTN/pFRG oscillations under different conditions. Here we describe a reduced model that maintains the essential features and architecture of the large-scale model, but relies on simplified activity-based descriptions of neural populations. This simplification allowed us to use methods of dynamical systems theory, such as fast-slow decomposition, bifurcation analysis, and phase plane analysis, to elucidate the mechanisms and dynamics of synchronization between the RTN/pFRG and BötC/pre-BötC oscillations. Three physiologically relevant behaviors have been analyzed: emergence and quantal acceleration of late-E oscillations during hypercapnia, transformation of the late-E activity into a biphasic-E activity during hypercapnic hypoxia, and quantal slowing of BötC/pre-BötC oscillations with the reduction of pre-BötC excitability. Each behavior is elicited by gradual changes in excitatory drives or other model parameters, reflecting specific changes in metabolic and/or physiological conditions. Our results provide important theoretical insights into interactions between RTN/pFRG and BötC/pre-BötC oscillations and the role of these interactions in the control of breathing under different metabolic conditions. PMID:20927576
Quasi-decadal Oscillation in the CMIP5 and CMIP3 Climate Model Simulations: California Case
NASA Astrophysics Data System (ADS)
Wang, J.; Yin, H.; Reyes, E.; Chung, F. I.
2014-12-01
The ongoing three drought years in California are reminding us of two other historical long drought periods: 1987-1992 and 1928-1934. This kind of interannual variability is corresponding to the dominating 7-15 yr quasi-decadal oscillation in precipitation and streamflow in California. When using global climate model projections to assess the climate change impact on water resources planning in California, it is natural to ask if global climate models are able to reproduce the observed interannual variability like 7-15 yr quasi-decadal oscillation. Further spectral analysis to tree ring retrieved precipitation and historical precipitation record proves the existence of 7-15 yr quasi-decadal oscillation in California. But while implementing spectral analysis to all the CMIP5 and CMIP3 global climate model historical simulations using wavelet analysis approach, it was found that only two models in CMIP3 , CGCM 2.3.2a of MRI and NCAP PCM1.0, and only two models in CMIP5, MIROC5 and CESM1-WACCM, have statistically significant 7-15 yr quasi-decadal oscillations in California. More interesting, the existence of 7-15 yr quasi-decadal oscillation in the global climate model simulation is also sensitive to initial conditions. 12-13 yr quasi-decadal oscillation occurs in one ensemble run of CGCM 2.3.2a of MRI but does not exist in the other four ensemble runs.
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.
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.
Veledina, Alexandra; Poutanen, Juri; Ingram, Adam E-mail: juri.poutanen@oulu.fi
2013-12-01
Recent observations of accreting black holes reveal the presence of quasi-periodic oscillations (QPO) in the optical power density spectra. The corresponding oscillation periods match those found in X-rays, implying a common origin. Among the numerous suggested X-ray QPO mechanisms, some may also work in the optical. However, their relevance to the broadband—optical through X-ray—spectral properties have not been investigated. For the first time, we discuss the QPO mechanism in the context of the self-consistent spectral model. We propose that the QPOs are produced by Lense-Thirring precession of the hot accretion flow, whose outer parts radiate in optical wavelengths. At the same time, its innermost parts are emitting X-rays, which explains the observed connection of QPO periods. We predict that the X-ray and optical QPOs should be either in phase or shifted by half a period, depending on the observer position. We investigate the QPO harmonic content and find that the variability amplitudes at the fundamental frequency are larger in the optical, while the X-rays are expected to have strong harmonics. We then discuss the QPO spectral dependence and compare the expectations to the existing data.
Seismic model of Mars. 2. Free oscillations and travel times
NASA Astrophysics Data System (ADS)
Gudkova, Tamara; Lognonne, Philippe; Raevskiy, Sergey; Zharkov, Vladimir
When constructing an interior structure model of a planet, it is common used method to describe the model by a restricted set of parameters: the thickness of the crust, the location of phase transitions, the core radius. The variation of these parameters originates from the uncertainties in temperature profile, composition, elastic and anelastic properties of relevant minerals. Water content should also be considered as a compositional variable in the mantle. Olivine and its high pressure phases, wadsleyite and ringwoodite are particularly important as they constitute about 60 wt% of the Martian mantle and have probably large capacity for water in the Martian mantle (Zharkov and Gudkova, 2014). At present Mars’ internal density distribution is constrained by the recent estimates of the moment of inertia and the Love number k _{2} (Konoplive et al., 2011). Below we use the data from Earth studies and laboratory data (Mao et al., 2010, 2011, 2012,extrapolated for P-T conditions in Mars, and show how the admixture of water in the main Martian minerals influences velocity drops at phase transition boundaries in Martian interiors and study the effects of hydration on the periods of free oscillations and travel times for P, PcP, S, ScS waves , which could serve as additional constraints, if upcoming seismic experiments are successful, as they can potentially constrain mantle composition and make more precise the location of transition zones. It is of importance to determine the depth of the phase transitions in the mantle, as it will fix the temperature profile in Mars. Our analysis is based on a trial seismic model M14_3 from (Zharkov et al., 2009). The crust is 50 km thick (with density of 2.9 g/cm (3) ), the molar ratio Fe/(Fe+Mg) in the mantle is 0.20, the Fe-Ni core contains 70 mol % H in addition to 14 wt % S with radius of 1800 km. The bulk Fe/Si ratio is close to chondritic 1.7. The upper mantle extends down to 1590 km depth. Olivine-wadsleite transition zone
Campbell, Kirby R; Campagnola, Paul J
2017-03-02
Extensive remodeling of the extracellular matrix (ECM) occurs in many epithelial cancers. For example, in ovarian cancer, upregulation of collagen isoform type III has been linked to invasive forms of the disease, and this change may be a potential biomarker. To examine this possibility, we implemented wavelength-dependent second harmonic generation circular dichroism (SHG-CD) imaging microscopy to quantitatively determine changes in chirality in ECM models comprised of different Col I/Col III composition. In these models, Col III was varied between 0 and 40%, and we found increasing Col III results in reduced net chirality, consistent with structural biology studies of Col I and III in tissues where the isoforms comingle in the same fibrils. We further examined the wavelength dependence of the SHG-CD to both optimize the response and gain insight into the underlying mechanism. We found using shorter SHG excitation wavelengths resulted in increased SHG-CD sensitivity, where this is consistent with the electric-dipole-coupled oscillator model suggested previously for the nonlinear chirality response from thin films. Moreover, the sensitivity is further consistent with the wavelength dependency of SHG intensity fit to a two-state model of the two-photon absorption in collagen. We also provide experimental calibration protocols to implement the SHG-CD modality on a laser scanning microscope. We last suggest that the technique has broad applicability in probing a wide range of diseased states with changes in collagen molecular structure.
Unsteady Pressure Measurements on Oscillating Models in European Wind Tunnels.
1980-03-01
EFFECTIVE TUBE DIAMETER 1.5 * EXPERIMENT 0j 1. 0. Frequency ,Hz 50 100 1*50 200 1500 2000 Figure 1 Experimental and Theoretical Results for a Single i...NORA 17 III CONCLUDING REMARKS 18* IV REFERENCES 19 P7 ,.-- ii i 7 LIST OF ILLUSTRATIONS FIGURE PAGE 1 Experimental and Theoretical Results for a...and Experimental Centerline Pressures in Chordwise Bending 71 48 Rigid Wing with Oscillating Control Surface 72 49 Supersonic Pressure Due to Control
Theoretical model of fishbone oscillations in magnetically confined plasmas
Coppi, B.; Porcelli, F.
1986-11-03
The onset of electromagnetic oscillations that are observed in magnetically confined plasmas where beams of fast neutrals are injected is associated with the excitation of a mode with poloidal wave number m/sup 0/ = 1 and phase velocity equal to the core-ion diamagnetic velocity. The resonant interaction of the mode with the beam ions is viewed as a form of dissipation that allows the release of the mode excitation energy, related to the gradient of the plasma pressure.
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.
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.
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
NASA Astrophysics Data System (ADS)
Steuernagel, Ole
2014-06-01
In quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us to understand either from the viewpoint of the other. Here we show that all general time-dependent solutions of the free-particle Schrödinger equation can be mapped to solutions of the Schrödinger equation for harmonic potentials, both the trapping oscillator and the inverted "oscillator". This map is fully invertible and therefore induces an isomorphism between both types of system, they are equivalent. A composition of the map and its inverse allows us to map from one harmonic oscillator to another with a different spring constant and different center position. The map is independent of the state of the system, consisting only of a coordinate transformation and multiplication by a form factor, and can be chosen such that the state is identical in both systems at one point in time. This transition point in time can be chosen freely, the wave function of the particle evolving in time in one system before the transition point can therefore be linked up smoothly with the wave function for the other system and its future evolution after the transition point. Such a cut-and-paste procedure allows us to describe the instantaneous changes of the environment a particle finds itself in. Transitions from free to trapped systems, between harmonic traps of different spring constants or center positions, or, from harmonic binding to repulsive harmonic potentials are straightforwardly modelled. This includes some time-dependent harmonic potentials. The mappings introduced here are computationally more efficient than either state-projection or harmonic oscillator propagator techniques conventionally employed when describing instantaneous (non-adiabatic) changes of a quantum particle's environment.
Decay-less kink oscillations in coronal loops
NASA Astrophysics Data System (ADS)
Anfinogentov, S.; Nisticò, G.; Nakariakov, V. M.
2013-12-01
Context. Kink oscillations of coronal loops in an off-limb active region are detected with the Imaging Assembly Array (AIA) instruments of the Solar Dynamics Observatory (SDO) at 171 Å. Aims: We aim to measure periods and amplitudes of kink oscillations of different loops and to determinate the evolution of the oscillation phase along the oscillating loop. Methods: Oscillating coronal loops were visually identified in the field of view of SDO/AIA and STEREO/EUVI-A: the loop length was derived by three-dimensional analysis. Several slits were taken along the loops to assemble time-distance maps. We identified oscillatory patterns and retrieved periods and amplitudes of the oscillations. We applied the cross-correlation technique to estimate the phase shift between oscillations at different segments of oscillating loops. Results: We found that all analysed loops show low-amplitude undamped transverse oscillations. Oscillation periods of loops in the same active region range from 2.5 to 11 min, and are different for different loops. The displacement amplitude is lower than 1 Mm. The oscillation phase is constant along each analysed loop. The spatial structure of the phase of the oscillations corresponds to the fundamental standing kink mode. We conclude that the observed behaviour is consistent with the empirical model in terms of a damped harmonic resonator affected by a non-resonant continuously operating external force. A movie is available in electronic form at http://www.aanda.org
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.