Wave Driven Non-linear Flow Oscillator for the 22-Year Solar Cycle

NASA Technical Reports Server (NTRS)

Mayr, Hans G.; Wolff, Charles L.; Hartle, Richard E.; Einaudi, Franco (Technical Monitor)

2000-01-01

In the Earth's atmosphere, a zonal flow oscillation is observed with periods between 20 and 32 months, the Quasi Biennial Oscillation. This oscillation does not require external time dependent forcing but is maintained by non-linear wave momentum deposition. It is proposed that such a mechanism also drives long-period oscillations in planetary and stellar interiors. We apply this mechanism to generate a flow oscillation for the 22-year solar cycle. The oscillation would occur just below the convective envelope where waves can propagate. Using scale analysis, we present results from a simplified model that incorporates Hines' gravity wave parameterization. Wave amplitudes less than 10 m/s can produce reversing zonal flows of 25 m/s that should be sufficient to generate a corresponding oscillation in the poloidal magnetic field. Low buoyancy frequency and the associated increase in turbulence help to produce the desired oscillation period of the flow.

Computing anticipatory systems with incursion and hyperincursion

NASA Astrophysics Data System (ADS)

Dubois, Daniel M.

1998-07-01

An anticipatory system is a system which contains a model of itself and/or of its environment in view of computing its present state as a function of the prediction of the model. With the concepts of incursion and hyperincursion, anticipatory discrete systems can be modelled, simulated and controlled. By definition an incursion, an inclusive or implicit recursion, can be written as: x(t+1)=F[…,x(t-1),x(t),x(t+1),…] where the value of a variable x(t+1) at time t+1 is a function of this variable at past, present and future times. This is an extension of recursion. Hyperincursion is an incursion with multiple solutions. For example, chaos in the Pearl-Verhulst map model: x(t+1)=a.x(t).[1-x(t)] is controlled by the following anticipatory incursive model: x(t+1)=a.x(t).[1-x(t+1)] which corresponds to the differential anticipatory equation: dx(t)/dt=a.x(t).[1-x(t+1)]-x(t). The main part of this paper deals with the discretisation of differential equation systems of linear and non-linear oscillators. The non-linear oscillator is based on the Lotka-Volterra equations model. The discretisation is made by incursion. The incursive discrete equation system gives the same stability condition than the original differential equations without numerical instabilities. The linearisation of the incursive discrete non-linear Lotka-Volterra equation system gives rise to the classical harmonic oscillator. The incursive discretisation of the linear oscillator is similar to define backward and forward discrete derivatives. A generalized complex derivative is then considered and applied to the harmonic oscillator. Non-locality seems to be a property of anticipatory systems. With some mathematical assumption, the Schrödinger quantum equation is derived for a particle in a uniform potential. Finally an hyperincursive system is given in the case of a neural stack memory.

Stochastic Multiresonance for a Fractional Linear Oscillator with Quadratic Trichotomous Noise

NASA Astrophysics Data System (ADS)

Zhu, Jian-Qu; Jin, Wei-Dong; Zheng, Gao; Guo, Feng

2017-11-01

The stochastic multiresonance behavior for a fractional linear oscillator with random system frequency is investigated. The fluctuation of the system frequency is a quadratic trichotomous noise, the memory kernel of the fractional oscillator is modeled as a Mittag-Leffler function. Based on linear system theory, applying Laplace transform and the definition of fractional derivative, the expression of the system output amplitude (SPA) is obtained. Stochastic multiresonance phenomenon is found on the curves of SPA versus the memory time and the memory exponent of the fractional oscillator, as well as versus the trichotomous noise amplitude. The SPA depends non-monotonically on the stationary probability of the trichotomous noise, on the viscous damping coefficient and system characteristic frequency of the oscillator, as well as on the driving frequency of external force. Supported by National Natural Science Foundation of China under Grant No. 61134002

The Pendulum: A Paradigm for the Linear Oscillator

ERIC Educational Resources Information Center

Newburgh, Ronald

2004-01-01

The simple pendulum is a model for the linear oscillator. The usual mathematical treatment of the problem begins with a differential equation that one solves with the techniques of the differential calculus, a formal process that tends to obscure the physics. In this paper we begin with a kinematic description of the motion obtained by experiment…

On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

NASA Astrophysics Data System (ADS)

BOERTJENS, G. J.; VAN HORSSEN, W. T.

2000-08-01

In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.

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.

Linear oscillation of gas bubbles in a viscoelastic material under ultrasound irradiation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hamaguchi, Fumiya; Ando, Keita, E-mail: kando@mech.keio.ac.jp

2015-11-15

Acoustically forced oscillation of spherical gas bubbles in a viscoelastic material is studied through comparisons between experiments and linear theory. An experimental setup has been designed to visualize bubble dynamics in gelatin gels using a high-speed camera. A spherical gas bubble is created by focusing an infrared laser pulse into (gas-supersaturated) gelatin gels. The bubble radius (up to 150 μm) under mechanical equilibrium is controlled by gradual mass transfer of gases across the bubble interface. The linearized bubble dynamics are studied from the observation of spherical bubble oscillation driven by low-intensity, planar ultrasound driven at 28 kHz. It follows frommore » the experiment for an isolated bubble that the frequency response in its volumetric oscillation was shifted to the high frequency side and its peak was suppressed as the gelatin concentration increases. The measurement is fitted to the linearized Rayleigh–Plesset equation coupled with the Voigt constitutive equation that models the behavior of linear viscoelastic solids; the fitting yields good agreement by tuning unknown values of the viscosity and rigidity, indicating that more complex phenomena including shear thinning, stress relaxation, and retardation do not play an important role for the small-amplitude oscillations. Moreover, the cases for bubble-bubble and bubble-wall systems are studied. The observed interaction effect on the linearized dynamics can be explained as well by a set of the Rayleigh–Plesset equations coupled through acoustic radiation among these systems. This suggests that this experimental setup can be applied to validate the model of bubble dynamics with more complex configuration such as a cloud of bubbles in viscoelastic materials.« less

The measurement of linear frequency drift in oscillators

NASA Astrophysics Data System (ADS)

Barnes, J. A.

1985-04-01

A linear drift in frequency is an important element in most stochastic models of oscillator performance. Quartz crystal oscillators often have drifts in excess of a part in ten to the tenth power per day. Even commercial cesium beam devices often show drifts of a few parts in ten to the thirteenth per year. There are many ways to estimate the drift rates from data samples (e.g., regress the phase on a quadratic; regress the frequency on a linear; compute the simple mean of the first difference of frequency; use Kalman filters with a drift term as one element in the state vector; and others). Although most of these estimators are unbiased, they vary in efficiency (i.e., confidence intervals). Further, the estimation of confidence intervals using the standard analysis of variance (typically associated with the specific estimating technique) can give amazingly optimistic results. The source of these problems is not an error in, say, the regressions techniques, but rather the problems arise from correlations within the residuals. That is, the oscillator model is often not consistent with constraints on the analysis technique or, in other words, some specific analysis techniques are often inappropriate for the task at hand. The appropriateness of a specific analysis technique is critically dependent on the oscillator model and can often be checked with a simple whiteness test on the residuals.

Resonance frequencies of lipid-shelled microbubbles in the regime of nonlinear oscillations

PubMed Central

Doinikov, Alexander A.; Haac, Jillian F.; Dayton, Paul A.

2009-01-01

Knowledge of resonant frequencies of contrast microbubbles is important for the optimization of ultrasound contrast imaging and therapeutic techniques. To date, however, there are estimates of resonance frequencies of contrast microbubbles only for the regime of linear oscillation. The present paper proposes an approach for evaluating resonance frequencies of contrast agent microbubbles in the regime of nonlinear oscillation. The approach is based on the calculation of the time-averaged oscillation power of the radial bubble oscillation. The proposed procedure was verified for free bubbles in the frequency range 1–4 MHz and then applied to lipid-shelled microbubbles insonified with a single 20-cycle acoustic pulse at two values of the acoustic pressure amplitude, 100 kPa and 200 kPa, and at four frequencies: 1.5, 2.0, 2.5, and 3.0 MHz. It is shown that, as the acoustic pressure amplitude is increased, the resonance frequency of a lipid-shelled microbubble tends to decrease in comparison with its linear resonance frequency. Analysis of existing shell models reveals that models that treat the lipid shell as a linear viscoelastic solid appear may be challenged to provide the observed tendency in the behavior of the resonance frequency at increasing acoustic pressure. The conclusion is drawn that the further development of shell models could be improved by the consideration of nonlinear rheological laws. PMID:18977009

Comparison of heaving buoy and oscillating flap wave energy converters

NASA Astrophysics Data System (ADS)

Abu Bakar, Mohd Aftar; Green, David A.; Metcalfe, Andrew V.; Najafian, G.

2013-04-01

Waves offer an attractive source of renewable energy, with relatively low environmental impact, for communities reasonably close to the sea. Two types of simple wave energy converters (WEC), the heaving buoy WEC and the oscillating flap WEC, are studied. Both WECs are considered as simple energy converters because they can be modelled, to a first approximation, as single degree of freedom linear dynamic systems. In this study, we estimate the response of both WECs to typical wave inputs; wave height for the buoy and corresponding wave surge for the flap, using spectral methods. A nonlinear model of the oscillating flap WEC that includes the drag force, modelled by the Morison equation is also considered. The response to a surge input is estimated by discrete time simulation (DTS), using central difference approximations to derivatives. This is compared with the response of the linear model obtained by DTS and also validated using the spectral method. Bendat's nonlinear system identification (BNLSI) technique was used to analyze the nonlinear dynamic system since the spectral analysis was only suitable for linear dynamic system. The effects of including the nonlinear term are quantified.

Meridionally propagating interannual-to-interdecadal variability in a linear ocean-atmosphere model

NASA Technical Reports Server (NTRS)

Mehta, Vikram M.

1992-01-01

Meridional oscillation modes in a global, primitive-equation coupled ocean-atmosphere model have been analyzed in order to determine whether they contain such meridionally propagating modes as surface-pressure perturbations with years-to-decades oscillation periods. A two-layer global ocean model and a two-level global atmosphere model were then formulated. For realistic parameter values and basic states, meridional modes oscillating at periods of several years to several decades are noted to be present in the coupled ocean-atmosphere model; the oscillation periods, travel times, and meridional structures of surface pressure perturbations in one of the modes are found to be comparable to the corresponding characteristics of observed sea-level pressure perturbations.

Predator-prey model for the self-organization of stochastic oscillators in dual populations

NASA Astrophysics Data System (ADS)

Moradi, Sara; Anderson, Johan; Gürcan, Ozgür D.

2015-12-01

A predator-prey model of dual populations with stochastic oscillators is presented. A linear cross-coupling between the two populations is introduced following the coupling between the motions of a Wilberforce pendulum in two dimensions: one in the longitudinal and the other in torsional plain. Within each population a Kuramoto-type competition between the phases is assumed. Thus, the synchronization state of the whole system is controlled by these two types of competitions. The results of the numerical simulations show that by adding the linear cross-coupling interactions predator-prey oscillations between the two populations appear, which results in self-regulation of the system by a transfer of synchrony between the two populations. The model represents several important features of the dynamical interplay between the drift wave and zonal flow turbulence in magnetically confined plasmas, and a novel interpretation of the coupled dynamics of drift wave-zonal flow turbulence using synchronization of stochastic oscillator is discussed.

Comparative study of popular objective functions for damping power system oscillations in multimachine system.

PubMed

Islam, Naz Niamul; Hannan, M A; Shareef, Hussain; Mohamed, Azah; Salam, M A

2014-01-01

Power oscillation damping controller is designed in linearized model with heuristic optimization techniques. Selection of the objective function is very crucial for damping controller design by optimization algorithms. In this research, comparative analysis has been carried out to evaluate the effectiveness of popular objective functions used in power system oscillation damping. Two-stage lead-lag damping controller by means of power system stabilizers is optimized using differential search algorithm for different objective functions. Linearized model simulations are performed to compare the dominant mode's performance and then the nonlinear model is continued to evaluate the damping performance over power system oscillations. All the simulations are conducted in two-area four-machine power system to bring a detailed analysis. Investigated results proved that multiobjective D-shaped function is an effective objective function in terms of moving unstable and lightly damped electromechanical modes into stable region. Thus, D-shape function ultimately improves overall system damping and concurrently enhances power system reliability.

Chemical oscillator as a generalized Rayleigh oscillator.

PubMed

Ghosh, Shyamolina; Ray, Deb Shankar

2013-10-28

We derive the conditions under which a set of arbitrary two dimensional autonomous kinetic equations can be reduced to the form of a generalized Rayleigh oscillator which admits of limit cycle solution. This is based on a linear transformation of field variables which can be found by inspection of the kinetic equations. We illustrate the scheme with the help of several chemical and bio-chemical oscillator models to show how they can be cast as a generalized Rayleigh oscillator.

Using oceanic-atmospheric oscillations for long lead time streamflow forecasting

NASA Astrophysics Data System (ADS)

Kalra, Ajay; Ahmad, Sajjad

2009-03-01

We present a data-driven model, Support Vector Machine (SVM), for long lead time streamflow forecasting using oceanic-atmospheric oscillations. The SVM is based on statistical learning theory that uses a hypothesis space of linear functions based on Kernel approach and has been used to predict a quantity forward in time on the basis of training from past data. The strength of SVM lies in minimizing the empirical classification error and maximizing the geometric margin by solving inverse problem. The SVM model is applied to three gages, i.e., Cisco, Green River, and Lees Ferry in the Upper Colorado River Basin in the western United States. Annual oceanic-atmospheric indices, comprising Pacific Decadal Oscillation (PDO), North Atlantic Oscillation (NAO), Atlantic Multidecadal Oscillation (AMO), and El Nino-Southern Oscillations (ENSO) for a period of 1906-2001 are used to generate annual streamflow volumes with 3 years lead time. The SVM model is trained with 86 years of data (1906-1991) and tested with 10 years of data (1992-2001). On the basis of correlation coefficient, root means square error, and Nash Sutcliffe Efficiency Coefficient the model shows satisfactory results, and the predictions are in good agreement with measured streamflow volumes. Sensitivity analysis, performed to evaluate the effect of individual and coupled oscillations, reveals a strong signal for ENSO and NAO indices as compared to PDO and AMO indices for the long lead time streamflow forecast. Streamflow predictions from the SVM model are found to be better when compared with the predictions obtained from feedforward back propagation artificial neural network model and linear regression.

Linear control of oscillator and amplifier flows*

NASA Astrophysics Data System (ADS)

Schmid, Peter J.; Sipp, Denis

2016-08-01

Linear control applied to fluid systems near an equilibrium point has important applications for many flows of industrial or fundamental interest. In this article we give an exposition of tools and approaches for the design of control strategies for globally stable or unstable flows. For unstable oscillator flows a feedback configuration and a model-based approach is proposed, while for stable noise-amplifier flows a feedforward setup and an approach based on system identification is advocated. Model reduction and robustness issues are addressed for the oscillator case; statistical learning techniques are emphasized for the amplifier case. Effective suppression of global and convective instabilities could be demonstrated for either case, even though the system-identification approach results in a superior robustness to off-design conditions.

Oscillatory Reduction in Option Pricing Formula Using Shifted Poisson and Linear Approximation

NASA Astrophysics Data System (ADS)

Nur Rachmawati, Ro'fah; Irene; Budiharto, Widodo

2014-03-01

Option is one of derivative instruments that can help investors improve their expected return and minimize the risks. However, the Black-Scholes formula is generally used in determining the price of the option does not involve skewness factor and it is difficult to apply in computing process because it produces oscillation for the skewness values close to zero. In this paper, we construct option pricing formula that involve skewness by modified Black-Scholes formula using Shifted Poisson model and transformed it into the form of a Linear Approximation in the complete market to reduce the oscillation. The results are Linear Approximation formula can predict the price of an option with very accurate and successfully reduce the oscillations in the calculation processes.

A Linear Model of Phase-Dependent Power Correlations in Neuronal Oscillations

PubMed Central

Eriksson, David; Vicente, Raul; Schmidt, Kerstin

2011-01-01

Recently, it has been suggested that effective interactions between two neuronal populations are supported by the phase difference between the oscillations in these two populations, a hypothesis referred to as “communication through coherence” (CTC). Experimental work quantified effective interactions by means of the power correlations between the two populations, where power was calculated on the local field potential and/or multi-unit activity. Here, we present a linear model of interacting oscillators that accounts for the phase dependency of the power correlation between the two populations and that can be used as a reference for detecting non-linearities such as gain control. In the experimental analysis, trials were sorted according to the coupled phase difference of the oscillators while the putative interaction between oscillations was taking place. Taking advantage of the modeling, we further studied the dependency of the power correlation on the uncoupled phase difference, connection strength, and topology. Since the uncoupled phase difference, i.e., the phase relation before the effective interaction, is the causal variable in the CTC hypothesis we also describe how power correlations depend on that variable. For uni-directional connectivity we observe that the width of the uncoupled phase dependency is broader than for the coupled phase. Furthermore, the analytical results show that the characteristics of the phase dependency change when a bidirectional connection is assumed. The width of the phase dependency indicates which oscillation frequencies are optimal for a given connection delay distribution. We propose that a certain width enables a stimulus-contrast dependent extent of effective long-range lateral connections. PMID:21808618

The dynamics of two linearly coupled Goodwin oscillators

NASA Astrophysics Data System (ADS)

Antonova, A. O.; Reznik, S. N.; Todorov, M. D.

2017-10-01

In this paper the Puu model of the interaction of Goodwin's business cycles for two regions is reconsidered. We investigated the effect of the accelerator coefficients and the Hicksian 'ceiling' and 'floor' parameters on the time dynamics of incomes for different values of marginal propensity to import. The cases when the periods of isolated Goodwin's cycles are close, and when they differ approximately twice are considered. By perturbation theory we obtained the formulas for slowly varying amplitudes and phase difference of weakly nonlinear coupled Goodwin oscillations. The coupled oscillations of two Goodwin's cycles with piecewise linear accelerators with only 'floor' are considered.

Transients in the synchronization of asymmetrically coupled oscillator arrays

NASA Astrophysics Data System (ADS)

Cantos, C. E.; Hammond, D. K.; Veerman, J. J. P.

2016-09-01

We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a certain parameter regime Ω. As corollaries we show that minimizing the transients requires considering non-symmetric coupling, and that within Ω the computed linear growth in N of the transients is independent of (reasonable) boundary conditions.

Modeling and analysis of several classes of self-oscillating inverters. I - State-plane representations. II - Model extension, classification, and duality relationships

NASA Technical Reports Server (NTRS)

Lee, F. C. Y.; Wilson, T. G.

1982-01-01

The present investigation is concerned with an important class of power conditioning networks, taking into account self-oscillating dc-to-square-wave transistor inverters. The considered circuits are widely used both as the principal power converting and processing means in many systems and as low-power analog-to-discrete-time converters for controlling the switching of the output-stage semiconductors in a variety of power conditioning systems. Aspects of piecewise-linear modeling are discussed, taking into consideration component models, and an equivalent-circuit model. Questions of singular point analysis and state plane representation are also investigated, giving attention to limit cycles, starting circuits, the region of attraction, a hard oscillator, and a soft oscillator.

Two-Dimensional Array Beam Scanning Via Externally and Mutually Injection Locked Coupled Oscillators

NASA Technical Reports Server (NTRS)

Pogorzelski, Ronald J.

2000-01-01

Some years ago, Stephan proposed an approach to one dimensional (linear) phased array beam steering which requires only a single phase shifter. This involves the use of a linear array of voltage-controlled electronic oscillators coupled to nearest neighbors. The oscillators are mutually injection locked by controlling their coupling and tuning appropriately. Stephan's approach consists of deriving two signals from a master oscillator, one signal phase shifted with respect to the other by means of a single phase shifter. These two signals are injected into the end oscillators of the array. The result is a linear phase progression across the oscillator array. Thus, if radiating elements are connected to each oscillator and spaced uniformly along a line, they will radiate a beam at an angle to that line determined by the phase gradient which is, in turn, determined by the phase difference between the injection signals.The beam direction is therefore controlled by adjusting this phase difference. Recently, Pogorzelski and York presented a formulation which facilitates theoretical analysis of the above beam steering technique. This was subsequently applied by Pogorzelski in analysis of two dimensional beam steering using perimeter detuning of a coupled oscillator array. The formulation is based on a continuum model in which the oscillator phases are represented by a continuous function satisfying a partial differential equation of diffusion type. This equation can be solved via the Laplace transform and the resulting solution exhibits the dynamic behavior of the array as the beam is steered. Stephan's beam steering technique can be similarly generalized to two-dimensional arrays in which the beam control signals are applied to the oscillators on the perimeter of the array. In this paper the continuum model for this two-dimensional case is developed and the dynamic solution for the corresponding aperture phase function is obtained. The corresponding behavior of the resulting far-zone radiation pattern is displayed as well.

Properties of finite difference models of non-linear conservative oscillators

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1988-01-01

Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.

Nonstandard neutrino self-interactions in a supernova and fast flavor conversions

NASA Astrophysics Data System (ADS)

Dighe, Amol; Sen, Manibrata

2018-02-01

We study the effects of nonstandard self-interactions (NSSI) of neutrinos streaming out of a core-collapse supernova. We show that with NSSI, the standard linear stability analysis gives rise to linearly as well as exponentially growing solutions. For a two-box spectrum, we demonstrate analytically that flavor-preserving NSSI lead to a suppression of bipolar collective oscillations. In the intersecting four-beam model, we show that flavor-violating NSSI can lead to fast oscillations even when the angle between the neutrino and antineutrino beams is obtuse, which is forbidden in the standard model. This leads to the new possibility of fast oscillations in a two-beam system with opposing neutrino-antineutrino fluxes, even in the absence of any spatial inhomogeneities. Finally, we solve the full nonlinear equations of motion in the four-beam model numerically, and explore the interplay of fast and slow flavor conversions in the long-time behavior, in the presence of NSSI.

Free oscillations in a climate model with ice-sheet dynamics

NASA Technical Reports Server (NTRS)

Kallen, E.; Crafoord, C.; Ghil, M.

1979-01-01

A study of stable periodic solutions to a simple nonlinear model of the ocean-atmosphere-ice system is presented. The model has two dependent variables: ocean-atmosphere temperature and latitudinal extent of the ice cover. No explicit dependence on latitude is considered in the model. Hence all variables depend only on time and the model consists of a coupled set of nonlinear ordinary differential equations. The globally averaged ocean-atmosphere temperature in the model is governed by the radiation balance. The reflectivity to incoming solar radiation, i.e., the planetary albedo, includes separate contributions from sea ice and from continental ice sheets. The major physical mechanisms active in the model are (1) albedo-temperature feedback, (2) continental ice-sheet dynamics and (3) precipitation-rate variations. The model has three-equilibrium solutions, two of which are linearly unstable, while one is linearly stable. For some choices of parameters, the stability picture changes and sustained, finite-amplitude oscillations obtain around the previously stable equilibrium solution. The physical interpretation of these oscillations points to the possibility of internal mechanisms playing a role in glaciation cycles.

LASR-Guided Variability Subtraction: The Linear Algorithm for Significance Reduction of Stellar Seismic Activity

NASA Astrophysics Data System (ADS)

Horvath, Sarah; Myers, Sam; Ahlers, Johnathon; Barnes, Jason W.

2017-10-01

Stellar seismic activity produces variations in brightness that introduce oscillations into transit light curves, which can create challenges for traditional fitting models. These oscillations disrupt baseline stellar flux values and potentially mask transits. We develop a model that removes these oscillations from transit light curves by minimizing the significance of each oscillation in frequency space. By removing stellar variability, we prepare each light curve for traditional fitting techniques. We apply our model to $\\delta$-Scuti KOI-976 and demonstrate that our variability subtraction routine successfully allows for measuring bulk system characteristics using traditional light curve fitting. These results open a new window for characterizing bulk system parameters of planets orbiting seismically active stars.

Experimental study of the oscillation of spheres in an acoustic levitator.

PubMed

Andrade, Marco A B; Pérez, Nicolás; Adamowski, Julio C

2014-10-01

The spontaneous oscillation of solid spheres in a single-axis acoustic levitator is experimentally investigated by using a high speed camera to record the position of the levitated sphere as a function of time. The oscillations in the axial and radial directions are systematically studied by changing the sphere density and the acoustic pressure amplitude. In order to interpret the experimental results, a simple model based on a spring-mass system is applied in the analysis of the sphere oscillatory behavior. This model requires the knowledge of the acoustic pressure distribution, which was obtained numerically by using a linear finite element method (FEM). Additionally, the linear acoustic pressure distribution obtained by FEM was compared with that measured with a laser Doppler vibrometer. The comparison between numerical and experimental pressure distributions shows good agreement for low values of pressure amplitude. When the pressure amplitude is increased, the acoustic pressure distribution becomes nonlinear, producing harmonics of the fundamental frequency. The experimental results of the spheres oscillations for low pressure amplitudes are consistent with the results predicted by the simple model based on a spring-mass system.

Linear transformation and oscillation criteria for Hamiltonian systems

NASA Astrophysics Data System (ADS)

Zheng, Zhaowen

2007-08-01

Using a linear transformation similar to the Kummer transformation, some new oscillation criteria for linear Hamiltonian systems are established. These results generalize and improve the oscillation criteria due to I.S. Kumari and S. Umanaheswaram [I. Sowjaya Kumari, S. Umanaheswaram, Oscillation criteria for linear matrix Hamiltonian systems, J. Differential Equations 165 (2000) 174-198], Q. Yang et al. [Q. Yang, R. Mathsen, S. Zhu, Oscillation theorems for self-adjoint matrix Hamiltonian systems, J. Differential Equations 190 (2003) 306-329], and S. Chen and Z. Zheng [Shaozhu Chen, Zhaowen Zheng, Oscillation criteria of Yan type for linear Hamiltonian systems, Comput. Math. Appl. 46 (2003) 855-862]. These criteria also unify many of known criteria in literature and simplify the proofs.

Numerical Study of the Complex Temporal Pattern of Spontaneous Oscillation in Bullfrog Saccular Hair Cells

NASA Astrophysics Data System (ADS)

Roongthumskul, Yuttana; Fredrickson-Hemsing, Lea; Kao, Albert; Bozovic, Dolores

2011-11-01

Hair bundles of the bullfrog sacculus display spontaneous oscillations that show complex temporal profiles. Quiescent intervals are typically interspersed with oscillations, analogous to bursting behavior observed in neural systems. By introducing slow calcium dynamics into the theoretical model of bundle mechanics, we reproduce numerically the multi-mode oscillations and explore the effects of internal parameters on the temporal profiles and the frequency tuning of their linear response functions. We also study the effects of mechanical overstimulation on the oscillatory behavior.

RF Frequency Oscillations in the Early Stages of Vacuum Arc Collapse

NASA Technical Reports Server (NTRS)

Griffin, Steven T.; Thio, Y. C. Francis

2003-01-01

RF frequency oscillations may be produced in a typical capacitive charging / discharging pulsed power system. These oscillations may be benign, parasitic, destructive or crucial to energy deposition. In some applications, proper damping of oscillations may be critical to proper plasma formation. Because the energy deposited into the plasma is a function of plasma and circuit conditions, the entire plasma / circuit system needs to be considered as a unit To accomplish this, the initiation of plasma is modeled as a time-varying, non-linear element in a circuit analysis model. The predicted spectra are compared to empirical power density spectra including those obtained from vacuum arcs.

Free piston variable-stroke linear-alternator generator

DOEpatents

Haaland, Carsten M.

1998-01-01

A free-piston variable stroke linear-alternator AC power generator for a combustion engine. An alternator mechanism and oscillator system generates AC current. The oscillation system includes two oscillation devices each having a combustion cylinder and a flying turnbuckle. The flying turnbuckle moves in accordance with the oscillation device. The alternator system is a linear alternator coupled between the two oscillation devices by a slotted connecting rod.

Temperature compensation via cooperative stability in protein degradation

NASA Astrophysics Data System (ADS)

Peng, Yuanyuan; Hasegawa, Yoshihiko; Noman, Nasimul; Iba, Hitoshi

2015-08-01

Temperature compensation is a notable property of circadian oscillators that indicates the insensitivity of the oscillator system's period to temperature changes; the underlying mechanism, however, is still unclear. We investigated the influence of protein dimerization and cooperative stability in protein degradation on the temperature compensation ability of two oscillators. Here, cooperative stability means that high-order oligomers are more stable than their monomeric counterparts. The period of an oscillator is affected by the parameters of the dynamic system, which in turn are influenced by temperature. We adopted the Repressilator and the Atkinson oscillator to analyze the temperature sensitivity of their periods. Phase sensitivity analysis was employed to evaluate the period variations of different models induced by perturbations to the parameters. Furthermore, we used experimental data provided by other studies to determine the reasonable range of parameter temperature sensitivity. We then applied the linear programming method to the oscillatory systems to analyze the effects of protein dimerization and cooperative stability on the temperature sensitivity of their periods, which reflects the ability of temperature compensation in circadian rhythms. Our study explains the temperature compensation mechanism for circadian clocks. Compared with the no-dimer mathematical model and linear model for protein degradation, our theoretical results show that the nonlinear protein degradation caused by cooperative stability is more beneficial for realizing temperature compensation of the circadian clock.

A 1-D model of the nonlinear dynamics of the human lumbar intervertebral disc

NASA Astrophysics Data System (ADS)

Marini, Giacomo; Huber, Gerd; Püschel, Klaus; Ferguson, Stephen J.

2017-01-01

Lumped parameter models of the spine have been developed to investigate its response to whole body vibration. However, these models assume the behaviour of the intervertebral disc to be linear-elastic. Recently, the authors have reported on the nonlinear dynamic behaviour of the human lumbar intervertebral disc. This response was shown to be dependent on the applied preload and amplitude of the stimuli. However, the mechanical properties of a standard linear elastic model are not dependent on the current deformation state of the system. The aim of this study was therefore to develop a model that is able to describe the axial, nonlinear quasi-static response and to predict the nonlinear dynamic characteristics of the disc. The ability to adapt the model to an individual disc's response was a specific focus of the study, with model validation performed against prior experimental data. The influence of the numerical parameters used in the simulations was investigated. The developed model exhibited an axial quasi-static and dynamic response, which agreed well with the corresponding experiments. However, the model needs further improvement to capture additional peculiar characteristics of the system dynamics, such as the change of mean point of oscillation exhibited by the specimens when oscillating in the region of nonlinear resonance. Reference time steps were identified for specific integration scheme. The study has demonstrated that taking into account the nonlinear-elastic behaviour typical of the intervertebral disc results in a predicted system oscillation much closer to the physiological response than that provided by linear-elastic models. For dynamic analysis, the use of standard linear-elastic models should be avoided, or restricted to study cases where the amplitude of the stimuli is relatively small.

Signatures of nonlinearity in single cell noise-induced oscillations.

PubMed

Thomas, Philipp; Straube, Arthur V; Timmer, Jens; Fleck, Christian; Grima, Ramon

2013-10-21

A class of theoretical models seeks to explain rhythmic single cell data by postulating that they are generated by intrinsic noise in biochemical systems whose deterministic models exhibit only damped oscillations. The main features of such noise-induced oscillations are quantified by the power spectrum which measures the dependence of the oscillatory signal's power with frequency. In this paper we derive an approximate closed-form expression for the power spectrum of any monostable biochemical system close to a Hopf bifurcation, where noise-induced oscillations are most pronounced. Unlike the commonly used linear noise approximation which is valid in the macroscopic limit of large volumes, our theory is valid over a wide range of volumes and hence affords a more suitable description of single cell noise-induced oscillations. Our theory predicts that the spectra have three universal features: (i) a dominant peak at some frequency, (ii) a smaller peak at twice the frequency of the dominant peak and (iii) a peak at zero frequency. Of these, the linear noise approximation predicts only the first feature while the remaining two stem from the combination of intrinsic noise and nonlinearity in the law of mass action. The theoretical expressions are shown to accurately match the power spectra determined from stochastic simulations of mitotic and circadian oscillators. Furthermore it is shown how recently acquired single cell rhythmic fibroblast data displays all the features predicted by our theory and that the experimental spectrum is well described by our theory but not by the conventional linear noise approximation. © 2013 Elsevier Ltd. All rights reserved.

Free piston variable-stroke linear-alternator generator

DOEpatents

Haaland, C.M.

1998-12-15

A free-piston variable stroke linear-alternator AC power generator for a combustion engine is described. An alternator mechanism and oscillator system generates AC current. The oscillation system includes two oscillation devices each having a combustion cylinder and a flying turnbuckle. The flying turnbuckle moves in accordance with the oscillation device. The alternator system is a linear alternator coupled between the two oscillation devices by a slotted connecting rod. 8 figs.

A new Hysteretic Nonlinear Energy Sink (HNES)

NASA Astrophysics Data System (ADS)

Tsiatas, George C.; Charalampakis, Aristotelis E.

2018-07-01

The behavior of a new Hysteretic Nonlinear Energy Sink (HNES) coupled to a linear primary oscillator is investigated in shock mitigation. Apart from a small mass and a nonlinear elastic spring of the Duffing oscillator, the HNES is also comprised of a purely hysteretic and a linear elastic spring of potentially negative stiffness, connected in parallel. The Bouc-Wen model is used to describe the force produced by both the purely hysteretic and linear elastic springs. Coupling the primary oscillator with the HNES, three nonlinear equations of motion are derived in terms of the two displacements and the dimensionless hysteretic variable, which are integrated numerically using the analog equation method. The performance of the HNES is examined by quantifying the percentage of the initially induced energy in the primary system that is passively transferred and dissipated by the HNES. Remarkable results are achieved for a wide range of initial input energies. The great performance of the HNES is mostly evidenced when the linear spring stiffness takes on negative values.

Signal Processing in Periodically Forced Gradient Frequency Neural Networks

PubMed Central

Kim, Ji Chul; Large, Edward W.

2015-01-01

Oscillatory instability at the Hopf bifurcation is a dynamical phenomenon that has been suggested to characterize active non-linear processes observed in the auditory system. Networks of oscillators poised near Hopf bifurcation points and tuned to tonotopically distributed frequencies have been used as models of auditory processing at various levels, but systematic investigation of the dynamical properties of such oscillatory networks is still lacking. Here we provide a dynamical systems analysis of a canonical model for gradient frequency neural networks driven by a periodic signal. We use linear stability analysis to identify various driven behaviors of canonical oscillators for all possible ranges of model and forcing parameters. The analysis shows that canonical oscillators exhibit qualitatively different sets of driven states and transitions for different regimes of model parameters. We classify the parameter regimes into four main categories based on their distinct signal processing capabilities. This analysis will lead to deeper understanding of the diverse behaviors of neural systems under periodic forcing and can inform the design of oscillatory network models of auditory signal processing. PMID:26733858

Spectral modification of seismic waves propagating through solids exhibiting a resonance frequency: a 1-D coupled wave propagation-oscillation model

NASA Astrophysics Data System (ADS)

Frehner, Marcel; Schmalholz, Stefan M.; Podladchikov, Yuri

2009-02-01

A 1-D model is presented that couples the microscale oscillations of non-wetting fluid blobs in a partially saturated poroelastic medium with the macroscale wave propagation through the elastic skeleton. The fluid oscillations are caused by surface tension forces that act as the restoring forces driving the oscillations. The oscillations are described mathematically with the equation for a linear oscillator and the wave propagation is described with the 1-D elastic wave equation. Coupling is done using Hamilton's variational principle for continuous systems. The resulting linear system of two partial differential equations is solved numerically with explicit finite differences. Numerical simulations are used to analyse the effect of solids exhibiting internal oscillations, and consequently a resonance frequency, on seismic waves propagating through such media. The phase velocity dispersion relation shows a higher phase velocity in the high-frequency limit and a lower phase velocity in the low-frequency limit. At the resonance frequency a singularity in the dispersion relation occurs. Seismic waves can initiate oscillations of the fluid by transferring energy from solid to fluid at the resonance frequency. Due to this transfer, the spectral amplitude of the solid particle velocity decreases at the resonance frequency. After initiation, the oscillatory movement of the fluid continuously transfers energy at the resonance frequency back to the solid. Therefore, the spectral amplitude of the solid particle velocity is increased at the resonance frequency. Once initiated, fluid oscillations decrease in amplitude with increasing time. Consequently, the spectral peak of the solid particle velocity at the resonance frequency decreases with time.

Structural health monitoring based on sensitivity vector fields and attractor morphing.

PubMed

Yin, Shih-Hsun; Epureanu, Bogdan I

2006-09-15

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we analyse the morphology (deformation and movement) of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Present studies of such problems are based on linear theories. In contrast, the presented approach using nonlinear dynamics has the potential of enhancing accuracy and sensitivity of detection.

Negative Coulomb damping, limit cycles, and self-oscillation of the vocal folds

NASA Astrophysics Data System (ADS)

Fulcher, Lewis P.; Scherer, Ronald C.; Melnykov, Artem; Gateva, Vesela; Limes, Mark E.

2006-05-01

An effective one-mass model of phonation is developed. It borrows the salient features of the classic two-mass model of human speech developed by Ishizaka, Matsudaira, and Flanagan. Their model is based on the idea that the oscillating vocal folds maintain their motion by deriving energy from the flow of air through the glottis. We argue that the essence of the action of the aerodynamic forces on the vocal folds is captured by negative Coulomb damping, which acts on the oscillator to energize it. A viscous force is added to include the effects of tissue damping. The solutions to this single oscillator model show that when it is excited by negative Coulomb damping, it will reach a limit cycle. Displacements, phase portraits, and energy histories are presented for two underdamped linear oscillators. A nonlinear force is added so that the variations of the fundamental frequency and the open quotient with lung pressure are comparable to the behavior of the two-mass model.

Predator-prey model for the self-organization of stochastic oscillators in dual populations

NASA Astrophysics Data System (ADS)

Moradi, Sara; Anderson, Johan; Gürcan, Ozgur D.

A predator-prey model of dual populations with stochastic oscillators is presented. A linear cross-coupling between the two populations is introduced that follows the coupling between the motions of a Wilberforce pendulum in two dimensions: one in the longitudinal and the other in torsional plain. Within each population a Kuramoto type competition between the phases is assumed. Thus, the synchronization state of the whole system is controlled by these two types of competitions. The results of the numerical simulations show that by adding the linear cross-coupling interactions predator-prey oscillations between the two populations appear which results in self-regulation of the system by a transfer of synchrony between the two populations. The model represents several important features of the dynamical interplay between the drift wave and zonal flow turbulence in magnetically confined plasmas, and a novel interpretation of the coupled dynamics of drift wave-zonal flow turbulence using synchronization of stochastic oscillator is discussed. Sara Moradi has benefited from a mobility grant funded by the Belgian Federal Science Policy Office and the MSCA of the European Commission (FP7-PEOPLE-COFUND-2008 nº 246540).

Mathematical models of bipolar disorder

NASA Astrophysics Data System (ADS)

Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.

2009-07-01

We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.

Multivariate Time Series Decomposition into Oscillation Components.

PubMed

Matsuda, Takeru; Komaki, Fumiyasu

2017-08-01

Many time series are considered to be a superposition of several oscillation components. We have proposed a method for decomposing univariate time series into oscillation components and estimating their phases (Matsuda & Komaki, 2017 ). In this study, we extend that method to multivariate time series. We assume that several oscillators underlie the given multivariate time series and that each variable corresponds to a superposition of the projections of the oscillators. Thus, the oscillators superpose on each variable with amplitude and phase modulation. Based on this idea, we develop gaussian linear state-space models and use them to decompose the given multivariate time series. The model parameters are estimated from data using the empirical Bayes method, and the number of oscillators is determined using the Akaike information criterion. Therefore, the proposed method extracts underlying oscillators in a data-driven manner and enables investigation of phase dynamics in a given multivariate time series. Numerical results show the effectiveness of the proposed method. From monthly mean north-south sunspot number data, the proposed method reveals an interesting phase relationship.

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…

Time Series Decomposition into Oscillation Components and Phase Estimation.

PubMed

Matsuda, Takeru; Komaki, Fumiyasu

2017-02-01

Many time series are naturally considered as a superposition of several oscillation components. For example, electroencephalogram (EEG) time series include oscillation components such as alpha, beta, and gamma. We propose a method for decomposing time series into such oscillation components using state-space models. Based on the concept of random frequency modulation, gaussian linear state-space models for oscillation components are developed. In this model, the frequency of an oscillator fluctuates by noise. Time series decomposition is accomplished by this model like the Bayesian seasonal adjustment method. Since the model parameters are estimated from data by the empirical Bayes' method, the amplitudes and the frequencies of oscillation components are determined in a data-driven manner. Also, the appropriate number of oscillation components is determined with the Akaike information criterion (AIC). In this way, the proposed method provides a natural decomposition of the given time series into oscillation components. In neuroscience, the phase of neural time series plays an important role in neural information processing. The proposed method can be used to estimate the phase of each oscillation component and has several advantages over a conventional method based on the Hilbert transform. Thus, the proposed method enables an investigation of the phase dynamics of time series. Numerical results show that the proposed method succeeds in extracting intermittent oscillations like ripples and detecting the phase reset phenomena. We apply the proposed method to real data from various fields such as astronomy, ecology, tidology, and neuroscience.

Nonlinear evolution of baryon acoustic oscillations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crocce, Martin; Institut de Ciencies de l'Espai, IEEC-CSIC, Campus UAB, Facultat de Ciencies, Torre C5 par-2, Barcelona 08193; Scoccimarro, Roman

2008-01-15

We study the nonlinear evolution of baryon acoustic oscillations in the dark matter power spectrum and the correlation function using renormalized perturbation theory. In a previous paper we showed that renormalized perturbation theory successfully predicts the damping of acoustic oscillations; here we extend our calculation to the enhancement of power due to mode coupling. We show that mode coupling generates additional oscillations that are out of phase with those in the linear spectrum, leading to shifts in the scales of oscillation nodes defined with respect to a smooth spectrum. When Fourier transformed, these out-of-phase oscillations induce percent-level shifts in themore » acoustic peak of the two-point correlation function. We present predictions for these shifts as a function of redshift; these should be considered as a robust lower limit to the more realistic case that includes, in addition, redshift distortions and galaxy bias. We show that these nonlinear effects occur at very large scales, leading to a breakdown of linear theory at scales much larger than commonly thought. We discuss why virialized halo profiles are not responsible for these effects, which can be understood from basic physics of gravitational instability. Our results are in excellent agreement with numerical simulations, and can be used as a starting point for modeling baryon acoustic oscillations in future observations. To meet this end, we suggest a simple physically motivated model to correct for the shifts caused by mode coupling.« less

Design of Linear Control System for Wind Turbine Blade Fatigue Testing

NASA Astrophysics Data System (ADS)

Toft, Anders; Roe-Poulsen, Bjarke; Christiansen, Rasmus; Knudsen, Torben

2016-09-01

This paper proposes a linear method for wind turbine blade fatigue testing at Siemens Wind Power. The setup consists of a blade, an actuator (motor and load mass) that acts on the blade with a sinusoidal moment, and a distribution of strain gauges to measure the blade flexure. Based on the frequency of the sinusoidal input, the blade will start oscillating with a given gain, hence the objective of the fatigue test is to make the blade oscillate with a controlled amplitude. The system currently in use is based on frequency control, which involves some non-linearities that make the system difficult to control. To make a linear controller, a different approach has been chosen, namely making a controller which is not regulating on the input frequency, but on the input amplitude. A non-linear mechanical model for the blade and the motor has been constructed. This model has been simplified based on the desired output, namely the amplitude of the blade. Furthermore, the model has been linearised to make it suitable for linear analysis and control design methods. The controller is designed based on a simplified and linearised model, and its gain parameter determined using pole placement. The model variants have been simulated in the MATLAB toolbox Simulink, which shows that the controller design based on the simple model performs adequately with the non-linear model. Moreover, the developed controller solves the robustness issue found in the existent solution and also reduces the needed energy for actuation as it always operates at the blade eigenfrequency.

The general linear inverse problem - Implication of surface waves and free oscillations for earth structure.

NASA Technical Reports Server (NTRS)

Wiggins, R. A.

1972-01-01

The discrete general linear inverse problem reduces to a set of m equations in n unknowns. There is generally no unique solution, but we can find k linear combinations of parameters for which restraints are determined. The parameter combinations are given by the eigenvectors of the coefficient matrix. The number k is determined by the ratio of the standard deviations of the observations to the allowable standard deviations in the resulting solution. Various linear combinations of the eigenvectors can be used to determine parameter resolution and information distribution among the observations. Thus we can determine where information comes from among the observations and exactly how it constraints the set of possible models. The application of such analyses to surface-wave and free-oscillation observations indicates that (1) phase, group, and amplitude observations for any particular mode provide basically the same type of information about the model; (2) observations of overtones can enhance the resolution considerably; and (3) the degree of resolution has generally been overestimated for many model determinations made from surface waves.

Stimulus-induced transitions between spike-wave discharges and spindles with the modulation of thalamic reticular nucleus.

PubMed

Fan, Denggui; Wang, Qingyun; Su, Jianzhong; Xi, Hongguang

2017-12-01

It is believed that thalamic reticular nucleus (TRN) controls spindles and spike-wave discharges (SWD) in seizure or sleeping processes. The dynamical mechanisms of spatiotemporal evolutions between these two types of activity, however, are not well understood. In light of this, we first use a single-compartment thalamocortical neural field model to investigate the effects of TRN on occurrence of SWD and its transition. Results show that the increasing inhibition from TRN to specific relay nuclei (SRN) can lead to the transition of system from SWD to slow-wave oscillation. Specially, it is shown that stimulations applied in the cortical neuronal populations can also initiate the SWD and slow-wave oscillation from the resting states under the typical inhibitory intensity from TRN to SRN. Then, we expand into a 3-compartment coupled thalamocortical model network in linear and circular structures, respectively, to explore the spatiotemporal evolutions of wave states in different compartments. The main results are: (i) for the open-ended model network, SWD induced by stimulus in the first compartment can be transformed into sleep-like slow UP-DOWN and spindle states as it propagates into the downstream compartments; (ii) for the close-ended model network, weak stimulations performed in the first compartment can result in the consistent experimentally observed spindle oscillations in all three compartments; in contrast, stronger periodic single-pulse stimulations applied in the first compartment can induce periodic transitions between SWD and spindle oscillations. Detailed investigations reveal that multi-attractor coexistence mechanism composed of SWD, spindles and background state underlies these state evolutions. What's more, in order to demonstrate the state evolution stability with respect to the topological structures of neural network, we further expand the 3-compartment coupled network into 10-compartment coupled one, with linear and circular structures, and nearest-neighbor (NN) coupled network as well as its realization of small-world (SW) topology via random rewiring, respectively. Interestingly, for the cases of linear and circular connetivities, qualitatively similar results were obtained in addition to the more irregularity of firings. However, SWD can be eventually transformed into the consistent low-amplitude oscillations for both NN and SW networks. In particular, SWD evolves into the slow spindling oscillations and background tonic oscillations within the NN and SW network, respectively. Our modeling and simulation studies highlight the effect of network topology in the evolutions of SWD and spindling oscillations, which provides new insights into the mechanisms of cortical seizures development.

Power loss of an oscillating electric dipole in a quantum plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghaderipoor, L.; Mehramiz, A.

2012-12-15

A system of linearized quantum plasma equations (quantum hydrodynamic model) has been used for investigating the dispersion equation for electrostatic waves in the plasma. Furthermore, dispersion relations and their modifications due to quantum effects are used for calculating the power loss of an oscillating electric dipole. Finally, the results are compared in quantum and classical regimes.

Transient Modeling of Hybrid Rocket Low Frequency Instabilities

NASA Technical Reports Server (NTRS)

Karabeyoglu, M. Arif; DeZilwa, Shane; Cantwell, Brian; Zilliac, Greg

2003-01-01

A comprehensive dynamic model of a hybrid rocket has been developed in order to understand and predict the transient behavior including instabilities. A linearized version of the transient model predicted the low-frequency chamber pressure oscillations that are commonly observed in hybrids. The source of the instabilities is based on a complex coupling of thermal transients in the solid fuel, wall heat transfer blocking due to fuel regression rate and the transients in the boundary layer that forms on the fuel surface. The oscillation frequencies predicted by the linearized theory are in very good agreement with 43 motor test results obtained from the hybrid propulsion literature. The motor test results used in the comparison cover a very wide spectrum of parameters including: 1) four separate research and development programs, 2) three different oxidizers (LOX, GOX, N2O), 3) a wide range of motor dimensions (i.e. from 5 inch diameter to 72 inch diameter) and operating conditions and 4) several fuel formulations. A simple universal scaling formula for the frequency of the primary oscillation mode is suggested.

Comparative study of microwave radiation-induced magnetoresistive oscillations induced by circularly- and linearly- polarized photo-excitation

PubMed Central

Ye, Tianyu; Liu, Han-Chun; Wang, Zhuo; Wegscheider, W.; Mani, Ramesh G.

2015-01-01

A comparative study of the radiation-induced magnetoresistance oscillations in the high mobility GaAs/AlGaAs heterostructure two dimensional electron system (2DES) under linearly- and circularly- polarized microwave excitation indicates a profound difference in the response observed upon rotating the microwave launcher for the two cases, although circularly polarized microwave radiation induced magnetoresistance oscillations observed at low magnetic fields are similar to the oscillations observed with linearly polarized radiation. For the linearly polarized radiation, the magnetoresistive response is a strong sinusoidal function of the launcher rotation (or linear polarization) angle, θ. For circularly polarized radiation, the oscillatory magnetoresistive response is hardly sensitive to θ. PMID:26450679

Comparative study of microwave radiation-induced magnetoresistive oscillations induced by circularly- and linearly- polarized photo-excitation.

PubMed

Ye, Tianyu; Liu, Han-Chun; Wang, Zhuo; Wegscheider, W; Mani, Ramesh G

2015-10-09

A comparative study of the radiation-induced magnetoresistance oscillations in the high mobility GaAs/AlGaAs heterostructure two dimensional electron system (2DES) under linearly- and circularly- polarized microwave excitation indicates a profound difference in the response observed upon rotating the microwave launcher for the two cases, although circularly polarized microwave radiation induced magnetoresistance oscillations observed at low magnetic fields are similar to the oscillations observed with linearly polarized radiation. For the linearly polarized radiation, the magnetoresistive response is a strong sinusoidal function of the launcher rotation (or linear polarization) angle, θ. For circularly polarized radiation, the oscillatory magnetoresistive response is hardly sensitive to θ.

Pressure wave propagation studies for oscillating cascades

NASA Technical Reports Server (NTRS)

Huff, Dennis L.

1992-01-01

The unsteady flow field around an oscillating cascade of flat plates is studied using a time marching Euler code. Exact solutions based on linear theory serve as model problems to study pressure wave propagation in the numerical solution. The importance of using proper unsteady boundary conditions, grid resolution, and time step is demonstrated. Results show that an approximate non-reflecting boundary condition based on linear theory does a good job of minimizing reflections from the inflow and outflow boundaries and allows the placement of the boundaries to be closer than cases using reflective boundary conditions. Stretching the boundary to dampen the unsteady waves is another way to minimize reflections. Grid clustering near the plates does a better job of capturing the unsteady flow field than cases using uniform grids as long as the CFL number is less than one for a sufficient portion of the grid. Results for various stagger angles and oscillation frequencies show good agreement with linear theory as long as the grid is properly resolved.

Modeling Two-Oscillator Circadian Systems Entrained by Two Environmental Cycles

PubMed Central

Oda, Gisele A.; Friesen, W. Otto

2011-01-01

Several experimental studies have altered the phase relationship between photic and non-photic environmental, 24 h cycles (zeitgebers) in order to assess their role in the synchronization of circadian rhythms. To assist in the interpretation of the complex activity patterns that emerge from these “conflicting zeitgeber” protocols, we present computer simulations of coupled circadian oscillators forced by two independent zeitgebers. This circadian system configuration was first employed by Pittendrigh and Bruce (1959), to model their studies of the light and temperature entrainment of the eclosion oscillator in Drosophila. Whereas most of the recent experiments have restricted conflicting zeitgeber experiments to two experimental conditions, by comparing circadian oscillator phases under two distinct phase relationships between zeitgebers (usually 0 and 12 h), Pittendrigh and Bruce compared eclosion phase under 12 distinct phase relationships, spanning the 24 h interval. Our simulations using non-linear differential equations replicated complex non-linear phenomena, such as “phase jumps” and sudden switches in zeitgeber preferences, which had previously been difficult to interpret. Our simulations reveal that these phenomena generally arise when inter-oscillator coupling is high in relation to the zeitgeber strength. Manipulations in the structural symmetry of the model indicated that these results can be expected to apply to a wide range of system configurations. Finally, our studies recommend the use of the complete protocol employed by Pittendrigh and Bruce, because different system configurations can generate similar results when a “conflicting zeitgeber experiment” incorporates only two phase relationships between zeitgebers. PMID:21886835

A New Forced Oscillation Capability for the Transonic Dynamics Tunnel

NASA Technical Reports Server (NTRS)

Piatak, David J.; Cleckner, Craig S.

2002-01-01

A new forced oscillation system has been installed and tested at NASA Langley Research Center's Transonic Dynamics Tunnel (TDT). The system is known as the Oscillating Turntable (OTT) and has been designed for the purpose of oscillating, large semispan models in pitch at frequencies up to 40 Hz to acquire high-quality unsteady pressure and loads data. Precisely controlled motions of a wind-tunnel model on the OTT can yield unsteady aerodynamic phenomena associated with flutter, limit cycle oscillations, shock dynamics, and non-linear aerodynamic effects on many vehicle configurations. This paper will discuss general design and components of the OTT and will present test data from performance testing and from research tests on two rigid semispan wind-tunnel models. The research tests were designed to challenge the OTT over a wide range of operating conditions while acquiring unsteady pressure data on a small rectangular supercritical wing and a large supersonic transport wing. These results will be presented to illustrate the performance capabilities, consistency of oscillations, and usefulness of the OTT as a research tool.

Elastic robot control - Nonlinear inversion and linear stabilization

NASA Technical Reports Server (NTRS)

Singh, S. N.; Schy, A. A.

1986-01-01

An approach to the control of elastic robot systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law u(d) is derived such that in the closed-loop system independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law u(s) is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u(d) + u(s).

An efficient model for coupling structural vibrations with acoustic radiation

NASA Technical Reports Server (NTRS)

Frendi, Abdelkader; Maestrello, Lucio; Ting, LU

1993-01-01

The scattering of an incident wave by a flexible panel is studied. The panel vibration is governed by the nonlinear plate equations while the loading on the panel, which is the pressure difference across the panel, depends on the reflected and transmitted waves. Two models are used to calculate this structural-acoustic interaction problem. One solves the three dimensional nonlinear Euler equations for the flow-field coupled with the plate equations (the fully coupled model). The second uses the linear wave equation for the acoustic field and expresses the load as a double integral involving the panel oscillation (the decoupled model). The panel oscillation governed by a system of integro-differential equations is solved numerically and the acoustic field is then defined by an explicit formula. Numerical results are obtained using the two models for linear and nonlinear panel vibrations. The predictions given by these two models are in good agreement but the computational time needed for the 'fully coupled model' is 60 times longer than that for 'the decoupled model'.

Analysis of 2D THz-Raman spectroscopy using a non-Markovian Brownian oscillator model with nonlinear system-bath interactions.

PubMed

Ikeda, Tatsushi; Ito, Hironobu; Tanimura, Yoshitaka

2015-06-07

We explore and describe the roles of inter-molecular vibrations employing a Brownian oscillator (BO) model with linear-linear (LL) and square-linear (SL) system-bath interactions, which we use to analyze two-dimensional (2D) THz-Raman spectra obtained by means of molecular dynamics (MD) simulations. In addition to linear infrared absorption (1D IR), we calculated 2D Raman-THz-THz, THz-Raman-THz, and THz-THz-Raman signals for liquid formamide, water, and methanol using an equilibrium non-equilibrium hybrid MD simulation. The calculated 1D IR and 2D THz-Raman signals are compared with results obtained from the LL+SL BO model applied through use of hierarchal Fokker-Planck equations with non-perturbative and non-Markovian noise. We find that all of the qualitative features of the 2D profiles of the signals obtained from the MD simulations are reproduced with the LL+SL BO model, indicating that this model captures the essential features of the inter-molecular motion. We analyze the fitted 2D profiles in terms of anharmonicity, nonlinear polarizability, and dephasing time. The origins of the echo peaks of the librational motion and the elongated peaks parallel to the probe direction are elucidated using optical Liouville paths.

Wavelets, non-linearity and turbulence in fusion plasmas

NASA Astrophysics Data System (ADS)

van Milligen, B. Ph.

Introduction Linear spectral analysis tools Wavelet analysis Wavelet spectra and coherence Joint wavelet phase-frequency spectra Non-linear spectral analysis tools Wavelet bispectra and bicoherence Interpretation of the bicoherence Analysis of computer-generated data Coupled van der Pol oscillators A large eddy simulation model for two-fluid plasma turbulence A long wavelength plasma drift wave model Analysis of plasma edge turbulence from Langmuir probe data Radial coherence observed on the TJ-IU torsatron Bicoherence profile at the L/H transition on CCT Conclusions

Oscillation criteria for half-linear dynamic equations on time scales

NASA Astrophysics Data System (ADS)

Hassan, Taher S.

2008-09-01

This paper is concerned with oscillation of the second-order half-linear dynamic equation(r(t)(x[Delta])[gamma])[Delta]+p(t)x[gamma](t)=0, on a time scale where [gamma] is the quotient of odd positive integers, r(t) and p(t) are positive rd-continuous functions on . Our results solve a problem posed by [R.P. Agarwal, D. O'Regan, S.H. Saker, Philos-type oscillation criteria for second-order half linear dynamic equations, Rocky Mountain J. Math. 37 (2007) 1085-1104; S.H. Saker, Oscillation criteria of second order half-linear dynamic equations on time scales, J. Comput. Appl. Math. 177 (2005) 375-387] and our results in the special cases when and involve and improve some oscillation results for second-order differential and difference equations; and when , and , etc., our oscillation results are essentially newE Some examples illustrating the importance of our results are also included.

Approximating a nonlinear advanced-delayed equation from acoustics

NASA Astrophysics Data System (ADS)

Teodoro, M. Filomena

2016-10-01

We approximate the solution of a particular non-linear mixed type functional differential equation from physiology, the mucosal wave model of the vocal oscillation during phonation. The mathematical equation models a superficial wave propagating through the tissues. The numerical scheme is adapted from the work presented in [1, 2, 3], using homotopy analysis method (HAM) to solve the non linear mixed type equation under study.

Probing the non-linear transient response of a carbon nanotube mechanical oscillator

NASA Astrophysics Data System (ADS)

Willick, Kyle; Tang, Xiaowu Shirley; Baugh, Jonathan

2017-11-01

Carbon nanotube (CNT) electromechanical resonators have demonstrated unprecedented sensitivities for detecting small masses and forces. The detection speed in a cryogenic setup is usually limited by the CNT contact resistance and parasitic capacitance of cabling. We report the use of a cold heterojunction bipolar transistor amplifying circuit near the device to measure the mechanical amplitude at microsecond timescales. A Coulomb rectification scheme, in which the probe signal is at much lower frequency than the mechanical drive signal, allows investigation of the strongly non-linear regime. The behaviour of transients in both the linear and non-linear regimes is observed and modeled by including Duffing and non-linear damping terms in a harmonic oscillator equation. We show that the non-linear regime can result in faster mechanical response times, on the order of 10 μs for the device and circuit presented, potentially enabling the magnetic moments of single molecules to be measured within their spin relaxation and dephasing timescales.

Receptors as a master key for synchronization of rhythms

NASA Astrophysics Data System (ADS)

Nagano, Seido

2004-03-01

A simple, but general scheme to achieve synchronization of rhythms was derived. The scheme has been inductively generalized from the modelling study of cellular slime mold. It was clarified that biological receptors work as apparatuses that can convert external stimulus to the form of nonlinear interaction within individual oscillators. Namely, the mathematical model receptor works as a nonlinear coupling apparatus between nonlinear oscillators. Thus, synchronization is achieved as a result of competition between two kinds of non-linearities, and to achieve synchronization, even a small external stimulation via model receptors can change the characteristics of individual oscillators significantly. The derived scheme is very simple mathematically, but it is a very powerful scheme as numerically demonstrated. The biological receptor scheme should significantly help understanding of synchronization phenomena in biology since groups of limit cycle oscillators and receptors are ubiquitous in biological systems. Reference: S. Nagano, Phys Rev. E67, 056215(2003)

Comparative study of microwave radiation-induced magnetoresistive oscillations induced by circularly- and linearly- polarized photo-excitation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ye, Tianyu; Liu, Han -Chun; Wang, Zhuo

A comparative study of the radiation-induced magnetoresistance oscillations in the high mobility GaAs/AlGaAs heterostructure two dimensional electron system (2DES) under linearly- and circularly- polarized microwave excitation indicates a profound difference in the response observed upon rotating the microwave launcher for the two cases, although circularly polarized microwave radiation induced magnetoresistance oscillations observed at low magnetic fields are similar to the oscillations observed with linearly polarized radiation. For the linearly polarized radiation, the magnetoresistive response is a strong sinusoidal function of the launcher rotation (or linear polarization) angle, θ. As a result, for circularly polarized radiation, the oscillatory magnetoresistive response ismore » hardly sensitive to θ.« less

Comparative study of microwave radiation-induced magnetoresistive oscillations induced by circularly- and linearly- polarized photo-excitation

DOE PAGES

Ye, Tianyu; Liu, Han -Chun; Wang, Zhuo; ...

2015-10-09

A comparative study of the radiation-induced magnetoresistance oscillations in the high mobility GaAs/AlGaAs heterostructure two dimensional electron system (2DES) under linearly- and circularly- polarized microwave excitation indicates a profound difference in the response observed upon rotating the microwave launcher for the two cases, although circularly polarized microwave radiation induced magnetoresistance oscillations observed at low magnetic fields are similar to the oscillations observed with linearly polarized radiation. For the linearly polarized radiation, the magnetoresistive response is a strong sinusoidal function of the launcher rotation (or linear polarization) angle, θ. As a result, for circularly polarized radiation, the oscillatory magnetoresistive response ismore » hardly sensitive to θ.« less

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 field. For the large length scales of the Sun, the flow cycle period tends to be very long. The period, however, can be made to be 22 years, provided the buoyancy frequency (stability) is sufficiently small, thus placing the proposed flow near the base of the convection zone where a dynamo is now believed to operate.

Exact folded-band chaotic oscillator.

PubMed

Corron, Ned J; Blakely, Jonathan N

2012-06-01

An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.

Quasi-optical theory of relativistic surface-wave oscillators with one-dimensional and two-dimensional periodic planar structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ginzburg, N. S.; Zaslavsky, V. Yu.; Institute of Applied Physics of Russian Academy of Sciences, 46 Ulyanov St., Nizhny Novgorod 603950

2013-11-15

Within the framework of a quasi-optical approach, we develop 2D and 3D self-consistent theory of relativistic surface-wave oscillators. Presenting the radiation field as a sum of two counter-propagating wavebeams coupled on a shallow corrugated surface, we describe formation of an evanescent slow wave. Dispersion characteristics of the evanescent wave following from this method are in good compliance with those found from the direct cst simulations. Considering excitation of the slow wave by a sheet electron beam, we simulate linear and nonlinear stages of interaction, which allows us to determine oscillation threshold conditions, electron efficiency, and output coupling. The transition frommore » the model of surface-wave oscillator operating in the π-mode regime to the canonical model of relativistic backward wave oscillator is considered. We also described a modified scheme of planar relativistic surface-wave oscillators exploiting two-dimensional periodic gratings. Additional transverse propagating waves emerging on these gratings synchronize the emission from a wide sheet rectilinear electron beam allowing realization of a Cherenkov millimeter-wave oscillators with subgigawatt output power level.« less

Discrete-Time Mapping for an Impulsive Goodwin Oscillator with Three Delays

NASA Astrophysics Data System (ADS)

Churilov, Alexander N.; Medvedev, Alexander; Zhusubaliyev, Zhanybai T.

A popular biomathematics model of the Goodwin oscillator has been previously generalized to a more biologically plausible construct by introducing three time delays to portray the transport phenomena arising due to the spatial distribution of the model states. The present paper addresses a similar conversion of an impulsive version of the Goodwin oscillator that has found application in mathematical modeling, e.g. in endocrine systems with pulsatile hormone secretion. While the cascade structure of the linear continuous part pertinent to the Goodwin oscillator is preserved in the impulsive Goodwin oscillator, the static nonlinear feedback of the former is substituted with a pulse modulation mechanism thus resulting in hybrid dynamics of the closed-loop system. To facilitate the analysis of the mathematical model under investigation, a discrete mapping propagating the continuous state variables through the firing times of the impulsive feedback is derived. Due to the presence of multiple time delays in the considered model, previously developed mapping derivation approaches are not applicable here and a novel technique is proposed and applied. The mapping captures the dynamics of the original hybrid system and is instrumental in studying complex nonlinear phenomena arising in the impulsive Goodwin oscillator. A simulation example is presented to demonstrate the utility of the proposed approach in bifurcation analysis.

On temporal dynamics of Sn2P2S6 oscillation in semi-linear cavity.

PubMed

Arciszewski, D; Shumelyuk, A; Odoulov, S

2013-06-01

Experimental measurements and calculations revealed an unusual type of oscillation dynamics of Sn(2)P(2)S(6) in the semi-linear cavity. It consists of a pronounced saw-tooth modulation of oscillation intensity--although it is not 100% in contrast--with the cw component being shifted in frequency with respect to the pump wave. This effect is attributed to the hybrid mode of two semi-linear oscillation geometries, one with a single pump wave and the other with two counterpropagating pump waves.

Observation of linear-polarization-sensitivity in the microwave-radiation-induced magnetoresistance oscillations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mani, R. G.; Ramanayaka, A. N.; Wegscheider, W.

2013-12-04

We examine the linear polarization sensitivity of the radiation- induced magneto-resistance oscillations by investigating the effect of rotating in-situ the electric field of linearly polarized microwaves relative to the current, in the GaAs/AlGaAs system. We find that the frequency and the phase of the photo-excited magneto-resistance oscillations are insensitive to the polarization. On the other hand, the amplitude of the resistance oscillations are strongly sensitive to the relative orientation between the microwave antenna and the current-axis in the specimen.

Extensions of the Ferry shear wave model for active linear and nonlinear microrheology

PubMed Central

Mitran, Sorin M.; Forest, M. Gregory; Yao, Lingxing; Lindley, Brandon; Hill, David B.

2009-01-01

The classical oscillatory shear wave model of Ferry et al. [J. Polym. Sci. 2:593-611, (1947)] is extended for active linear and nonlinear microrheology. In the Ferry protocol, oscillation and attenuation lengths of the shear wave measured from strobe photographs determine storage and loss moduli at each frequency of plate oscillation. The microliter volumes typical in biology require modifications of experimental method and theory. Microbead tracking replaces strobe photographs. Reflection from the top boundary yields counterpropagating modes which are modeled here for linear and nonlinear viscoelastic constitutive laws. Furthermore, bulk imposed strain is easily controlled, and we explore the onset of normal stress generation and shear thinning using nonlinear viscoelastic models. For this paper, we present the theory, exact linear and nonlinear solutions where possible, and simulation tools more generally. We then illustrate errors in inverse characterization by application of the Ferry formulas, due to both suppression of wave reflection and nonlinearity, even if there were no experimental error. This shear wave method presents an active and nonlinear analog of the two-point microrheology of Crocker et al. [Phys. Rev. Lett. 85: 888 - 891 (2000)]. Nonlocal (spatially extended) deformations and stresses are propagated through a small volume sample, on wavelengths long relative to bead size. The setup is ideal for exploration of nonlinear threshold behavior. PMID:20011614

Vocal fold tissue failure: preliminary data and constitutive modeling.

PubMed

Chan, Roger W; Siegmund, Thomas

2004-08-01

In human voice production (phonation), linear small-amplitude vocal fold oscillation occurs only under restricted conditions. Physiologically, phonation more often involves large-amplitude oscillation associated with tissue stresses and strains beyond their linear viscoelastic limits, particularly in the lamina propria extracellular matrix (ECM). This study reports some preliminary measurements of tissue deformation and failure response of the vocal fold ECM under large-strain shear The primary goal was to formulate and test a novel constitutive model for vocal fold tissue failure, based on a standard-linear cohesive-zone (SL-CZ) approach. Tissue specimens of the sheep vocal fold mucosa were subjected to torsional deformation in vitro, at constant strain rates corresponding to twist rates of 0.01, 0.1, and 1.0 rad/s. The vocal fold ECM demonstrated nonlinear stress-strain and rate-dependent failure response with a failure strain as low as 0.40 rad. A finite-element implementation of the SL-CZ model was capable of capturing the rate dependence in these preliminary data, demonstrating the model's potential for describing tissue failure. Further studies with additional tissue specimens and model improvements are needed to better understand vocal fold tissue failure.

Modelling vertical human walking forces using self-sustained oscillator

NASA Astrophysics Data System (ADS)

Kumar, Prakash; Kumar, Anil; Racic, Vitomir; Erlicher, Silvano

2018-01-01

This paper proposes a model of a self-sustained oscillator which can generate reliably the vertical contact force between the feet of a healthy pedestrian and the supporting flat rigid surface. The model is motivated by the self-sustained nature of the walking process, i.e. a pedestrian generates the required inner energy to sustain its repetitive body motion. The derived model is a fusion of the well-known Rayleigh, Van der Pol and Duffing oscillators. Some additional nonlinear terms are added to produce both the odd and even harmonics observed in the experimentally measured force data. The model parameters were derived from force records due to twelve pedestrians walking on an instrumented treadmill at ten speeds using a linear least square technique. The stability analysis was performed using the energy balance method and perturbation method. The results obtained from the model show a good agreement with the experimental results.

Synchronization and desynchronization in a network of locally coupled Wilson-Cowan oscillators.

PubMed

Campbell, S; Wang, D

1996-01-01

A network of Wilson-Cowan (WC) oscillators is constructed, and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis. The network is a 2D matrix, where each oscillator is coupled only to its neighbors. We show analytically that a chain of locally coupled oscillators (the piecewise linear approximation to the WC oscillator) synchronizes, and we present a technique to rapidly entrain finite numbers of oscillators. The coupling strengths change on a fast time scale based on a Hebbian rule. A global separator is introduced which receives input from and sends feedback to each oscillator in the matrix. The global separator is used to desynchronize different oscillator groups. Unlike many other models, the properties of this network emerge from local connections that preserve spatial relationships among components and are critical for encoding Gestalt principles of feature grouping. The ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure/ground segregation based on oscillatory correlation.

Linear-algebraic bath transformation for simulating complex open quantum systems

DOE PAGES

Huh, Joonsuk; Mostame, Sarah; Fujita, Takatoshi; ...

2014-12-02

In studying open quantum systems, the environment is often approximated as a collection of non-interacting harmonic oscillators, a configuration also known as the star-bath model. It is also well known that the star-bath can be transformed into a nearest-neighbor interacting chain of oscillators. The chain-bath model has been widely used in renormalization group approaches. The transformation can be obtained by recursion relations or orthogonal polynomials. Based on a simple linear algebraic approach, we propose a bath partition strategy to reduce the system-bath coupling strength. As a result, the non-interacting star-bath is transformed into a set of weakly coupled multiple parallelmore » chains. Furthermore, the transformed bath model allows complex problems to be practically implemented on quantum simulators, and it can also be employed in various numerical simulations of open quantum dynamics.« less

The Madden-Julian Oscillation and the Indo-Pacific Warm Pool

NASA Astrophysics Data System (ADS)

Raymond, David J.; Fuchs, Željka

2018-04-01

A minimal model of the interaction of the Madden-Julian oscillation (MJO) with the Indo-Pacific warm pool is presented. This model is based on the linear superposition of the flow associated with a highly simplified treatment of the MJO plus the flow induced by the warm pool itself. Both of these components parameterize rainfall as proportional to the column water vapor, which in turn is governed by a linearized moisture equation in which WISHE (wind induced surface heat exchange) plays a governing role. The MJO component has maximum growth rate for planetary wavenumber 1 and is equatorially trapped with purely zonal winds. The warm pool component exhibits a complex flow pattern, differing significantly from the classical Gill model as a result of the mean easterly flow. The combination of the two produce a flow that reproduces many aspects of the observed global flow associated with the MJO.

The Effects of Magnetic-Field Geometry on Longitudinal Oscillations of Solar Prominences: Cross-Sectional Area Variation for Thin Tubes

NASA Technical Reports Server (NTRS)

Luna, M.; Diaz, A. J.; Oliver, R.; Terradas, J.; Karpen, J.

2016-01-01

Solar prominences are subject to both field-aligned (longitudinal) and transverse oscillatory motions, as evidenced by an increasing number of observations. Large-amplitude longitudinal motions provide valuable information on the geometry of the filament channel magnetic structure that supports the cool prominence plasma against gravity. Our pendulum model, in which the restoring force is the gravity projected along the dipped field lines of the magnetic structure, best explains these oscillations. However, several factors can influence the longitudinal oscillations, potentially invalidating the pendulum model. Aims. The aim of this work is to study the influence of large-scale variations in the magnetic field strength along the field lines, i.e., variations of the cross-sectional area along the flux tubes supporting prominence threads. Methods. We studied the normal modes of several flux tube configurations, using linear perturbation analysis, to assess the influence of different geometrical parameters on the oscillation properties. Results. We found that the influence of the symmetric and asymmetric expansion factors on longitudinal oscillations is small.Conclusions. We conclude that the longitudinal oscillations are not significantly influenced by variations of the cross-section of the flux tubes, validating the pendulum model in this context.

Temporal coordination and adaptation to rate change in music performance.

PubMed

Loehr, Janeen D; Large, Edward W; Palmer, Caroline

2011-08-01

People often coordinate their actions with sequences that exhibit temporal variability and unfold at multiple periodicities. We compared oscillator- and timekeeper-based accounts of temporal coordination by examining musicians' coordination of rhythmic musical sequences with a metronome that gradually changed rate at the end of a musical phrase (Experiment 1) or at the beginning of a phrase (Experiment 2). The rhythms contained events that occurred at the same periodic rate as the metronome and at half the period. Rate change consisted of a linear increase or decrease in intervals between metronome onsets. Musicians coordinated their performances better with a metronome that decreased than increased in tempo (as predicted by an oscillator model), at both beginnings and ends of musical phrases. Model performance was tested with an oscillator period or timekeeper interval set to the same period as the metronome (1:1 coordination) or half the metronome period (2:1 coordination). Only the oscillator model was able to predict musicians' coordination at both periods. These findings suggest that coordination is based on internal neural oscillations that entrain to external sequences.

Oscillations and stability of numerical solutions of the heat conduction equation

NASA Technical Reports Server (NTRS)

Kozdoba, L. A.; Levi, E. V.

1976-01-01

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

Reconstructing baryon oscillations: A Lagrangian theory perspective

NASA Astrophysics Data System (ADS)

Padmanabhan, Nikhil; White, Martin; Cohn, J. D.

2009-03-01

Recently Eisenstein and collaborators introduced a method to “reconstruct” the linear power spectrum from a nonlinearly evolved galaxy distribution in order to improve precision in measurements of baryon acoustic oscillations. We reformulate this method within the Lagrangian picture of structure formation, to better understand what such a method does, and what the resulting power spectra are. We show that reconstruction does not reproduce the linear density field, at second order. We however show that it does reduce the damping of the oscillations due to nonlinear structure formation, explaining the improvements seen in simulations. Our results suggest that the reconstructed power spectrum is potentially better modeled as the sum of three different power spectra, each dominating over different wavelength ranges and with different nonlinear damping terms. Finally, we also show that reconstruction reduces the mode-coupling term in the power spectrum, explaining why miscalibrations of the acoustic scale are reduced when one considers the reconstructed power spectrum.

Preliminary Analysis of an Oscillating Surge Wave Energy Converter with Controlled Geometry: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tom, Nathan; Lawson, Michael; Yu, Yi-Hsiang

The aim of this paper is to present a novel wave energy converter device concept that is being developed at the National Renewable Energy Laboratory. The proposed concept combines an oscillating surge wave energy converter with active control surfaces. These active control surfaces allow for the device geometry to be altered, which leads to changes in the hydrodynamic properties. The device geometry will be controlled on a sea state time scale and combined with wave-to-wave power-take-off control to maximize power capture, increase capacity factor, and reduce design loads. The paper begins with a traditional linear frequency domain analysis of themore » device performance. Performance sensitivity to foil pitch angle, the number of activated foils, and foil cross section geometry is presented to illustrate the current design decisions; however, it is understood from previous studies that modeling of current oscillating wave energy converter designs requires the consideration of nonlinear hydrodynamics and viscous drag forces. In response, a nonlinear model is presented that highlights the shortcomings of the linear frequency domain analysis and increases the precision in predicted performance.« less

Precise measurement of coupling strength and high temperature quantum effect in a nonlinearly coupled qubit-oscillator system

NASA Astrophysics Data System (ADS)

Ge, Li; Zhao, Nan

2018-04-01

We study the coherence dynamics of a qubit coupled to a harmonic oscillator with both linear and quadratic interactions. As long as the linear coupling strength is much smaller than the oscillator frequency, the long time behavior of the coherence is dominated by the quadratic coupling strength g 2. The coherence decays and revives at a period , with the width of coherence peak decreasing as the temperature increases, hence providing a way to measure g 2 precisely without cooling. Unlike the case of linear coupling, here the coherence dynamics never reduces to the classical limit in which the oscillator is classical. Finally, the validity of linear coupling approximation is discussed and the coherence under Hahn-echo is evaluated.

Coupled Leidenfrost states as a monodisperse granular clock

NASA Astrophysics Data System (ADS)

Liu, Rui; Yang, Mingcheng; Chen, Ke; Hou, Meiying; To, Kiwing

2016-08-01

Using an event-driven molecular dynamics simulation, we show that simple monodisperse granular beads confined in coupled columns may oscillate as a different type of granular clock. To trigger this oscillation, the system needs to be driven against gravity into a density-inverted state, with a high-density clustering phase supported from below by a gaslike low-density phase (Leidenfrost effect) in each column. Our analysis reveals that the density-inverted structure and the relaxation dynamics between the phases can amplify any small asymmetry between the columns, and lead to a giant oscillation. The oscillation occurs only for an intermediate range of the coupling strength, and the corresponding phase diagram can be universally described with a characteristic height of the density-inverted structure. A minimal two-phase model is proposed and a linear stability analysis shows that the triggering mechanism of the oscillation can be explained as a switchable two-parameter Andronov-Hopf bifurcation. Numerical solutions of the model also reproduce similar oscillatory dynamics to the simulation results.

Adaptive oscillator networks with conserved overall coupling: Sequential firing and near-synchronized states

NASA Astrophysics Data System (ADS)

Picallo, Clara B.; Riecke, Hermann

2011-03-01

Motivated by recent observations in neuronal systems we investigate all-to-all networks of nonidentical oscillators with adaptive coupling. The adaptation models spike-timing-dependent plasticity in which the sum of the weights of all incoming links is conserved. We find multiple phase-locked states that fall into two classes: near-synchronized states and splay states. Among the near-synchronized states are states that oscillate with a frequency that depends only very weakly on the coupling strength and is essentially given by the frequency of one of the oscillators, which is, however, neither the fastest nor the slowest oscillator. In sufficiently large networks the adaptive coupling is found to develop effective network topologies dominated by one or two loops. This results in a multitude of stable splay states, which differ in their firing sequences. With increasing coupling strength their frequency increases linearly and the oscillators become less synchronized. The essential features of the two classes of states are captured analytically in perturbation analyses of the extended Kuramoto model used in the simulations.

Experimental Robot Model Adjustments Based on Force–Torque Sensor Information

PubMed Central

2018-01-01

The computational complexity of humanoid robot balance control is reduced through the application of simplified kinematics and dynamics models. However, these simplifications lead to the introduction of errors that add to other inherent electro-mechanic inaccuracies and affect the robotic system. Linear control systems deal with these inaccuracies if they operate around a specific working point but are less precise if they do not. This work presents a model improvement based on the Linear Inverted Pendulum Model (LIPM) to be applied in a non-linear control system. The aim is to minimize the control error and reduce robot oscillations for multiple working points. The new model, named the Dynamic LIPM (DLIPM), is used to plan the robot behavior with respect to changes in the balance status denoted by the zero moment point (ZMP). Thanks to the use of information from force–torque sensors, an experimental procedure has been applied to characterize the inaccuracies and introduce them into the new model. The experiments consist of balance perturbations similar to those of push-recovery trials, in which step-shaped ZMP variations are produced. The results show that the responses of the robot with respect to balance perturbations are more precise and the mechanical oscillations are reduced without comprising robot dynamics. PMID:29534477

A hydrodynamic model of the oscillating screen viscometer

NASA Technical Reports Server (NTRS)

Davis, A. M. J.

1993-01-01

The viscometer consists of an oscillating screen immersed in a fluid and free to rotate about an axis in its plane. The viscosity can be determined from the measured ratio of the periodic driving force to the screen motion when an adequate hydrodynamical model of the immersed oscillator is available. The screen is formed by a square mesh of thin wire whose dimensions invite comparison with asymptotic results for narrow hollow bodies translating in Stokes flow. These indicate that the closed hole structure of the grid plays an important role in determining its motion. It is shown that this role diminishes as the frequency increases. The computed results, obtained from a system of linear equations, are consistent with experimental values over the appropriate range of frequency.

Clusters in nonsmooth oscillator networks

NASA Astrophysics Data System (ADS)

Nicks, Rachel; Chambon, Lucie; Coombes, Stephen

2018-03-01

For coupled oscillator networks with Laplacian coupling, the master stability function (MSF) has proven a particularly powerful tool for assessing the stability of the synchronous state. Using tools from group theory, this approach has recently been extended to treat more general cluster states. However, the MSF and its generalizations require the determination of a set of Floquet multipliers from variational equations obtained by linearization around a periodic orbit. Since closed form solutions for periodic orbits are invariably hard to come by, the framework is often explored using numerical techniques. Here, we show that further insight into network dynamics can be obtained by focusing on piecewise linear (PWL) oscillator models. Not only do these allow for the explicit construction of periodic orbits, their variational analysis can also be explicitly performed. The price for adopting such nonsmooth systems is that many of the notions from smooth dynamical systems, and in particular linear stability, need to be modified to take into account possible jumps in the components of Jacobians. This is naturally accommodated with the use of saltation matrices. By augmenting the variational approach for studying smooth dynamical systems with such matrices we show that, for a wide variety of networks that have been used as models of biological systems, cluster states can be explicitly investigated. By way of illustration, we analyze an integrate-and-fire network model with event-driven synaptic coupling as well as a diffusively coupled network built from planar PWL nodes, including a reduction of the popular Morris-Lecar neuron model. We use these examples to emphasize that the stability of network cluster states can depend as much on the choice of single node dynamics as it does on the form of network structural connectivity. Importantly, the procedure that we present here, for understanding cluster synchronization in networks, is valid for a wide variety of systems in biology, physics, and engineering that can be described by PWL oscillators.

Graph partitions and cluster synchronization in networks of oscillators

PubMed Central

Schaub, Michael T.; O’Clery, Neave; Billeh, Yazan N.; Delvenne, Jean-Charles; Lambiotte, Renaud; Barahona, Mauricio

2017-01-01

Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable Partitions of the network graph and their associated quotient graphs. We exploit this graph-theoretical concept to study the phenomenon of cluster synchronization, in which different groups of nodes converge to distinct behaviors. We derive conditions and properties of networks in which such clustered behavior emerges, and show that the ensuing dynamics is the result of the localization of the eigenvectors of the associated graph Laplacians linked to the existence of invariant subspaces. The framework is applied to both linear and non-linear models, first for the standard case of networks with positive edges, before being generalized to the case of signed networks with both positive and negative interactions. We illustrate our results with examples of both signed and unsigned graphs for consensus dynamics and for partial synchronization of oscillator networks under the master stability function as well as Kuramoto oscillators. PMID:27781454

Bistable energy harvesting enhancement with an auxiliary linear oscillator

NASA Astrophysics Data System (ADS)

Harne, R. L.; Thota, M.; Wang, K. W.

2013-12-01

Recent work has indicated that linear vibrational energy harvesters with an appended degree-of-freedom (DOF) may be advantageous for introducing new dynamic forms to extend the operational bandwidth. Given the additional interest in bistable harvester designs, which exhibit a propitious snap through effect from one stable state to the other, it is a logical extension to explore the influence of an added DOF to a bistable system. However, bistable snap through is not a resonant phenomenon, which tempers the presumption that the dynamics induced by an additional DOF on bistable designs would inherently be beneficial as for linear systems. This paper presents two analytical formulations to assess the fundamental and superharmonic steady-state dynamics of an excited bistable energy harvester to which is attached an auxiliary linear oscillator. From an energy harvesting perspective, the model predicts that the additional linear DOF uniformly amplifies the bistable harvester response magnitude and generated power for excitation frequencies less than the attachment’s resonance while improved power density spans a bandwidth below this frequency. Analyses predict bandwidths having co-existent responses composed of a unique proportion of fundamental and superharmonic dynamics. Experiments validate key analytical predictions and observe the ability for the coupled system to develop an advantageous multi-harmonic interwell response when the initial conditions are insufficient for continuous high-energy orbit at the excitation frequency. Overall, the addition of an auxiliary linear oscillator to a bistable harvester is found to be an effective means of enhancing the energy harvesting performance and robustness.

Membrane potential dynamics of grid cells

PubMed Central

Domnisoru, Cristina; Kinkhabwala, Amina A.; Tank, David W.

2014-01-01

During navigation, grid cells increase their spike rates in firing fields arranged on a strikingly regular triangular lattice, while their spike timing is often modulated by theta oscillations. Oscillatory interference models of grid cells predict theta amplitude modulations of membrane potential during firing field traversals, while competing attractor network models predict slow depolarizing ramps. Here, using in-vivo whole-cell recordings, we tested these models by directly measuring grid cell intracellular potentials in mice running along linear tracks in virtual reality. Grid cells had large and reproducible ramps of membrane potential depolarization that were the characteristic signature tightly correlated with firing fields. Grid cells also exhibited intracellular theta oscillations that influenced their spike timing. However, the properties of theta amplitude modulations were not consistent with the view that they determine firing field locations. Our results support cellular and network mechanisms in which grid fields are produced by slow ramps, as in attractor models, while theta oscillations control spike timing. PMID:23395984

Aerodynamics of a linear oscillating cascade

NASA Technical Reports Server (NTRS)

Buffum, Daniel H.; Fleeter, Sanford

1990-01-01

The steady and unsteady aerodynamics of a linear oscillating cascade are investigated using experimental and computational methods. Experiments are performed to quantify the torsion mode oscillating cascade aerodynamics of the NASA Lewis Transonic Oscillating Cascade for subsonic inlet flowfields using two methods: simultaneous oscillation of all the cascaded airfoils at various values of interblade phase angle, and the unsteady aerodynamic influence coefficient technique. Analysis of these data and correlation with classical linearized unsteady aerodynamic analysis predictions indicate that the wind tunnel walls enclosing the cascade have, in some cases, a detrimental effect on the cascade unsteady aerodynamics. An Euler code for oscillating cascade aerodynamics is modified to incorporate improved upstream and downstream boundary conditions and also the unsteady aerodynamic influence coefficient technique. The new boundary conditions are shown to improve the unsteady aerodynamic influence coefficient technique. The new boundary conditions are shown to improve the unsteady aerodynamic predictions of the code, and the computational unsteady aerodynamic influence coefficient technique is shown to be a viable alternative for calculation of oscillating cascade aerodynamics.

Multiple time scale analysis of pressure oscillations in solid rocket motors

NASA Astrophysics Data System (ADS)

Ahmed, Waqas; Maqsood, Adnan; Riaz, Rizwan

2018-03-01

In this study, acoustic pressure oscillations for single and coupled longitudinal acoustic modes in Solid Rocket Motor (SRM) are investigated using Multiple Time Scales (MTS) method. Two independent time scales are introduced. The oscillations occur on fast time scale whereas the amplitude and phase changes on slow time scale. Hopf bifurcation is employed to investigate the properties of the solution. The supercritical bifurcation phenomenon is observed for linearly unstable system. The amplitude of the oscillations result from equal energy gain and loss rates of longitudinal acoustic modes. The effect of linear instability and frequency of longitudinal modes on amplitude and phase of oscillations are determined for both single and coupled modes. For both cases, the maximum amplitude of oscillations decreases with the frequency of acoustic mode and linear instability of SRM. The comparison of analytical MTS results and numerical simulations demonstrate an excellent agreement.

A study of nonlinear dynamics of single- and two-phase flow oscillations

NASA Astrophysics Data System (ADS)

Mawasha, Phetolo Ruby

The dynamics of single- and two-phase flows in channels can be contingent on nonlinearities which are not clearly understood. These nonlinearities could be interfacial forces between the flowing fluid and its walls, variations in fluid properties, growth of voids, etc. The understanding of nonlinear dynamics of fluid flow is critical in physical systems which can undergo undesirable system operating scenarios such an oscillatory behavior which may lead to component failure. A nonlinear lumped mathematical model of a surge tank with a constant inlet flow into the tank and an outlet flow through a channel is derived from first principles. The model is used to demonstrate that surge tanks with inlet and outlet flows contribute to oscillatory behavior in laminar, turbulent, single-phase, and two-phase flow systems. Some oscillations are underdamped while others are self-sustaining. The mechanisms that are active in single-phase oscillations with no heating are presented using specific cases of simplified models. Also, it is demonstrated how an external mechanism such as boiling contributes to the oscillations observed in two-phase flow and gives rise to sustained oscillations (or pressure drop oscillations). A description of the pressure drop oscillation mechanism is presented using the steady state pressure drop versus mass flow rate characteristic curve of the heated channel, available steady state pressure drop versus mass flow rate from the surge tank, and the transient pressure drop versus mass flow rate limit cycle. Parametric studies are used to verify the theoretical pressure drop oscillations model using experimental data by Yuncu's (1990). The following contributions are unique: (1) comparisons of nonlinear pressure drop oscillation models with and without the effect of the wall thermal heat capacity and (2) comparisons of linearized pressure drop oscillation models with and without the effect of the wall thermal heat capacity to identify stability boundaries.

Analysis of the linearity of half periods of the Lorentz pendulum

NASA Astrophysics Data System (ADS)

Wickramasinghe, T.; Ochoa, R.

2005-05-01

We analyze the motion of the Lorentz pendulum, a simple pendulum whose length is changed at a constant rate k. We show both analytically and numerically that the half period Tn, the time between half oscillations as measured from midpoint to midpoint, increases linearly with the oscillation number n such that Tn+1-Tn≈kπ2/2g, where g is the acceleration due to gravity. A video camera is used to record the motion of the oscillating bob of the pendulum and verify the linearity of Tn with oscillation number. The theory and the experiment are suitable for an advanced undergraduate laboratory.

Modulation linearization of a frequency-modulated voltage controlled oscillator, part 3

NASA Technical Reports Server (NTRS)

Honnell, M. A.

1975-01-01

An analysis is presented for the voltage versus frequency characteristics of a varactor modulated VHF voltage controlled oscillator in which the frequency deviation is linearized by using the nonlinear characteristics of a field effect transistor as a signal amplifier. The equations developed are used to calculate the oscillator output frequency in terms of pertinent circuit parameters. It is shown that the nonlinearity exponent of the FET has a pronounced influence on frequency deviation linearity, whereas the junction exponent of the varactor controls total frequency deviation for a given input signal. A design example for a 250 MHz frequency modulated oscillator is presented.

An oscillating wave energy converter with nonlinear snap-through Power-Take-Off systems in regular waves

NASA Astrophysics Data System (ADS)

Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei

2016-07-01

Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.

Modelling a Simple Mechanical System.

ERIC Educational Resources Information Center

Morland, Tim

1999-01-01

Provides an example of the modeling power of Mathematics, demonstrated in a piece of A-Level student coursework which was undertaken as part of the MEI Structured Mathematics scheme. A system of two masses and two springs oscillating in one dimension is found to be accurately modeled by a system of linear differential equations. (Author/ASK)

Physical understanding of complex multiscale biochemical models via algorithmic simplification: Glycolysis in Saccharomyces cerevisiae

NASA Astrophysics Data System (ADS)

Kourdis, Panayotis D.; Steuer, Ralf; Goussis, Dimitris A.

2010-09-01

Large-scale models of cellular reaction networks are usually highly complex and characterized by a wide spectrum of time scales, making a direct interpretation and understanding of the relevant mechanisms almost impossible. We address this issue by demonstrating the benefits provided by model reduction techniques. We employ the Computational Singular Perturbation (CSP) algorithm to analyze the glycolytic pathway of intact yeast cells in the oscillatory regime. As a primary object of research for many decades, glycolytic oscillations represent a paradigmatic candidate for studying biochemical function and mechanisms. Using a previously published full-scale model of glycolysis, we show that, due to fast dissipative time scales, the solution is asymptotically attracted on a low dimensional manifold. Without any further input from the investigator, CSP clarifies several long-standing questions in the analysis of glycolytic oscillations, such as the origin of the oscillations in the upper part of glycolysis, the importance of energy and redox status, as well as the fact that neither the oscillations nor cell-cell synchronization can be understood in terms of glycolysis as a simple linear chain of sequentially coupled reactions.

Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Freitas, Celso, E-mail: cbnfreitas@gmail.com; Macau, Elbert, E-mail: elbert.macau@inpe.br; Pikovsky, Arkady, E-mail: pikovsky@uni-potsdam.de

2015-04-15

We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the fullmore » synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.« less

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.

Oscillations in a Linearly Stratified Salt Solution

ERIC Educational Resources Information Center

Heavers, Richard M.

2007-01-01

Our physics students like to watch a ball bouncing underwater. They do this by dropping a weighted plastic ball into a 1000-ml cylinder filled with a linearly stratified salt-water solution at room temperature. The ball oscillates and comes to rest at about mid-depth. Its motion is analogous to the damped vertical oscillations of a mass hanging…

Enhanced localized energetic ion losses resulting from first-orbit linear and non-linear interactions with Alfvén eigenmodes in DIII-D

DOE PAGES

Chen, Xi; Heidbrink, William W.; Kramer, Gerrit J.; ...

2014-08-04

Two key insights into interactions between Alfvén eigenmodes (AEs) and energetic particles in the plasma core are gained from measurements and modeling of first-orbit beam-ion loss in DIII-D. First, the neutral beam-ion first-orbit losses are enhanced by AEs and a single AE can cause large fast-ion displacement. The coherent losses are from born trapped full energy beam-ions being non-resonantly scattered by AEs onto loss orbits within their first poloidal transit. The loss amplitudes scale linearly with the mode amplitude but the slope is different for different modes. The radial displacement of fast-ions by individual AEs can be directly inferred frommore » the measurements. Second, oscillations in the beam-ion first-orbit losses are observed at the sum, difference, and harmonic frequencies of two independent AEs. These oscillations are not plasma modes and are absent in magnetic, density, and temperature fluctuations. The origin of the non-linearity as a wave-particle coupling is confirmed through bi-coherence analysis, which is clearly observed because the coherences are preserved by the first-orbit loss mechanism. Finally, an analytic model and full orbit simulations show that the non-linear features seen in the loss signal can be explained by a non-linear interaction between the fast ions and the two independent AEs.« less

Enhanced localized energetic ion losses resulting from first-orbit linear and non-linear interactions with Alfvén eigenmodes in DIII-D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, X.; General Atomics, P.O. Box 85608, San Diego, California 92186; Heidbrink, W. W.

2014-08-15

Two key insights into interactions between Alfvén eigenmodes (AEs) and energetic particles in the plasma core are gained from measurements and modeling of first-orbit beam-ion loss in DIII-D. First, the neutral beam-ion first-orbit losses are enhanced by AEs and a single AE can cause large fast-ion displacement. The coherent losses are from born trapped full energy beam-ions being non-resonantly scattered by AEs onto loss orbits within their first poloidal transit. The loss amplitudes scale linearly with the mode amplitude but the slope is different for different modes. The radial displacement of fast-ions by individual AEs can be directly inferred frommore » the measurements. Second, oscillations in the beam-ion first-orbit losses are observed at the sum, difference, and harmonic frequencies of two independent AEs. These oscillations are not plasma modes and are absent in magnetic, density, and temperature fluctuations. The origin of the non-linearity as a wave-particle coupling is confirmed through bi-coherence analysis, which is clearly observed because the coherences are preserved by the first-orbit loss mechanism. An analytic model and full orbit simulations show that the non-linear features seen in the loss signal can be explained by a non-linear interaction between the fast ions and the two independent AEs.« less

Theoretical analysis of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator

NASA Astrophysics Data System (ADS)

Shin, Y. M.; Ryskin, N. M.; Won, J. H.; Han, S. T.; Park, G. S.

2006-03-01

The basic theory of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator consisting of two two-cavity klystron amplifiers reversely coupled through input/output slots is theoretically investigated. Application of Kirchhoff's laws to the coupled equivalent RLC circuit model of the device provides four nonlinear coupled equations, which are the first-order time-delayed differential equations. Analytical solutions obtained through linearization of the equations provide oscillation frequencies and thresholds of four fundamental eigenstates, symmetric/antisymmetric 0/π modes. Time-dependent output signals are numerically analyzed with variation of the beam current, and a self-modulation mechanism and transition to chaos scenario are examined. The oscillator shows a much stronger multistability compared to a delayed feedback klystron oscillator owing to the competitions among more diverse eigenmodes. A fully developed chaos region also appears at a relatively lower beam current, ˜3.5Ist, compared to typical vacuum tube oscillators (10-100Ist), where Ist is a start-oscillation current.

The effect of delays on filament oscillations and stability

NASA Astrophysics Data System (ADS)

van den Oord, G. H. J.; Schutgens, N. A. J.; Kuperus, M.

1998-11-01

We discuss the linear response of a filament to perturbations, taking the finite communication time between the filament and the photosphere into account. The finite communication time introduces delays in the system. Recently Schutgens (1997ab) investigated the solutions of the delay equation for vertical perturbations. In this paper we expand his analysis by considering also horizontal and coupled oscillations. The latter occur in asymmetric coronal fields. We also discuss the effect of Alfven wave emission on filament oscillations and show that wave emission is important for stabilizing filaments. We introduce a fairly straightforward method to study the solutions of delay equations as a function of the filament-photosphere communication time. A solution can be described by a linear combination of damped harmonic oscillations each characterized by a frequency, a damping/growth time and, accordingly, a quality factor. As a secondary result of our analysis we show that, within the context of line current models, Kippenhahn/Schlüter-type filament equilibria can never be stable in the horizontal and the vertical direction at the same time but we also demonstrate that Kuperus/Raadu-type equilibria can account for both an inverse or a normal polarity signature. The diagnostic value of our analysis for determining, e.g., the filament current from observations of oscillating filaments is discussed.

Bifurcation of quiescent H-mode to a wide pedestal regime in DIII-D and advances in the understanding of edge harmonic oscillations

DOE PAGES

Chen, Xi; Burrell, K. H.; Osborne, T. H.; ...

2017-06-14

New experimental studies and modelling of the coherent edge harmonic oscillation (EHO), which regulates the conventional Quiescent H-mode (QH-mode) edge, validate the proposed hypothesis of edge rotational shear in destabilizing the low-n kink-peeling mode as the additional drive mechanism for the EHO. The observed minimum edge E×B shear required for the EHO decreases linearly with pedestal collisionalitymore » $$\

Cross-diffusion-induced subharmonic spatial resonances in a predator-prey system

NASA Astrophysics Data System (ADS)

Gambino, G.; Lombardo, M. C.; Sammartino, M.

2018-01-01

In this paper we investigate the complex dynamics originated by a cross-diffusion-induced subharmonic destabilization of the fundamental subcritical Turing mode in a predator-prey reaction-diffusion system. The model we consider consists of a two-species Lotka-Volterra system with linear diffusion and a nonlinear cross-diffusion term in the predator equation. The taxis term in the search strategy of the predator is responsible for the onset of complex dynamics. In fact, our model does not exhibit any Hopf or wave instability, and on the basis of the linear analysis one should only expect stationary patterns; nevertheless, the presence of the nonlinear cross-diffusion term is able to induce a secondary instability: due to a subharmonic spatial resonance, the stationary primary branch bifurcates to an out-of-phase oscillating solution. Noticeably, the strong resonance between the harmonic and the subharmonic is able to generate the oscillating pattern albeit the subharmonic is below criticality. We show that, as the control parameter is varied, the oscillating solution (sub T mode) can undergo a sequence of secondary instabilities, generating a transition toward chaotic dynamics. Finally, we investigate the emergence of sub T -mode solutions on two-dimensional domains: when the fundamental mode describes a square pattern, subharmonic resonance originates oscillating square patterns. In the case of subcritical Turing hexagon solutions, the internal interactions with a subharmonic mode are able to generate the so-called "twinkling-eyes" pattern.

Smoothly deformed light

NASA Technical Reports Server (NTRS)

Stenholm, Stig

1993-01-01

A single mode cavity is deformed smoothly to change its electromagnetic eigenfrequency. The system is modeled as a simple harmonic oscillator with a varying period. The Wigner function of the problem is obtained exactly by starting with a squeezed initial state. The result is evaluated for a linear change of the cavity length. The approach to the adiabatic limit is investigated. The maximum squeezing is found to occur for smooth change lasting only a fraction of the oscillational period. However, only a factor of two improvement over the adiabatic result proves to be possible. The sudden limit cannot be investigated meaningfully within the model.

A new chaotic oscillator with free control

NASA Astrophysics Data System (ADS)

Li, Chunbiao; Sprott, Julien Clinton; Akgul, Akif; Iu, Herbert H. C.; Zhao, Yibo

2017-08-01

A novel chaotic system is explored in which all terms are quadratic except for a linear function. The slope of the linear function rescales the amplitude and frequency of the variables linearly while its zero intercept allows offset boosting for one of the variables. Therefore, a free-controlled chaotic oscillation can be obtained with any desired amplitude, frequency, and offset by an easy modification of the linear function. When implemented as an electronic circuit, the corresponding chaotic signal can be controlled by two independent potentiometers, which is convenient for constructing a chaos-based application system. To the best of our knowledge, this class of chaotic oscillators has never been reported.

Wind tunnel wall effects in a linear oscillating cascade

NASA Technical Reports Server (NTRS)

Buffum, Daniel H.; Fleeter, Sanford

1991-01-01

Experiments in a linear oscillating cascade reveal that the wind tunnel walls enclosing the airfoils have, in some cases, a detrimental effect on the oscillating cascade aerodynamics. In a subsonic flow field, biconvex airfoils are driven simultaneously in harmonic, torsion-mode oscillations for a range of interblade phase angle values. It is found that the cascade dynamic periodicity - the airfoil to airfoil variation in unsteady surface pressure - is good for some values of interblade phase angle but poor for others. Correlation of the unsteady pressure data with oscillating flat plate cascade predictions is generally good for conditions where the periodicity is good and poor where the periodicity is poor. Calculations based upon linearized unsteady aerodynamic theory indicate that pressure waves reflected from the wind tunnel walls are responsible for the cases where there is poor periodicity and poor correlation with the predictions.

Non-resonant dynamic stark control of vibrational motion with optimized laser pulses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thomas, Esben F.; Henriksen, Niels E.

2016-06-28

The term dynamic Stark control (DSC) has been used to describe methods of quantum control related to the dynamic Stark effect, i.e., a time-dependent distortion of energy levels. Here, we employ analytical models that present clear and concise interpretations of the principles behind DSC. Within a linearly forced harmonic oscillator model of vibrational excitation, we show how the vibrational amplitude is related to the pulse envelope, and independent of the carrier frequency of the laser pulse, in the DSC regime. Furthermore, we shed light on the DSC regarding the construction of optimal pulse envelopes — from a time-domain as wellmore » as a frequency-domain perspective. Finally, in a numerical study beyond the linearly forced harmonic oscillator model, we show that a pulse envelope can be constructed such that a vibrational excitation into a specific excited vibrational eigenstate is accomplished. The pulse envelope is constructed such that high intensities are avoided in order to eliminate the process of ionization.« less

A simple mechanical system mimicking phase transitions in a one-dimensional medium

NASA Astrophysics Data System (ADS)

Charru, François

1997-11-01

We study a simple mechanical oscillator the bifurcations of which illustrate first- and second-order phase transitions. The phase diagram of the oscillator exhibits a coexistence curve. This curve ends at a critical point, where three critical exponents can be defined. A metronome may be used to illustrate the main results. We then consider a linear array of such oscillators with elastic coupling, which is governed by the damped Klein - Gordon equation. The classical solutions of this equation, such as fronts propagating in an unstable or in a metastable state, can be guessed at and discussed from the point of view of a mechanical model.

Oscillator Strengths and Predissociation Widths for Rydberg Transitions in Carbon Monoxide

NASA Technical Reports Server (NTRS)

Federman, Steven R.; Sheffer, Y.; Eidelsberg, Michele; Lemaire, Jean-Louis; Fillion, Jean-Hugues; Rostas, Francois; Ruiz, J.

2006-01-01

CO is used as a probe of astronomical environments ranging from planetary atmospheres and comets to interstellar clouds and the envelopes surrounding stars near the end of their lives. One of the processes controlling the CO abundance and the ratio of its isotopomers is photodissociation. Accurate oscillator strengths for Rydberg transitions are needed for modeling this process. Absorption bands were analyzed by synthesizing the profiles with codes developed independently in Meudon and Toledo. Each synthetic spectrum was adjusted to match the experimental one in a non-linear least-squares fitting procedure with the band oscillator strength, the line width (instrumental and predissociation.

Damping of prominence longitudinal oscillations due to mass accretion

NASA Astrophysics Data System (ADS)

Ruderman, Michael S.; Luna, Manuel

2016-06-01

We study the damping of longitudinal oscillations of a prominence thread caused by the mass accretion. We suggested a simple model describing this phenomenon. In this model we considered a thin curved magnetic tube filled with the plasma. The prominence thread is in the central part of the tube and it consists of dense cold plasma. The parts of the tube at the two sides of the thread are filled with hot rarefied plasma. We assume that there are flows of rarefied plasma toward the thread caused by the plasma evaporation at the magnetic tube footpoints. Our main assumption is that the hot plasma is instantaneously accommodated by the thread when it arrives at the thread, and its temperature and density become equal to those of the thread. Then we derive the system of ordinary differential equations describing the thread dynamics. We solve this system of ordinary differential equations in two particular cases. In the first case we assume that the magnetic tube is composed of an arc of a circle with two straight lines attached to its ends such that the whole curve is smooth. A very important property of this model is that the equations describing the thread oscillations are linear for any oscillation amplitude. We obtain the analytical solution of the governing equations. Then we obtain the analytical expressions for the oscillation damping time and periods. We find that the damping time is inversely proportional to the accretion rate. The oscillation periods increase with time. We conclude that the oscillations can damp in a few periods if the inclination angle is sufficiently small, not larger that 10°, and the flow speed is sufficiently large, not less that 30 km s-1. In the second model we consider the tube with the shape of an arc of a circle. The thread oscillates with the pendulum frequency dependent exclusively on the radius of curvature of the arc. The damping depends on the mass accretion rate and the initial mass of the threads, that is the mass of the thread at the moment when it is perturbed. First we consider small amplitude oscillations and use the linear description. Then we consider nonlinear oscillations and assume that the damping is slow, meaning that the damping time is much larger that the characteristic oscillation time. The thread oscillations are described by the solution of the nonlinear pendulum problem with slowly varying amplitude. The nonlinearity reduces the damping time, however this reduction is small. Again the damping time is inversely proportional to the accretion rate. We also obtain that the oscillation periods decrease with time. However even for the largest initial oscillation amplitude considered in our article the period reduction does not exceed 20%. We conclude that the mass accretion can damp the motion of the threads rapidly. Thus, this mechanism can explain the observed strong damping of large-amplitude longitudinal oscillations. In addition, the damping time can be used to determine the mass accretion rate and indirectly the coronal heating.

Low-Dimensional Model of a Cylinder Wake

NASA Astrophysics Data System (ADS)

Luchtenburg, Mark; Cohen, Kelly; Siegel, Stefan; McLaughlin, Tom

2003-11-01

In a two-dimensional cylinder wake, self-excited oscillations in the form of periodic shedding of vortices are observed above a critical Reynolds number of about 47. These flow-induced non-linear oscillations lead to some undesirable effects associated with unsteady pressures such as fluid-structure interactions. An effective way of suppressing the self-excited flow oscillations is by the incorporation of closed-loop flow control. In this effort, a low dimensional, proper orthogonal decomposition (POD) model is based on data obtained from direct numerical simulations of the Navier Stokes equations for the two dimensional circular cylinder wake at a Reynolds number of 100. Three different conditions are examined, namely, the unforced wake experiencing steady-state vortex shedding, the transient behavior of the unforced wake at the startup of the simulation, and transient response to open-loop harmonic forcing by translation. We discuss POD mode selection and the number of modes that need to be included in the low-dimensional model. It is found that the transient dynamics need to be represented by a coupled system that includes an aperiodic mean-flow mode, an aperiodic shift mode and the periodic von Karman modes. Finally, a least squares mapping method is introduced to develop the non-linear state equations. The predictive capability of the state equations demonstrates the ability of the above approach to model the transient dynamics of the wake.

Forecasting of Machined Surface Waviness on the Basis of Self-oscillations Analysis

NASA Astrophysics Data System (ADS)

Belov, E. B.; Leonov, S. L.; Markov, A. M.; Sitnikov, A. A.; Khomenko, V. A.

2017-01-01

The paper states a problem of providing quality of geometrical characteristics of machined surfaces, which makes it necessary to forecast the occurrence and amount of oscillations appearing in the course of mechanical treatment. Objectives and tasks of the research are formulated. Sources of oscillation onset are defined: these are coordinate connections and nonlinear dependence of cutting force on the cutting velocity. A mathematical model of forecasting steady-state self-oscillations is investigated. The equation of the cutter tip motion is a system of two second-order nonlinear differential equations. The paper shows an algorithm describing a harmonic linearization method which allows for a significant reduction of the calculation time. In order to do that it is necessary to determine the amplitude of oscillations, frequency and a steady component of the first harmonic. Software which allows obtaining data on surface waviness parameters is described. The paper studies an example of the use of the developed model in semi-finished lathe machining of the shaft made from steel 40H which is a part of the BelAZ wheel electric actuator unit. Recommendations on eliminating self-oscillations in the process of shaft cutting and defect correction of the surface waviness are given.

Observation of Droplet Size Oscillations in a Two Phase Fluid under Shear Flow

NASA Astrophysics Data System (ADS)

Courbin, Laurent; Panizza, Pascal

2004-11-01

It is well known that complex fluids exhibit strong couplings between their microstructure and the flow field. Such couplings may lead to unusual non linear rheological behavior. Because energy is constantly brought to the system, richer dynamic behavior such as non linear oscillatory or chaotic response is expected. We report on the observation of droplet size oscillations at fixed shear rate. At low shear rates, we observe two steady states for which the droplet size results from a balance between capillary and viscous stress. For intermediate shear rates, the droplet size becomes a periodic function of time. We propose a phenomenological model to account for the observed phenomenon and compare numerical results to experimental data.

Decaying and decayless transverse oscillations of a coronal loop

NASA Astrophysics Data System (ADS)

Nisticò, G.; Nakariakov, V. M.; Verwichte, E.

2013-04-01

Aims: We investigate kink oscillations of loops observed in an active region with the Atmospheric Imaging Assembly (AIA) instrument on board the Solar Dynamics Observatory (SDO) spacecraft before and after a flare. Methods: The oscillations were depicted and analysed with time-distance maps, extracted from the cuts taken parallel or perpendicular to the loop axis. Moving loops were followed in time with steadily moving slits. The period of oscillations and its time variation were determined by best-fitting harmonic functions. Results: We show that before and well after the occurrence of the flare, the loops experience low-amplitude decayless oscillations. The flare and the coronal mass ejection associated to it trigger large-amplitude oscillations that decay exponentially in time. The periods of the kink oscillations in both regimes (about 240 s) are similar. An empirical model of the phenomenon in terms of a damped linear oscillator excited by a continuous low-amplitude harmonic driver and by an impulsive high-amplitude driver is found to be consistent with the observations. Two movies are available in electronic form at http://www.aanda.org

Standing waves, clustering, and phase waves in 1D simulations of kinetic relaxation oscillations in NO+NH 3 on Pt(1 0 0) coupled by diffusion

NASA Astrophysics Data System (ADS)

Uecker, Hannes

2004-04-01

The Lombardo-Imbihl-Fink (LFI) ODE model of the NO+NH 3 reaction on a Pt(1 0 0) surface shows stable relaxation oscillations with very sharp transitions for temperatures T between 404 and 433 K. Here we study numerically the effect of linear diffusive coupling of these oscillators in one spatial dimension. Depending on the parameters and initial conditions we find a rich variety of spatio-temporal patterns which we group into four main regimes: bulk oscillations (BOs), standing waves (SW), phase clusters (PC), and phase waves (PW). Two key ingredients for SW and PC are identified, namely the relaxation type of the ODE oscillations and a nonlocal (and nonglobal) coupling due to relatively fast diffusion of the kinetically slaved variables NH 3 and H. In particular, the latter replaces the global coupling through the gas phase used to obtain SW and PC in models of related surface reactions. The PW exist only under the assumption of (relatively) slow diffusion of NH 3 and H.

Nonlinear state-space modelling of the kinematics of an oscillating circular cylinder in a fluid flow

NASA Astrophysics Data System (ADS)

Decuyper, J.; De Troyer, T.; Runacres, M. C.; Tiels, K.; Schoukens, J.

2018-01-01

The flow-induced vibration of bluff bodies is an important problem of many marine, civil, or mechanical engineers. In the design phase of such structures, it is vital to obtain good predictions of the fluid forces acting on the structure. Current methods rely on computational fluid dynamic simulations (CFD), with a too high computational cost to be effectively used in the design phase or for control applications. Alternative methods use heuristic mathematical models of the fluid forces, but these lack the accuracy (they often assume the system to be linear) or flexibility to be useful over a wide operating range. In this work we show that it is possible to build an accurate, flexible and low-computational-cost mathematical model using nonlinear system identification techniques. This model is data driven: it is trained over a user-defined region of interest using data obtained from experiments or simulations, or both. Here we use a Van der Pol oscillator as well as CFD simulations of an oscillating circular cylinder to generate the training data. Then a discrete-time polynomial nonlinear state-space model is fit to the data. This model relates the oscillation of the cylinder to the force that the fluid exerts on the cylinder. The model is finally validated over a wide range of oscillation frequencies and amplitudes, both inside and outside the so-called lock-in region. We show that forces simulated by the model are in good agreement with the data obtained from CFD.

Does the entorhinal cortex use the Fourier transform?

PubMed Central

Orchard, Jeff; Yang, Hao; Ji, Xiang

2013-01-01

Some neurons in the entorhinal cortex (EC) fire bursts when the animal occupies locations organized in a hexagonal grid pattern in their spatial environment. Place cells have also been observed, firing bursts only when the animal occupies a particular region of the environment. Both of these types of cells exhibit theta-cycle modulation, firing bursts in the 4–12 Hz range. Grid cells fire bursts of action potentials that precess with respect to the theta cycle, a phenomenon dubbed “theta precession.” Various models have been proposed to explain these phenomena, and how they relate to navigation. Among the most promising are the oscillator interference models. The bank-of-oscillators model proposed by Welday et al. (2011) exhibits all these features. However, their simulations are based on theoretical oscillators, and not implemented entirely with spiking neurons. We extend their work in a number of ways. First, we place the oscillators in a frequency domain and reformulate the model in terms of Fourier theory. Second, this perspective suggests a division of labor for implementing spatial maps: position vs. map layout. The animal's position is encoded in the phases of the oscillators, while the spatial map shape is encoded implicitly in the weights of the connections between the oscillators and the read-out nodes. Third, it reveals that the oscillator phases all need to conform to a linear relationship across the frequency domain. Fourth, we implement a partial model of the EC using spiking leaky integrate-and-fire (LIF) neurons. Fifth, we devise new coupling mechanisms, enlightened by the global phase constraint, and show they are capable of keeping spiking neural oscillators in consistent formation. Our model demonstrates place cells, grid cells, and phase precession. The Fourier model also gives direction for future investigations, such as integrating sensory feedback to combat drift, or explaining why grid cells exist at all. PMID:24376415

Linear and nonlinear winter atmospheric responses to extreme phases of low frequency Pacific sea surface temperature variability

NASA Astrophysics Data System (ADS)

Cao, Dandan; Wu, Qigang; Hu, Aixue; Yao, Yonghong; Liu, Shizuo; Schroeder, Steven R.; Yang, Fucheng

2018-02-01

This study examines Northern Hemisphere winter (DJFM) atmospheric responses to opposite strong phases of interdecadal (low frequency, LF) Pacific sea surface temperature (SST) forcing, which resembles El Niño-Southern Oscillation (ENSO) on a longer time scale, in observations and GFDL and CAM4 model simulations. Over the Pacific-North America (PNA) sector, linear observed responses of 500-hPa height (Z500) anomalies resemble the PNA teleconnection pattern, but show a PNA-like nonlinear response because of a westward Z500 shift in the negative (LF-) relative to the positive LF (LF+) phase. Significant extratropical linear responses include a North Atlantic Oscillation (NAO)-like Z500 anomaly, a dipole-like Z500 anomaly over northern Eurasia associated with warming over mid-high latitude Eurasia, and a Southern Annular anomaly pattern associated with warming in southern land areas. Significant nonlinear Z500 responses also include a NAO-like anomaly pattern. Models forced by LF+ and LF- SST anomalies reproduce many aspects of observed linear and nonlinear responses over the Pacific-North America sector, and linear responses over southern land, but not in the North Atlantic-European sector and Eurasia. Both models simulate PNA-like linear responses in the North Pacific-North America region similar to observed, but show larger PNA-like LF+ responses, resulting in a PNA nonlinear response. The nonlinear PNA responses result from both nonlinear western tropical Pacific rainfall changes and extratropical transient eddy feedbacks. With LF tropical Pacific forcing only (LFTP+ and LFTP-, climatological SST elsewhere), CAM4 simulates a significant NAO response to LFTP-, including a linear negative and nonlinear positive NAO response.

Umbral oscillations as resonant modes of magneto-atmospheric waves. [in sunspots

NASA Technical Reports Server (NTRS)

Scheuer, M. A.; Thomas, J. H.

1981-01-01

Umbral oscillations in sunspots are identified as a resonant response of the umbral atmosphere to forcing by oscillatory convection in the subphotosphere. The full, linearized equations for magnetoatmospheric waves are solved numerically for a detailed model of the umbral atmosphere, for both forced and free oscillations. Resonant 'fast' modes are found, the lowest mode having a period of 153 s, typical of umbral oscillations. A comparison is made with a similar analysis by Uchida and Sakurai (1975), who calculated resonant modes using an approximate ('quasi-Alfven') form of the wave equations. Whereas both analyses give an appropriate value for the period of oscillation, several new features of the motion follow from the full equations. The resonant modes are due to upward reflection in the subphotosphere (due to increasing sound speed) and downward reflection in the photosphere and low chromosphere (due to increasing Alfven speed); downward reflection at the chromosphere-corona transition is unimportant for these modes.

Network-induced oscillatory behavior in material flow networks and irregular business cycles

NASA Astrophysics Data System (ADS)

Helbing, Dirk; Lämmer, Stefen; Witt, Ulrich; Brenner, Thomas

2004-11-01

Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of power grids remains to be explored. Based on a simple model of supply networks, we offer an interpretation of instabilities and oscillations observed in biological, ecological, economic, and engineering systems. We find that most supply networks display damped oscillations, even when their units—and linear chains of these units—behave in a nonoscillatory way. Moreover, networks of damped oscillators tend to produce growing oscillations. This surprising behavior offers, for example, a different interpretation of business cycles and of oscillating or pulsating processes. The network structure of material flows itself turns out to be a source of instability, and cyclical variations are an inherent feature of decentralized adjustments.

Photoinduced fluorescence intensity oscillation in a reaction-diffusion cell containing a colloidal quantum dot dispersion

NASA Astrophysics Data System (ADS)

Komoto, Atsushi; Maenosono, Shinya

2006-09-01

The nonlinear spontaneous oscillation of photoluminescence (PL) intensity in an ensemble of semiconductor quantum dots (QDs), which differs from the fluorescence intermittency of a single QD, is investigated. The PL intensity in a QD dispersion slowly oscillates with time under continuous illumination. The oscillatory behavior is found to vary with changing QD concentration, solvent viscosity, volume fraction of irradiated region, and irradiation intensity. On the basis of the Gray-Scott model [Chemical Oscillation and Instabilities: Non-linear Chemical Kinetics (Clarendon, Oxford, 1994); J. Phys. Chem. 89, 22 (1985); Chem. Eng. Sci. 42, 307 (1987)], and its comparison with the experimental results, it is revealed that the following processes are important for PL oscillation: (1) mass transfer of QDs between the illuminated and dark regions, (2) autocatalytic formation of vacant sites on QD surfaces via photodesorption of ligand molecules, and (3) passivation of vacant sites via photoadsorption of water molecules.

Photoinduced fluorescence intensity oscillation in a reaction-diffusion cell containing a colloidal quantum dot dispersion.

PubMed

Komoto, Atsushi; Maenosono, Shinya

2006-09-21

The nonlinear spontaneous oscillation of photoluminescence (PL) intensity in an ensemble of semiconductor quantum dots (QDs), which differs from the fluorescence intermittency of a single QD, is investigated. The PL intensity in a QD dispersion slowly oscillates with time under continuous illumination. The oscillatory behavior is found to vary with changing QD concentration, solvent viscosity, volume fraction of irradiated region, and irradiation intensity. On the basis of the Gray-Scott model [Chemical Oscillation and Instabilities: Non-linear Chemical Kinetics (Clarendon, Oxford, 1994); J. Phys. Chem. 89, 22 (1985); Chem. Eng. Sci. 42, 307 (1987)], and its comparison with the experimental results, it is revealed that the following processes are important for PL oscillation: (1) mass transfer of QDs between the illuminated and dark regions, (2) autocatalytic formation of vacant sites on QD surfaces via photodesorption of ligand molecules, and (3) passivation of vacant sites via photoadsorption of water molecules.

Realistic Features in Analysing the Effect of the Seismic Motion upon Localized Structures Considering Base Isolation Influence on Their Dynamic Behaviour

NASA Astrophysics Data System (ADS)

Apostol, Bogdan Felix; Florin Balan, Stefan; Ionescu, Constantin

2017-12-01

The effects of the earthquakes on buildings and the concept of seismic base isolation are investigated by using the model of the vibrating bar embedded at one end. The normal modes and the eigenfrequencies of the bar are highlighted and the amplification of the response due to the excitation of the normal modes (eigenmodes) is computed. The effect is much enhanced at resonance, for oscillating shocks which contain eigenfrequencies of the bar. Also, the response of two linearly joined bars with one end embedded is calculated. It is shown that for very different elastic properties the eigenfrequencies are due mainly to the “softer” bar. The effect of the base isolation in seismic structural engineering is assessed by formulating the model of coupled harmonic oscillators, as a simplified model for the structure building-foundation viewed as two coupled vibrating bars. The coupling decreases the lower eigenfrequencies of the structure and increases the higher ones. Similar amplification factors are derived for coupled oscillators at resonance with an oscillating shock.

Identification and Control of Non-Linear Time-Varying Dynamical Systems Using Artificial Neural Networks

DTIC Science & Technology

1992-09-01

finding an inverse plant such as was done by Bertrand [BD91] and by Levin, Gewirtzman and Inbar in a binary type inverse controller [LGI91], to self tuning...gain robust control. 2) Self oscillating adaptive controller. 3) Gain scheduling. 4) Self tuning. 5) Model-reference adaptive systems. Although the...of multidimensional systems (CS881 as well as aircraft [HG90]. The self oscillating method is also a feedback based mechanism, utilizing a relay in the

On the Effect of Variability on Fermi, Pasta and Ulam Matrices

NASA Astrophysics Data System (ADS)

Nelson, Heather; Choubey, Bhaskar

The first numerical experiment by Fermi, Pasta, Ulam and Tsingou in 1955 observed recurrence in an array of non-linear systems. This has led to a large number of nonlinear numerical experiments with various new results from a chain of ideal oscillators. FPUT arrays consists of linear oscillators connected nonlinearly which leads to recurrence of energy mode with time. However, if such a system were to be physically constructed, inherent process variations would introduce a manufacturing tolerance into the parameters of the system. This abstract reports investigation into the effects of these tolerances on the FPU matrices. It has been observed that tolerance in the oscillators can degrade the observance of recurrence and with a chain of even 64 oscillators, recurrence cannot be observed with tolerances more than 10%. It has also been observed that linear oscillators tolerances have more effects on recurrence than those of the nonlinear coupling. Even with very small tolerances of +/- 1% on the linear components, one start to observe variations in the quality and magnitude of the recurrence and at +/- 5%, recurrence is starting to break down.

The chimera state in colloidal phase oscillators with hydrodynamic interaction

NASA Astrophysics Data System (ADS)

Hamilton, Evelyn; Bruot, Nicolas; Cicuta, Pietro

2017-12-01

The chimera state is the incongruous situation where coherent and incoherent populations coexist in sets of identical oscillators. Using driven non-linear oscillators interacting purely through hydrodynamic forces at low Reynolds number, previously studied as a simple model of motile cilia supporting waves, we find concurrent incoherent and synchronised subsets in small arrays. The chimeras seen in simulation display a "breathing" aspect, reminiscent of uniformly interacting phase oscillators. In contrast to other systems where chimera has been observed, this system has a well-defined interaction metric, and we know that the emergent dynamics inherit the symmetry of the underlying Oseen tensor eigenmodes. The chimera state can thus be connected to a superposition of eigenstates, whilst considering the mean interaction strength within and across subsystems allows us to make a connection to more generic (and abstract) chimeras in populations of Kuramoto phase oscillators. From this work, we expect the chimera state to emerge in experimental observations of oscillators coupled through hydrodynamic forces.

Investigation of oscillating cascade aerodynamics by an experimental influence coefficient technique

NASA Technical Reports Server (NTRS)

Buffum, Daniel H.; Fleeter, Sanford

1988-01-01

Fundamental experiments are performed in the NASA Lewis Transonic Oscillating Cascade Facility to investigate the torsion mode unsteady aerodynamics of a biconvex airfoil cascade at realistic values of the reduced frequency for all interblade phase angles at a specified mean flow condition. In particular, an unsteady aerodynamic influence coefficient technique is developed and utilized in which only one airfoil in the cascade is oscillated at a time and the resulting airfoil surface unsteady pressure distribution measured on one dynamically instrumented airfoil. The unsteady aerodynamics of an equivalent cascade with all airfoils oscillating at a specified interblade phase angle are then determined through a vector summation of these data. These influence coefficient determined oscillation cascade data are correlated with data obtained in this cascade with all airfoils oscillating at several interblade phase angle values. The influence coefficients are then utilized to determine the unsteady aerodynamics of the cascade for all interblade phase angles, with these unique data subsequently correlated with predictions from a linearized unsteady cascade model.

Wave Driven Non-Linear Flow Oscillator for the 22-Year Solar Cycle

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Wolff, C. L.; Hartle, R. E.; Einaudi, Franco (Technical Monitor)

2000-01-01

We propose that waves generate an oscillation in the Sun to account for the 22-year magnetic cycle. The mechanism we envision is analogous to that driving the Quasi Biennial Oscillation (QBO) observed in the terrestrial atmosphere, which is well understood in principal. Planetary waves and gravity waves deposit momentum in the background atmosphere and accelerate the flow under viscous dissipation. Analysis shows that such a momentum source represents a non-linearity of third or generally odd order, which generates also the fundamental frequency/period so that an oscillation is maintained without external time dependent forcing. For the Sun, we propose that the wave driven oscillation would occur just below the convection region, where the buoyancy frequency or convective stability becomes small to favor wave breaking and wave mean flow interaction. Using scale analysis to extrapolate from terrestrial to solar conditions, we present results from a simplified analytical model, applied to the equator, that incorporates Hines'Doppler Spread Parameterization for gravity waves (GW). Based on a parametric study, we conclude: (1) Depending on the adopted horizontal wavelengths of GW's, wave amplitudes < 10 m/s can be made to produce oscillating zonal winds of about 25 m/s that should be large enough to generate a corresponding oscillation in the main poloidal magnetic field; (2) The oscillation period can be made to be 22 years provided the buoyancy frequency (stability) is sufficiently small, which would place the oscillating wind field near the base of the convection region; (3) In this region, the turbulence associated with wave processes would be enhanced by low stability, and this also helps to produce the desired oscillation period and generate the dynamo currents that would produce the reversing magnetic field. We suggest that the above mechanism may also drive other long-period metronomes in planetary and stellar interiors.

A comparison of linear respiratory system models based on parameter estimates from PRN forced oscillation data.

PubMed

Diong, B; Grainger, J; Goldman, M; Nazeran, H

2009-01-01

The forced oscillation technique offers some advantages over spirometry for assessing pulmonary function. It requires only passive patient cooperation; it also provides data in a form, frequency-dependent impedance, which is very amenable to engineering analysis. In particular, the data can be used to obtain parameter estimates for electric circuit-based models of the respiratory system, which can in turn aid the detection and diagnosis of various diseases/pathologies. In this study, we compare the least-squares error performance of the RIC, extended RIC, augmented RIC, augmented RIC+I(p), DuBois, Nagels and Mead models in fitting 3 sets of impedance data. These data were obtained by pseudorandom noise forced oscillation of healthy subjects, mild asthmatics and more severe asthmatics. We found that the aRIC+I(p) and DuBois models yielded the lowest fitting errors (for the healthy subjects group and the 2 asthmatic patient groups, respectively) without also producing unphysiologically large component estimates.

Three-step approach for prediction of limit cycle pressure oscillations in combustion chambers of gas turbines

NASA Astrophysics Data System (ADS)

Iurashev, Dmytro; Campa, Giovanni; Anisimov, Vyacheslav V.; Cosatto, Ezio

2017-11-01

Currently, gas turbine manufacturers frequently face the problem of strong acoustic combustion driven oscillations inside combustion chambers. These combustion instabilities can cause extensive wear and sometimes even catastrophic damages to combustion hardware. This requires prevention of combustion instabilities, which, in turn, requires reliable and fast predictive tools. This work presents a three-step method to find stability margins within which gas turbines can be operated without going into self-excited pressure oscillations. As a first step, a set of unsteady Reynolds-averaged Navier-Stokes simulations with the Flame Speed Closure (FSC) model implemented in the OpenFOAM® environment are performed to obtain the flame describing function of the combustor set-up. The standard FSC model is extended in this work to take into account the combined effect of strain and heat losses on the flame. As a second step, a linear three-time-lag-distributed model for a perfectly premixed swirl-stabilized flame is extended to the nonlinear regime. The factors causing changes in the model parameters when applying high-amplitude velocity perturbations are analysed. As a third step, time-domain simulations employing a low-order network model implemented in Simulink® are performed. In this work, the proposed method is applied to a laboratory test rig. The proposed method permits not only the unsteady frequencies of acoustic oscillations to be computed, but the amplitudes of such oscillations as well. Knowing the amplitudes of unstable pressure oscillations, it is possible to determine how these oscillations are harmful to the combustor equipment. The proposed method has a low cost because it does not require any license for computational fluid dynamics software.

Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

PubMed Central

Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; D'Incerti, Ludovico

2015-01-01

In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D2), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes. PMID:25833429

Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: lminati@istituto-besta.it; Center for Mind/Brain Sciences, University of Trento, Trento; Chiesa, Pietro

In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D{sub 2}), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequencymore » activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.« less

Linear Proof-Mass Actuator

NASA Technical Reports Server (NTRS)

Holloway, Sidney E., III; Crossley, Edward A.; Miller, James B.; Jones, Irby W.; Davis, C. Calvin; Behun, Vaughn D.; Goodrich, Lewis R., Sr.

1995-01-01

Linear proof-mass actuator (LPMA) is friction-driven linear mass actuator capable of applying controlled force to structure in outer space to damp out oscillations. Capable of high accelerations and provides smooth, bidirectional travel of mass. Design eliminates gears and belts. LPMA strong enough to be used terrestrially where linear actuators needed to excite or damp out oscillations. High flexibility designed into LPMA by varying size of motors, mass, and length of stroke, and by modifying control software.

Transverse kink oscillations in the presence of twist

NASA Astrophysics Data System (ADS)

Terradas, J.; Goossens, M.

2012-12-01

Context. Magnetic twist is thought to play an important role in coronal loops. The effects of magnetic twist on stable magnetohydrodynamic (MHD) waves is poorly understood because they are seldom studied for relevant cases. Aims: The goal of this work is to study the fingerprints of magnetic twist on stable transverse kink oscillations. Methods: We numerically calculated the eigenmodes of propagating and standing MHD waves for a model of a loop with magnetic twist. The azimuthal component of the magnetic field was assumed to be small in comparison to the longitudinal component. We did not consider resonantly damped modes or kink instabilities in our analysis. Results: For a nonconstant twist the frequencies of the MHD wave modes are split, which has important consequences for standing waves. This is different from the degenerated situation for equilibrium models with constant twist, which are characterised by an azimuthal component of the magnetic field that linearly increases with the radial coordinate. Conclusions: In the presence of twist standing kink solutions are characterised by a change in polarisation of the transverse displacement along the tube. For weak twist, and in the thin tube approximation, the frequency of standing modes is unaltered and the tube oscillates at the kink speed of the corresponding straight tube. The change in polarisation is linearly proportional to the degree of twist. This has implications with regard to observations of kink modes, since the detection of this variation in polarisation can be used as an indirect method to estimate the twist in oscillating loops.

Vibronic coupling simulations for linear and nonlinear optical processes: Theory

NASA Astrophysics Data System (ADS)

Silverstein, Daniel W.; Jensen, Lasse

2012-02-01

A comprehensive vibronic coupling model based on the time-dependent wavepacket approach is derived to simulate linear optical processes, such as one-photon absorbance and resonance Raman scattering, and nonlinear optical processes, such as two-photon absorbance and resonance hyper-Raman scattering. This approach is particularly well suited for combination with first-principles calculations. Expressions for the Franck-Condon terms, and non-Condon effects via the Herzberg-Teller coupling approach in the independent-mode displaced harmonic oscillator model are presented. The significance of each contribution to the different spectral types is discussed briefly.

Characterizing Observed Limit Cycles in the Cassini Main Engine Guidance Control System

NASA Technical Reports Server (NTRS)

Rizvi, Farheen; Weitl, Raquel M.

2011-01-01

The Cassini spacecraft dynamics-related telemetry during long Main Engine (ME) burns has indicated the presence of stable limit cycles between 0.03-0.04 Hz frequencies. These stable limit cycles cause the spacecraft to possess non-zero oscillating rates for extended periods of time. This indicates that the linear ME guidance control system does not model the complete dynamics of the spacecraft. In this study, we propose that the observed limit cycles in the spacecraft dynamics telemetry appear from a stable interaction between the unmodeled nonlinear elements in the ME guidance control system. Many nonlinearities in the control system emerge from translating the linear engine gimbal actuator (EGA) motion into a spacecraft rotation. One such nonlinearity comes from the gear backlash in the EGA system, which is the focus of this paper. The limit cycle characteristics and behavior can be predicted by modeling this gear backlash nonlinear element via a describing function and studying the interaction of this describing function with the overall dynamics of the spacecraft. The linear ME guidance controller and gear backlash nonlinearity are modeled analytically. The frequency, magnitude, and nature of the limit cycle are obtained from the frequency response of the ME guidance controller and nonlinear element. In addition, the ME guidance controller along with the nonlinearity is simulated. The simulation response contains a limit cycle with similar characterstics as predicted analytically: 0.03-0.04 Hz frequency and stable, sustained oscillations. The analytical and simulated limit cycle responses are compared to the flight telemetry for long burns such as the Saturn Orbit Insertion and Main Engine Orbit Trim Maneuvers. The analytical and simulated limit cycle characteristics compare well with the actual observed limit cycles in the flight telemetry. Both have frequencies between 0.03-0.04 Hz and stable oscillations. This work shows that the stable limit cycles occur due to the interaction between the unmodeled nonlinear elements and linear ME guidance controller.

Effect of wind tunnel acoustic modes on linear oscillating cascade aerodynamics

NASA Technical Reports Server (NTRS)

Buffum, Daniel H.; Fleeter, Sanford

1993-01-01

The aerodynamics of a biconvex airfoil cascade oscillating in torsion is investigated using the unsteady aerodynamic influence coefficient technique. For subsonic flow and reduced frequencies as large as 0.9, airfoil surface unsteady pressures resulting from oscillation of one of the airfoils are measured using flush-mounted high-frequency-response pressure transducers. The influence coefficient data are examined in detail and then used to predict the unsteady aerodynamics of a cascade oscillating at various interblade phase angles. These results are correlated with experimental data obtained in the traveling-wave mode of oscillation and linearized analysis predictions. It is found that the unsteady pressure disturbances created by an oscillating airfoil excite wind tunnel acoustic modes which have detrimental effects on the experimental data. Acoustic treatment is proposed to rectify this problem.

ExoMars Entry Demonstrator Module Dynamic Stability

NASA Astrophysics Data System (ADS)

Dormieux, Marc; Gulhan, Ali; Berner, Claude

2011-05-01

In the frame of ExoMars DM aerodynamics characterization, pitch damping derivatives determination is required as it drives the parachute deployment conditions. Series of free-flight and free- oscillation tests (captive model) have been conducted with particular attention for data reduction. 6 Degrees- of-Freedom (DoF) analysis tools require the knowledge of local damping derivatives. In general ground tests do not provide them directly but only effective damping derivatives. Free-flight (ballistic range) tests with full oscillations around trim angle have been performed at ISL for 0.5

Linearly Polarized Single-Frequency Oscillations of Laser-Diode-Pumped Microchip Ceramic Nd:YAG Lasers with Forced Ince-Gaussian Mode Operations

NASA Astrophysics Data System (ADS)

Otsuka, Kenju; Nemoto, Kana; Kamikariya, Koji; Miyasaka, Yoshihiko; Chu, Shu-Chun

2007-09-01

Detailed oscillation spectra and polarization properties have been examined in laser-diode-pumped (LD-pumped) microchip ceramic (i.e., polycrystalline) Nd:YAG lasers and the inherent segregation of lasing patterns into local modes possessing different polarization states was observed. Single-frequency linearly-polarized stable oscillations were realized by forcing the laser to Ince-Gaussian mode operations by adjusting azimuthal cavity symmetry.

Chimera states in an ensemble of linearly locally coupled bistable oscillators

NASA Astrophysics Data System (ADS)

Shchapin, D. S.; Dmitrichev, A. S.; Nekorkin, V. I.

2017-11-01

Chimera states in a system with linear local connections have been studied. The system is a ring ensemble of analog bistable self-excited oscillators with a resistive coupling. It has been shown that the existence of chimera states is not due to the nonidentity of oscillators and noise, which is always present in real experiments, but is due to the nonlinear dynamics of the system on invariant tori with various dimensions.

Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes

ERIC Educational Resources Information Center

Steele, Joel S.; Ferrer, Emilio

2011-01-01

We examine emotion self-regulation and coregulation in romantic couples using daily self-reports of positive and negative affect. We fit these data using a damped linear oscillator model specified as a latent differential equation to investigate affect dynamics at the individual level and coupled influences for the 2 partners in each couple.…

A Simplified Theory of Coupled Oscillator Array Phase Control

NASA Technical Reports Server (NTRS)

Pogorzelski, R. J.; York, R. A.

1997-01-01

Linear and planar arrays of coupled oscillators have been proposed as means of achieving high power rf sources through coherent spatial power combining. In such - applications, a uniform phase distribution over the aperture is desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Notable among these are linear phase distributions resulting in steering of the output rf beam away from the broadside direction. The theory describing the operation of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. This has made it difficult to develop an intuitive understanding of the impact of oscillator tuning on phase control and has thus impeded practical application. In this work a simpl!fied theory is developed which facilitates intuitive understanding by establishing an analog of the phase control problem in terms of electrostatics.

Oscillation of satellite droplets in an Oldroyd-B viscoelastic liquid jet

NASA Astrophysics Data System (ADS)

Li, Fang; Yin, Xie-Yuan; Yin, Xie-Zhen

2017-01-01

A one-dimensional numerical simulation is carried out to study the oscillation characteristics of satellite droplets in the beads-on-a-string structure of an Oldroyd-B viscoelastic liquid jet. The oscillation of satellite droplets is compared with the linear oscillation of a single viscoelastic droplet. It is found that, contrary to the predictions of linear theory, the period of oscillation of satellite droplets decreases with time, despite the increase in droplet volume. The mechanism may lie in the existence of the filament, which exerts an extra resistance on droplets. On the other hand, the oscillation of droplets does not influence very much the thinning of the filament. The influence of the axial wave number, viscosity, and elasticity on the oscillation of satellite droplets is examined. Increasing the wave number may result in the decrease in the period and the increase in the decay rate of oscillation, while increasing viscosity may lead to the increase in both the period and the decay rate of oscillation. Elasticity is shown to suppress the oscillation at large wave numbers, but its influence is limited at small wave numbers.

Nonlinear aeroservoelastic analysis of a controlled multiple-actuated-wing model with free-play

NASA Astrophysics Data System (ADS)

Huang, Rui; Hu, Haiyan; Zhao, Yonghui

2013-10-01

In this paper, the effects of structural nonlinearity due to free-play in both leading-edge and trailing-edge outboard control surfaces on the linear flutter control system are analyzed for an aeroelastic model of three-dimensional multiple-actuated-wing. The free-play nonlinearities in the control surfaces are modeled theoretically by using the fictitious mass approach. The nonlinear aeroelastic equations of the presented model can be divided into nine sub-linear modal-based aeroelastic equations according to the different combinations of deflections of the leading-edge and trailing-edge outboard control surfaces. The nonlinear aeroelastic responses can be computed based on these sub-linear aeroelastic systems. To demonstrate the effects of nonlinearity on the linear flutter control system, a single-input and single-output controller and a multi-input and multi-output controller are designed based on the unconstrained optimization techniques. The numerical results indicate that the free-play nonlinearity can lead to either limit cycle oscillations or divergent motions when the linear control system is implemented.

The Damping Rates of Embedded Oscillating Starless Cores

NASA Astrophysics Data System (ADS)

Broderick, Avery E.; Narayan, Ramesh; Keto, Eric; Lada, Charles J.

2008-08-01

In a previous paper we demonstrated that nonradial hydrodynamic oscillations of a thermally supported (Bonnor-Ebert) sphere embedded in a low-density, high-temperature medium persist for many periods. The predicted column density variations and molecular spectral line profiles are similar to those observed in the Bok globule B68, suggesting that the motions in some starless cores may be oscillating perturbations on a thermally supported equilibrium structure. Such oscillations can produce molecular line maps which mimic rotation, collapse, or expansion and, thus, could make determining the dynamical state from such observations alone difficult. However, while B68 is embedded in a very hot, low-density medium, many starless cores are not, having interior/exterior density contrasts closer to unity. In this paper we investigate the oscillation damping rate as a function of the exterior density. For concreteness we use the same interior model employed by Broderick et al., with varying models for the exterior gas. We also develop a simple analytical formalism, based on the linear perturbation analysis of the oscillations, which predicts the contribution to the damping rates due to the excitation of sound waves in the external medium. We find that the damping rate of oscillations on globules in dense molecular environments is always many periods, corresponding to hundreds of thousands of years and persisting over the inferred lifetimes of the globules.

Transmission of arterial oxygen partial pressure oscillations to the cerebral microcirculation in a porcine model of acute lung injury caused by cyclic recruitment and derecruitment.

PubMed

Klein, K U; Boehme, S; Hartmann, E K; Szczyrba, M; Heylen, L; Liu, T; David, M; Werner, C; Markstaller, K; Engelhard, K

2013-02-01

Cyclic recruitment and derecruitment (R/D) play a key role in the pathomechanism of acute lung injury (ALI) leading to respiration-dependent oscillations of arterial partial pressure of oxygen (Pa(O(2))). These Pa(O(2)) oscillations could also be forwarded to the cerebral microcirculation. In 12 pigs, partial pressure of oxygen was measured in the thoracic aorta (Pa(O(2))) and subcortical cerebral tissue (Pbr(O(2))). Cerebral cortical haemoglobin oxygen saturation (Sbr(O(2))), cerebral blood flow (CBF), and peripheral haemoglobin saturation (Sp(O(2))) were assessed by spectroscopy and laser Doppler flowmetry. Measurements at different fractions of inspired oxygen (F(I(O(2)))) were performed at baseline and during cyclic R/D. frequency domain analysis, the Mann-Whitney test, linear models to test the influence of Pa(O(2)) and systolic arterial pressure (SAP) oscillations on cerebral measurements. Parameters [mean (SD)] remained stable during baseline. Pa(O(2)) oscillations [10.6 (8) kPa, phase(reference)], systemic arterial pressure (SAP) oscillations [20 (9) mm Hg, phase(Pa(O(2))-SAP) -33 (72)°], and Sp(O(2))oscillations [1.9 (1.7)%, phase(Pa(O(2))-Sp(O(2))) 264 (72)°] were detected during lung R/D at 1.0. Pa(O(2)) oscillations decreased [2.7 (3.5) kPa, P=0.0008] and Sp(O(2)) oscillations increased [6.8 (3.9)%, P=0.0014] at F(I(O(2))) 0.3. In the brain, synchronized Pbr(O(2)) oscillations [0.6 (0.4) kPa, phase(Pa(O(2))-Pbr(O(2))) 90 (39)°], Sbr(O(2)) oscillations [4.1 (1.5)%, phase(Pa(O(2))-Sbr(O(2))) 182 (54)°], and CBF oscillations [198 (176) AU, phase(Pa(O(2))-CBF) 201 (63)°] occurred that were dependent on Pa(O(2)) and SAP oscillations. Pa(O(2)) oscillations caused by cyclic R/D are transmitted to the cerebral microcirculation in a porcine model of ALI. These cyclic oxygen alterations could play a role in the crosstalk of acute lung and brain injury.

An improved understanding of the natural resonances of moonpools contained within floating rigid-bodies: Theory and application to oscillating water column devices

DOE PAGES

Bull, Diana L.

2015-09-23

The fundamental interactions between waves, a floating rigid-body, and a moonpool that is selectively open to atmosphere or enclosed to purposefully induce pressure fluctuations are investigated. The moonpool hydrodynamic characteristics and the hydrodynamic coupling to the rigid-body are derived implicitly through reciprocity relations on an array of field points. By modeling the free surface of the moonpool in this manner, an explicit hydrodynamic coupling term is included in the equations of motion. This coupling results in the migration of the moonpool's natural resonance frequency from the piston frequency to a new frequency when enclosed in a floating rigid-body. Two geometriesmore » that highlight distinct aspects of marine vessels and oscillating water column (OWC) renewable energy devices are analyzed to reveal the coupled natural resonance migration. The power performance of these two OWCs in regular waves is also investigated. The air chamber is enclosed and a three-dimensional, linear, frequency domain performance model that links the rigid-body to the moonpool through a linear resistive control strategy is detailed. Furthermore, an analytic expression for the optimal linear resistive control values in regular waves is presented.« less

Beer bottle whistling: a stochastic Hopf bifurcation

NASA Astrophysics Data System (ADS)

Boujo, Edouard; Bourquard, Claire; Xiong, Yuan; Noiray, Nicolas

2017-11-01

Blowing in a bottle to produce sound is a popular and yet intriguing entertainment. We reproduce experimentally the common observation that the bottle ``whistles'', i.e. produces a distinct tone, for large enough blowing velocity and over a finite interval of blowing angle. For a given set of parameters, the whistling frequency stays constant over time while the acoustic pressure amplitude fluctuates. Transverse oscillations of the shear layer in the bottle's neck are clearly identified with time-resolved particle image velocimetry (PIV) and proper orthogonal decomposition (POD). To account for these observations, we develop an analytical model of linear acoustic oscillator (the air in the bottle) subject to nonlinear stochastic forcing (the turbulent jet impacting the bottle's neck). We derive a stochastic differential equation and, from the associated Fokker-Planck equation and the measured acoustic pressure signals, we identify the model's parameters with an adjoint optimization technique. Results are further validated experimentally, and allow us to explain (i) the occurrence of whistling in terms of linear instability, and (ii) the amplitude of the limit cycle as a competition between linear growth rate, noise intensity, and nonlinear saturation. E. B. and N. N. acknowledge support by Repower and the ETH Zurich Foundation.

An improved understanding of the natural resonances of moonpools contained within floating rigid-bodies: Theory and application to oscillating water column devices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bull, Diana L.

The fundamental interactions between waves, a floating rigid-body, and a moonpool that is selectively open to atmosphere or enclosed to purposefully induce pressure fluctuations are investigated. The moonpool hydrodynamic characteristics and the hydrodynamic coupling to the rigid-body are derived implicitly through reciprocity relations on an array of field points. By modeling the free surface of the moonpool in this manner, an explicit hydrodynamic coupling term is included in the equations of motion. This coupling results in the migration of the moonpool's natural resonance frequency from the piston frequency to a new frequency when enclosed in a floating rigid-body. Two geometriesmore » that highlight distinct aspects of marine vessels and oscillating water column (OWC) renewable energy devices are analyzed to reveal the coupled natural resonance migration. The power performance of these two OWCs in regular waves is also investigated. The air chamber is enclosed and a three-dimensional, linear, frequency domain performance model that links the rigid-body to the moonpool through a linear resistive control strategy is detailed. Furthermore, an analytic expression for the optimal linear resistive control values in regular waves is presented.« less

Control Surface Interaction Effects of the Active Aeroelastic Wing Wind Tunnel Model

NASA Technical Reports Server (NTRS)

Heeg, Jennifer

2006-01-01

This paper presents results from testing the Active Aeroelastic Wing wind tunnel model in NASA Langley s Transonic Dynamics Tunnel. The wind tunnel test provided an opportunity to study aeroelastic system behavior under combined control surface deflections, testing for control surface interaction effects. Control surface interactions were observed in both static control surface actuation testing and dynamic control surface oscillation testing. The primary method of evaluating interactions was examination of the goodness of the linear superposition assumptions. Responses produced by independently actuating single control surfaces were combined and compared with those produced by simultaneously actuating and oscillating multiple control surfaces. Adjustments to the data were required to isolate the control surface influences. Using dynamic data, the task increases, as both the amplitude and phase have to be considered in the data corrections. The goodness of static linear superposition was examined and analysis of variance was used to evaluate significant factors influencing that goodness. The dynamic data showed interaction effects in both the aerodynamic measurements and the structural measurements.

Modeling walker synchronization on the Millennium Bridge.

PubMed

Eckhardt, Bruno; Ott, Edward; Strogatz, Steven H; Abrams, Daniel M; McRobie, Allan

2007-02-01

On its opening day the London Millennium footbridge experienced unexpected large amplitude wobbling subsequent to the migration of pedestrians onto the bridge. Modeling the stepping of the pedestrians on the bridge as phase oscillators, we obtain a model for the combined dynamics of people and the bridge that is analytically tractable. It provides predictions for the phase dynamics of individual walkers and for the critical number of people for the onset of oscillations. Numerical simulations and analytical estimates reproduce the linear relation between pedestrian force and bridge velocity as observed in experiments. They allow prediction of the amplitude of bridge motion, the rate of relaxation to the synchronized state and the magnitude of the fluctuations due to a finite number of people.

Curved-flow, rolling-flow, and oscillatory pure-yawing wind-tunnel test methods for determination of dynamic stability derivatives

NASA Technical Reports Server (NTRS)

Chambers, J. R.; Grafton, S. B.; Lutze, F. H.

1981-01-01

Dynamic stability derivatives are evaluated on the basis of rolling-flow, curved-flow and snaking tests. Attention is given to the hardware associated with curved-flow, rolling-flow and oscillatory pure-yawing wind-tunnel tests. It is found that the snaking technique, when combined with linear- and forced-oscillation methods, yields an important method for evaluating beta derivatives for current configurations at high angles of attack. Since the rolling flow model is fixed during testing, forced oscillations may be imparted to the model, permitting the measurement of damping and cross-derivatives. These results, when coupled with basic rolling-flow or rotary-balance data, yield a highly accurate mathematical model for studies of incipient spin and spin entry.

Modeling high-order synchronization epochs and transitions in the cardiovascular system

NASA Astrophysics Data System (ADS)

García-Álvarez, David; Bahraminasab, Alireza; Stefanovska, Aneta; McClintock, Peter V. E.

2007-12-01

We study a system consisting of two coupled phase oscillators in the presence of noise. This system is used as a model for the cardiorespiratory interaction in wakefulness and anaesthesia. We show that longrange correlated noise produces transitions between epochs with different n:m synchronisation ratios, as observed in the cardiovascular system. Also, we see that, the smaller the noise (specially the one acting on the slower oscillator), the bigger the synchronisation time, exactly as happens in anaesthesia compared with wakefulness. The dependence of the synchronisation time on the couplings, in the presence of noise, is studied; such dependence is softened by low-frequency noise. We show that the coupling from the slow oscillator to the fast one (respiration to heart) plays a more important role in synchronisation. Finally, we see that the isolines with same synchronisation time seem to be a linear combination of the two couplings.

Unified Theory for Aircraft Handling Qualities and Adverse Aircraft-Pilot Coupling

NASA Technical Reports Server (NTRS)

Hess, R. A.

1997-01-01

A unified theory for aircraft handling qualities and adverse aircraft-pilot coupling or pilot-induced oscillations is introduced. The theory is based on a structural model of the human pilot. A methodology is presented for the prediction of (1) handling qualities levels; (2) pilot-induced oscillation rating levels; and (3) a frequency range in which pilot-induced oscillations are likely to occur. Although the dynamics of the force-feel system of the cockpit inceptor is included, the methodology will not account for effects attributable to control sensitivity and is limited to single-axis tasks and, at present, to linear vehicle models. The theory is derived from the feedback topology of the structural model and an examination of flight test results for 32 aircraft configurations simulated by the U.S. Air Force/CALSPAN NT-33A and Total In-Flight Simulator variable stability aircraft. An extension to nonlinear vehicle dynamics such as that encountered with actuator saturation is discussed.

Minimal model for tag-based cooperation

NASA Astrophysics Data System (ADS)

Traulsen, Arne; Schuster, Heinz Georg

2003-10-01

Recently, Riolo et al. [Nature (London) 414, 441 (2001)] showed by computer simulations that cooperation can arise without reciprocity when agents donate only to partners who are sufficiently similar to themselves. One striking outcome of their simulations was the observation that the number of tolerant agents that support a wide range of players was not constant in time, but showed characteristic fluctuations. The cause and robustness of these tides of tolerance remained to be explored. Here we clarify the situation by solving a minimal version of the model of Riolo et al. It allows us to identify a net surplus of random changes from intolerant to tolerant agents as a necessary mechanism that produces these oscillations of tolerance, which segregate different agents in time. This provides a new mechanism for maintaining different agents, i.e., for creating biodiversity. In our model the transition to the oscillating state is caused by a saddle node bifurcation. The frequency of the oscillations increases linearly with the transition rate from tolerant to intolerant agents.

Roll Damping Derivatives from Generalized Lifting-Surface Theory and Wind Tunnel Forced-Oscillation Tests

NASA Technical Reports Server (NTRS)

Pototzky, Anthony S; Murphy, Patrick C.

2014-01-01

Improving aerodynamic models for adverse loss-of-control conditions in flight is an area being researched under the NASA Aviation Safety Program. Aerodynamic models appropriate for loss of control conditions require a more general mathematical representation to predict nonlinear unsteady behaviors. As more general aerodynamic models are studied that include nonlinear higher order effects, the possibility of measurements that confound aerodynamic and structural responses are probable. In this study an initial step is taken to look at including structural flexibility in analysis of rigid-body forced-oscillation testing that accounts for dynamic rig, sting and balance flexibility. Because of the significant testing required and associated costs in a general study, it makes sense to capitalize on low cost analytical methods where possible, especially where structural flexibility can be accounted for by a low cost method. This paper provides an initial look at using linear lifting surface theory applied to rigid-body aircraft roll forced-oscillation tests.

Observations of decay-less low-amplitude kink oscillations of EUV coronal loops

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe; Nakariakov, Valery; Anfinogentov, Sergey

The high spatial and temporal resolution observations at Extreme Ultra-Violet (EUV) wavelengths from the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) reveal new features in kink oscillations of coronal loops. We show that, in addition to the well-known rapidly decaying oscillations, a new type of kink waves is present, characterized by low-amplitude and undamped oscillations, that we define as decay-less. Typical periods range from 2.5 to 12 min in both regimes and are different for different loops, increasing with the loop length. Estimates of the loop lengths are supported by three dimensional reconstruction of the loop geometry. The amplitude for the decay-less regime is about 1 Mm, close to the spatial resolution of the AIA instruments. The oscillation phase, measured by the cross-correlation method, is found to be constant along each analysed loop, and the spatial structure of the phase of the oscillations corresponds to the fundamental standing kink mode. We show that the observed behaviours are consistent with the empirical model of a damped linear oscillator excited by a continuous low-amplitude harmonic driver, in addition to an eventual impulsive high-amplitude driver. The observed life-time of the oscillations is likely to be determined by the observational conditions rather than any physical damping. However, the balance between the driving and damping is a necessary ingredient of this model. The properties of this type of transverse oscillations make them interesting object of study in the framework of resonant absorption theory and coronal heating process.

High-Order Shock-Capturing Methods for Modeling Dynamics of the Solar Atmosphere

NASA Technical Reports Server (NTRS)

Bryson, Steve; Kosovichev, Alexander; Levy, Doron

2004-01-01

We use one-dimensional high-order central shock capturing numerical methods to study the response of various model solar atmospheres to forcing at the solar surface. The dynamics of the atmosphere is modeled with the Euler equations in a variable-sized flux tube in the presence of gravity. We study dynamics of the atmosphere suggestive of spicule formation and coronal oscillations. These studies are performed on observationally-derived model atmospheres above the quiet sun and above sunspots. To perform these simulations, we provide a new extension of existing second- and third- order shock-capturing methods to irregular grids. We also solve the problem of numerically maintaining initial hydrostatic balance via the introduction of new variables in the model equations and a careful initialization mechanism. We find several striking results: all model atmospheres respond to a single impulsive perturbation with several strong shock waves consistent with the rebound-shock model. These shock waves lift material and the transition region well into the initial corona, and the sensitivity of this lift to the initial impulse depends non-linearly on the details of the atmosphere model. We also reproduce an observed 3-minute coronal oscillation above sunspots compared to 5-minute oscillations above the quiet sun.

Enhanced Sensitivity of Novel Surface Acoustic Wave Microelectromechanical System-Interdigital Transducer Gyroscope

NASA Astrophysics Data System (ADS)

Wang, Wen; Oh, Haekwan; Lee, Keekeun; Yoon, Sungjin; Yang, Sangsik

2009-06-01

In this paper, we present a novel microelectromechanical system-interdigital transducer (MEMS-IDT) surface acoustic wave (SAW) gyroscope with an 80 MHz central frequency on a 128° YX LiNbO3 wafer. The developed MEMS-IDT gyroscope is composed of a two-port SAW resonator, a dual delay line oscillator, and metallic dots. The SAW resonator provides a stable standing wave, and the vibrating metallic dot at an antinode of the standing wave induces the second SAW in the normal direction of its vibrating axis. The dual delay line oscillator detects the Coriolis force by comparing the resonant frequencies between two oscillators through the interference effect. The coupling of mode (COM) modeling was used to extract the optimal design parameters prior to fabrication. In the electrical testing by the network analyzer, the fabricated SAW resonator and delay lines showed low insertion loss and similar operation frequencies between a resonator and delay lines. When the device was rotated, the resonant frequency differences between two oscillators linearly varied owing to the Coriolis force. The obtained sensitivity was approximately 119 Hz deg-1 s-1 in the angular rate range of 0-1000 deg/s. Satisfactory linearity and superior directivity were also observed in the test.

Investigation of diocotron modes in toroidally trapped electron plasmas using non-destructive method

NASA Astrophysics Data System (ADS)

Lachhvani, Lavkesh; Pahari, Sambaran; Sengupta, Sudip; Yeole, Yogesh G.; Bajpai, Manu; Chattopadhyay, P. K.

2017-10-01

Experiments with trapped electron plasmas in a SMall Aspect Ratio Toroidal device (SMARTEX-C) have demonstrated a flute-like mode represented by oscillations on capacitive (wall) probes. Although analogous to diocotron mode observed in linear electron traps, the mode evolution in toroids can have interesting consequences due to the presence of in-homogeneous magnetic field. In SMARTEX-C, the probe signals are observed to undergo transition from small, near-sinusoidal oscillations to large amplitude, non-linear "double-peaked" oscillations. To interpret the wall probe signal and bring forth the dynamics, an expression for the induced current on the probe for an oscillating charge is derived, utilizing Green's Reciprocation Theorem. Equilibrium position, poloidal velocity of the charge cloud, and charge content of the cloud, required to compute the induced current, are estimated from the experiments. Signal through capacitive probes is thereby computed numerically for possible charge cloud trajectories. In order to correlate with experiments, starting with an intuitive guess of the trajectory, the model is evolved and tweaked to arrive at a signal consistent with experimentally observed probe signals. A possible vortex like dynamics is predicted, hitherto unexplored in toroidal geometries, for a limited set of experimental observations from SMARTEX-C. Though heuristic, a useful interpretation of capacitive probe data in terms of charge cloud dynamics is obtained.

Radiating Fröhlich system as a model of cellular electromagnetism.

PubMed

Šrobár, Fedor

2015-01-01

Oscillating polar entities inside the biological cells, most notably microtubules, are bound to emit electromagnetic radiation. This phenomenon is described by Fröhlich kinetic equations expressing, in terms of quantum occupancy numbers of each discrete collective oscillatory mode, the balance between incoming metabolic energy flow and losses due to linear and non-linear interactions with the thermal environs of the oscillators. Hitherto, radiation losses have not been introduced as part of the balance; it was assumed that they were proportional to the modal occupation numbers. It is demonstrated that this formulation is incorrect and the radiation losses must be taken into account in the kinetic equations explicitly. Results of a numerical study of kinetic equations, enlarged in this sense, are presented for the case of three coupled oscillators which was shown to evince the essential attributes of the Fröhlich systems. Oscillator eigenfrequencies were chosen, alternatively, to fall into the MHz and the THz frequency domains. It was found that large radiation levels destroy the main hallmark of the Fröhlich systems, the energy condensation in the lowest frequency mode. The system then functions as a convertor of metabolic energy into radiation. At more moderate radiation levels, both energy condensation and significant radiation can coexist. Possible consequences for the cell physiology are suggested.

Incomplete data based parameter identification of nonlinear and time-variant oscillators with fractional derivative elements

NASA Astrophysics Data System (ADS)

Kougioumtzoglou, Ioannis A.; dos Santos, Ketson R. M.; Comerford, Liam

2017-09-01

Various system identification techniques exist in the literature that can handle non-stationary measured time-histories, or cases of incomplete data, or address systems following a fractional calculus modeling. However, there are not many (if any) techniques that can address all three aforementioned challenges simultaneously in a consistent manner. In this paper, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear and time-variant oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear sub-systems. In this regard, the oscillator is transformed into an equivalent MISO system in the wavelet domain. Next, a recently developed L1-norm minimization procedure based on compressive sensing theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Finally, these wavelet coefficients are utilized to determine appropriately defined time- and frequency-dependent wavelet based frequency response functions and related oscillator parameters. Several linear and nonlinear time-variant systems with fractional derivative elements are used as numerical examples to demonstrate the reliability of the technique even in cases of noise corrupted and incomplete data.

A simple model of intraseasonal oscillations

NASA Astrophysics Data System (ADS)

Fuchs, Željka; Raymond, David J.

2017-06-01

The intraseasonal oscillations and in particular the MJO have been and still remain a "holy grail" of today's atmospheric science research. Why does the MJO propagate eastward? What makes it unstable? What is the scaling for the MJO, i.e., why does it prefer long wavelengths or planetary wave numbers 1-3? What is the westward moving component of the intraseasonal oscillation? Though linear WISHE has long been discounted as a plausible model for intraseasonal oscillations and the MJO, the version we have developed explains many of the observed features of those phenomena, in particular, the preference for large zonal scale. In this model version, the moisture budget and the increase of precipitation with tropospheric humidity lead to a "moisture mode." The destabilization of the large-scale moisture mode occurs via WISHE only and there is no need to postulate large-scale radiatively induced instability or negative effective gross moist stability. Our WISHE-moisture theory leads to a large-scale unstable eastward propagating mode in n = -1 case and a large-scale unstable westward propagating mode in n = 1 case. We suggest that the n = -1 case might be connected to the MJO and the observed westward moving disturbance to the observed equatorial Rossby mode.

Linear analysis of auto-organization in Hebbian neural networks.

PubMed

Carlos Letelier, J; Mpodozis, J

1995-01-01

The self-organization of neurotopies where neural connections follow Hebbian dynamics is framed in terms of linear operator theory. A general and exact equation describing the time evolution of the overall synaptic strength connecting two neural laminae is derived. This linear matricial equation, which is similar to the equations used to describe oscillating systems in physics, is modified by the introduction of non-linear terms, in order to capture self-organizing (or auto-organizing) processes. The behavior of a simple and small system, that contains a non-linearity that mimics a metabolic constraint, is analyzed by computer simulations. The emergence of a simple "order" (or degree of organization) in this low-dimensionality model system is discussed.

Linearization of Conservative Nonlinear Oscillators

ERIC Educational Resources Information Center

Belendez, A.; Alvarez, M. L.; Fernandez, E.; Pascual, I.

2009-01-01

A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…

Undamped transverse oscillations of coronal loops as a self-oscillatory process

NASA Astrophysics Data System (ADS)

Nakariakov, V. M.; Anfinogentov, S. A.; Nisticò, G.; Lee, D.-H.

2016-06-01

Context. Standing transverse oscillations of coronal loops are observed to operate in two regimes: rapidly decaying, large amplitude oscillations and undamped small amplitude oscillations. In the latter regime the damping should be compensated by energy supply, which allows the loop to perform almost monochromatic oscillations with almost constant amplitude and phase. Different loops oscillate with different periods. The oscillation amplitude does not show dependence on the loop length or the oscillation period. Aims: We aim to develop a low-dimensional model explaining the undamped kink oscillations as a self-oscillatory process caused by the effect of negative friction. The source of energy is an external quasi-steady flow, for example, supergranulation motions near the loop footpoints or external flows in the corona. Methods: We demonstrate that the interaction of a quasi-steady flow with a loop can be described by a Rayleigh oscillator equation that is a non-linear ordinary differential equation, with the damping and resonant terms determined empirically. Results: Small-amplitude self-oscillatory solutions to the Rayleigh oscillator equation are harmonic signals of constant amplitude, which is consistent with the observed properties of undamped kink oscillations. The period of self-oscillations is determined by the frequency of the kink mode. The damping by dissipation and mode conversion is compensated by the continuous energy deposition at the frequency of the natural oscillation. Conclusions: We propose that undamped kink oscillations of coronal loops may be caused by the interaction of the loops with quasi-steady flows, and hence are self-oscillations, which is analogous to producing a tune by moving a bow across a violin string.

Symmetry breaking, Josephson oscillation and self-trapping in a self-bound three-dimensional quantum ball.

PubMed

Adhikari, S K

2017-11-22

We study spontaneous symmetry breaking (SSB), Josephson oscillation, and self-trapping in a stable, mobile, three-dimensional matter-wave spherical quantum ball self-bound by attractive two-body and repulsive three-body interactions. The SSB is realized by a parity-symmetric (a) one-dimensional (1D) double-well potential or (b) a 1D Gaussian potential, both along the z axis and no potential along the x and y axes. In the presence of each of these potentials, the symmetric ground state dynamically evolves into a doubly-degenerate SSB ground state. If the SSB ground state in the double well, predominantly located in the first well (z > 0), is given a small displacement, the quantum ball oscillates with a self-trapping in the first well. For a medium displacement one encounters an asymmetric Josephson oscillation. The asymmetric oscillation is a consequence of SSB. The study is performed by a variational and a numerical solution of a non-linear mean-field model with 1D parity-symmetric perturbations.

Delay decomposition approach to [Formula: see text] filtering analysis of genetic oscillator networks with time-varying delays.

PubMed

Revathi, V M; Balasubramaniam, P

2016-04-01

In this paper, the [Formula: see text] filtering problem is treated for N coupled genetic oscillator networks with time-varying delays and extrinsic molecular noises. Each individual genetic oscillator is a complex dynamical network that represents the genetic oscillations in terms of complicated biological functions with inner or outer couplings denote the biochemical interactions of mRNAs, proteins and other small molecules. Throughout the paper, first, by constructing appropriate delay decomposition dependent Lyapunov-Krasovskii functional combined with reciprocal convex approach, improved delay-dependent sufficient conditions are obtained to ensure the asymptotic stability of the filtering error system with a prescribed [Formula: see text] performance. Second, based on the above analysis, the existence of the designed [Formula: see text] filters are established in terms of linear matrix inequalities with Kronecker product. Finally, numerical examples including a coupled Goodwin oscillator model are inferred to illustrate the effectiveness and less conservatism of the proposed techniques.

Theoretical analysis of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shin, Y.M.; Ryskin, N.M.; Won, J.H.

The basic theory of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator consisting of two two-cavity klystron amplifiers reversely coupled through input/output slots is theoretically investigated. Application of Kirchhoff's laws to the coupled equivalent RLC circuit model of the device provides four nonlinear coupled equations, which are the first-order time-delayed differential equations. Analytical solutions obtained through linearization of the equations provide oscillation frequencies and thresholds of four fundamental eigenstates, symmetric/antisymmetric 0/{pi} modes. Time-dependent output signals are numerically analyzed with variation of the beam current, and a self-modulation mechanism and transition to chaos scenario are examined. The oscillatormore » shows a much stronger multistability compared to a delayed feedback klystron oscillator owing to the competitions among more diverse eigenmodes. A fully developed chaos region also appears at a relatively lower beam current, {approx}3.5I{sub st}, compared to typical vacuum tube oscillators (10-100I{sub st}), where I{sub st} is a start-oscillation current.« less

Order parameter analysis of synchronization transitions on star networks

NASA Astrophysics Data System (ADS)

Chen, Hong-Bin; Sun, Yu-Ting; Gao, Jian; Xu, Can; Zheng, Zhi-Gang

2017-12-01

The collective behaviors of populations of coupled oscillators have attracted significant attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynamical mechanism of collective synchronizations, by adopting the star-topology of coupled oscillators as a prototype system. The order parameter equation of star-linked phase oscillators can be obtained in terms of the Watanabe-Strogatz transformation, Ott-Antonsen ansatz, and the ensemble order parameter approach. Different solutions of the order parameter equation correspond to the diverse collective states, and different bifurcations reveal various transitions among these collective states. The properties of various transitions in the star-network model are revealed by using tools of nonlinear dynamics such as time reversibility analysis and linear stability analysis.

Analysis of Quasi-periodic Oscillations and Time Lag in Ultraluminous X-Ray Sources with XMM-Newton

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Zi-Jian; Xiao, Guang-Cheng; Zhang, Shu

We investigated the power density spectrum (PDS) and time lag of ultraluminous X-ray sources (ULXs) observed by XMM-Newton . We determined the PDSs for each ULX and found that five of them show intrinsic variability due to obvious quasi-periodic oscillations (QPOs) of mHz–1 Hz, consistent with previous reports. We further investigated these five ULXs to determine their possible time lag. The ULX QPOs exhibit a soft time lag that is linearly related to the QPO frequency. We discuss the likelihood of the ULX QPOs being type-C QPO analogs, and the time lag models. The ULXs might harbor intermediate-mass black holesmore » if their QPOs are type-C QPO analogs. We suggest that the soft lag and the linearity may be due to reverberation.« less

Traveling solitons in long-range oscillator chains

NASA Astrophysics Data System (ADS)

Miloshevich, George; Nguenang, Jean Pierre; Dauxois, Thierry; Khomeriki, Ramaz; Ruffo, Stefano

2017-03-01

We investigate the existence and propagation of solitons in a long-range extension of the quartic Fermi-Pasta-Ulam (FPU) chain of anharmonic oscillators. The coupling in the linear term decays as a power-law with an exponent 1<α ≤slant 3 . We obtain an analytic perturbative expression of traveling envelope solitons by introducing a non linear Schrödinger equation for the slowly varying amplitude of short wavelength modes. Due to the non analytic properties of the dispersion relation, it is crucial to develop the theory using discrete difference operators. Those properties are also the ultimate reason why kink-solitons may exist but are unstable, at variance with the short-range FPU model. We successfully compare these approximate analytic results with numerical simulations for the value α =2 which was chosen as a case study.

River Devices to Recover Energy with Advanced Materials (River DREAM)

DOE Office of Scientific and Technical Information (OSTI.GOV)

McMahon, Daniel P.

2013-07-03

The purpose of this project is to develop a generator called a Galloping Hydroelectric Energy Extraction Device (GHEED). It uses a galloping prism to convert water flow into linear motion. This motion is converted into electricity via a dielectric elastomer generator (DEG). The galloping mechanism and the DEG are combined to create a system to effectively generate electricity. This project has three research objectives: 1. Oscillator development and design a. Characterize galloping behavior, evaluate control surface shape change on oscillator performance and demonstrate shape change with water flow change. 2. Dielectric Energy Generator (DEG) characterization and modeling a. Characterize andmore » model the performance of the DEG based on oscillator design 3. Galloping Hydroelectric Energy Extraction Device (GHEED) system modeling and integration a. Create numerical models for construction of a system performance model and define operating capabilities for this approach Accomplishing these three objectives will result in the creation of a model that can be used to fully define the operating parameters and performance capabilities of a generator based on the GHEED design. This information will be used in the next phase of product development, the creation of an integrated laboratory scale generator to confirm model predictions.« less

El Niño Southern Oscillation (ENSO) and dysentery in Shandong province, China.

PubMed

Zhang, Ying; Bi, Peng; Wang, Guoyong; Hiller, Janet E

2007-01-01

To investigate the impact of the El Niño Southern Oscillation (ENSO) on dysentery transmission, the relationship between monthly dysentery cases in Shandong Province of China and the monthly Southern Oscillation Index (SOI), a broad index of ENSO, was examined over the period 1991-2003. Spearman correlations and generalized linear models were calculated to detect the association between the SOI and dysentery cases. Data from 1991 to 2001 were used to estimate the parameters, while data from 2002 to 2003 were used to test the forecasting ability of the model. After controlling for seasonality, autocorrelation, and a time-lagged effect, the results indicate that there was a significant negative association between the number of dysentery cases and the SOI, with a lagged effect of 2 months. A one-standard-deviation decrease in the SOI might cause up to 207 more dysentery cases per month in Shandong Province. This is the first report of the impact of the Southern Oscillation on dysentery risk in China, indicating that the SOI may be a useful early indicator of potential dysentery risk in Shandong Province.

Impact of Friedel oscillations on vapor-liquid equilibria and supercritical properties in two and three dimensions

NASA Astrophysics Data System (ADS)

Desgranges, Caroline; Huber, Landon; Delhommelle, Jerome

2016-07-01

We determine the impact of the Friedel oscillations on the phase behavior, critical properties, and thermodynamic contours in films [two dimensions (2 D )] and bulk phases [three dimensions (3 D )]. Using expanded Wang-Landau simulations, we calculate the grand-canonical partition function and, in turn, the thermodynamic properties of systems modeled with a linear combination of the Lennard-Jones and Dzugutov potentials, weighted by a parameter X (0

Model based control of dynamic atomic force microscope.

PubMed

Lee, Chibum; Salapaka, Srinivasa M

2015-04-01

A model-based robust control approach is proposed that significantly improves imaging bandwidth for the dynamic mode atomic force microscopy. A model for cantilever oscillation amplitude and phase dynamics is derived and used for the control design. In particular, the control design is based on a linearized model and robust H(∞) control theory. This design yields a significant improvement when compared to the conventional proportional-integral designs and verified by experiments.

Magnetization of a quantum spin system induced by a linear polarized laser

NASA Astrophysics Data System (ADS)

Zvyagin, A. A.

2015-08-01

It is shown that a linear polarized laser can cause magnetization of a spin system with magnetic anisotropy, the distinguished axis of which is perpendicular to the polarization of the laser field. In the dynamical regime the magnetization oscillates around the nonzero value determined by the parameters of the system. Oscillations have the frequency of the laser field, modulated by the lower Rabi-like frequencies. In the steady-state regime, for a large time scale greater than the characteristic relaxation time, the Rabi-like oscillations are damped, and the magnetization oscillates with the frequency of the laser field around the value which is determined by the relaxation rate also. Analytic results are presented for the spin-1/2 chain. The most direct manifestation of such a behavior can be observed in spin-1/2 Ising chain materials if the linear polarization of the laser field is chosen to be perpendicular to the Ising axis.

Theoretical studies of solar oscillations

NASA Technical Reports Server (NTRS)

Goldreich, P.

1980-01-01

Possible sources for the excitation of the solar 5 minute oscillations were investigated and a linear non-adiabatic stability code was applied to a preliminary study of the solar g-modes with periods near 160 minutes. Although no definitive conclusions concerning the excitation of these modes were reached, the excitation of the 5 minute oscillations by turbulent stresses in the convection zone remains a viable possibility. Theoretical calculations do not offer much support for the identification of the 160 minute global solar oscillation (reported by several independent observers) as a solar g-mode. A significant advance was made in attempting to reconcile mixing-length theory with the results of the calculations of linearly unstable normal modes. Calculations show that in a convective envelope prepared according to mixing length theory, the only linearly unstable modes are those which correspond to the turbulent eddies which are the basic element of the heuristic mixing length theory.

Baryon acoustic oscillations in 2D. II. Redshift-space halo clustering in N-body simulations

NASA Astrophysics Data System (ADS)

Nishimichi, Takahiro; Taruya, Atsushi

2011-08-01

We measure the halo power spectrum in redshift space from cosmological N-body simulations, and test the analytical models of redshift distortions particularly focusing on the scales of baryon acoustic oscillations. Remarkably, the measured halo power spectrum in redshift space exhibits a large-scale enhancement in amplitude relative to the real-space clustering, and the effect becomes significant for the massive or highly biased halo samples. These findings cannot be simply explained by the so-called streaming model frequently used in the literature. By contrast, a physically motivated perturbation theory model developed in the previous paper reproduces the halo power spectrum very well, and the model combining a simple linear scale-dependent bias can accurately characterize the clustering anisotropies of halos in two dimensions, i.e., line-of-sight and its perpendicular directions. The results highlight the significance of nonlinear coupling between density and velocity fields associated with two competing effects of redshift distortions, i.e., Kaiser and Finger-of-God effects, and a proper account of this effect would be important in accurately characterizing the baryon acoustic oscillations in two dimensions.

Thermohaline circulation and its box models simulation

NASA Astrophysics Data System (ADS)

Bazyura, Kateryna; Polonsky, Alexander; Sannikov, Viktor

2014-05-01

Ocean Thermochaline circulation (THC) is the part of large-scale World Ocean circulation and one of the main climate system components. It is generated by global meridional density gradients, which are controlled by surface heat and freshwater fluxes. THC regulates climate variability on different timescales (from decades to thousands years) [Stocker (2000), Clark (2002)]. Study of paleoclimatic evidences of abrupt and dramatic changes in ocean-atmosphere system in the past (such as, Dansgaard-Oeschger and Heinrich events or Younger Dryas, see e.g., [Rahmstorf (2002), Alley & Clark(1999)]) shows that these events are connected with THC regimes. At different times during last 120,000 years, three THC modes have prevailed in the Atlantic. They can be labeled as stadial, interstadial and Heinrich modes or as cold, warm and off mode. THC collapse (or thermohaline catastrophe) can be one of the consequences of global warming (including modern anthropogenic climate changes occurring at the moment). The ideas underlying different box-model studies, possibility of thermochaline catastrophe in present and past are discussed in this presentation. Response of generalized four box model of North Atlantic thermohaline circulation [developing the model of Griffies & Tzippermann (1995)] on periodic, stochastic and linear forcing is studied in details. To estimate climatic parameters of the box model we used monthly salinity and temperature data of ECMWF operational Ocean Reanalysis System 3 (ORA-S3) and data from atmospheric NCEP/NCAR reanalysis on precipitation, and heat fluxes for 1959-2011. Mean values, amplitude of seasonal cycle, amplitudes and periods of typical interdecadal oscillations, white noise level, linear trend coefficients and their significance level were estimated for every hydrophysical parameter. In response to intense freshwater or heat forcing, THC regime can change resulting in thermohaline catastrophe. We analyze relevant thresholds of external forcing in cases of using linear and nonlinear seawater state equation. In the frame of four-box model it is shown that: 1) The occurrence of the thermohaline catastrophe, which is likely happened at Younger Dryas period or developed as Heinrich events in the past, is improbable in modern climate epoch. 2) Choice of nonlinear seawater equitation of state leads to stabilization of warm mode of THC, which corresponds to modern climate state. 3) Typical white noise in heat and freshwater fluxes leads to generation of multidecadal oscillations of volume transport. Time-scale of these oscillations coincides with Atlantic Multidecadal oscillation periodicity. So, it is shown that that recent climate is characterized by quasi-periodical stable multidecadal THC warm regime. Stocker, T. F., 2000: Past and future reorganisations in the climate system. Quat. Sci.Rev, Vol. 19, P.301-319. Clark U., 2002: The role of the thermohaline circulation in abrupt climate change. Nature. Vol. 415, P.863-869. Rahmstorf S., 2002: Ocean circulation and climate during the past 120000 years. Nature. Vol. 419, P.207-214. Alley, R. B. & Clark, P. U., 1999: The deglaciation of the Northern Hemisphere: a global perspective. Annu.Rev. Earth Planet. Sci. Vol. 27, P.149-182. Griffies S.M., Tziperman E., 1995: A linear thermohaline oscillator driven by stochastic atmospheric forcing. Journal of Climate. Vol. 8. P. 2440-2453.

Quantum conductance oscillation in linear monatomic silicon chains

NASA Astrophysics Data System (ADS)

Liu, Fu-Ti; Cheng, Yan; Yang, Fu-Bin; Chen, Xiang-Rong

2014-02-01

The conductance of linear silicon atomic chains with n=1-8 atoms sandwiched between Au electrodes is investigated by using the density functional theory combined with non-equilibrium Green's function. The results show that the conductance oscillates with a period of two atoms as the number of atoms in the chain is varied. We optimize the geometric structure of nanoscale junctions in different distances, and obtain that the average bond-length of silicon atoms in each chain at equilibrium positions is 2.15±0.03 Å. The oscillation of average Si-Si bond-length can explain the conductance oscillation from the geometric structure of atomic chains. We calculate the transmission spectrum of the chains in the equilibrium positions, and explain the conductance oscillation from the electronic structure. The transport channel is mainly contributed by px and py orbital electrons of silicon atoms. The even-odd oscillation is robust under external voltage up to 1.2 V.

Dielectric response in Bloch’s hydrodynamic model of an electron-ion plasma

NASA Astrophysics Data System (ADS)

Ishikawa, K.; Felderhof, B. U.

The linear response of an electron-ion plasma to an applied oscillating electric field is studied within the framework of Bloch’s classical hydrodynamic model. The ions are assumed to be fixed in space and distributed according to a known probability distribution. The linearized equations of motion for electron density and flow velocity are studied with the aid of a multiple scattering analysis and cluster expansion. This allows systematic reduction of the many-ion problem to a composition of few-ion problems, and shows how the longitudinal dielectric response function can in principle be calculated.

Growth rate in the dynamical dark energy models.

PubMed

Avsajanishvili, Olga; Arkhipova, Natalia A; Samushia, Lado; Kahniashvili, Tina

Dark energy models with a slowly rolling cosmological scalar field provide a popular alternative to the standard, time-independent cosmological constant model. We study the simultaneous evolution of background expansion and growth in the scalar field model with the Ratra-Peebles self-interaction potential. We use recent measurements of the linear growth rate and the baryon acoustic oscillation peak positions to constrain the model parameter [Formula: see text] that describes the steepness of the scalar field potential.

Evolution of the linear-polarization-angle-dependence of the radiation-induced magnetoresistance-oscillations with microwave power

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ye, Tianyu; Mani, R. G.; Wegscheider, W.

2014-11-10

We examine the role of the microwave power in the linear polarization angle dependence of the microwave radiation induced magnetoresistance oscillations observed in the high mobility GaAs/AlGaAs two dimensional electron system. The diagonal resistance R{sub xx} was measured at the fixed magnetic fields of the photo-excited oscillatory extrema of R{sub xx} as a function of both the microwave power, P, and the linear polarization angle, θ. Color contour plots of such measurements demonstrate the evolution of the lineshape of R{sub xx} versus θ with increasing microwave power. We report that the non-linear power dependence of the amplitude of the radiation-inducedmore » magnetoresistance oscillations distorts the cosine-square relation between R{sub xx} and θ at high power.« less

Analysis of albedo versus cloud fraction relationships in liquid water clouds using heuristic models and large eddy simulation

NASA Astrophysics Data System (ADS)

Feingold, Graham; Balsells, Joseph; Glassmeier, Franziska; Yamaguchi, Takanobu; Kazil, Jan; McComiskey, Allison

2017-07-01

The relationship between the albedo of a cloudy scene A and cloud fraction fc is studied with the aid of heuristic models of stratocumulus and cumulus clouds. Existing work has shown that scene albedo increases monotonically with increasing cloud fraction but that the relationship varies from linear to superlinear. The reasons for these differences in functional dependence are traced to the relationship between cloud deepening and cloud widening. When clouds deepen with no significant increase in fc (e.g., in solid stratocumulus), the relationship between A and fc is linear. When clouds widen as they deepen, as in cumulus cloud fields, the relationship is superlinear. A simple heuristic model of a cumulus cloud field with a power law size distribution shows that the superlinear A-fc behavior is traced out either through random variation in cloud size distribution parameters or as the cloud field oscillates between a relative abundance of small clouds (steep slopes on a log-log plot) and a relative abundance of large clouds (flat slopes). Oscillations of this kind manifest in large eddy simulation of trade wind cumulus where the slope and intercept of the power law fit to the cloud size distribution are highly correlated. Further analysis of the large eddy model-generated cloud fields suggests that cumulus clouds grow larger and deeper as their underlying plumes aggregate; this is followed by breakup of large plumes and a tendency to smaller clouds. The cloud and thermal size distributions oscillate back and forth approximately in unison.

High Frequency Chandler Wobble Excitation

NASA Astrophysics Data System (ADS)

Seitz, F.; Stuck, J.; Thomas, M.

2003-04-01

Variations of Earth rotation on sub-daily to secular timescales are caused by mass redistributions in the Earth system as a consequence of geophysical processes and gravitational influences. Forced oscillations of polar motion are superposed by free oscillations of the Earth, i.e. the Chandler wobble and the free core nutation. In order to study the interactions between externally induced polar motion and the Earth's free oscillations, a non-linear gyroscopic model has been developed. In most of the former investigations on polar motion, the Chandler wobble is introduced as a damped oscillation with predetermined frequency and amplitude. However, as the effect of rotational deformation is a backcoupling mechanism of polar motion on the Earth's rotational dynamics, both period and amplitude of the Chandler wobble are time-dependent when regarding additional excitations from, e.g., atmospheric or oceanic mass redistributions. The gyroscopic model is free of any explicit information concerning amplitude, phase, and period of free oscillations. The characteristics of the Earth's free oscillation is reproduced by the model from rheological and geometrical parameters and rotational deformation is taken into account. This enables to study the time variable Chandler oscillation when the gyro is forced with atmospheric and oceanic angular momentum from the global atmospheric ECHAM3-T21 general circulation model together with the ocean model for circulation and tides OMCT driven by ECHAM including surface pressure. Besides, mass redistributions in the Earth's body due to gravitational and loading deformations are regarded and external torques exerted by Moon and Sun are considered. The numerical results of the gyro are significantly related with the geodetically observed time series of polar motion published by the IERS. It is shown that the consistent excitation is capable to counteract the damping and thus to maintain the Chandler amplitude. Spectral analyses of the ECHAM and OMCT forcing fields give no hint for increased excitation power in the Chandler band. Thus it is assumed, that continuous high frequency excitation due to stochastic weather phenomena is responsible for the perpetuation of the Chandler wobble.

Clausius inequality beyond the weak-coupling limit: the quantum Brownian oscillator.

PubMed

Kim, Ilki; Mahler, Günter

2010-01-01

We consider a quantum linear oscillator coupled at an arbitrary strength to a bath at an arbitrary temperature. We find an exact closed expression for the oscillator density operator. This state is noncanonical but can be shown to be equivalent to that of an uncoupled linear oscillator at an effective temperature T*(eff) with an effective mass and an effective spring constant. We derive an effective Clausius inequality deltaQ*(eff)< or =T*(eff)dS , where deltaQ*(eff) is the heat exchanged between the effective (weakly coupled) oscillator and the bath, and S represents a thermal entropy of the effective oscillator, being identical to the von-Neumann entropy of the coupled oscillator. Using this inequality (for a cyclic process in terms of a variation of the coupling strength) we confirm the validity of the second law. For a fixed coupling strength this inequality can also be tested for a process in terms of a variation of either the oscillator mass or its spring constant. Then it is never violated. The properly defined Clausius inequality is thus more robust than assumed previously.

Interaction with a field: a simple integrable model with backreaction

NASA Astrophysics Data System (ADS)

Mouchet, Amaury

2008-09-01

The classical model of an oscillator linearly coupled to a string captures, for a low price in technique, many general features of more realistic models for describing a particle interacting with a field or an atom in an electromagnetic cavity. The scattering matrix and the asymptotic in and out-waves on the string can be computed exactly and the phenomenon of resonant scattering can be introduced in the simplest way. The dissipation induced by the coupling of the oscillator to the string can be studied completely. In the case of a d'Alembert string, the backreaction leads to an Abraham-Lorentz-Dirac-like equation. In the case of a Klein-Gordon string, one can see explicitly how radiation governs the (meta)stability of the (quasi)bounded mode.

On the Role of Surface Friction in Tropical Intraseasonal Oscillation

NASA Technical Reports Server (NTRS)

Chao, Winston C.; Chen, Baode

1999-01-01

The Madden-Julian oscillation (MJO), or the tropical intraseasonal oscillation, has attracted much attention, ever since its discovery in the early seventies for reasons of both scientific understanding and practical forecasts. Among the theoretical interpretations of the MJO, the wave-CISK (conditional instability of the second kind) mechanism is the most popular. The basic idea of the wave-CISK interpretation is that the cooperation between the low-level convergence associated with the eastward moving Kelvin wave and the cumulus convection generates an eastward moving Kelvin-wave-like mode. Later it was recognized that the MJO has an important Rossby-wave-like component. However linear analysis and numerical simulations based on it (even when conditional heating is used) have revealed two problems with the wave-CISK interpretation; i.e., excessive speed and the most preferred scale being zero or grid scale. Chao (1995) presented a discussion of these problems and attributed these problems to the particular type of expression for the cumulus heating used in the linear analyses and numerical studies (i.e., the convective heating is proportional to low-level convergence and a fixed vertical heating profile). It should be pointed out that in the relatively successful simulation of MJO with general circulation models the problem of grid scale being the most preferred scale does not appear and die problem of excessive speed is not as severe as in the linear analysis.

Period doubling and other nonlinear phenomena in volcanic earthquakes and tremor

USGS Publications Warehouse

Julian, B.R.

2000-01-01

Evidence of subharmonic period-doubling cascades has recently been recognized in seismograms of volcanic tremor from several volcanoes. This phenomenon occurs only in nonlinear systems, and is the commonest route by which such systems change from periodic to chaotic behavior. It is predicted to occur in a model of volcanic tremor excitation by flow-induced vibration, and it might well also occur in other volcano-seismic source process. If the possibility of period doubling is not taken into account in interpreting spectra of tremor and long-period earthquakes, then low-frequency "sub-harmonic" oscillations may be mis-identified as normal modes of a linear acoustic resonator, leading to errors of an order of magnitude or more in inferred magma-body dimensions. This example illustrates the importance of nonlinear phenomena in attempts to understand volcano-seismic phenomena physically. Linear systems are fundamentally incapable of causing earthquakes or exciting tremor, so nonlinearity is essential to any theory of volcano-seismic phenomena. Nonlinear processes are in many respects qualitatively different from linear ones. A few of their characteristics that might be relevant in volcanoes include the possibility: (1) that damping might increase, rather than decrease, oscillation frequencies; and (2) that these frequencies might be functions of the amplitude of oscillation, so that temporal variations in spectral peak frequencies might not be manifestations of changes of conditions within the magmatic system.

Recurrent jellyfish blooms are a consequence of global oscillations.

PubMed

Condon, Robert H; Duarte, Carlos M; Pitt, Kylie A; Robinson, Kelly L; Lucas, Cathy H; Sutherland, Kelly R; Mianzan, Hermes W; Bogeberg, Molly; Purcell, Jennifer E; Decker, Mary Beth; Uye, Shin-ichi; Madin, Laurence P; Brodeur, Richard D; Haddock, Steven H D; Malej, Alenka; Parry, Gregory D; Eriksen, Elena; Quiñones, Javier; Acha, Marcelo; Harvey, Michel; Arthur, James M; Graham, William M

2013-01-15

A perceived recent increase in global jellyfish abundance has been portrayed as a symptom of degraded oceans. This perception is based primarily on a few case studies and anecdotal evidence, but a formal analysis of global temporal trends in jellyfish populations has been missing. Here, we analyze all available long-term datasets on changes in jellyfish abundance across multiple coastal stations, using linear and logistic mixed models and effect-size analysis to show that there is no robust evidence for a global increase in jellyfish. Although there has been a small linear increase in jellyfish since the 1970s, this trend was unsubstantiated by effect-size analysis that showed no difference in the proportion of increasing vs. decreasing jellyfish populations over all time periods examined. Rather, the strongest nonrandom trend indicated jellyfish populations undergo larger, worldwide oscillations with an approximate 20-y periodicity, including a rising phase during the 1990s that contributed to the perception of a global increase in jellyfish abundance. Sustained monitoring is required over the next decade to elucidate with statistical confidence whether the weak increasing linear trend in jellyfish after 1970 is an actual shift in the baseline or part of an oscillation. Irrespective of the nature of increase, given the potential damage posed by jellyfish blooms to fisheries, tourism, and other human industries, our findings foretell recurrent phases of rise and fall in jellyfish populations that society should be prepared to face.

Making chaotic behavior in a damped linear harmonic oscillator

NASA Astrophysics Data System (ADS)

Konishi, Keiji

2001-06-01

The present Letter proposes a simple control method which makes chaotic behavior in a damped linear harmonic oscillator. This method is a modified scheme proposed in paper by Wang and Chen (IEEE CAS-I 47 (2000) 410) which presents an anti-control method for making chaotic behavior in discrete-time linear systems. We provide a systematic procedure to design parameters and sampling period of a feedback controller. Furthermore, we show that our method works well on numerical simulations.

Reconstruction of real-space linear matter power spectrum from multipoles of BOSS DR12 results

NASA Astrophysics Data System (ADS)

Lee, Seokcheon

2018-02-01

Recently, the power spectrum (PS) multipoles using the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 (DR12) sample are analyzed [1]. The based model for the analysis is the so-called TNS quasi-linear model and the analysis provides the multipoles up to the hexadecapole [2]. Thus, one might be able to recover the real-space linear matter PS by using the combinations of multipoles to investigate the cosmology [3]. We provide the analytic form of the ratio of quadrupole (hexadecapole) to monopole moments of the quasi-linear PS including the Fingers-of-God (FoG) effect to recover the real-space PS in the linear regime. One expects that observed values of the ratios of multipoles should be consistent with those of the linear theory at large scales. Thus, we compare the ratios of multipoles of the linear theory, including the FoG effect with the measured values. From these, we recover the linear matter power spectra in real-space. These recovered power spectra are consistent with the linear matter power spectra.

Experimental and analytical investigations of longitudinal combustion instability in a continuously variable resonance combustor (CVRC)

NASA Astrophysics Data System (ADS)

Yu, Yen Ching

An analytical model based on linearized Euler equations (LEE) is developed and used in conjunction with a validating experiment to study combustion instability. The LEE model features mean flow effects, entropy waves, adaptability for more physically-realistic boundary conditions, and is generalized for multiple-domain conditions. The model calculates spatial modes, resonant frequencies and linear growth rates of the overall system. The predicted resonant frequencies and spatially-resolved mode shapes agree with the experimental data from a longitudinally-unstable model rocket combustor to within 7%. Different gaseous fuels (methane, ethylene, and hydrogen) were tested under fixed geometry. Tests with hydrogen were stable, whereas ethylene, methane, and JP-8 were increasingly unstable. A novel method for obtaining large amounts of stability data under variable resonance conditions in a single test was demonstrated. The continuously variable resonance combustor (CVRC) incorporates a traversing choked axial oxidizer inlet to vary the overall combustion system resonance. The CVRC experiment successfully demonstrates different level of instability, transitions between stability levels, and identifies the most stable and unstable geometric combination. Pressure oscillation amplitudes ranged from less than 10% of mean pressure to greater than 60%. At low amplitudes, measured resonant frequency changed with inlet location but at high amplitude the measured resonance frequency matched the frequency of the combustion chamber. As the system transitions from linear to non-linear instability, the higher harmonics of the fundamental resonant mode appear nearly simultaneously. Transient, high-amplitude, broadband noise, at lower frequencies (on the order of 200 Hz) are also observed. Conversely, as the system transitions back to a more linear stability regime, the higher harmonics disappear sequentially, led by the highest order. Good agreements between analytical and experimental results are attained by treating the experiment as quasi-stationary. The stability characteristics from the high frequency measurements are further analyzed using filtered pressure traces, spectrograms, power spectral density plots, and oscillation decrements. Future works recommended include: direct measurements, such as chemiluminescence or high-speed imaging to examine the unsteady combustion processes; three-way comparisons between the acoustic-based, linear Euler-based, and non-linear Euler/RANS model; use the high fidelity computation to investigate the forcing terms modeled in the acoustic-based model.

Neuromorphic computing with nanoscale spintronic oscillators

PubMed Central

Torrejon, Jacob; Riou, Mathieu; Araujo, Flavio Abreu; Tsunegi, Sumito; Khalsa, Guru; Querlioz, Damien; Bortolotti, Paolo; Cros, Vincent; Fukushima, Akio; Kubota, Hitoshi; Yuasa, Shinji; Stiles, M. D.; Grollier, Julie

2017-01-01

Neurons in the brain behave as non-linear oscillators, which develop rhythmic activity and interact to process information1. Taking inspiration from this behavior to realize high density, low power neuromorphic computing will require huge numbers of nanoscale non-linear oscillators. Indeed, a simple estimation indicates that, in order to fit a hundred million oscillators organized in a two-dimensional array inside a chip the size of a thumb, their lateral dimensions must be smaller than one micrometer. However, despite multiple theoretical proposals2–5, and several candidates such as memristive6 or superconducting7 oscillators, there is no proof of concept today of neuromorphic computing with nano-oscillators. Indeed, nanoscale devices tend to be noisy and to lack the stability required to process data in a reliable way. Here, we show experimentally that a nanoscale spintronic oscillator8,9 can achieve spoken digit recognition with accuracies similar to state of the art neural networks. We pinpoint the regime of magnetization dynamics leading to highest performance. These results, combined with the exceptional ability of these spintronic oscillators to interact together, their long lifetime, and low energy consumption, open the path to fast, parallel, on-chip computation based on networks of oscillators. PMID:28748930

Model of Wave Driven Flow Oscillation for Solar Cycle

NASA Technical Reports Server (NTRS)

Mayr, Hans G.; Wolff, Charles L.; Einaudi, Franco (Technical Monitor)

2001-01-01

At low latitudes in the Earth's atmosphere, the observed zonal flow velocities are dominated by the semi-annual and quasi-biennial oscillations with periods of 6 months and 20 to 32 months respectively. These terrestrial oscillations, the SAO and QBO respectively, are driven by wave-mean flow interactions due to upward propagating planetary-scale waves (periods of days) and small-scale gravity waves (periods of hours). We are proposing (see also Mayr et al., GRL, 2001) that such a mechanism may drive long period oscillations (reversing flows) in stellar and planetary interiors, and we apply it to the Sun. The reversing flows would occur below the convective envelope where waves can propagate. We apply a simplified, one dimensional, analytical flow model that incorporates a gravity wave parameterization due to Hines (1997). Based on this analysis, our estimates show that relatively small wave amplitudes less than 10 m/s can produce zonal flow amplitudes of 20 m/s, which should be sufficient to generate the observed variations in the magnetic field. To produce the 22-year period of oscillation, a low buoyancy frequency must be chosen, and this places the proposed flow in a region that is close to (and below) the base of the convective envelope. Enhanced turbulence associated with this low stability should help to generate the dynamo currents. With larger stability at deeper levels in the solar interior, the model can readily produce also oscillations with much longer periods. To provide an understanding of the fluid dynamics involved, we present numerical results from a 2D model for the terrestrial atmosphere that exemplify the non-linear nature of the wave interaction for which a mechanical analog is the escapement mechanism of the clock.

Stochastic multiresonance for a fractional linear oscillator with time-delayed kernel and quadratic noise

NASA Astrophysics Data System (ADS)

Guo, Feng; Wang, Xue-Yuan; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Zhang, Zheng-Yu; Huang, Xu-Hui

2017-12-01

The stochastic resonance for a fractional oscillator with time-delayed kernel and quadratic trichotomous noise is investigated. Applying linear system theory and Laplace transform, the system output amplitude (SPA) for the fractional oscillator is obtained. It is found that the SPA is a periodical function of the kernel delayed-time. Stochastic multiplicative phenomenon appears on the SPA versus the driving frequency, versus the noise amplitude, and versus the fractional exponent. The non-monotonous dependence of the SPA on the system parameters is also discussed.

A model for large amplitude oscillations of coated bubbles accounting for buckling and rupture

NASA Astrophysics Data System (ADS)

Marmottant, Philippe; van der Meer, Sander; Emmer, Marcia; Versluis, Michel; de Jong, Nico; Hilgenfeldt, Sascha; Lohse, Detlef

2005-12-01

We present a model applicable to ultrasound contrast agent bubbles that takes into account the physical properties of a lipid monolayer coating on a gas microbubble. Three parameters describe the properties of the shell: a buckling radius, the compressibility of the shell, and a break-up shell tension. The model presents an original non-linear behavior at large amplitude oscillations, termed compression-only, induced by the buckling of the lipid monolayer. This prediction is validated by experimental recordings with the high-speed camera Brandaris 128, operated at several millions of frames per second. The effect of aging, or the resultant of repeated acoustic pressure pulses on bubbles, is predicted by the model. It corrects a flaw in the shell elasticity term previously used in the dynamical equation for coated bubbles. The break-up is modeled by a critical shell tension above which gas is directly exposed to water.

Spontaneous Oscillations and Waves during Chemical Vapor Deposition of InN

NASA Astrophysics Data System (ADS)

Jiang, F.; Munkholm, A.; Wang, R.-V.; Streiffer, S. K.; Thompson, Carol; Fuoss, P. H.; Latifi, K.; Elder, K. R.; Stephenson, G. B.

2008-08-01

We report observations of self-sustaining spatiotemporal chemical oscillations during metal-organic chemical vapor deposition of InN onto GaN. Under constant supply of vapor precursors trimethylindium and NH3, the condensed-phase cycles between crystalline islands of InN and elemental In droplets. Propagating fronts between regions of InN and In occur with linear, circular, and spiral geometries. The results are described by a model in which the nitrogen activity produced by surface-catalyzed NH3 decomposition varies with the exposed surface areas of GaN, InN, and In.

Spontaneous oscillations and waves during chemical vapor deposition of InN.

PubMed

Jiang, F; Munkholm, A; Wang, R-V; Streiffer, S K; Thompson, Carol; Fuoss, P H; Latifi, K; Elder, K R; Stephenson, G B

2008-08-22

We report observations of self-sustaining spatiotemporal chemical oscillations during metal-organic chemical vapor deposition of InN onto GaN. Under constant supply of vapor precursors trimethylindium and NH3, the condensed-phase cycles between crystalline islands of InN and elemental In droplets. Propagating fronts between regions of InN and In occur with linear, circular, and spiral geometries. The results are described by a model in which the nitrogen activity produced by surface-catalyzed NH3 decomposition varies with the exposed surface areas of GaN, InN, and In.

An Apparatus to Demonstrate Linear and Nonlinear Oscillations of a Pendulum

ERIC Educational Resources Information Center

Mayer, V. V.; Varaksina, E. I.

2016-01-01

A physical pendulum with a magnetic load is proposed for comparison of linear and nonlinear oscillations. The magnetic load is repelled by permanent magnets which are disposed symmetrically relative to the load. It is established that positions of the pendulum and the magnets determine the dependence of restoring force on displacement of the load.…

Solution of the Schrodinger Equation for a Diatomic Oscillator Using Linear Algebra: An Undergraduate Computational Experiment

ERIC Educational Resources Information Center

Gasyna, Zbigniew L.

2008-01-01

Computational experiment is proposed in which a linear algebra method is applied to the solution of the Schrodinger equation for a diatomic oscillator. Calculations of the vibration-rotation spectrum for the HCl molecule are presented and the results show excellent agreement with experimental data. (Contains 1 table and 1 figure.)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Asplund, Curtis T., E-mail: ca2621@columbia.edu; Berenstein, David, E-mail: dberens@physics.ucsb.edu

We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that the entanglement entropy, after tracing over half of the oscillators, generically asymptotes to linear growth at a rate given by the sum of the positive Lyapunov exponents of the system. These exponents give a classical entropy growth rate, in the sense of Kolmogorov, Sinai and Pesin. We also calculate the dependence of this entropy on linear mixtures of the oscillator Hilbert-space factors, to investigate themore » dependence of the entanglement entropy on the choice of coarse graining. We find that for almost all choices the asymptotic growth rate is the same.« less

Completely monolithic linearly polarized high-power fiber laser oscillator

NASA Astrophysics Data System (ADS)

Belke, Steffen; Becker, Frank; Neumann, Benjamin; Ruppik, Stefan; Hefter, Ulrich

2014-03-01

We have demonstrated a linearly polarized cw all-in-fiber oscillator providing 1 kW of output power and a polarization extinction ratio (PER) of up to 21.7 dB. The design of the laser oscillator is simple and consists of an Ytterbium-doped polarization maintaining large mode area (PLMA) fiber and suitable fiber Bragg gratings (FBG) in matching PLMA fibers. The oscillator has nearly diffraction-limited beam quality (M² < 1.2). Pump power is delivered via a high power 6+1:1 pump coupler. The slope efficiency of the laser is 75 %. The electro/optical efficiency of the complete laser system is ~30 % and hence in the range of Rofin's cw non-polarized fiber lasers. Choosing an adequate bending diameter for the Yb-doped PLMA fiber, one polarization mode as well as higher order modes are sufficiently supressed1. Resulting in a compact and robust linearly polarized high power single mode laser without external polarizing components. Linearly polarized lasers are well established for one dimensional cutting or welding applications. Using beam shaping optics radially polarized laser light can be generated to be independent from the angle of incident to the processing surface. Furthermore, high power linearly polarized laser light is fundamental for nonlinear frequency conversion of nonlinear materials.

Feedback stabilization of an oscillating vertical cylinder by POD Reduced-Order Model

NASA Astrophysics Data System (ADS)

Tissot, Gilles; Cordier, Laurent; Noack, Bernd R.

2015-01-01

The objective is to demonstrate the use of reduced-order models (ROM) based on proper orthogonal decomposition (POD) to stabilize the flow over a vertically oscillating circular cylinder in the laminar regime (Reynolds number equal to 60). The 2D Navier-Stokes equations are first solved with a finite element method, in which the moving cylinder is introduced via an ALE method. Since in fluid-structure interaction, the POD algorithm cannot be applied directly, we implemented the fictitious domain method of Glowinski et al. [1] where the solid domain is treated as a fluid undergoing an additional constraint. The POD-ROM is classically obtained by projecting the Navier-Stokes equations onto the first POD modes. At this level, the cylinder displacement is enforced in the POD-ROM through the introduction of Lagrange multipliers. For determining the optimal vertical velocity of the cylinder, a linear quadratic regulator framework is employed. After linearization of the POD-ROM around the steady flow state, the optimal linear feedback gain is obtained as solution of a generalized algebraic Riccati equation. Finally, when the optimal feedback control is applied, it is shown that the flow converges rapidly to the steady state. In addition, a vanishing control is obtained proving the efficiency of the control approach.

Recent Developments in the Analysis of Couple Oscillator Arrays

NASA Technical Reports Server (NTRS)

Pogorzelski, Ronald J.

2000-01-01

This presentation considers linear arrays of coupled oscillators. Our purpose in coupling oscillators together is to achieve high radiated power through the spatial power combining which results when the oscillators are injection locked to each other. York, et. al. have shown that, left to themselves, the ensemble of injection locked oscillators oscillate at the average of the tuning frequencies of all the oscillators. Coupling these arrays achieves high radiated power through coherent spatial power combining. The coupled oscillators are usually designed to produce constant aperture phase. Oscillators are injection locked to each other or to a master oscillator to produce coherent radiation. Oscillators do not necessarily oscillate at their tuning frequency.

Chaotic Oscillations of Second Order Linear Hyperbolic Equations with Nonlinear Boundary Conditions: A Factorizable but Noncommutative Case

NASA Astrophysics Data System (ADS)

Li, Liangliang; Huang, Yu; Chen, Goong; Huang, Tingwen

If a second order linear hyperbolic partial differential equation in one-space dimension can be factorized as a product of two first order operators and if the two first order operators commute, with one boundary condition being the van der Pol type and the other being linear, one can establish the occurrence of chaos when the parameters enter a certain regime [Chen et al., 2014]. However, if the commutativity of the two first order operators fails to hold, then the treatment in [Chen et al., 2014] no longer works and significant new challenges arise in determining nonlinear boundary conditions that engenders chaos. In this paper, we show that by incorporating a linear memory effect, a nonlinear van der Pol boundary condition can cause chaotic oscillations when the parameter enters a certain regime. Numerical simulations illustrating chaotic oscillations are also presented.

Magnetic quantization in monolayer bismuthene

NASA Astrophysics Data System (ADS)

Chen, Szu-Chao; Chiu, Chih-Wei; Lin, Hui-Chi; Lin, Ming-Fa

The magnetic quantization in monolayer bismuthene is investigated by the generalized tight-binding model. The quite large Hamiltonian matrix is built from the tight-binding functions of the various sublattices, atomic orbitals and spin states. Due to the strong spin orbital coupling and sp3 bonding, monolayer bismuthene has the diverse low-lying energy bands such as the parabolic, linear and oscillating energy bands. The main features of band structures are further reflected in the rich magnetic quantization. Under a uniform perpendicular magnetic field (Bz) , three groups of Landau levels (LLs) with distinct features are revealed near the Fermi level. Their Bz-dependent energy spectra display the linear, square-root and non-monotonous dependences, respectively. These LLs are dominated by the combinations of the 6pz orbital and (6px,6py) orbitals as a result of strong sp3 bonding. Specifically, the LL anti-crossings only occur between LLs originating from the oscillating energy band.

Oscillator strengths, first-order properties, and nuclear gradients for local ADC(2).

PubMed

Schütz, Martin

2015-06-07

We describe theory and implementation of oscillator strengths, orbital-relaxed first-order properties, and nuclear gradients for the local algebraic diagrammatic construction scheme through second order. The formalism is derived via time-dependent linear response theory based on a second-order unitary coupled cluster model. The implementation presented here is a modification of our previously developed algorithms for Laplace transform based local time-dependent coupled cluster linear response (CC2LR); the local approximations thus are state specific and adaptive. The symmetry of the Jacobian leads to considerable simplifications relative to the local CC2LR method; as a result, a gradient evaluation is about four times less expensive. Test calculations show that in geometry optimizations, usually very similar geometries are obtained as with the local CC2LR method (provided that a second-order method is applicable). As an exemplary application, we performed geometry optimizations on the low-lying singlet states of chlorophyllide a.

Chaos and Robustness in a Single Family of Genetic Oscillatory Networks

PubMed Central

Fu, Daniel; Tan, Patrick; Kuznetsov, Alexey; Molkov, Yaroslav I.

2014-01-01

Genetic oscillatory networks can be mathematically modeled with delay differential equations (DDEs). Interpreting genetic networks with DDEs gives a more intuitive understanding from a biological standpoint. However, it presents a problem mathematically, for DDEs are by construction infinitely-dimensional and thus cannot be analyzed using methods common for systems of ordinary differential equations (ODEs). In our study, we address this problem by developing a method for reducing infinitely-dimensional DDEs to two- and three-dimensional systems of ODEs. We find that the three-dimensional reductions provide qualitative improvements over the two-dimensional reductions. We find that the reducibility of a DDE corresponds to its robustness. For non-robust DDEs that exhibit high-dimensional dynamics, we calculate analytic dimension lines to predict the dependence of the DDEs’ correlation dimension on parameters. From these lines, we deduce that the correlation dimension of non-robust DDEs grows linearly with the delay. On the other hand, for robust DDEs, we find that the period of oscillation grows linearly with delay. We find that DDEs with exclusively negative feedback are robust, whereas DDEs with feedback that changes its sign are not robust. We find that non-saturable degradation damps oscillations and narrows the range of parameter values for which oscillations exist. Finally, we deduce that natural genetic oscillators with highly-regular periods likely have solely negative feedback. PMID:24667178

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks

PubMed Central

Mori, Hiroki; Okuyama, Yuji; Asada, Minoru

2017-01-01

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the “information networks” different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed. PMID:28796797

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks.

PubMed

Park, Jihoon; Mori, Hiroki; Okuyama, Yuji; Asada, Minoru

2017-01-01

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the "information networks" different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.

Chimera regimes in a ring of oscillators with local nonlinear interaction

NASA Astrophysics Data System (ADS)

Shepelev, Igor A.; Zakharova, Anna; Vadivasova, Tatiana E.

2017-03-01

One of important problems concerning chimera states is the conditions of their existence and stability. Until now, it was assumed that chimeras could arise only in ensembles with nonlocal character of interactions. However, this assumption is not exactly right. In some special cases chimeras can be realized for local type of coupling [1-3]. We propose a simple model of ensemble with local coupling when chimeras are realized. This model is a ring of linear oscillators with the local nonlinear unidirectional interaction. Chimera structures in the ring are found using computer simulations for wide area of values of parameters. Diagram of the regimes on plane of control parameters is plotted and scenario of chimera destruction are studied when the parameters are changed.

Visualization of vortex structures and analysis of frequency of PVC

NASA Astrophysics Data System (ADS)

Gesheva, E. S.; Shtork, S. I.; Alekseenko, S. V.

2018-03-01

The paper presents the results of the study of large-scale vortex structures in a model chamber. Methods of forming quasi-stationary vortices of various shapes by changing the geometric parameters of the chamber have been proposed. In the model chamber with a tangential swirl of the flow, a rectilinear vortex, single helical and double helical vortices were obtained. The double helical structure of the vortex is unique due to its immovability around the axis of the chamber. The resulting structures slowly oscillate around their own axes, which is called the vortex core precession; while the oscillation frequency depends linearly on the liquid flow rate. The use of stationary vortex structures in power plants will increase the efficiency of combustion chambers and reduce slagging.

Piezoelectric Non-Linear Nanomechanical Temperature and Acceleration Insensitive Clocks (PENNTAC) Phase 1 Evaluation and Plans for Phase 2

DTIC Science & Technology

2013-05-01

95.2 dBc/Hz, (c) - 94.2 dBc/Hz. Fig. 4: Mechanically compensated AlN resonators. A thin oxide layer is used to completely cancel the linear...pumped is represented by a non-linear capacitor. This capacitor will be first implemented via a varactor and then substituted by a purely mechanical...demonstrate the advantages of a parametric oscillator: (i) we will first use an external electronic varactor to prove that a parametric oscillator

Complex metabolic oscillations in plants forced by harmonic irradiance.

PubMed Central

Nedbal, Ladislav; Brezina, Vítezslav

2002-01-01

Plants exposed to harmonically modulated irradiance, approximately 1 + cos(omegat), exhibit a complex periodic pattern of chlorophyll fluorescence emission that can be deconvoluted into a steady-state component, a component that is modulated with the frequency of the irradiance (omega), and into at least two upper harmonic components (2omega and 3omega). A model is proposed that accounts for the upper harmonics in fluorescence emission by nonlinear negative feedback regulation of photosynthesis. In contrast to simpler linear models, the model predicts that the steady-state fluorescence component will depend on the frequency of light modulation, and that amplitudes of all fluorescence components will exhibit resonance peak(s) when the irradiance frequency is tuned to an internal frequency of a regulatory component. The experiments confirmed that the upper harmonic components appear and exhibit distinct resonant peaks. The frequency of autonomous oscillations observed earlier upon an abrupt increase in CO(2) concentration corresponds to the sharpest of the resonant peaks of the forced oscillations. We propose that the underlying principles are general for a wide spectrum of negative-feedback regulatory mechanisms. The analysis by forced harmonic oscillations will enable us to examine internal dynamics of regulatory processes that have not been accessible to noninvasive fluorescence monitoring to date. PMID:12324435

Unsteady-flow-field predictions for oscillating cascades

NASA Technical Reports Server (NTRS)

Huff, Dennis L.

1991-01-01

The unsteady flow field around an oscillating cascade of flat plates with zero stagger was studied by using a time marching Euler code. This case had an exact solution based on linear theory and served as a model problem for studying pressure wave propagation in the numerical solution. The importance of using proper unsteady boundary conditions, grid resolution, and time step size was shown for a moderate reduced frequency. Results show that an approximate nonreflecting boundary condition based on linear theory does a good job of minimizing reflections from the inflow and outflow boundaries and allows the placement of the boundaries to be closer to the airfoils than when reflective boundaries are used. Stretching the boundary to dampen the unsteady waves is another way to minimize reflections. Grid clustering near the plates captures the unsteady flow field better than when uniform grids are used as long as the 'Courant Friedrichs Levy' (CFL) number is less than 1 for a sufficient portion of the grid. Finally, a solution based on an optimization of grid, CFL number, and boundary conditions shows good agreement with linear theory.

1.5  kW ytterbium-doped single-transverse-mode, linearly polarized monolithic fiber master oscillator power amplifier.

PubMed

Huang, Long; Ma, Pengfei; Tao, Rumao; Shi, Chen; Wang, Xiaolin; Zhou, Pu

2015-04-01

A linearly polarized monolithic fiber laser based on a master oscillator power amplifier structure with a master oscillator and a one-stage power amplifier is reported. We design a homemade oscillator based on the theory that, in the coiled gain fiber, the higher modes and the polarized mode of the fundamental mode along the fast axis are suppressed effectively because of their obviously higher bend loss than that of the polarized mode of the fundamental mode along the slow axis. The oscillator operates at 1080 nm, launching a 30 W seed laser with a high polarization extinction ratio of 19 dB into the power amplifier via a mode field adapter. The power amplifier utilizes Yb-doped polarization-maintaining fiber of 20/400  μm, which produces nearly diffraction-limited output power of about 1.5 kW with an optical-optical efficiency of 81.5% and a polarization extinction ratio of 13.8 dB. Both the M(x)² factor and the M(y)² factor of the collimated beam are measured to be about 1.2. The spectral width of the output power is broadened approximately linearly, and the full width at half maximum of the spectrum at the maximum output power is about 5.8 nm. It is known as the highest linearly polarized output power to the best of our knowledge.

On the interannual oscillations in the northern temperate total ozone

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krzyscin, J.W.

1994-07-01

The interannual variations in total ozone are studied using revised Dobson total ozone records (1961-1990) from 17 stations located within the latitude band 30 deg N - 60 deg N. To obtain the quasi-biennial oscillation (QBO), El Nino-Southern Oscillation (ENSO), and 11-year solar cycle manifestation in the `northern temperate` total ozone data, various multiple regression models are constructed by the least squares fitting to the observed ozone. The statistical relationships between the selected indices of the atmospheric variabilities and total ozone are described in the linear and nonlinear regression models. Nonlinear relationships to the predictor variables are found. That is,more » the total ozone variations are statistically modeled by nonlinear terms accounting for the coupling between QBO and ENSO, QBO and solar activity, and ENSO and solar activity. It is suggested that large reduction of total ozone values over the `northern temperate` region occurs in cold season when a strong ENSO warm event meets the west phase of the QBO during the period of high solar activity.« less

Spatial proximity effects on the excitation of sheath RF voltages by evanescent slow waves in the ion cyclotron range of frequencies

NASA Astrophysics Data System (ADS)

Colas, Laurent; Lu, Ling-Feng; Křivská, Alena; Jacquot, Jonathan; Hillairet, Julien; Helou, Walid; Goniche, Marc; Heuraux, Stéphane; Faudot, Eric

2017-02-01

We investigate theoretically how sheath radio-frequency (RF) oscillations relate to the spatial structure of the near RF parallel electric field E ∥ emitted by ion cyclotron (IC) wave launchers. We use a simple model of slow wave (SW) evanescence coupled with direct current (DC) plasma biasing via sheath boundary conditions in a 3D parallelepiped filled with homogeneous cold magnetized plasma. Within a ‘wide-sheath’ asymptotic regime, valid for large-amplitude near RF fields, the RF part of this simple RF  +  DC model becomes linear: the sheath oscillating voltage V RF at open field line boundaries can be re-expressed as a linear combination of individual contributions by every emitting point in the input field map. SW evanescence makes individual contributions all the larger as the wave emission point is located closer to the sheath walls. The decay of |V RF| with the emission point/sheath poloidal distance involves the transverse SW evanescence length and the radial protrusion depth of lateral boundaries. The decay of |V RF| with the emitter/sheath parallel distance is quantified as a function of the parallel SW evanescence length and the parallel connection length of open magnetic field lines. For realistic geometries and target SOL plasmas, poloidal decay occurs over a few centimeters. Typical parallel decay lengths for |V RF| are found to be smaller than IC antenna parallel extension. Oscillating sheath voltages at IC antenna side limiters are therefore mainly sensitive to E ∥ emission by active or passive conducting elements near these limiters, as suggested by recent experimental observations. Parallel proximity effects could also explain why sheath oscillations persist with antisymmetric strap toroidal phasing, despite the parallel antisymmetry of the radiated field map. They could finally justify current attempts at reducing the RF fields induced near antenna boxes to attenuate sheath oscillations in their vicinity.

Decentralized Fuzzy MPC on Spatial Power Control of a Large PHWR

NASA Astrophysics Data System (ADS)

Liu, Xiangjie; Jiang, Di; Lee, Kwang Y.

2016-08-01

Reliable power control for stabilizing the spatial oscillations is quite important for ensuring the safe operation of a modern pressurized heavy water reactor (PHWR), since these spatial oscillations can cause “flux tilting” in the reactor core. In this paper, a decentralized fuzzy model predictive control (DFMPC) is proposed for spatial control of PHWR. Due to the load dependent dynamics of the nuclear power plant, fuzzy modeling is used to approximate the nonlinear process. A fuzzy Lyapunov function and “quasi-min-max” strategy is utilized in designing the DFMPC, to reduce the conservatism. The plant-wide stability is achieved by the asymptotically positive realness constraint (APRC) for this decentralized MPC. The solving optimization problem is based on a receding horizon scheme involving the linear matrix inequalities (LMIs) technique. Through dynamic simulations, it is demonstrated that the designed DFMPC can effectively suppress spatial oscillations developed in PHWR, and further, shows the advantages over the typical parallel distributed compensation (PDC) control scheme.

Synchronization of Coupled Mechanical Oscillators

NASA Astrophysics Data System (ADS)

Kennedy, Linda; Andereck, Barbara

2007-10-01

The Kuramoto model is used to describe synchronization of non-linear oscillators in biological, chemical, and physics systems. Using identical metronomes with similar frequencies on a movable platform, as per J. Pantaleone Am. J. Phys. 70, 992 (2002), we hope to realize a mechanical example of this model. A variety of materials were used for the movable platforms that coupled the metronomes. Platforms were either allowed to roll on cylindrical supports or suspended in pendulum fashion from the ceiling. Metronomes were started out of phase and allowed to synchronize. Measurements by PASCO photogates monitored by a LabView program were used to determine the phase difference between the two metronomes as a function of time. The dynamics of the metronome coupling was described by two second-order differential equations involving four key parameters: platform coupling, oscillation angle, damping/driving strength, and intrinsic frequency difference. Outstanding agreement between theory and experiment was achieved when the vertical motion of the platform and metronomes was included in the governing equations.

Electronically Tunable Differential Integrator: Linear Voltage Controlled Quadrature Oscillator.

PubMed

Nandi, Rabindranath; Pattanayak, Sandhya; Venkateswaran, Palaniandavar; Das, Sagarika

2015-01-01

A new electronically tunable differential integrator (ETDI) and its extension to voltage controlled quadrature oscillator (VCQO) design with linear tuning law are proposed; the active building block is a composite current feedback amplifier with recent multiplication mode current conveyor (MMCC) element. Recently utilization of two different kinds of active devices to form a composite building block is being considered since it yields a superior functional element suitable for improved quality circuit design. The integrator time constant (τ) and the oscillation frequency (ω o ) are tunable by the control voltage (V) of the MMCC block. Analysis indicates negligible phase error (θ e ) for the integrator and low active ω o -sensitivity relative to the device parasitic capacitances. Satisfactory experimental verifications on electronic tunability of some wave shaping applications by the integrator and a double-integrator feedback loop (DIFL) based sinusoid oscillator with linear f o variation range of 60 KHz~1.8 MHz at low THD of 2.1% are verified by both simulation and hardware tests.

The Biharmonic Oscillator and Asymmetric Linear Potentials: From Classical Trajectories to Momentum-Space Probability Densities in the Extreme Quantum Limit

ERIC Educational Resources Information Center

Ruckle, L. J.; Belloni, M.; Robinett, R. W.

2012-01-01

The biharmonic oscillator and the asymmetric linear well are two confining power-law-type potentials for which complete bound-state solutions are possible in both classical and quantum mechanics. We examine these problems in detail, beginning with studies of their trajectories in position and momentum space, evaluation of the classical probability…

Self-motion magnitude estimation during linear oscillation - Changes with head orientation and following fatigue

NASA Technical Reports Server (NTRS)

Parker, D. E.; Wood, D. L.; Gulledge, W. L.; Goodrich, R. L.

1979-01-01

Two types of experiments concerning the estimated magnitude of self-motion during exposure to linear oscillation on a parallel swing are described in this paper. Experiment I examined changes in magnitude estimation as a function of variation of the subject's head orientation, and Experiments II a, II b, and II c assessed changes in magnitude estimation performance following exposure to sustained, 'intense' linear oscillation (fatigue-inducting stimulation). The subjects' performance was summarized employing Stevens' power law R = k x S to the nth, where R is perceived self-motion magnitude, k is a constant, S is amplitude of linear oscillation, and n is an exponent). The results of Experiment I indicated that the exponents, n, for the magnitude estimation functions varied with head orientation and were greatest when the head was oriented 135 deg off the vertical. In Experiments II a-c, the magnitude estimation function exponents were increased following fatigue. Both types of experiments suggest ways in which the vestibular system's contribution to a spatial orientation perceptual system may vary. This variability may be a contributing factor to the development of pilot/astronaut disorientation and may also be implicated in the occurrence of motion sickness.

What Controls ENSO-Amplitude Diversity in Climate Models?

NASA Astrophysics Data System (ADS)

Wengel, C.; Dommenget, D.; Latif, M.; Bayr, T.; Vijayeta, A.

2018-02-01

Climate models depict large diversity in the strength of the El Niño/Southern Oscillation (ENSO) (ENSO amplitude). Here we investigate ENSO-amplitude diversity in the Coupled Model Intercomparison Project Phase 5 (CMIP5) by means of the linear recharge oscillator model, which reduces ENSO dynamics to a two-dimensional problem in terms of eastern equatorial Pacific sea surface temperature anomalies (T) and equatorial Pacific upper ocean heat content anomalies (h). We find that a large contribution to ENSO-amplitude diversity originates from stochastic forcing. Further, significant interactions exist between the stochastic forcing and the growth rates of T and h with competing effects on ENSO amplitude. The joint consideration of stochastic forcing and growth rates explains more than 80% of the ENSO-amplitude variance within CMIP5. Our results can readily explain the lack of correlation between the Bjerknes Stability index, a measure of the growth rate of T, and ENSO amplitude in a multimodel ensemble.

Drifts and Environmental Disturbances in Atomic Clock Subsystems: Quantifying Local Oscillator, Control Loop, and Ion Resonance Interactions.

PubMed

Enzer, Daphna G; Diener, William A; Murphy, David W; Rao, Shanti R; Tjoelker, Robert L

2017-03-01

Linear ion trap frequency standards are among the most stable continuously operating frequency references and clocks. Depending on the application, they have been operated with a variety of local oscillators (LOs), including quartz ultrastable oscillators, hydrogen-masers, and cryogenic sapphire oscillators. The short-, intermediate-, and long-term stability of the frequency output is a complicated function of the fundamental performances, the time dependence of environmental disturbances, the atomic interrogation algorithm, the implemented control loop, and the environmental sensitivity of the LO and the atomic system components. For applications that require moving these references out of controlled lab spaces and into less stable environments, such as fieldwork or spaceflight, a deeper understanding is needed of how disturbances at different timescales impact the various subsystems of the clock and ultimately the output stability. In this paper, we analyze which perturbations have an impact and to what degree. We also report on a computational model of a control loop, which keeps the microwave source locked to the ion resonance. This model is shown to agree with laboratory measurements of how well the feedback removes various disturbances and also with a useful analytic approach we developed for predicting these impacts.

Wave fluctuations in the system with some Yang-Mills condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prokhorov, G., E-mail: zhoraprox@yandex.ru; Pasechnik, R., E-mail: Roman.Pasechnik@thep.lu.se; Vereshkov, G., E-mail: gveresh@gmail.com

2016-12-15

Self-consistent dynamics of non-homogeneous fluctuations and homogeneous and isotropic condensate of Yang–Mills fields was investigated in zero, linear and quasilinear approximations over the wave modes in the framework of N = 4 supersymmetric model in Hamilton gauge in quasiclassical theory. The models with SU(2), SU(3) and SU(4) gauge groups were considered. Particle production effect and effect of generation of longitudinal oscillations were obtained.

Second- and third-harmonic generation in metal-based structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scalora, M.; Akozbek, N.; Bloemer, M. J.

We present a theoretical approach to the study of second- and third-harmonic generation from metallic structures and nanocavities filled with a nonlinear material in the ultrashort pulse regime. We model the metal as a two-component medium, using the hydrodynamic model to describe free electrons and Lorentz oscillators to account for core electron contributions to both the linear dielectric constant and harmonic generation. The active nonlinear medium that may fill a metallic nanocavity, or be positioned between metallic layers in a stack, is also modeled using Lorentz oscillators and surface phenomena due to symmetry breaking are taken into account. We studymore » the effects of incident TE- and TM-polarized fields and show that a simple reexamination of the basic equations reveals additional, exploitable dynamical features of nonlinear frequency conversion in plasmonic nanostructures.« less

Linear stability analysis of collective neutrino oscillations without spurious modes

NASA Astrophysics Data System (ADS)

Morinaga, Taiki; Yamada, Shoichi

2018-01-01

Collective neutrino oscillations are induced by the presence of neutrinos themselves. As such, they are intrinsically nonlinear phenomena and are much more complex than linear counterparts such as the vacuum or Mikheyev-Smirnov-Wolfenstein oscillations. They obey integro-differential equations, for which it is also very challenging to obtain numerical solutions. If one focuses on the onset of collective oscillations, on the other hand, the equations can be linearized and the technique of linear analysis can be employed. Unfortunately, however, it is well known that such an analysis, when applied with discretizations of continuous angular distributions, suffers from the appearance of so-called spurious modes: unphysical eigenmodes of the discretized linear equations. In this paper, we analyze in detail the origin of these unphysical modes and present a simple solution to this annoying problem. We find that the spurious modes originate from the artificial production of pole singularities instead of a branch cut on the Riemann surface by the discretizations. The branching point singularities on the Riemann surface for the original nondiscretized equations can be recovered by approximating the angular distributions with polynomials and then performing the integrals analytically. We demonstrate for some examples that this simple prescription does remove the spurious modes. We also propose an even simpler method: a piecewise linear approximation to the angular distribution. It is shown that the same methodology is applicable to the multienergy case as well as to the dispersion relation approach that was proposed very recently.

Linear dynamic coupling in geared rotor systems

NASA Technical Reports Server (NTRS)

David, J. W.; Mitchell, L. D.

1986-01-01

The effects of high frequency oscillations caused by the gear mesh, on components of a geared system that can be modeled as rigid discs are analyzed using linear dynamic coupling terms. The coupled, nonlinear equations of motion for a disc attached to a rotating shaft are presented. The results of a trial problem analysis show that the inclusion of the linear dynamic coupling terms can produce significant changes in the predicted response of geared rotor systems, and that the produced sideband responses are greater than the unbalanced response. The method is useful in designing gear drives for heavy-lift helicopters, industrial speed reducers, naval propulsion systems, and heavy off-road equipment.

Direct reading inductance meter

NASA Technical Reports Server (NTRS)

Kolby, R. B. (Inventor)

1977-01-01

A direct reading inductance meter comprised of a crystal oscillator and an LC tuned oscillator is presented. The oscillators function respectively to generate a reference frequency, f(r), and to generate an initial frequency, f(0), which when mixed produce a difference equal to zero. Upon connecting an inductor of small unknown value in the LC circuit to change its resonant frequency to f(x), a difference frequency (f(r)-f(x)) is produced that is very nearly a linear function of the inductance of the inductor. The difference frequency is measured and displayed on a linear scale in units of inductance.

Effect of parameter mismatch on the dynamics of strongly coupled self sustained oscillators.

PubMed

Chakrabarty, Nilaj; Jain, Aditya; Lal, Nijil; Das Gupta, Kantimay; Parmananda, Punit

2017-01-01

In this paper, we present an experimental setup and an associated mathematical model to study the synchronization of two self-sustained, strongly coupled, mechanical oscillators (metronomes). The effects of a small detuning in the internal parameters, namely, damping and frequency, have been studied. Our experimental system is a pair of spring wound mechanical metronomes; coupled by placing them on a common base, free to move along a horizontal direction. We designed a photodiode array based non-contact, non-magnetic position detection system driven by a microcontroller to record the instantaneous angular displacement of each oscillator and the small linear displacement of the base, coupling the two. In our system, the mass of the oscillating pendula forms a significant fraction of the total mass of the system, leading to strong coupling of the oscillators. We modified the internal mechanism of the spring-wound "clockwork" slightly, such that the natural frequency and the internal damping could be independently tuned. Stable synchronized and anti-synchronized states were observed as the difference in the parameters was varied in the experiments. The simulation results showed a rapid increase in the phase difference between the two oscillators beyond a certain threshold of parameter mismatch. Our simple model of the escapement mechanism did not reproduce a complete 180° out of phase state. However, the numerical simulations show that increased mismatch in parameters leads to a synchronized state with a large phase difference.

Why noise is useful in functional and neural mechanisms of interval timing?

PubMed Central

2013-01-01

Background The ability to estimate durations in the seconds-to-minutes range - interval timing - is essential for survival, adaptation and its impairment leads to severe cognitive and/or motor dysfunctions. The response rate near a memorized duration has a Gaussian shape centered on the to-be-timed interval (criterion time). The width of the Gaussian-like distribution of responses increases linearly with the criterion time, i.e., interval timing obeys the scalar property. Results We presented analytical and numerical results based on the striatal beat frequency (SBF) model showing that parameter variability (noise) mimics behavioral data. A key functional block of the SBF model is the set of oscillators that provide the time base for the entire timing network. The implementation of the oscillators block as simplified phase (cosine) oscillators has the additional advantage that is analytically tractable. We also checked numerically that the scalar property emerges in the presence of memory variability by using biophysically realistic Morris-Lecar oscillators. First, we predicted analytically and tested numerically that in a noise-free SBF model the output function could be approximated by a Gaussian. However, in a noise-free SBF model the width of the Gaussian envelope is independent of the criterion time, which violates the scalar property. We showed analytically and verified numerically that small fluctuations of the memorized criterion time leads to scalar property of interval timing. Conclusions Noise is ubiquitous in the form of small fluctuations of intrinsic frequencies of the neural oscillators, the errors in recording/retrieving stored information related to criterion time, fluctuation in neurotransmitters’ concentration, etc. Our model suggests that the biological noise plays an essential functional role in the SBF interval timing. PMID:23924391

Stochastic oscillations in models of epidemics on a network of cities

NASA Astrophysics Data System (ADS)

Rozhnova, G.; Nunes, A.; McKane, A. J.

2011-11-01

We carry out an analytic investigation of stochastic oscillations in a susceptible-infected-recovered model of disease spread on a network of n cities. In the model a fraction fjk of individuals from city k commute to city j, where they may infect, or be infected by, others. Starting from a continuous-time Markov description of the model the deterministic equations, which are valid in the limit when the population of each city is infinite, are recovered. The stochastic fluctuations about the fixed point of these equations are derived by use of the van Kampen system-size expansion. The fixed point structure of the deterministic equations is remarkably simple: A unique nontrivial fixed point always exists and has the feature that the fraction of susceptible, infected, and recovered individuals is the same for each city irrespective of its size. We find that the stochastic fluctuations have an analogously simple dynamics: All oscillations have a single frequency, equal to that found in the one-city case. We interpret this phenomenon in terms of the properties of the spectrum of the matrix of the linear approximation of the deterministic equations at the fixed point.

Modelling hydrological extremes under non-stationary conditions using climate covariates

NASA Astrophysics Data System (ADS)

Vasiliades, Lampros; Galiatsatou, Panagiota; Loukas, Athanasios

2013-04-01

Extreme value theory is a probabilistic theory that can interpret the future probabilities of occurrence of extreme events (e.g. extreme precipitation and streamflow) using past observed records. Traditionally, extreme value theory requires the assumption of temporal stationarity. This assumption implies that the historical patterns of recurrence of extreme events are static over time. However, the hydroclimatic system is nonstationary on time scales that are relevant to extreme value analysis, due to human-mediated and natural environmental change. In this study the generalized extreme value (GEV) distribution is used to assess nonstationarity in annual maximum daily rainfall and streamflow timeseries at selected meteorological and hydrometric stations in Greece and Cyprus. The GEV distribution parameters (location, scale, and shape) are specified as functions of time-varying covariates and estimated using the conditional density network (CDN) as proposed by Cannon (2010). The CDN is a probabilistic extension of the multilayer perceptron neural network. Model parameters are estimated via the generalized maximum likelihood (GML) approach using the quasi-Newton BFGS optimization algorithm, and the appropriate GEV-CDN model architecture for the selected meteorological and hydrometric stations is selected by fitting increasingly complicated models and choosing the one that minimizes the Akaike information criterion with small sample size correction. For all case studies in Greece and Cyprus different formulations are tested with combinational cases of stationary and nonstationary parameters of the GEV distribution, linear and non-linear architecture of the CDN and combinations of the input climatic covariates. Climatic indices such as the Southern Oscillation Index (SOI), which describes atmospheric circulation in the eastern tropical pacific related to El Niño Southern Oscillation (ENSO), the Pacific Decadal Oscillation (PDO) index that varies on an interdecadal rather than interannual time scale and the atmospheric circulation patterns as expressed by the North Atlantic Oscillation (NAO) index are used to express the GEV parameters as functions of the covariates. Results show that the nonstationary GEV model can be an efficient tool to take into account the dependencies between extreme value random variables and the temporal evolution of the climate.

Nonlinear Dynamic Modeling and Controls Development for Supersonic Propulsion System Research

NASA Technical Reports Server (NTRS)

Connolly, Joseph W.; Kopasakis, George; Paxson, Daniel E.; Stuber, Eric; Woolwine, Kyle

2012-01-01

This paper covers the propulsion system component modeling and controls development of an integrated nonlinear dynamic simulation for an inlet and engine that can be used for an overall vehicle (APSE) model. The focus here is on developing a methodology for the propulsion model integration, which allows for controls design that prevents inlet instabilities and minimizes the thrust oscillation experienced by the vehicle. Limiting thrust oscillations will be critical to avoid exciting vehicle aeroelastic modes. Model development includes both inlet normal shock position control and engine rotor speed control for a potential supersonic commercial transport. A loop shaping control design process is used that has previously been developed for the engine and verified on linear models, while a simpler approach is used for the inlet control design. Verification of the modeling approach is conducted by simulating a two-dimensional bifurcated inlet and a representative J-85 jet engine previously used in a NASA supersonics project. Preliminary results are presented for the current supersonics project concept variable cycle turbofan engine design.

Different coupled atmosphere-recharge oscillator Low Order Models for ENSO: a projection approach.

NASA Astrophysics Data System (ADS)

Bianucci, Marco; Mannella, Riccardo; Merlino, Silvia; Olivieri, Andrea

2016-04-01

El Ninõ-Southern Oscillation (ENSO) is a large scale geophysical phenomenon where, according to the celebrated recharge oscillator model (ROM), the Ocean slow variables given by the East Pacific Sea Surface Temperature (SST) and the average thermocline depth (h), interact with some fast "irrelevant" ones, representing mostly the atmosphere (the westerly wind burst and the Madden-Julian Oscillation). The fast variables are usually inserted in the model as an external stochastic forcing. In a recent work (M. Bianucci, "Analytical probability density function for the statistics of the ENSO phenomenon: asymmetry and power law tail" Geophysical Research Letters, under press) the author, using a projection approach applied to general deterministic coupled systems, gives a physically reasonable explanation for the use of stochastic models for mimicking the apparent random features of the ENSO phenomenon. Moreover, in the same paper, assuming that the interaction between the ROM and the fast atmosphere is of multiplicative type, i.e., it depends on the SST variable, an analytical expression for the equilibrium density function of the anomaly SST is obtained. This expression fits well the data from observations, reproducing the asymmetry and the power law tail of the histograms of the NINÕ3 index. Here, using the same theoretical approach, we consider and discuss different kind of interactions between the ROM and the other perturbing variables, and we take into account also non linear ROM as a low order model for ENSO. The theoretical and numerical results are then compared with data from observations.

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

2018-04-01

Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

The excitation and characteristic frequency of the long-period volcanic event: An approach based on an inhomogeneous autoregressive model of a linear dynamic system

USGS Publications Warehouse

Nakano, M.; Kumagai, H.; Kumazawa, M.; Yamaoka, K.; Chouet, B.A.

1998-01-01

We present a method to quantify the source excitation function and characteristic frequencies of long-period volcanic events. The method is based on an inhomogeneous autoregressive (AR) model of a linear dynamic system, in which the excitation is assumed to be a time-localized function applied at the beginning of the event. The tail of an exponentially decaying harmonic waveform is used to determine the characteristic complex frequencies of the event by the Sompi method. The excitation function is then derived by operating an AR filter constructed from the characteristic frequencies to the entire seismogram of the event, including the inhomogeneous part of the signal. We apply this method to three long-period events at Kusatsu-Shirane Volcano, central Japan, whose waveforms display simple decaying monochromatic oscillations except for the beginning of the events. We recover time-localized excitation functions lasting roughly 1 s at the start of each event and find that the estimated functions are very similar to each other at all the stations of the seismic network for each event. The phases of the characteristic oscillations referred to the estimated excitation function fall within a narrow range for almost all the stations. These results strongly suggest that the excitation and mode of oscillation are both dominated by volumetric change components. Each excitation function starts with a pronounced dilatation consistent with a sudden deflation of the volumetric source which may be interpreted in terms of a choked-flow transport mechanism. The frequency and Q of the characteristic oscillation both display a temporal evolution from event to event. Assuming a crack filled with bubbly water as seismic source for these events, we apply the Van Wijngaarden-Papanicolaou model to estimate the acoustic properties of the bubbly liquid and find that the observed changes in the frequencies and Q are consistently explained by a temporal change in the radii of the bubbles characterizing the bubbly water in the crack.

Multiple spatially localized dynamical states in friction-excited oscillator chains

NASA Astrophysics Data System (ADS)

Papangelo, A.; Hoffmann, N.; Grolet, A.; Stender, M.; Ciavarella, M.

2018-03-01

Friction-induced vibrations are known to affect many engineering applications. Here, we study a chain of friction-excited oscillators with nearest neighbor elastic coupling. The excitation is provided by a moving belt which moves at a certain velocity vd while friction is modelled with an exponentially decaying friction law. It is shown that in a certain range of driving velocities, multiple stable spatially localized solutions exist whose dynamical behavior (i.e. regular or irregular) depends on the number of oscillators involved in the vibration. The classical non-repeatability of friction-induced vibration problems can be interpreted in light of those multiple stable dynamical states. These states are found within a "snaking-like" bifurcation pattern. Contrary to the classical Anderson localization phenomenon, here the underlying linear system is perfectly homogeneous and localization is solely triggered by the friction nonlinearity.

Linear canonical transformations of coherent and squeezed states in the Wigner phase space

NASA Technical Reports Server (NTRS)

Han, D.; Kim, Y. S.; Noz, Marilyn E.

1988-01-01

It is shown that classical linear canonical transformations are possible in the Wigner phase space. Coherent and squeezed states are shown to be linear canonical transforms of the ground-state harmonic oscillator. It is therefore possible to evaluate the Wigner functions for coherent and squeezed states from that for the harmonic oscillator. Since the group of linear canonical transformations has a subgroup whose algebraic property is the same as that of the (2+1)-dimensional Lorentz group, it may be possible to test certain properties of the Lorentz group using optical devices. A possible experiment to measure the Wigner rotation angle is discussed.

Recurrent jellyfish blooms are a consequence of global oscillations

PubMed Central

Condon, Robert H.; Duarte, Carlos M.; Pitt, Kylie A.; Robinson, Kelly L.; Lucas, Cathy H.; Sutherland, Kelly R.; Mianzan, Hermes W.; Bogeberg, Molly; Purcell, Jennifer E.; Decker, Mary Beth; Uye, Shin-ichi; Madin, Laurence P.; Brodeur, Richard D.; Haddock, Steven H. D.; Malej, Alenka; Parry, Gregory D.; Eriksen, Elena; Quiñones, Javier; Acha, Marcelo; Harvey, Michel; Arthur, James M.; Graham, William M.

2013-01-01

A perceived recent increase in global jellyfish abundance has been portrayed as a symptom of degraded oceans. This perception is based primarily on a few case studies and anecdotal evidence, but a formal analysis of global temporal trends in jellyfish populations has been missing. Here, we analyze all available long-term datasets on changes in jellyfish abundance across multiple coastal stations, using linear and logistic mixed models and effect-size analysis to show that there is no robust evidence for a global increase in jellyfish. Although there has been a small linear increase in jellyfish since the 1970s, this trend was unsubstantiated by effect-size analysis that showed no difference in the proportion of increasing vs. decreasing jellyfish populations over all time periods examined. Rather, the strongest nonrandom trend indicated jellyfish populations undergo larger, worldwide oscillations with an approximate 20-y periodicity, including a rising phase during the 1990s that contributed to the perception of a global increase in jellyfish abundance. Sustained monitoring is required over the next decade to elucidate with statistical confidence whether the weak increasing linear trend in jellyfish after 1970 is an actual shift in the baseline or part of an oscillation. Irrespective of the nature of increase, given the potential damage posed by jellyfish blooms to fisheries, tourism, and other human industries, our findings foretell recurrent phases of rise and fall in jellyfish populations that society should be prepared to face. PMID:23277544

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

NASA Astrophysics Data System (ADS)

Pritula, G. M.; Petrenko, E. V.; Usatenko, O. V.

2018-02-01

A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.

Electron-phonon thermalization in a scalable method for real-time quantum dynamics

NASA Astrophysics Data System (ADS)

Rizzi, Valerio; Todorov, Tchavdar N.; Kohanoff, Jorge J.; Correa, Alfredo A.

2016-01-01

We present a quantum simulation method that follows the dynamics of out-of-equilibrium many-body systems of electrons and oscillators in real time. Its cost is linear in the number of oscillators and it can probe time scales from attoseconds to hundreds of picoseconds. Contrary to Ehrenfest dynamics, it can thermalize starting from a variety of initial conditions, including electronic population inversion. While an electronic temperature can be defined in terms of a nonequilibrium entropy, a Fermi-Dirac distribution in general emerges only after thermalization. These results can be used to construct a kinetic model of electron-phonon equilibration based on the explicit quantum dynamics.

Multi-Baker Map as a Model of Digital PD Control

NASA Astrophysics Data System (ADS)

Csernák, Gábor; Gyebrószki, Gergely; Stépán, Gábor

Digital stabilization of unstable equilibria of linear systems may lead to small amplitude stochastic-like oscillations. We show that these vibrations can be related to a deterministic chaotic dynamics induced by sampling and quantization. A detailed analytical proof of chaos is presented for the case of a PD controlled oscillator: it is shown that there exists a finite attracting domain in the phase-space, the largest Lyapunov exponent is positive and the existence of a Smale horseshoe is also pointed out. The corresponding two-dimensional micro-chaos map is a multi-baker map, i.e. it consists of a finite series of baker’s maps.

Linear time-varying models can reveal non-linear interactions of biomolecular regulatory networks using multiple time-series data.

PubMed

Kim, Jongrae; Bates, Declan G; Postlethwaite, Ian; Heslop-Harrison, Pat; Cho, Kwang-Hyun

2008-05-15

Inherent non-linearities in biomolecular interactions make the identification of network interactions difficult. One of the principal problems is that all methods based on the use of linear time-invariant models will have fundamental limitations in their capability to infer certain non-linear network interactions. Another difficulty is the multiplicity of possible solutions, since, for a given dataset, there may be many different possible networks which generate the same time-series expression profiles. A novel algorithm for the inference of biomolecular interaction networks from temporal expression data is presented. Linear time-varying models, which can represent a much wider class of time-series data than linear time-invariant models, are employed in the algorithm. From time-series expression profiles, the model parameters are identified by solving a non-linear optimization problem. In order to systematically reduce the set of possible solutions for the optimization problem, a filtering process is performed using a phase-portrait analysis with random numerical perturbations. The proposed approach has the advantages of not requiring the system to be in a stable steady state, of using time-series profiles which have been generated by a single experiment, and of allowing non-linear network interactions to be identified. The ability of the proposed algorithm to correctly infer network interactions is illustrated by its application to three examples: a non-linear model for cAMP oscillations in Dictyostelium discoideum, the cell-cycle data for Saccharomyces cerevisiae and a large-scale non-linear model of a group of synchronized Dictyostelium cells. The software used in this article is available from http://sbie.kaist.ac.kr/software

Characterization of linear interfacial waves in a turbulent gas-liquid pipe flow

NASA Astrophysics Data System (ADS)

Ayati, A. A.; Farias, P. S. C.; Azevedo, L. F. A.; de Paula, I. B.

2017-06-01

The evolution of interfacial waves on a stratified flow was investigated experimentally for air-water flow in a horizontal pipe. Waves were introduced in the liquid level of stratified flow near the pipe entrance using an oscillating plate. The mean height of liquid layer and the fluctuations superimposed on this mean level were captured using high speed cameras. Digital image processing techniques were used to detect instantaneous interfaces along the pipe. The driving signal of the oscillating plate was controlled by a D/A board that was synchronized with acquisitions. This enabled to perform phase-locked acquisitions and to use ensemble average procedures. Thereby, it was possible to measure the temporal and spatial evolution of the disturbances introduced in the flow. In addition, phase-locked measurements of the velocity field in the liquid layer were performed using standard planar Particle Image Velocimetry (PIV). The velocity fields were extracted at a fixed streamwise location, whereas the measurements of the liquid level were performed at several locations along the pipe. The assessment of the setup was important for validation of the methodology proposed in this work, since it aimed at providing results for further comparisons with theoretical models and numerical simulations. Therefore, the work focuses on validation and characterization of interfacial waves within the linear regime. Results show that under controlled conditions, the wave development can be well captured and reproduced. In addition, linear waves were observed for liquid level oscillations lower than about 1.5% of the pipe diameter. It was not possible to accurately define an amplitude threshold for the appearance of nonlinear effects because it strongly depended on the wave frequency. According to the experimental findings, longer waves display characteristics similar to linear waves, while short ones exhibit a more complex evolution, even for low amplitudes.

Conditions and Linear Stability Analysis at the Transition to Synchronization of Three Coupled Phase Oscillators in a Ring

NASA Astrophysics Data System (ADS)

El-Nashar, Hassan F.

2017-06-01

We consider a system of three nonidentical coupled phase oscillators in a ring topology. We explore the conditions that must be satisfied in order to obtain the phases at the transition to a synchrony state. These conditions lead to the correct mathematical expressions of phases that aid to find a simple analytic formula for critical coupling when the oscillators transit to a synchronization state having a common frequency value. The finding of a simple expression for the critical coupling allows us to perform a linear stability analysis at the transition to the synchronization stage. The obtained analytic forms of the eigenvalues show that the three coupled phase oscillators with periodic boundary conditions transit to a synchrony state when a saddle-node bifurcation occurs.

Assessing Aircraft Susceptibility to Nonlinear Aircraft-Pilot Coupling/Pilot-Induced Oscillations

NASA Technical Reports Server (NTRS)

Hess, R.A.; Stout, P. W.

1997-01-01

A unified approach for assessing aircraft susceptibility to aircraft-pilot coupling (or pilot-induced oscillations) which was previously reported in the literature and applied to linear systems is extended to nonlinear systems, with emphasis upon vehicles with actuator rate saturation. The linear methodology provided a tool for predicting: (1) handling qualities levels, (2) pilot-induced oscillation rating levels and (3) a frequency range in which pilot-induced oscillations are likely to occur. The extension to nonlinear systems provides a methodology for predicting the latter two quantities. Eight examples are presented to illustrate the use of the technique. The dearth of experimental flight-test data involving systematic variation and assessment of the effects of actuator rate limits presently prevents a more thorough evaluation of the methodology.

A linearization time-domain CMOS smart temperature sensor using a curvature compensation oscillator.

PubMed

Chen, Chun-Chi; Chen, Hao-Wen

2013-08-28

This paper presents an area-efficient time-domain CMOS smart temperature sensor using a curvature compensation oscillator for linearity enhancement with a -40 to 120 °C temperature range operability. The inverter-based smart temperature sensors can substantially reduce the cost and circuit complexity of integrated temperature sensors. However, a large curvature exists on the temperature-to-time transfer curve of the inverter-based delay line and results in poor linearity of the sensor output. For cost reduction and error improvement, a temperature-to-pulse generator composed of a ring oscillator and a time amplifier was used to generate a thermal sensing pulse with a sufficient width proportional to the absolute temperature (PTAT). Then, a simple but effective on-chip curvature compensation oscillator is proposed to simultaneously count and compensate the PTAT pulse with curvature for linearization. With such a simple structure, the proposed sensor possesses an extremely small area of 0.07 mm2 in a TSMC 0.35-mm CMOS 2P4M digital process. By using an oscillator-based scheme design, the proposed sensor achieves a fine resolution of 0.045 °C without significantly increasing the circuit area. With the curvature compensation, the inaccuracy of -1.2 to 0.2 °C is achieved in an operation range of -40 to 120 °C after two-point calibration for 14 packaged chips. The power consumption is measured as 23 mW at a sample rate of 10 samples/s.

Analysis of graphic representation ability in oscillation phenomena

NASA Astrophysics Data System (ADS)

Dewi, A. R. C.; Putra, N. M. D.; Susilo

2018-03-01

This study aims to investigates how the ability of students to representation graphs of linear function and harmonic function in understanding of oscillation phenomena. Method of this research used mix methods with concurrent embedded design. The subjects were 35 students of class X MIA 3 SMA 1 Bae Kudus. Data collection through giving essays and interviews that lead to the ability to read and draw graphs in material of Hooke's law and oscillation characteristics. The results of study showed that most of the students had difficulty in drawing graph of linear function and harmonic function of deviation with time. Students’ difficulties in drawing the graph of linear function is the difficulty of analyzing the variable data needed in graph making, confusing the placement of variable data on the coordinate axis, the difficulty of determining the scale interval on each coordinate, and the variation of how to connect the dots forming the graph. Students’ difficulties in representing the graph of harmonic function is to determine the time interval of sine harmonic function, the difficulty to determine the initial deviation point of the drawing, the difficulty of finding the deviation equation of the case of oscillation characteristics and the confusion to different among the maximum deviation (amplitude) with the length of the spring caused the load.Complexity of the characteristic attributes of the oscillation phenomena graphs, students tend to show less well the ability of graphical representation of harmonic functions than the performance of the graphical representation of linear functions.

Low-Power Photothermal Self-Oscillation of Bimetallic Nanowires.

PubMed

De Alba, Roberto; Abhilash, T S; Rand, Richard H; Craighead, Harold G; Parpia, Jeevak M

2017-07-12

We investigate the nonlinear mechanics of a bimetallic, optically absorbing SiN-Nb nanowire in the presence of incident laser light and a reflecting Si mirror. Situated in a standing wave of optical intensity and subject to photothermal forces, the nanowire undergoes self-induced oscillations at low incident light thresholds of <1 μW due to engineered strong temperature-position (T-z) coupling. Along with inducing self-oscillation, laser light causes large changes to the mechanical resonant frequency ω 0 and equilibrium position z 0 that cannot be neglected. We present experimental results and a theoretical model for the motion under laser illumination. In the model, we solve the governing nonlinear differential equations by perturbative means to show that self-oscillation amplitude is set by the competing effects of direct T-z coupling and 2ω 0 parametric excitation due to T-ω 0 coupling. We then study the linearized equations of motion to show that the optimal thermal time constant τ for photothermal feedback is τ → ∞ rather than the previously reported ω 0 τ = 1. Lastly, we demonstrate photothermal quality factor (Q) enhancement of driven motion as a means to counteract air damping. Understanding photothermal effects on nano- and micromechanical devices, as well as nonlinear aspects of optics-based motion detection, can enable new device applications as oscillators or other electronic elements with smaller device footprints and less stringent ambient vacuum requirements.

Endogenous Business Cycle Dynamics within Metzlers Inventory Model: Adding an Inventory Floor.

PubMed

Sushko, Irina; Wegener, Michael; Westerhoff, Frank; Zaklan, Georg

2009-04-01

Metzlers inventory model may produce dampened fluctuations in economic activity, thus contributing to our understanding of business cycle dynamics. For some parameter combinations, however, the model generates oscillations with increasing amplitude, implying that the inventory stock of firms eventually turns negative. Taking this observation into account, we reformulate Metzlers model by simply putting a floor to the inventory level. Within the new piecewise linear model, endogenous business cycle dynamics may now be triggered via a center bifurcation, i.e. for certain parameter combinations production changes are (quasi-)periodic.

Nonlinear pulse propagation in InAs/InP quantum dot optical amplifiers: Rabi oscillations in the presence of nonresonant nonlinearities

NASA Astrophysics Data System (ADS)

Karni, O.; Mishra, A. K.; Eisenstein, G.; Reithmaier, J. P.

2015-03-01

We study the interplay between coherent light-matter interactions and nonresonant pulse propagation effects when ultrashort pulses propagate in room-temperature quantum dot (QD) semiconductor optical amplifiers (SOAs). The signatures observed on a pulse envelope after propagating in a transparent SOA, when coherent Rabi oscillations are absent, highlight the contribution of two-photon absorption (TPA), and its accompanying Kerr-like effect, as well as of linear dispersion, to the modification of the pulse complex electric field profile. These effects are incorporated into our previously developed finite-difference time-domain comprehensive model that describes the interaction between the pulses and the QD SOA. The present generalized model is used to investigate the combined effect of coherent and nonresonant phenomena in the gain and absorption regimes of the QD SOA. It confirms that in the QD SOA we examined, linear dispersion in the presence of the Kerr-like effect causes pulse compression, which counteracts the pulse peak suppression due to TPA, and also modifies the patterns which the coherent Rabi oscillations imprint on the pulse envelope under both gain and absorption conditions. The inclusion of these effects leads to a better fit with experiments and to a better understanding of the interplay among the various mechanisms so as to be able to better analyze more complex future experiments of coherent light-matter interaction induced by short pulses propagating along an SOA.

The Design of a 100 GHz CARM (Cyclotron Auto-Resonance Maser) Oscillator Experiment

DTIC Science & Technology

1988-09-14

pulsed-power system must be considered. A model of the voltage pulse that consists of a linear voltage rise from zero to the operating voltage...to vary as the voltage to the 3/2 power in order to model space-charge limited flow from a relativistic diode.. As the current rises in the pulse, the...distribution due to a space-charge-limited, laminar flow of electrons based on a one-dimensional, planar, relativistic model . From the charge distribution

Information-geometric measures estimate neural interactions during oscillatory brain states

PubMed Central

Nie, Yimin; Fellous, Jean-Marc; Tatsuno, Masami

2014-01-01

The characterization of functional network structures among multiple neurons is essential to understanding neural information processing. Information geometry (IG), a theory developed for investigating a space of probability distributions has recently been applied to spike-train analysis and has provided robust estimations of neural interactions. Although neural firing in the equilibrium state is often assumed in these studies, in reality, neural activity is non-stationary. The brain exhibits various oscillations depending on cognitive demands or when an animal is asleep. Therefore, the investigation of the IG measures during oscillatory network states is important for testing how the IG method can be applied to real neural data. Using model networks of binary neurons or more realistic spiking neurons, we studied how the single- and pairwise-IG measures were influenced by oscillatory neural activity. Two general oscillatory mechanisms, externally driven oscillations and internally induced oscillations, were considered. In both mechanisms, we found that the single-IG measure was linearly related to the magnitude of the external input, and that the pairwise-IG measure was linearly related to the sum of connection strengths between two neurons. We also observed that the pairwise-IG measure was not dependent on the oscillation frequency. These results are consistent with the previous findings that were obtained under the equilibrium conditions. Therefore, we demonstrate that the IG method provides useful insights into neural interactions under the oscillatory condition that can often be observed in the real brain. PMID:24605089

Information-geometric measures estimate neural interactions during oscillatory brain states.

PubMed

Nie, Yimin; Fellous, Jean-Marc; Tatsuno, Masami

2014-01-01

The characterization of functional network structures among multiple neurons is essential to understanding neural information processing. Information geometry (IG), a theory developed for investigating a space of probability distributions has recently been applied to spike-train analysis and has provided robust estimations of neural interactions. Although neural firing in the equilibrium state is often assumed in these studies, in reality, neural activity is non-stationary. The brain exhibits various oscillations depending on cognitive demands or when an animal is asleep. Therefore, the investigation of the IG measures during oscillatory network states is important for testing how the IG method can be applied to real neural data. Using model networks of binary neurons or more realistic spiking neurons, we studied how the single- and pairwise-IG measures were influenced by oscillatory neural activity. Two general oscillatory mechanisms, externally driven oscillations and internally induced oscillations, were considered. In both mechanisms, we found that the single-IG measure was linearly related to the magnitude of the external input, and that the pairwise-IG measure was linearly related to the sum of connection strengths between two neurons. We also observed that the pairwise-IG measure was not dependent on the oscillation frequency. These results are consistent with the previous findings that were obtained under the equilibrium conditions. Therefore, we demonstrate that the IG method provides useful insights into neural interactions under the oscillatory condition that can often be observed in the real brain.

Controlling the onset of Hopf bifurcation in the Hodgkin-Huxley model

NASA Astrophysics Data System (ADS)

Xie, Yong; Chen, Luonan; Kang, Yan Mei; Aihara, Kazuyuki

2008-06-01

It is a challenging problem to establish safe and simple therapeutic methods for various complicated diseases of the nervous system, particularly dynamical diseases such as epilepsy, Alzheimer’s disease, and Parkinson’s disease. From the viewpoint of nonlinear dynamical systems, a dynamical disease can be considered to be caused by a bifurcation induced by a change in the values of one or more regulating parameter. Therefore, the theory of bifurcation control may have potential applications in the diagnosis and therapy of dynamical diseases. In this study, we employ a washout filter-aided dynamic feedback controller to control the onset of Hopf bifurcation in the Hodgkin-Huxley (HH) model. Specifically, by the control scheme, we can move the Hopf bifurcation to a desired point irrespective of whether the corresponding steady state is stable or unstable. In other words, we are able to advance or delay the Hopf bifurcation, so as to prevent it from occurring in a certain range of the externally applied current. Moreover, we can control the criticality of the bifurcation and regulate the oscillation amplitude of the bifurcated limit cycle. In the controller, there are only two terms: the linear term and the nonlinear cubic term. We show that while the former determines the location of the Hopf bifurcation, the latter regulates the criticality of the Hopf bifurcation. According to the conditions of the occurrence of Hopf bifurcation and the bifurcation stability coefficient, we can analytically deduce the linear term and the nonlinear cubic term, respectively. In addition, we also show that mixed-mode oscillations (MMOs), featuring slow action potential generation, which are frequently observed in both experiments and models of chemical and biological systems, appear in the controlled HH model. It is well known that slow firing rates in single neuron models could be achieved only by type-I neurons. However, the controlled HH model is still classified as a type-II neuron, as is the original HH model. We explain that the occurrence of MMOs can be related to the presence of the canard explosion where a small oscillation grows through a sequence of canard cycles to a relaxation oscillation as the control parameter moves through an interval of exponentially small width.

Using an elastic magnifier to increase power output and performance of heart-beat harvesters

NASA Astrophysics Data System (ADS)

Galbier, Antonio C.; Karami, M. Amin

2017-09-01

Embedded piezoelectric energy harvesting (PEH) systems in medical pacemakers have been a growing and innovative research area. The goal of these systems, at present, is to remove the pacemaker battery, which makes up 60%-80% of the unit, and replace it with a sustainable power source. This requires that energy harvesting systems provide sufficient power, 1-3 μW, for operating a pacemaker. The goal of this work is to develop, test, and simulate cantilevered energy harvesters with a linear elastic magnifier (LEM). This research hopes to provide insight into the interaction between pacemaker energy harvesters and the heart. By introducing the elastic magnifier into linear and nonlinear systems oscillations of the tip are encouraged into high energy orbits and large tip deflections. A continuous nonlinear model is presented for the bistable piezoelectric energy harvesting (BPEH) system and a one-degree-of-freedom linear mass-spring-damper model is presented for the elastic magnifier. The elastic magnifier will not consider the damping negligible, unlike most models. A physical model was created for the bistable structure and formed to an elastic magnifier. A hydrogel was designed for the experimental model for the LEM. Experimental results show that the BPEH coupled with a LEM (BPEH + LEM) produces more power at certain input frequencies and operates a larger bandwidth than a PEH, BPEH, and a standard piezoelectric energy harvester with the elastic magnifier (PEH + LEM). Numerical simulations are consistent with these results. It was observed that the system enters high-energy and high orbit oscillations and that, ultimately, BPEH systems implemented in medical pacemakers can, if designed properly, have enhanced performance if positioned over the heart.

Single frequency 1083nm ytterbium doped fiber master oscillator power amplifier laser.

PubMed

Huang, Shenghong; Qin, Guanshi; Shirakawa, Akira; Musha, Mitsuru; Ueda, Ken-Ichi

2005-09-05

Single frequency 1083nm ytterbium fiber master oscillator power amplifier system was demonstrated. The oscillator was a linear fiber cavity with loop mirror filter and polarization controller. The loop mirror with unpumped ytterbium fiber as a narrow bandwidth filter discriminated and selected laser longitudinal modes efficiently. Spatial hole burning effect was restrained by adjusting polarization controller appropriately in the linear cavity. The amplifier was 5 m ytterbium doped fiber pumped by 976nm pigtail coupled laser diode. The linewidth of the single frequency laser was about 2 KHz. Output power up to 177 mW was produced under the launched pump power of 332 mW.

Low-sensitivity, low-bounce, high-linearity current-controlled oscillator suitable for single-supply mixed-mode instrumentation system.

PubMed

Hwang, Yuh-Shyan; Kung, Che-Min; Lin, Ho-Cheng; Chen, Jiann-Jong

2009-02-01

A low-sensitivity, low-bounce, high-linearity current-controlled oscillator (CCO) suitable for a single-supply mixed-mode instrumentation system is designed and proposed in this paper. The designed CCO can be operated at low voltage (2 V). The power bounce and ground bounce generated by this CCO is less than 7 mVpp when the power-line parasitic inductance is increased to 100 nH to demonstrate the effect of power bounce and ground bounce. The power supply noise caused by the proposed CCO is less than 0.35% in reference to the 2 V supply voltage. The average conversion ratio KCCO is equal to 123.5 GHz/A. The linearity of conversion ratio is high and its tolerance is within +/-1.2%. The sensitivity of the proposed CCO is nearly independent of the power supply voltage, which is less than a conventional current-starved oscillator. The performance of the proposed CCO has been compared with the current-starved oscillator. It is shown that the proposed CCO is suitable for single-supply mixed-mode instrumentation systems.

Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay.

PubMed

Akimenko, Vitalii; Anguelov, Roumen

2017-12-01

In this paper we study the nonlinear age-structured model of a polycyclic two-phase population dynamics including delayed effect of population density growth on the mortality. Both phases are modelled as a system of initial boundary values problem for semi-linear transport equation with delay and initial problem for nonlinear delay ODE. The obtained system is studied both theoretically and numerically. Three different regimes of population dynamics for asymptotically stable states of autonomous systems are obtained in numerical experiments for the different initial values of population density. The quasi-periodical travelling wave solutions are studied numerically for the autonomous system with the different values of time delays and for the system with oscillating death rate and birth modulus. In both cases it is observed three types of travelling wave solutions: harmonic oscillations, pulse sequence and single pulse.

How to turn a genetic circuit into a synthetic tunable oscillator, or a bistable switch.

PubMed

Marucci, Lucia; Barton, David A W; Cantone, Irene; Ricci, Maria Aurelia; Cosma, Maria Pia; Santini, Stefania; di Bernardo, Diego; di Bernardo, Mario

2009-12-07

Systems and Synthetic Biology use computational models of biological pathways in order to study in silico the behaviour of biological pathways. Mathematical models allow to verify biological hypotheses and to predict new possible dynamical behaviours. Here we use the tools of non-linear analysis to understand how to change the dynamics of the genes composing a novel synthetic network recently constructed in the yeast Saccharomyces cerevisiae for In-vivo Reverse-engineering and Modelling Assessment (IRMA). Guided by previous theoretical results that make the dynamics of a biological network depend on its topological properties, through the use of simulation and continuation techniques, we found that the network can be easily turned into a robust and tunable synthetic oscillator or a bistable switch. Our results provide guidelines to properly re-engineering in vivo the network in order to tune its dynamics.

Instability of g-mode oscillations in white dwarf stars

NASA Technical Reports Server (NTRS)

Keeley, D. A.

1979-01-01

A white dwarf model with M = 6 solar masses, Te = 12,000 K, and L = 1.2 x 10 to the 31st erg/sec provided by Cox has been tested for linear stability of radial oscillations. The radial mode instability first reported for this model by Cox, et al. (1979) has been confirmed. The growth rates obtained are comparable to the rates found by Cox. A sequence of l = 2 g-modes has also been found to be unstable. The e-folding times range from around 10 to the 11th periods for a 137 second mode (1 radial node) to less than 100 periods for a 629 second mode (17 nodes). It is likely that the latter rate is too high because the eigenfunction has been forced to vanish at the non-zero inner radius of the model, at which the Brunt-Vaisala frequency is barely less than the mode frequency.

Dissecting the Function of Hippocampal Oscillations in a Human Anxiety Model

PubMed Central

Khemka, Saurabh

2017-01-01

Neural oscillations in hippocampus and medial prefrontal cortex (mPFC) are a hallmark of rodent anxiety models that build on conflict between approach and avoidance. Yet, the function of these oscillations, and their expression in humans, remain elusive. Here, we used magnetoencephalography (MEG) to investigate neural oscillations in a task that simulated approach–avoidance conflict, wherein 23 male and female human participants collected monetary tokens under a threat of virtual predation. Probability of threat was signaled by color and learned beforehand by direct experience. Magnitude of threat corresponded to a possible monetary loss, signaled as a quantity. We focused our analyses on an a priori defined region-of-interest, the bilateral hippocampus. Oscillatory power under conflict was linearly predicted by threat probability in a location consistent with right mid-hippocampus. This pattern was specific to the hippocampus, most pronounced in the gamma band, and not explained by spatial movement or anxiety-like behavior. Gamma power was modulated by slower theta rhythms, and this theta modulation increased with threat probability. Furthermore, theta oscillations in the same location showed greater synchrony with mPFC theta with increased threat probability. Strikingly, these findings were not seen in relation to an increase in threat magnitude, which was explicitly signaled as a quantity and induced similar behavioral responses as learned threat probability. Thus, our findings suggest that the expression of hippocampal and mPFC oscillatory activity in the context of anxiety is specifically linked to threat memory. These findings resonate with neurocomputational accounts of the role played by hippocampal oscillations in memory. SIGNIFICANCE STATEMENT We use a biologically relevant approach–avoidance conflict test in humans while recording neural oscillations with magnetoencephalography to investigate the expression and function of hippocampal oscillations in human anxiety. Extending nonhuman studies, we can assign a possible function to hippocampal oscillations in this task, namely threat memory communication. This blends into recent attempts to elucidate the role of brain synchronization in defensive responses to threat. PMID:28626018

An Aeroelastic Evaluation of the Flexible Thermal Protection System for an Inatable Aerodynamic Decelerator

NASA Astrophysics Data System (ADS)

Goldman, Benjamin D.

The purpose of this dissertation is to study the aeroelastic stability of a proposed flexible thermal protection system (FTPS) for the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). A flat, square FTPS coupon exhibits violent oscillations during experimental aerothermal testing in NASA's 8 Foot High Temperature Tunnel, leading to catastrophic failure. The behavior of the structural response suggested that aeroelastic flutter may be the primary instability mechanism, prompting further experimental investigation and theoretical model development. Using Von Karman's plate theory for the panel-like structure and piston theory aerodynamics, a set of aeroelastic models were developed and limit cycle oscillations (LCOs) were calculated at the tunnel flow conditions. Similarities in frequency content of the theoretical and experimental responses indicated that the observed FTPS oscillations were likely aeroelastic in nature, specifically LCO/flutter. While the coupon models can be used for comparison with tunnel tests, they cannot predict accurately the aeroelastic behavior of the FTPS in atmospheric flight. This is because the geometry of the flight vehicle is no longer a flat plate, but rather (approximately) a conical shell. In the second phase of this work, linearized Donnell conical shell theory and piston theory aerodynamics are used to calculate natural modes of vibration and flutter dynamic pressures for various structural models composed of one or more conical shells resting on several circumferential elastic supports. When the flight vehicle is approximated as a single conical shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case, as "hump-mode" flutter is possible. Aeroelastic models that consider the individual FTPS layers as separate shells exhibit asymmetric flutter at high dynamic pressures relative to the single shell models. Parameter studies also examine the effects of tension, shear modulus reduction, and elastic support stiffness. Limitations of a linear structural model and piston theory aerodynamics prompted a more elaborate evaluation of the flight configuration. Using nonlinear Donnell conical shell theory for the FTPS structure, the pressure buckling and aeroelastic limit cycle oscillations were studied for a single elastically-supported conical shell. While piston theory was used initially, a time-dependent correction factor was derived using transform methods and potential flow theory to calculate more accurately the low Mach number supersonic flow. Three conical shell geometries were considered: a 3-meter diameter 70° shell, a 3.7-meter 70° shell, and a 6-meter diameter 70° shell. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD vehicle. Though agreement between theoretical and experimental strains was poor, circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With piston theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. Pre-buckling pressure loads and the aerodynamic pressure correction factor were studied for all geometries, and these effects resulted in significantly lower flutter boundaries compared with piston theory alone. In the final phase of this work, the existing linear and nonlinear FTPS shell models were coupled with NASA's FUN3D Reynolds Averaged Navier Stokes CFD code, allowing for the most physically realistic flight predictions. For the linear shell structural model, the elastically-supported shell natural modes were mapped to a CFD grid of a 6-meter HIAD vehicle, and a linear structural dynamics solver internal to the CFD code was used to compute the aeroelastic response. Aerodynamic parameters for a proposed HIAD re-entry trajectory were obtained, and aeroelastic solutions were calculated at three points in the trajectory: Mach 1, Mach 2, and Mach 11 (peak dynamic pressure). No flutter was found at any of these conditions using the linear method, though oscillations (of uncertain origin) on the order of the shell thickness may be possible in the transonic regime. For the nonlinear shell structural model, a set of assumed sinusoidal modes were mapped to the CFD grid, and the linear structural dynamics equations were replaced by a nonlinear ODE solver for the conical shell equations. Successful calculation and restart of the nonlinear dynamic aeroelastic solutions was demonstrated. Preliminary results indicated that dynamic instabilities may be possible at Mach 1 and 2, with a completely stable solution at Mach 11, though further study is needed. A major benefit of this implementation is that the coefficients and mode shapes for the nonlinear conical shell may be replaced with those of other types of structures, greatly expanding the aeroelastic capabilities of FUN3D.

Complex dynamics in a simple model of pulsations for super-asymptotic giant branch stars.

PubMed

Munteanu, Andreea; Garcia-Berro, Enrique; Jose, Jordi; Petrisor, Emilia

2002-06-01

When intermediate mass stars reach their last stages of evolution they show pronounced oscillations. This phenomenon happens when these stars reach the so-called asymptotic giant branch (AGB), which is a region of the Hertzsprung-Russell diagram located at about the same region of effective temperatures but at larger luminosities than those of regular giant stars. The period of these oscillations depends on the mass of the star. There is growing evidence that these oscillations are highly correlated with mass loss and that, as the mass loss increases, the pulsations become more chaotic. In this paper we study a simple oscillator which accounts for the observed properties of this kind of stars. This oscillator was first proposed and studied in Icke et al. [Astron. Astrophys. 258, 341 (1992)] and we extend their study to the region of more massive and luminous stars -the region of super-AGB stars. The oscillator consists of a periodic nonlinear perturbation of a linear Hamiltonian system. The formalism of dynamical systems theory has been used to explore the associated Poincare map for the range of parameters typical of those stars. We have studied and characterized the dynamical behavior of the oscillator as the parameters of the model are varied, leading us to explore a sequence of local and global bifurcations. Among these, a tripling bifurcation is remarkable, which allows us to show that the Poincare map is a nontwist area preserving map. Meandering curves, hierarchical-islands traps and sticky orbits also show up. We discuss the implications of the stickiness phenomenon in the evolution and stability of the super-AGB stars. (c) 2002 American Institute of Physics.

The Duffin-Kemmer-Petiau oscillator

NASA Technical Reports Server (NTRS)

Nedjadi, Youcef; Barrett, Roger

1995-01-01

In view of current interest in relativistic spin-one systems and the recent work on the Dirac Oscillator, we introduce the Duffin-Kemmer-Petiau (DKP) equation obtained by using an external potential linear in r. Since, in the non-relativistic limit, the spin 1 representation leads to a harmonic oscillator with a spin-orbit coupling of the Thomas form, we call the equation the DKP oscillator. This oscillator is a relativistic generalization of the quantum harmonic oscillator for scalar and vector bosons. We show that it conserves total angular momentum and that it is exactly solvable. We calculate and discuss the eigenspectrum of the DKP oscillator in the spin 1 representation.

Stochastic bifurcations in the nonlinear parallel Ising model.

PubMed

Bagnoli, Franco; Rechtman, Raúl

2016-11-01

We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.

A Theoretical Probe for Excitation Mechanisms of Sun-like and Mira-like Oscillations of Stars

NASA Astrophysics Data System (ADS)

Xiong, Da-run; Deng, Li-cai

2013-01-01

The linear nonadiabatic oscillations for evolutionary models of 0.6- 3M8 stars are calculated by using a nonlocal and time-dependent convection theory. The results show that in the HR diagram the pulsation-unstable low- temperature stars on the right side of instability strip can be divided into two groups. One group indicates the Sun-like oscillation stars composed of the main- sequence dwarfs, sub-giants and red giants (RGs) of low and intermediate lu- minosities, which are unstable in the intermediate- and high-order (n ≥ 12) p- modes, and stable in the low-order (n ≤ 5) p-modes. Another group indicates the Mira-like stars composed of the bright RGs and asymptotic giant branch (AGB) stars, which are just contrary to Sun-like stars, unstable in low-order (n ≤ 5) p-modes and stable in the intermediate- and high-order (n ≥ 12) p-modes. The oscillations for the red edge of Cepheid (δ Scuti) instability strip, Sun-like and Mira-like stars can be explained uniformly by the coupling between convection and oscillation (CCO). For the low-temperature stars on the right side of in- stability strip, CCO is the dominant excitation and damping mechanism of the oscillations of low- and intermediate-order p-modes, and the turbulent stochas- tic excitation becomes important only for the high-order p-modes of Sun-like oscillations.

Dynamics of Relaxation Processes of Spontaneous Otoacoustic Emissions

NASA Astrophysics Data System (ADS)

Murphy, William James

The dynamical response of spontaneous otoacoustic emissions (SOAEs) to suppression by ipsilateral pulsed external tones of different frequencies and levels is investigated in nine female subjects under normal conditions and in four female subjects during periods when aspirin is being administered. A simple Van der Pol limit-cycle oscillator driven by an external tone is used as an interpretive model. Typical results for both the onset of, and recovery from suppression yield 1/r_1 (where -r_1 is the negative linear component of the damping function) in the range of 2-25 msec. In accordance with the predictions of the model: (a) the relaxation time for the onset of suppression increases with the amount of suppression induced by the external tone, (b) the values of r _1 and the amplitudes of the unsuppressed emissions exhibit an inverse correlation, (c) the values inferred for r_1 are not significantly dependent on the frequency of the pulsed suppressor tone and (d) the inferred r_1 values are not significantly dependent upon the amount of suppression. In investigations involving subjects under aspirin administration, the changes in the relaxation time constants indicate that the main effect of aspirin administration is to reduce the negative damping parameter r_1. The salicylate is apparently not metabolized in some subjects whose emissions are negligibly affected by aspirin administration. A modification of the single-oscillator model is used to describe pulsed suppression data obtained from a primary SOAE (2545 Hz) which is suppressed by a neighboring secondary emission (2895 Hz). The response of the SOAE amplitude during pulsed suppression is modeled by a pair of Van der Pol limit-cycle oscillators with the primary oscillator linearly coupled to the displacement of the secondary higher-frequency one. The relaxation time constants for the onset of, and recovery from, suppression are 4.5 and 4.8 msec, respectively, for the primary SOAE and 7.5 and 10.5 msec for the secondary one. Aspirin administration reduces the magnitude of the overshoot by reducing the level of the higher frequency SOAE and thereby eliminating the suppression of the lower frequency one.

Identifying Crucial Parameter Correlations Maintaining Bursting Activity

PubMed Central

Doloc-Mihu, Anca; Calabrese, Ronald L.

2014-01-01

Recent experimental and computational studies suggest that linearly correlated sets of parameters (intrinsic and synaptic properties of neurons) allow central pattern-generating networks to produce and maintain their rhythmic activity regardless of changing internal and external conditions. To determine the role of correlated conductances in the robust maintenance of functional bursting activity, we used our existing database of half-center oscillator (HCO) model instances of the leech heartbeat CPG. From the database, we identified functional activity groups of burster (isolated neuron) and half-center oscillator model instances and realistic subgroups of each that showed burst characteristics (principally period and spike frequency) similar to the animal. To find linear correlations among the conductance parameters maintaining functional leech bursting activity, we applied Principal Component Analysis (PCA) to each of these four groups. PCA identified a set of three maximal conductances (leak current, Leak; a persistent K current, K2; and of a persistent Na+ current, P) that correlate linearly for the two groups of burster instances but not for the HCO groups. Visualizations of HCO instances in a reduced space suggested that there might be non-linear relationships between these parameters for these instances. Experimental studies have shown that period is a key attribute influenced by modulatory inputs and temperature variations in heart interneurons. Thus, we explored the sensitivity of period to changes in maximal conductances of Leak, K2, and P, and we found that for our realistic bursters the effect of these parameters on period could not be assessed because when varied individually bursting activity was not maintained. PMID:24945358

Collisionless damping of flows in the TJ-II stellarator

NASA Astrophysics Data System (ADS)

Sánchez, E.; Kleiber, R.; Hatzky, R.; Borchardt, M.; Monreal, P.; Castejón, F.; López-Fraguas, A.; Sáez, X.; Velasco, J. L.; Calvo, I.; Alonso, A.; López-Bruna, D.

2013-01-01

The results of global linear gyrokinetic simulations of residual flows carried out with the code EUTERPE in the TJ-II three-dimensional geometry are reported. The linear response of the plasma to potential perturbations homogeneous in a magnetic surface shows several oscillation frequencies: a Geodesic-acoustic-mode-like frequency, in qualitative agreement with the formula given by Sugama and Watanabe (2006 Plasma Phys. 72 825), and a much lower frequency oscillation in agreement with the predictions of Mishchenko et al (2008 Phys. Plasmas 15 072309) and Helander et al (2011 Plasma Phys. Control. Fusion 53 054006) for stellarators. The dependence of both oscillations on ion and electron temperatures and the magnetic configuration is studied. The low-frequency oscillations are in the frequency range supporting the long-range correlations between potential signals experimentally observed in TJ-II.

Constraints on running vacuum model with H(z) and f σ8

NASA Astrophysics Data System (ADS)

Geng, Chao-Qiang; Lee, Chung-Chi; Yin, Lu

2017-08-01

We examine the running vacuum model with Λ (H) = 3 ν H2 + Λ0, where ν is the model parameter and Λ0 is the cosmological constant. From the data of the cosmic microwave background radiation, weak lensing and baryon acoustic oscillation along with the time dependent Hubble parameter H(z) and weighted linear growth f (z)σ8(z) measurements, we find that ν=(1.37+0.72-0.95)× 10-4 with the best fitted χ2 value slightly smaller than that in the ΛCDM model.

Synchronization in complex oscillator networks and smart grids.

PubMed

Dörfler, Florian; Chertkov, Michael; Bullo, Francesco

2013-02-05

The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A widely adopted model of a coupled oscillator network is characterized by a population of heterogeneous phase oscillators, a graph describing the interaction among them, and diffusive and sinusoidal coupling. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here, we present a unique, concise, and closed-form condition for synchronization of the fully nonlinear, nonequilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters; they are statistically correct for almost all networks; and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks, such as electrical power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex network scenarios and in smart grid applications.

Electromechanical oscillations in bilayer graphene

PubMed Central

Benameur, Muhammed M.; Gargiulo, Fernando; Manzeli, Sajedeh; Autès, Gabriel; Tosun, Mahmut; Yazyev, Oleg V.; Kis, Andras

2015-01-01

Nanoelectromechanical systems constitute a class of devices lying at the interface between fundamental research and technological applications. Realizing nanoelectromechanical devices based on novel materials such as graphene allows studying their mechanical and electromechanical characteristics at the nanoscale and addressing fundamental questions such as electron–phonon interaction and bandgap engineering. In this work, we realize electromechanical devices using single and bilayer graphene and probe the interplay between their mechanical and electrical properties. We show that the deflection of monolayer graphene nanoribbons results in a linear increase in their electrical resistance. Surprisingly, we observe oscillations in the electromechanical response of bilayer graphene. The proposed theoretical model suggests that these oscillations arise from quantum mechanical interference in the transition region induced by sliding of individual graphene layers with respect to each other. Our work shows that bilayer graphene conceals unexpectedly rich and novel physics with promising potential in applications based on nanoelectromechanical systems. PMID:26481767

Identical phase oscillators with global sinusoidal coupling evolve by Mobius group action.

PubMed

Marvel, Seth A; Mirollo, Renato E; Strogatz, Steven H

2009-12-01

Systems of N identical phase oscillators with global sinusoidal coupling are known to display low-dimensional dynamics. Although this phenomenon was first observed about 20 years ago, its underlying cause has remained a puzzle. Here we expose the structure working behind the scenes of these systems by proving that the governing equations are generated by the action of the Mobius group, a three-parameter subgroup of fractional linear transformations that map the unit disk to itself. When there are no auxiliary state variables, the group action partitions the N-dimensional state space into three-dimensional invariant manifolds (the group orbits). The N-3 constants of motion associated with this foliation are the N-3 functionally independent cross ratios of the oscillator phases. No further reduction is possible, in general; numerical experiments on models of Josephson junction arrays suggest that the invariant manifolds often contain three-dimensional regions of neutrally stable chaos.

GeV-scale hot sterile neutrino oscillations: a numerical solution

NASA Astrophysics Data System (ADS)

Ghiglieri, J.; Laine, M.

2018-02-01

The scenario of baryogenesis through GeV-scale sterile neutrino oscillations is governed by non-linear differential equations for the time evolution of a sterile neutrino density matrix and Standard Model lepton and baryon asymmetries. By employing up-to-date rate coefficients and a non-perturbatively estimated Chern-Simons diffusion rate, we present a numerical solution of this system, incorporating the full momentum and helicity dependences of the density matrix. The density matrix deviates significantly from kinetic equilibrium, with the IR modes equilibrating much faster than the UV modes. For equivalent input parameters, our final results differ moderately (˜50%) from recent benchmarks in the literature. The possibility of producing an observable baryon asymmetry is nevertheless confirmed. We illustrate the dependence of the baryon asymmetry on the sterile neutrino mass splitting and on the CP-violating phase measurable in active neutrino oscillation experiments.

Scattering of charged particles on two spatially separated time-periodic optical fields

NASA Astrophysics Data System (ADS)

Szabó, Lóránt Zs.; Benedict, Mihály G.; Földi, Péter

2017-12-01

We consider a monoenergetic beam of moving charged particles interacting with two separated oscillating electric fields. Time-periodic linear potential is assumed to model the light-particle interaction using a nonrelativistic, quantum mechanical description based on Gordon-Volkov states. Applying Floquet theory, we calculate transmission probabilities as a function of the laser field parameters. The transmission resonances in this Ramsey-like setup are interpreted as if they originated from a corresponding static double-potential barrier with heights equal to the ponderomotive potential resulting from the oscillating field. Due to the opening of new "Floquet channels," the resonances are repeated at input energies when the corresponding frequency is shifted by an integer multiple of the exciting frequency. These narrow resonances can be used as precise energy filters. The fine structure of the transmission spectra is determined by the phase difference between the two oscillating light fields, allowing for the optical control of the transmission.

Unsteady aerodynamics of an oscillating cascade in a compressible flow field

NASA Technical Reports Server (NTRS)

Buffum, Daniel H.; Boldman, Donald R.; Fleeter, Sanford

1987-01-01

Fundamental experiments were performed in the NASA Lewis Transonic Oscillating Cascade Facility to investigate and quantify the unsteady aerodynamics of a cascade of biconvex airfoils executing torsion-mode oscillations at realistic reduced frequencies. Flush-mounted, high-response miniature pressure transducers were used to measure the unsteady airfoil surface pressures. The pressures were measured for three interblade phase angles at two inlet Mach numbers, 0.65 and 0.80, and two incidence angles, 0 and 7 deg. The time-variant pressures were analyzed by means of discrete Fourier transform techniques, and these unique data were then compared with predictions from a linearized unsteady cascade model. The experimental results indicate that the interblade phase angle had a major effect on the chordwise distributions of the airfoil surface unsteady pressure, and that reduced frequency, incidence angle, and Mach number had a somewhat less significant effect.

Biomechanically Induced and Controller Coupled Oscillations Experienced on the F-16XL Aircraft During Rolling Maneuvers

NASA Technical Reports Server (NTRS)

Smith, John W.; Montgomery, Terry

1996-01-01

During rapid rolling maneuvers, the F-16 XL aircraft exhibits a 2.5 Hz lightly damped roll oscillation, perceived and described as 'roll ratcheting.' This phenomenon is common with fly-by-wire control systems, particularly when primary control is derived through a pedestal-mounted side-arm controller. Analytical studies have been conducted to model the nature of the integrated control characteristics. The analytical results complement the flight observations. A three-degree-of-freedom linearized set of aerodynamic matrices was assembled to simulate the aircraft plant. The lateral-directional control system was modeled as a linear system. A combination of two second-order transfer functions was derived to couple the lateral acceleration feed through effect of the operator's arm and controller to the roll stick force input. From the combined systems, open-loop frequency responses and a time history were derived, describing and predicting an analogous in-flight situation. This report describes the primary control, aircraft angular rate, and position time responses of the F-16 XL-2 aircraft during subsonic and high-dynamic-pressure rolling maneuvers. The analytical description of the pilot's arm and controller can be applied to other aircraft or simulations to assess roll ratcheting susceptibility.

Applicability of Time-Averaged Holography for Micro-Electro-Mechanical System Performing Non-Linear Oscillations

PubMed Central

Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas

2014-01-01

Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms. PMID:24451467

Propagation of acoustic waves in a stratified atmosphere, 1

NASA Technical Reports Server (NTRS)

Kalkofen, W.; Rossi, P.; Bodo, G.; Massaglia, S.

1994-01-01

This work is motivated by the chromospheric 3 minute oscillations observed in the K(sub 2v) bright points. We study acoustic gravity waves in a one-dimensional, gravitationally stratified, isothermal atmosphere. The oscillations are excited either by a velocity pulse imparted to a layer in an atmosphere of infinite vertical extent, or by a piston forming the lower boundary of a semi-infinite medium. We consider both linear and non-linear waves.

Compact high-efficiency 100-W-level diode-side-pumped Nd:YAG laser with linearly polarized TEM00 mode output.

PubMed

Xu, Yi-Ting; Xu, Jia-Lin; Guo, Ya-Ding; Yang, Feng-Tu; Chen, Yan-Zhong; Xu, Jian; Xie, Shi-Yong; Bo, Yong; Peng, Qin-Jun; Cui, Dafu; Xu, Zu-Yan

2010-08-20

We present a compact high-efficiency and high-average-power diode-side-pumped Nd:YAG rod laser oscillator operated with a linearly polarized fundamental mode. The oscillator resonator is based on an L-shaped convex-convex cavity with an improved module and a dual-rod configuration for birefringence compensation. Under a pump power of 344 W, a linearly polarized average output power of 101.4 W at 1064 nm is obtained, which corresponds to an optical-to-optical conversion efficiency of 29.4%. The laser is operated at a repetition rate of 400 Hz with a beam quality factor of M(2)=1.14. To the best of our knowledge, this is the highest optical-to-optical efficiency for a side-pumped TEM(00) Nd:YAG rod laser oscillator with a 100-W-level output ever reported.

Simplification and its consequences in biological modelling: conclusions from a study of calcium oscillations in hepatocytes.

PubMed

Hetherington, James P J; Warner, Anne; Seymour, Robert M

2006-04-22

Systems Biology requires that biological modelling is scaled up from small components to system level. This can produce exceedingly complex models, which obscure understanding rather than facilitate it. The successful use of highly simplified models would resolve many of the current problems faced in Systems Biology. This paper questions whether the conclusions of simple mathematical models of biological systems are trustworthy. The simplification of a specific model of calcium oscillations in hepatocytes is examined in detail, and the conclusions drawn from this scrutiny generalized. We formalize our choice of simplification approach through the use of functional 'building blocks'. A collection of models is constructed, each a progressively more simplified version of a well-understood model. The limiting model is a piecewise linear model that can be solved analytically. We find that, as expected, in many cases the simpler models produce incorrect results. However, when we make a sensitivity analysis, examining which aspects of the behaviour of the system are controlled by which parameters, the conclusions of the simple model often agree with those of the richer model. The hypothesis that the simplified model retains no information about the real sensitivities of the unsimplified model can be very strongly ruled out by treating the simplification process as a pseudo-random perturbation on the true sensitivity data. We conclude that sensitivity analysis is, therefore, of great importance to the analysis of simple mathematical models in biology. Our comparisons reveal which results of the sensitivity analysis regarding calcium oscillations in hepatocytes are robust to the simplifications necessarily involved in mathematical modelling. For example, we find that if a treatment is observed to strongly decrease the period of the oscillations while increasing the proportion of the cycle during which cellular calcium concentrations are rising, without affecting the inter-spike or maximum calcium concentrations, then it is likely that the treatment is acting on the plasma membrane calcium pump.

(Small) Resonant non-Gaussianities: Signatures of a Discrete Shift Symmetry in the Effective Field Theory of Inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Behbahani, Siavosh R.; /SLAC /Stanford U., Phys. Dept. /Boston U.; Dymarsky, Anatoly

2012-06-06

We apply the Effective Field Theory of Inflation to study the case where the continuous shift symmetry of the Goldstone boson {pi} is softly broken to a discrete subgroup. This case includes and generalizes recently proposed String Theory inspired models of Inflation based on Axion Monodromy. The models we study have the property that the 2-point function oscillates as a function of the wavenumber, leading to oscillations in the CMB power spectrum. The non-linear realization of time diffeomorphisms induces some self-interactions for the Goldstone boson that lead to a peculiar non-Gaussianity whose shape oscillates as a function of the wavenumber.more » We find that in the regime of validity of the effective theory, the oscillatory signal contained in the n-point correlation functions, with n > 2, is smaller than the one contained in the 2-point function, implying that the signature of oscillations, if ever detected, will be easier to find first in the 2-point function, and only then in the higher order correlation functions. Still the signal contained in higher-order correlation functions, that we study here in generality, could be detected at a subleading level, providing a very compelling consistency check for an approximate discrete shift symmetry being realized during inflation.« less

Inverted Spring Pendulum Driven by a Periodic Force: Linear versus Nonlinear Analysis

ERIC Educational Resources Information Center

Arinstein, A.; Gitterman, M.

2008-01-01

We analyse the stability of the spring inverted pendulum with the vertical oscillations of the suspension point. An important factor in the stability analysis is the interaction between radial and oscillating modes. In addition to the small oscillations near the upper position, the nonlinearity of the problem leads to the appearance of limit-cycle…

Doubly anharmonic oscillator under the topological effects of a screw dislocation

NASA Astrophysics Data System (ADS)

Bakke, Knut

2018-05-01

We consider an elastic medium with the distortion of a circular curve into a vertical spiral, and investigate the influence of this topological defect on the doubly anharmonic oscillator. We show that the Schrödinger equation for the doubly anharmonic oscillator in the presence of this linear topological defect can be solved analytically. We also obtain the exact expressions for the permitted energies of the ground state of the doubly anharmonic oscillator, and show that the topology of the screw dislocation modifies the spectrum of energy of the doubly anharmonic oscillator.

Interaction function of oscillating coupled neurons

PubMed Central

Dodla, Ramana; Wilson, Charles J.

2013-01-01

Large scale simulations of electrically coupled neuronal oscillators often employ the phase coupled oscillator paradigm to understand and predict network behavior. We study the nature of the interaction between such coupled oscillators using weakly coupled oscillator theory. By employing piecewise linear approximations for phase response curves and voltage time courses, and parameterizing their shapes, we compute the interaction function for all such possible shapes and express it in terms of discrete Fourier modes. We find that reasonably good approximation is achieved with four Fourier modes that comprise of both sine and cosine terms. PMID:24229210

INVESTIGATION OF NEW CONCEPTS AND LINEAR BEAM TECHNIQUES FOR MICROWAVE POWER GENERATION.

DTIC Science & Technology

ARSENIC ALLOYS, MILLIMETER WAVES, CAVITY RESONATORS, ELECTRON GUNS, ELECTRON DENSITY, EPITAXIAL GROWTH, OSCILLATORS, S BAND , X BAND , GERMANIUM...ELECTRIC FIELDS, SCATTERING, BRILLOUIN ZONES, RUBY, ELECTROSTRICTION, IONIZATION, MICROWAVE OSCILLATORS, KLYSTRONS , EXPERIMENTAL DESIGN.

Quantum Kramers model: Corrections to the linear response theory for continuous bath spectrum

NASA Astrophysics Data System (ADS)

Rips, Ilya

2017-01-01

Decay of the metastable state is analyzed within the quantum Kramers model in the weak-to-intermediate dissipation regime. The decay kinetics in this regime is determined by energy exchange between the unstable mode and the stable modes of thermal bath. In our previous paper [Phys. Rev. A 42, 4427 (1990), 10.1103/PhysRevA.42.4427], Grabert's perturbative approach to well dynamics in the case of the discrete bath [Phys. Rev. Lett. 61, 1683 (1988), 10.1103/PhysRevLett.61.1683] has been extended to account for the second order terms in the classical equations of motion (EOM) for the stable modes. Account of the secular terms reduces EOM for the stable modes to those of the forced oscillator with the time-dependent frequency (TDF oscillator). Analytic expression for the characteristic function of energy loss of the unstable mode has been derived in terms of the generating function of the transition probabilities for the quantum forced TDF oscillator. In this paper, the approach is further developed and applied to the case of the continuous frequency spectrum of the bath. The spectral density functions of the bath of stable modes are expressed in terms of the dissipative properties (the friction function) of the original bath. They simplify considerably for the one-dimensional systems, when the density of phonon states is constant. Explicit expressions for the fourth order corrections to the linear response theory result for the characteristic function of the energy loss and its cumulants are obtained for the particular case of the cubic potential with Ohmic (Markovian) dissipation. The range of validity of the perturbative approach in this case is determined (γ /ωb<0.26 ), which includes the turnover region. The dominant correction to the linear response theory result is associated with the "work function" and leads to reduction of the average energy loss and its dispersion. This reduction increases with the increasing dissipation strength (up to ˜10 % ) within the range of validity of the approach. We have also calculated corrections to the depopulation factor and the escape rate for the quantum and for the classical Kramers models. Results for the classical escape rate are in very good agreement with the numerical simulations for high barriers. The results can serve as an additional proof of the robustness and accuracy of the linear response theory.

Quantum Kramers model: Corrections to the linear response theory for continuous bath spectrum.

PubMed

Rips, Ilya

2017-01-01

Decay of the metastable state is analyzed within the quantum Kramers model in the weak-to-intermediate dissipation regime. The decay kinetics in this regime is determined by energy exchange between the unstable mode and the stable modes of thermal bath. In our previous paper [Phys. Rev. A 42, 4427 (1990)PLRAAN1050-294710.1103/PhysRevA.42.4427], Grabert's perturbative approach to well dynamics in the case of the discrete bath [Phys. Rev. Lett. 61, 1683 (1988)PRLTAO0031-900710.1103/PhysRevLett.61.1683] has been extended to account for the second order terms in the classical equations of motion (EOM) for the stable modes. Account of the secular terms reduces EOM for the stable modes to those of the forced oscillator with the time-dependent frequency (TDF oscillator). Analytic expression for the characteristic function of energy loss of the unstable mode has been derived in terms of the generating function of the transition probabilities for the quantum forced TDF oscillator. In this paper, the approach is further developed and applied to the case of the continuous frequency spectrum of the bath. The spectral density functions of the bath of stable modes are expressed in terms of the dissipative properties (the friction function) of the original bath. They simplify considerably for the one-dimensional systems, when the density of phonon states is constant. Explicit expressions for the fourth order corrections to the linear response theory result for the characteristic function of the energy loss and its cumulants are obtained for the particular case of the cubic potential with Ohmic (Markovian) dissipation. The range of validity of the perturbative approach in this case is determined (γ/ω_{b}<0.26), which includes the turnover region. The dominant correction to the linear response theory result is associated with the "work function" and leads to reduction of the average energy loss and its dispersion. This reduction increases with the increasing dissipation strength (up to ∼10%) within the range of validity of the approach. We have also calculated corrections to the depopulation factor and the escape rate for the quantum and for the classical Kramers models. Results for the classical escape rate are in very good agreement with the numerical simulations for high barriers. The results can serve as an additional proof of the robustness and accuracy of the linear response theory.

A theoretical evaluation of rigid baffles in suppression of combustion instability

NASA Technical Reports Server (NTRS)

Baer, M. R.; Mitchell, C. E.

1976-01-01

An analytical technique for the prediction of the effects of rigid baffles on the stability of liquid propellant combustors is presented. A three dimensional combustor model characterized by a concentrated combustion source at the chamber injector and a constant Mach number nozzle is used. The linearized partial differential equations describing the unsteady flow field are solved by an eigenfunction matching method. Boundary layer corrections to this unsteady flow are used to evaluate viscous and turbulence effects within the flow. An integral stability relationship is then employed to predict the decay rate of the oscillations. Results show that sufficient dissipation exists to indicate that the proper mechanism of baffle damping is a fluid dynamic loss. The response of the dissipation model to varying baffle blade length, mean flow Mach number and oscillation amplitude is examined.

Programming strategy for efficient modeling of dynamics in a population of heterogeneous cells.

PubMed

Hald, Bjørn Olav; Garkier Hendriksen, Morten; Sørensen, Preben Graae

2013-05-15

Heterogeneity is a ubiquitous property of biological systems. Even in a genetically identical population of a single cell type, cell-to-cell differences are observed. Although the functional behavior of a given population is generally robust, the consequences of heterogeneity are fairly unpredictable. In heterogeneous populations, synchronization of events becomes a cardinal problem-particularly for phase coherence in oscillating systems. The present article presents a novel strategy for construction of large-scale simulation programs of heterogeneous biological entities. The strategy is designed to be tractable, to handle heterogeneity and to handle computational cost issues simultaneously, primarily by writing a generator of the 'model to be simulated'. We apply the strategy to model glycolytic oscillations among thousands of yeast cells coupled through the extracellular medium. The usefulness is illustrated through (i) benchmarking, showing an almost linear relationship between model size and run time, and (ii) analysis of the resulting simulations, showing that contrary to the experimental situation, synchronous oscillations are surprisingly hard to achieve, underpinning the need for tools to study heterogeneity. Thus, we present an efficient strategy to model the biological heterogeneity, neglected by ordinary mean-field models. This tool is well posed to facilitate the elucidation of the physiologically vital problem of synchronization. The complete python code is available as Supplementary Information. bjornhald@gmail.com or pgs@kiku.dk Supplementary data are available at Bioinformatics online.

Electron-phonon thermalization in a scalable method for real-time quantum dynamics

DOE PAGES

Rizzi, Valerio; Todorov, Tchavdar N.; Kohanoff, Jorge J.; ...

2016-01-27

Here, we present a quantum simulation method that follows the dynamics of out-of-equilibrium many-body systems of electrons and oscillators in real time. Its cost is linear in the number of oscillators and it can probe time scales from attoseconds to hundreds of picoseconds. Contrary to Ehrenfest dynamics, it can thermalize starting from a variety of initial conditions, including electronic population inversion. While an electronic temperature can be defined in terms of a nonequilibrium entropy, a Fermi-Dirac distribution in general emerges only after thermalization. These results can be used to construct a kinetic model of electron-phonon equilibration based on the explicitmore » quantum dynamics.« less

Dispersion of the refractive index of a samarium-doped Se{sup 95}Te{sup 5} chalcogenide glassy semiconductor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Atayeva, S. U., E-mail: seva-atayeva@mail.ru; Mekhtiyeva, S. I.; Isayev, A. I.

2015-07-15

The transmission spectrum of a Se{sup 95}Te{sup 5} chalcogenide glassy semiconductor doped with samarium (0.05, 0.1, 0.25, 0.5, and 1 at %) is studied; the Swanepoel method and the single-oscillator model are used to determine the oscillator energy E{sup 0}, dispersion energy E{sup d}, optical width of the band gap E{sup g}, and linear (n) and nonlinear (n{sup 2}) refractive indices. The changes in the values of these parameters as a result of doping are attributed to modification of the local structure and to a change in the concentration of defect states.

Demonstration of Detection and Ranging Using Solvable Chaos

NASA Technical Reports Server (NTRS)

Corron, Ned J.; Stahl, Mark T.; Blakely, Jonathan N.

2013-01-01

Acoustic experiments demonstrate a novel approach to ranging and detection that exploits the properties of a solvable chaotic oscillator. This nonlinear oscillator includes an ordinary differential equation and a discrete switching condition. The chaotic waveform generated by this hybrid system is used as the transmitted waveform. The oscillator admits an exact analytic solution that can be written as the linear convolution of binary symbols and a single basis function. This linear representation enables coherent reception using a simple analog matched filter and without need for digital sampling or signal processing. An audio frequency implementation of the transmitter and receiver is described. Successful acoustic ranging measurements are presented to demonstrate the viability of the approach.

The detectability of baryonic acoustic oscillations in future galaxy surveys

NASA Astrophysics Data System (ADS)

Angulo, R. E.; Baugh, C. M.; Frenk, C. S.; Lacey, C. G.

2008-01-01

We assess the detectability of baryonic acoustic oscillation (BAO) in the power spectrum of galaxies using ultralarge volume N-body simulations of the hierarchical clustering of dark matter and semi-analytical modelling of galaxy formation. A step-by-step illustration is given of the various effects (non-linear fluctuation growth, peculiar motions, non-linear and scale-dependent bias) which systematically change the form of the galaxy power spectrum on large scales from the simple prediction of linear perturbation theory. Using a new method to extract the scale of the oscillations, we nevertheless find that the BAO approach gives an unbiased estimate of the sound horizon scale. Sampling variance remains the dominant source of error despite the huge volume of our simulation box (=2.41h-3Gpc3). We use our results to forecast the accuracy with which forthcoming surveys will be able to measure the sound horizon scale, s, and, hence constrain the dark energy equation of state parameter, w (with simplifying assumptions and without marginalizing over the other cosmological parameters). Pan-STARRS could potentially yield a measurement with an accuracy of Δs/s = 0.5-0.7 per cent (corresponding to Δw ~ 2-3 per cent), which is competitive with the proposed WFMOS survey (Δs/s = 1 per cent Δw ~ 4 per cent). Achieving Δw <= 1 per cent using BAO alone is beyond any currently commissioned project and will require an all-sky spectroscopic survey, such as would be undertaken by the SPACE mission concept under proposal to ESA.

Chaotic examination

NASA Astrophysics Data System (ADS)

Bildirici, Melike; Sonustun, Fulya Ozaksoy; Sonustun, Bahri

2018-01-01

In the regards of chaos theory, new concepts such as complexity, determinism, quantum mechanics, relativity, multiple equilibrium, complexity, (continuously) instability, nonlinearity, heterogeneous agents, irregularity were widely questioned in economics. It is noticed that linear models are insufficient for analyzing unpredictable, irregular and noncyclical oscillations of economies, and for predicting bubbles, financial crisis, business cycles in financial markets. Therefore, economists gave great consequence to use appropriate tools for modelling non-linear dynamical structures and chaotic behaviors of the economies especially in macro and the financial economy. In this paper, we aim to model the chaotic structure of exchange rates (USD-TL and EUR-TL). To determine non-linear patterns of the selected time series, daily returns of the exchange rates were tested by BDS during the period from January 01, 2002 to May 11, 2017 which covers after the era of the 2001 financial crisis. After specifying the non-linear structure of the selected time series, it was aimed to examine the chaotic characteristic for the selected time period by Lyapunov Exponents. The findings verify the existence of the chaotic structure of the exchange rate returns in the analyzed time period.

Oscillations in stellar atmospheres

NASA Technical Reports Server (NTRS)

Costa, A.; Ringuelet, A. E.; Fontenla, J. M.

1989-01-01

Atmospheric excitation and propagation of oscillations are analyzed for typical pulsating stars. The linear, plane-parallel approach for the pulsating atmosphere gives a local description of the phenomenon. From the local analysis of oscillations, the minimum frequencies are obtained for radially propagating waves. The comparison of the minimum frequencies obtained for a variety of stellar types is in good agreement with the observed periods of the oscillations. The role of the atmosphere in the globar stellar pulsations is thus emphasized.

A residual-based shock capturing scheme for the continuous/discontinuous spectral element solution of the 2D shallow water equations

NASA Astrophysics Data System (ADS)

Marras, Simone; Kopera, Michal A.; Constantinescu, Emil M.; Suckale, Jenny; Giraldo, Francis X.

2018-04-01

The high-order numerical solution of the non-linear shallow water equations is susceptible to Gibbs oscillations in the proximity of strong gradients. In this paper, we tackle this issue by presenting a shock capturing model based on the numerical residual of the solution. Via numerical tests, we demonstrate that the model removes the spurious oscillations in the proximity of strong wave fronts while preserving their strength. Furthermore, for coarse grids, it prevents energy from building up at small wave-numbers. When applied to the continuity equation to stabilize the water surface, the addition of the shock capturing scheme does not affect mass conservation. We found that our model improves the continuous and discontinuous Galerkin solutions alike in the proximity of sharp fronts propagating on wet surfaces. In the presence of wet/dry interfaces, however, the model needs to be enhanced with the addition of an inundation scheme which, however, we do not address in this paper.

Arm motion coupling during locomotion-like actions: An experimental study and a dynamic model

PubMed Central

Shapkova, E.Yu; Terekhov, A.V.; Latash, M.L.

2010-01-01

We studied the coordination of arm movements in standing persons who performed an out-of-phase arm-swinging task while stepping in place or while standing. The subjects were instructed to stop one of the arms in response to an auditory signal while trying to keep the rest of the movement pattern unchanged. A significant increase was observed in the amplitude of the arm that continued swinging under both the stepping and standing conditions. This increase was similar between the right and left arms. A dynamic model was developed including two coupled non-linear van der Pol oscillators. We assumed that stopping an arm did not eliminate the coupling but introduced a new constraint. Within the model, superposition of two factors, a command to stop the ongoing movement of one arm and the coupling between the two oscillators, has been able to account for the observed effects. The model makes predictions for future experiments. PMID:21628725

Adaptive and nonadaptive feedback control of global instabilities with application to a heated 2-D jet

NASA Astrophysics Data System (ADS)

Monkewitz, Peter A.; Mingori, D. L.

1992-04-01

Close to the onset of self-excited fluid oscillations the generic complex Ginzburg-Landau is proposed as the lowest order model for the plant. Its linear part which provides the stability boundaries is derived from first principles for both doubly-infinite and semi-infinite flow domains. Concentrating on a single global mode, the model is further simplified to the Stuart-Landau equation. For this latter model, a methodology is developed for the design of single-input single-output controllers. The so designed controllers have been implemented on a self-excited, heated two-dimensional jet with one hot wire as sensor and an acoustic speaker as actuator, and are shown to be effective within their limitations in suppressing or enhancing limit-cycle oscillations. Finally, the effect of of a controller designed to suppress the most unstable global mode on other modes is investigated experimentally in the wake of a cylinder at low Reynolds number, where an encouraging semi-quantitative correspondence to the Ginzburg-Landau model is found.

Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.

PubMed

Scott, M

2012-08-01

The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.

How enzymes can capture and transmit free energy from an oscillating electric field.

PubMed

Westerhoff, H V; Tsong, T Y; Chock, P B; Chen, Y D; Astumian, R D

1986-07-01

Recently, it has been demonstrated that free energy from an alternating electric field can drive the active transport of Rb+ by way of the Na+, K+-ATPase. In the present work, it is shown why many transmembrane enzymes can be expected to absorb free energy from an oscillating electric field and transduce that to chemical or transport work. In the theoretical analysis it turned out to be sufficient that (i) the catalytic process be accompanied by either net or cyclic charge translocation across the membrane and (ii) the stability of the enzyme states involved be asymmetric. Calculations based on a four-state model reveal that free-energy transduction occurs with sinusoidal, square-wave, and positive-only oscillating electric fields and for cases that exhibit either linear or exponential field-dependent rate constants. The results suggest that in addition to oscillating electric field-driven transport, the proposed mechanism can also be used to explain, in part, the "missing" free energy term in the cases in which ATP synthesis has been observed with insufficient transmembrane proton electrochemical potential difference.

How enzymes can capture and transmit free energy from an oscillating electric field.

PubMed Central

Westerhoff, H V; Tsong, T Y; Chock, P B; Chen, Y D; Astumian, R D

1986-01-01

Recently, it has been demonstrated that free energy from an alternating electric field can drive the active transport of Rb+ by way of the Na+, K+-ATPase. In the present work, it is shown why many transmembrane enzymes can be expected to absorb free energy from an oscillating electric field and transduce that to chemical or transport work. In the theoretical analysis it turned out to be sufficient that (i) the catalytic process be accompanied by either net or cyclic charge translocation across the membrane and (ii) the stability of the enzyme states involved be asymmetric. Calculations based on a four-state model reveal that free-energy transduction occurs with sinusoidal, square-wave, and positive-only oscillating electric fields and for cases that exhibit either linear or exponential field-dependent rate constants. The results suggest that in addition to oscillating electric field-driven transport, the proposed mechanism can also be used to explain, in part, the "missing" free energy term in the cases in which ATP synthesis has been observed with insufficient transmembrane proton electrochemical potential difference. PMID:2941758

Superharmonic resonances in a two-dimensional non-linear photonic-crystal nano-electro-mechanical oscillator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chowdhury, A.; Yeo, I.; Tsvirkun, V.

2016-04-18

We investigate the non-linear mechanical dynamics of a nano-optomechanical mirror formed by a suspended membrane pierced by a photonic crystal. By applying to the mirror a periodic electrostatic force induced by interdigitated electrodes integrated below the membrane, we evidence superharmonic resonances of our nano-electro-mechanical system; the constant phase shift of the oscillator across the resonance tongues is observed on the onset of principal harmonic and subharmonic excitation regimes.

Synchronization of mobile chaotic oscillator networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fujiwara, Naoya, E-mail: fujiwara@csis.u-tokyo.ac.jp; Kurths, Jürgen; Díaz-Guilera, Albert

We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to themore » transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.« less

Investigation of Hot Cracking Behavior in Transverse Mechanically Arc Oscillated Autogenous AA2014 T6 TIG Welds

NASA Astrophysics Data System (ADS)

Biradar, N. S.; Raman, R.

2012-09-01

Hot cracking studies on autogenous AA2014 T6 TIG welds were carried out. Significant cracking was observed during linear and circular welding test (CWT) on 4-mm-thick plates. Weld metal grain structure and amount of liquid distribution during the terminal stages of solidification were the key cause for hot cracking in aluminum welds. Square-wave AC TIG welding with transverse mechanical arc oscillation (TMAO) was employed to study the cracking behavior during linear and CWT. TMAO welds with amplitude = 0.9 mm and frequency = 0.5 Hz showed significant reduction in cracking tendency. The increase in cracking resistance in the arc-oscillated weld was attributed to grain refinement and improved weld bead morphology, which improved the weld metal ductility and uniformity, respectively, of residual tensile stresses that developed during welding. The obtained results were comparable to those of reported favorable results of electromagnetic arc oscillation.

A finite difference method for the solution of the transonic flow around harmonically oscillating wings

NASA Technical Reports Server (NTRS)

Ehlers, E. F.

1974-01-01

A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.

A statistical study of decaying kink oscillations detected using SDO/AIA

NASA Astrophysics Data System (ADS)

Goddard, C. R.; Nisticò, G.; Nakariakov, V. M.; Zimovets, I. V.

2016-01-01

Context. Despite intensive studies of kink oscillations of coronal loops in the last decade, a large-scale statistically significant investigation of the oscillation parameters has not been made using data from the Solar Dynamics Observatory (SDO). Aims: We carry out a statistical study of kink oscillations using extreme ultraviolet imaging data from a previously compiled catalogue. Methods: We analysed 58 kink oscillation events observed by the Atmospheric Imaging Assembly (AIA) on board SDO during its first four years of operation (2010-2014). Parameters of the oscillations, including the initial apparent amplitude, period, length of the oscillating loop, and damping are studied for 120 individual loop oscillations. Results: Analysis of the initial loop displacement and oscillation amplitude leads to the conclusion that the initial loop displacement prescribes the initial amplitude of oscillation in general. The period is found to scale with the loop length, and a linear fit of the data cloud gives a kink speed of Ck = (1330 ± 50) km s-1. The main body of the data corresponds to kink speeds in the range Ck = (800-3300) km s-1. Measurements of 52 exponential damping times were made, and it was noted that at least 21 of the damping profiles may be better approximated by a combination of non-exponential and exponential profiles rather than a purely exponential damping envelope. There are nine additional cases where the profile appears to be purely non-exponential and no damping time was measured. A scaling of the exponential damping time with the period is found, following the previously established linear scaling between these two parameters.

Latest astronomical constraints on some non-linear parametric dark energy models

NASA Astrophysics Data System (ADS)

Yang, Weiqiang; Pan, Supriya; Paliathanasis, Andronikos

2018-04-01

We consider non-linear redshift-dependent equation of state parameters as dark energy models in a spatially flat Friedmann-Lemaître-Robertson-Walker universe. To depict the expansion history of the universe in such cosmological scenarios, we take into account the large-scale behaviour of such parametric models and fit them using a set of latest observational data with distinct origin that includes cosmic microwave background radiation, Supernove Type Ia, baryon acoustic oscillations, redshift space distortion, weak gravitational lensing, Hubble parameter measurements from cosmic chronometers, and finally the local Hubble constant from Hubble space telescope. The fitting technique avails the publicly available code Cosmological Monte Carlo (COSMOMC), to extract the cosmological information out of these parametric dark energy models. From our analysis, it follows that those models could describe the late time accelerating phase of the universe, while they are distinguished from the Λ-cosmology.

Transient and chaotic low-energy transfers in a system with bistable nonlinearity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romeo, F., E-mail: francesco.romeo@uniroma1.it; Manevitch, L. I.; Bergman, L. A.

2015-05-15

The low-energy dynamics of a two-dof system composed of a grounded linear oscillator coupled to a lightweight mass by means of a spring with both cubic nonlinear and negative linear components is investigated. The mechanisms leading to intense energy exchanges between the linear oscillator, excited by a low-energy impulse, and the nonlinear attachment are addressed. For lightly damped systems, it is shown that two main mechanisms arise: Aperiodic alternating in-well and cross-well oscillations of the nonlinear attachment, and secondary nonlinear beats occurring once the dynamics evolves solely in-well. The description of the former dissipative phenomenon is provided in a two-dimensionalmore » projection of the phase space, where transitions between in-well and cross-well oscillations are associated with sequences of crossings across a pseudo-separatrix. Whereas the second mechanism is described in terms of secondary limiting phase trajectories of the nonlinear attachment under certain resonance conditions. The analytical treatment of the two aformentioned low-energy transfer mechanisms relies on the reduction of the nonlinear dynamics and consequent analysis of the reduced dynamics by asymptotic techniques. Direct numerical simulations fully validate our analytical predictions.« less

Lunisolar tidal force and its relationship to chlorophyll fluorescence in Arabidopsis thaliana.

PubMed

Fisahn, Joachim; Klingelé, Emile; Barlow, Peter

2015-01-01

The yield of chlorophyll fluorescence Ft was measured in leaves of Arabidopsis thaliana over periods of several days under conditions of continuous illumination (LL) without the application of saturating light pulses. After linearization of the time series of the chlorophyll fluorescence yield (ΔFt), oscillations became apparent with periodicities in the circatidal range. Alignments of these linearized time series ΔFt with the lunisolar tidal acceleration revealed high degrees of synchrony and phase congruence. Similar congruence with the lunisolar tide was obtained with the linearized quantum yield of PSII (ΔФII), recorded after application of saturating light pulses. These findings strongly suggest that there is an exogenous timekeeper which is a stimulus for the oscillations detected in both the linearized yield of chlorophyll fluorescence (ΔFt) and the linearized quantum yield of PSII (ΔФII).

Lunisolar tidal force and its relationship to chlorophyll fluorescence in Arabidopsis thaliana

PubMed Central

Fisahn, Joachim; Klingelé, Emile; Barlow, Peter

2015-01-01

The yield of chlorophyll fluorescence Ft was measured in leaves of Arabidopsis thaliana over periods of several days under conditions of continuous illumination (LL) without the application of saturating light pulses. After linearization of the time series of the chlorophyll fluorescence yield (ΔFt), oscillations became apparent with periodicities in the circatidal range. Alignments of these linearized time series ΔFt with the lunisolar tidal acceleration revealed high degrees of synchrony and phase congruence. Similar congruence with the lunisolar tide was obtained with the linearized quantum yield of PSII (ΔФII), recorded after application of saturating light pulses. These findings strongly suggest that there is an exogenous timekeeper which is a stimulus for the oscillations detected in both the linearized yield of chlorophyll fluorescence (ΔFt) and the linearized quantum yield of PSII (ΔФII). PMID:26376108

Mesospheric Non-Migrating Tides Generated With Planetary Waves. 1; Characteristics

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Mengel, J. G.; Talaat, E. L.; Porter, H. S.; Chan, K. L.

2003-01-01

We discuss results from a modeling study with our Numerical Spectral Model (NSM) that specifically deals with the non-migrating tides generated in the mesosphere. The NSM extends from the ground to the thermosphere, incorporates Hines' Doppler Spread Parameterization for small-scale gravity waves (GWs), and it describes the major dynamical features of the atmosphere including the wave driven equatorial oscillations (QBO and SAO), and the seasonal variations of tides and planetary waves. Accounting solely for the excitation sources of the solar migrating tides, the NSM generates through dynamical interactions also non-migrating tides in the mesosphere that are comparable in magnitude to those observed. Large non-migrating tides are produced in the diurnal and semi-diurnal oscillations for the zonal mean (m = 0) and in the semidiurnal oscillation for m = 1. In general, significant eastward and westward propagating tides are generated for all the zonal wave numbers m = 1 to 4. To identify the cause, the NSM is run without the solar heating for the zonal mean (m = 0), and the amplitudes of the resulting non-migrating tides are then negligibly small. In this case, the planetary waves are artificially suppressed, which are generated in the NSM through instabilities. This leads to the conclusion that the non-migrating tides are generated through non-linear interactions between planetary waves and migrating tides, as Forbes et al. and Talaat and Liberman had proposed. In an accompanying paper, we present results from numerical experiments, which indicate that gravity wave filtering contributes significantly to produce the non-linear coupling that is involved.

Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools.

PubMed

Siettos, Constantinos; Starke, Jens

2016-09-01

The extreme complexity of the brain naturally requires mathematical modeling approaches on a large variety of scales; the spectrum ranges from single neuron dynamics over the behavior of groups of neurons to neuronal network activity. Thus, the connection between the microscopic scale (single neuron activity) to macroscopic behavior (emergent behavior of the collective dynamics) and vice versa is a key to understand the brain in its complexity. In this work, we attempt a review of a wide range of approaches, ranging from the modeling of single neuron dynamics to machine learning. The models include biophysical as well as data-driven phenomenological models. The discussed models include Hodgkin-Huxley, FitzHugh-Nagumo, coupled oscillators (Kuramoto oscillators, Rössler oscillators, and the Hindmarsh-Rose neuron), Integrate and Fire, networks of neurons, and neural field equations. In addition to the mathematical models, important mathematical methods in multiscale modeling and reconstruction of the causal connectivity are sketched. The methods include linear and nonlinear tools from statistics, data analysis, and time series analysis up to differential equations, dynamical systems, and bifurcation theory, including Granger causal connectivity analysis, phase synchronization connectivity analysis, principal component analysis (PCA), independent component analysis (ICA), and manifold learning algorithms such as ISOMAP, and diffusion maps and equation-free techniques. WIREs Syst Biol Med 2016, 8:438-458. doi: 10.1002/wsbm.1348 For further resources related to this article, please visit the WIREs website. © 2016 Wiley Periodicals, Inc.

A Non-Linear Model for Elastic Dielectric Crystals with Mobile Vacancies

DTIC Science & Technology

2009-07-01

crystals, vacancies typically carry an electric charge [18,37]. Such charged vacancies notably influence dielectric properties and elec- trical loss...characteristics of capacitors, oscillators, and tunable fil- ters [19], for example those comprised of perovskite ceramic crystals such as barium titanate...thermomechanical and thermoelectrical couplings, respectively, and the final term capturing non-mechanical sources of heat energy. 3.3. Representative free energy

Inflaton fragmentation in E models of cosmological α -attractors

NASA Astrophysics Data System (ADS)

Hasegawa, Fuminori; Hong, Jeong-Pyong

2018-04-01

Cosmological α -attractors are observationally favored due to the asymptotic flatness of the potential. Since its flatness induces the negative pressure, the coherent oscillation of the inflaton field could fragment into quasistable localized objects called I-balls (or "oscillons"). We investigated the possibility of I-ball formation in E models of α -attractors. Using the linear analysis and the lattice simulations, we found that the instability sufficiently grows against the cosmic expansion and the inflaton actually fragments into the I-balls for α ≲10-3 .

Properties of QBO and SAO Generated by Gravity Waves

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Mengel, J. G.; Reddy, C. A.; Chan, K. L.; Porter, H. S.

1999-01-01

We present an extension for the 2D (zonal mean) version of our Numerical Spectral Mode (NSM) that incorporates Hines' Doppler spread parameterization (DSP) for small scale gravity waves (GW). This model is applied to describe the seasonal variations and the semi-annual and quasi-biennial oscillations (SAO and QBO). Our earlier model reproduced the salient features of the mean zonal circulation in the middle atmosphere, including the QBO extension into the upper mesosphere inferred from UARS measurements. In the present model we incorporate also tropospheric heating to reproduce the upwelling at equatorial latitudes associated with the Brewer-Dobson circulation that affects significantly the dynamics of the stratosphere as Dunkerton had pointed out. Upward vertical winds increase the period of the QBO observed from the ground. To compensate for that, one needs to increase the eddy diffusivity and the GW momentum flux, bringing the latter closer to values recommended in the DSP. The QBO period in the model is 30 months (mo), which is conducive to synchronize this oscillation with the seasonal cycle of solar forcing. Multi-year interannual oscillations are generated through wave filtering by the solar driven annual oscillation in the zonal circulation. Quadratic non-linearities generate interseasonal variations to produce a complicated pattern of variability associated with the QBO. The computed temperature amplitudes for the SAO and QBO are in substantial agreement with observations at equatorial and extratropical latitudes. At high latitudes, however, the observed QBO amplitudes are significantly larger, which may be a signature of propagating planetary waves not included in the present model. The assumption of hydrostatic equilibrium not being imposed, we find that the effects from the vertical Coriolis force associated with the equatorial oscillations are large for the vertical winds and significant for the temperature variations even outside the tropics but are relatively small for the zonal winds.

Modeling Tight Junction Dynamics and Oscillations

PubMed Central

Kassab, Fuad; Marques, Ricardo Paulino; Lacaz-Vieira, Francisco

2002-01-01

Tight junction (TJ) permeability responds to changes of extracellular Ca2+ concentration. This can be gauged through changes of the transepithelial electrical conductance (G) determined in the absence of apical Na+. The early events of TJ dynamics were evaluated by the fast Ca2+ switch assay (FCSA) (Lacaz-Vieira, 2000), which consists of opening the TJs by removing basal calcium (Ca2+ bl) and closing by returning Ca2+ bl to normal values. Oscillations of TJ permeability were observed when Ca2+ bl is removed in the presence of apical calcium (Ca2+ ap) and were interpreted as resulting from oscillations of a feedback control loop which involves: (a) a sensor (the Ca2+ binding sites of zonula adhaerens), (b) a control unit (the cell signaling machinery), and (c) an effector (the TJs). A mathematical model to explain the dynamical behavior of the TJs and oscillations was developed. The extracellular route (ER), which comprises the paracellular space in series with the submucosal interstitial fluid, was modeled as a continuous aqueous medium having the TJ as a controlled barrier located at its apical end. The ER was approximated as a linear array of cells. The most apical cell is separated from the apical solution by the TJ and this cell bears the Ca2+ binding sites of zonula adhaerens that control the TJs. According to the model, the control unit receives information from the Ca2+ binding sites and delivers a signal that regulates the TJ barrier. Ca2+ moves along the ER according to one-dimensional diffusion following Fick's second law. Across the TJ, Ca2+ diffusion follows Fick's first law. Our first approach was to simulate the experimental results in a semiquantitative way. The model tested against experiment results performed in the frog urinary bladder adequately predicts the responses obtained in different experimental conditions, such as: (a) TJ opening and closing in a FCSA, (b) opening by the presence of apical Ca2+ and attainment of a new steady-state, (c) the escape phase which follows the halt of TJ opening induced by apical Ca2+, (d) the oscillations of TJ permeability, and (e) the effect of Ca2+ ap concentration on the frequency of oscillations. PMID:12149284

On the Boundary Conditions at an Oscillating Contact Line: A Physical/Numerical Experimental Program

NASA Technical Reports Server (NTRS)

Perlin, Marc; Schultz, William W.

1996-01-01

We will pursue an improved physical understanding and mathematical model for the boundary condition at an oscillating contact line at high Reynolds number. We expect that the body force is locally unimportant for earth-based systems, and that the local behavior may dominate the mechanics of partially-filled reservoirs in the microgravity environment. One important space-based application for this contact-line study is for Faraday-waves. Oscillations in the direction of gravity (or acceleration) can dominate the fluid motion during take-off and reentry with large steady-state accelerations and in orbit, where fluctuations on the order of 10(exp -4)g occur about a zero mean. Our experience with Faraday waves has shown them to be 'cleaner' than those produced by vertical or horizontal oscillation of walls. They are easier to model analytically or computationally, and they do not have strong vortex formation at the bottom of the plate. Hence many, if not most, of the experiments will be performed in this manner. The importance of contact lines in the microgravity environment is well established. We will compare high resolution measurements of the velocity field (lO micro-m resolution) using particle-tracking and particle-image velocimetry as the fluid/fluid interface is approached from the lower fluid. The spatial gradients in the deviation provide additional means to determine an improved boundary condition and a measure of the slip region. Dissipation, the size of the eddy near the contact line, and hysteresis will be measured and compare to linear and nonlinear models of viscous and irrotational but dissipative models.

Association of climate drivers with rainfall in New South Wales, Australia, using Bayesian Model Averaging

NASA Astrophysics Data System (ADS)

Duc, Hiep Nguyen; Rivett, Kelly; MacSween, Katrina; Le-Anh, Linh

2017-01-01

Rainfall in New South Wales (NSW), located in the southeast of the Australian continent, is known to be influenced by four major climate drivers: the El Niño/Southern Oscillation (ENSO), the Interdecadal Pacific Oscillation (IPO), the Southern Annular Mode (SAM) and the Indian Ocean Dipole (IOD). Many studies have shown the influences of ENSO, IPO modulation, SAM and IOD on rainfall in Australia and on southeast Australia in particular. However, only limited work has been undertaken using a multiple regression framework to examine the extent of the combined effect of these climate drivers on rainfall. This paper analysed the role of these combined climate drivers and their interaction on the rainfall in NSW using Bayesian Model Averaging (BMA) to account for model uncertainty by considering each of the linear models across the whole model space which is equal to the set of all possible combinations of predictors to find the model posterior probabilities and their expected predictor coefficients. Using BMA for linear regression models, we are able to corroborate and confirm the results from many previous studies. In addition, the method gives the ranking order of importance and the probability of the association of each of the climate drivers and their interaction on the rainfall at a site. The ability to quantify the relative contribution of the climate drivers offers the key to understand the complex interaction of drivers on rainfall, or lack of rainfall in a region, such as the three big droughts in southeastern Australia which have been the subject of discussion and debate recently on their causes.

Oscillating-flow loss test results in rectangular heat exchanger passages

NASA Technical Reports Server (NTRS)

Wood, J. Gary

1991-01-01

Test results of oscillating flow losses in rectangular heat exchanger passages of various aspect ratios are given. This work was performed in support of the design of a free-piston Stirling engine (FPSE) for a dynamic space power conversion system. Oscillating flow loss testing was performed using an oscillating flow rig, which was based on a variable stroke and variable frequency linear drive motor. Tests were run over a range of oscillating flow parameters encompassing the flow regimes of the proposed engine design. Test results are presented in both tabular and graphical form and are compared against analytical predictions.

Tuning the synchronization of a network of weakly coupled self-oscillating gels via capacitors.

PubMed

Fang, Yan; Yashin, Victor V; Dickerson, Samuel J; Balazs, Anna C

2018-05-01

We consider a network of coupled oscillating units, where each unit comprises a self-oscillating polymer gel undergoing the Belousov-Zhabotinsky (BZ) reaction and an overlaying piezoelectric (PZ) cantilever. Through chemo-mechano-electrical coupling, the oscillations of the networked BZ-PZ units achieve in-phase or anti-phase synchronization, enabling, for example, the storage of information within the system. Herein, we develop numerical and computational models to show that the introduction of capacitors into the BZ-PZ system enhances the dynamical behavior of the oscillating network by yielding additional stable synchronization modes. We specifically show that the capacitors lead to a redistribution of charge in the system and alteration of the force that the PZ cantilevers apply to the underlying gel. Hence, the capacitors modify the strength of the coupling between the oscillators in the network. We utilize a linear stability analysis to determine the phase behavior of BZ-PZ networks encompassing different capacitances, force polarities, and number of units and then verify our findings with numerical simulations. Thus, through analytical calculations and numerical simulations, we determine the impact of the capacitors on the existence of the synchronization modes, their stability, and the rate of synchronization within these complex dynamical systems. The findings from our study can be used to design robotic materials that harness the materials' intrinsic, responsive properties to perform such functions as sensing, actuation, and information storage.

Tuning the synchronization of a network of weakly coupled self-oscillating gels via capacitors

NASA Astrophysics Data System (ADS)

Fang, Yan; Yashin, Victor V.; Dickerson, Samuel J.; Balazs, Anna C.

2018-05-01

We consider a network of coupled oscillating units, where each unit comprises a self-oscillating polymer gel undergoing the Belousov-Zhabotinsky (BZ) reaction and an overlaying piezoelectric (PZ) cantilever. Through chemo-mechano-electrical coupling, the oscillations of the networked BZ-PZ units achieve in-phase or anti-phase synchronization, enabling, for example, the storage of information within the system. Herein, we develop numerical and computational models to show that the introduction of capacitors into the BZ-PZ system enhances the dynamical behavior of the oscillating network by yielding additional stable synchronization modes. We specifically show that the capacitors lead to a redistribution of charge in the system and alteration of the force that the PZ cantilevers apply to the underlying gel. Hence, the capacitors modify the strength of the coupling between the oscillators in the network. We utilize a linear stability analysis to determine the phase behavior of BZ-PZ networks encompassing different capacitances, force polarities, and number of units and then verify our findings with numerical simulations. Thus, through analytical calculations and numerical simulations, we determine the impact of the capacitors on the existence of the synchronization modes, their stability, and the rate of synchronization within these complex dynamical systems. The findings from our study can be used to design robotic materials that harness the materials' intrinsic, responsive properties to perform such functions as sensing, actuation, and information storage.

Synthesizing Virtual Oscillators to Control Islanded Inverters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Brian B.; Sinha, Mohit; Ainsworth, Nathan G.

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 modelsmore » 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.« less

Sunspot Oscillations From The Chromosphere To The Corona

NASA Astrophysics Data System (ADS)

Brynildsen, N.; Maltby, P.; Fredvik, T.; Kjeldseth-Moe, O.

The behavior of the 3 minute sunspot oscillations is studied as a function of temper- ature through the transition region using observations with CDS/SOHO and TRACE. The oscillations occur above the umbra, with amplitudes increasing to a maximum near 200 000 K, then decreasing towards higher temperatures. Deviations from pure linear oscillations are present in several cases. Power spectra of the oscillations are remarkably similar in the chromosphere and through the transition region in contra- diction to the predictions of the sunspot filter theory. The 3 minute oscillations pene- trate to the low temperature end of the corona, where they are channeled into smaller areas coinciding with the endpoints of sunspot coronal loops. This differs from the transition zone where the oscillating region covers the umbra.

Energetics and optimum motion of oscillating lifting surfaces of finite span

NASA Technical Reports Server (NTRS)

Ahmadi, A. R.; Widnall, S. E.

1986-01-01

In certain modes of animal propulsion in nature, such as bird flight and fish swimming, the efficiency compared to man-made vehicles is very high. In such cases, wing and tail motions are typically associated with relatively high Reynolds numbers, where viscous effects are confined to a thin boundary layer at the surface and a thin trailing wake. The propulsive forces, which are generated primarily by the inertial forces, can be calculated from potential-flow theory using linearized unsteady-wing theory (for small-amplitude oscillations). In the present study, a recently developed linearized, low-frequency, unsteady lifting-line theory is employed to calculate the (sectional and total) energetic quantities and optimum motion of an oscillating wing of finite span.

Modeling Pharmacological Clock and Memory Patterns of Interval Timing in a Striatal Beat-Frequency Model with Realistic, Noisy Neurons

PubMed Central

Oprisan, Sorinel A.; Buhusi, Catalin V.

2011-01-01

In most species, the capability of perceiving and using the passage of time in the seconds-to-minutes range (interval timing) is not only accurate but also scalar: errors in time estimation are linearly related to the estimated duration. The ubiquity of scalar timing extends over behavioral, lesion, and pharmacological manipulations. For example, in mammals, dopaminergic drugs induce an immediate, scalar change in the perceived time (clock pattern), whereas cholinergic drugs induce a gradual, scalar change in perceived time (memory pattern). How do these properties emerge from unreliable, noisy neurons firing in the milliseconds range? Neurobiological information relative to the brain circuits involved in interval timing provide support for an striatal beat frequency (SBF) model, in which time is coded by the coincidental activation of striatal spiny neurons by cortical neural oscillators. While biologically plausible, the impracticality of perfect oscillators, or their lack thereof, questions this mechanism in a brain with noisy neurons. We explored the computational mechanisms required for the clock and memory patterns in an SBF model with biophysically realistic and noisy Morris–Lecar neurons (SBF–ML). Under the assumption that dopaminergic drugs modulate the firing frequency of cortical oscillators, and that cholinergic drugs modulate the memory representation of the criterion time, we show that our SBF–ML model can reproduce the pharmacological clock and memory patterns observed in the literature. Numerical results also indicate that parameter variability (noise) – which is ubiquitous in the form of small fluctuations in the intrinsic frequencies of neural oscillators within and between trials, and in the errors in recording/retrieving stored information related to criterion time – seems to be critical for the time-scale invariance of the clock and memory patterns. PMID:21977014

Intra-breath arterial oxygen oscillations detected by a fast oxygen sensor in an animal model of acute respiratory distress syndrome

PubMed Central

Formenti, F.; Chen, R.; McPeak, H.; Murison, P. J.; Matejovic, M.; Hahn, C. E. W.; Farmery, A. D.

2015-01-01

Background There is considerable interest in oxygen partial pressure (Po2) monitoring in physiology, and in tracking Po2 changes dynamically when it varies rapidly. For example, arterial Po2 (PaO2) can vary within the respiratory cycle in cyclical atelectasis (CA), where PaO2 is thought to increase and decrease during inspiration and expiration, respectively. A sensor that detects these PaO2 oscillations could become a useful diagnostic tool of CA during acute respiratory distress syndrome (ARDS). Methods We developed a fibreoptic Po2 sensor (<200 µm diameter), suitable for human use, that has a fast response time, and can measure Po2 continuously in blood. By altering the inspired fraction of oxygen (FIO2) from 21 to 100% in four healthy animal models, we determined the linearity of the sensor's signal over a wide range of PaO2 values in vivo. We also hypothesized that the sensor could measure rapid intra-breath PaO2 oscillations in a large animal model of ARDS. Results In the healthy animal models, PaO2 responses to changes in FIO2 were in agreement with conventional intermittent blood-gas analysis (n=39) for a wide range of PaO2 values, from 10 to 73 kPa. In the animal lavage model of CA, the sensor detected PaO2 oscillations, also at clinically relevant PaO2 levels close to 9 kPa. Conclusions We conclude that these fibreoptic PaO2 sensors have the potential to become a diagnostic tool for CA in ARDS. PMID:25631471

Disc-oscillation resonance and neutron star QPOs: 3:2 epicyclic orbital model

NASA Astrophysics Data System (ADS)

Urbanec, M.; Török, G.; Šrámková, E.; Čech, P.; Stuchlík, Z.; Bakala, P.

2010-11-01

The high-frequency quasi-periodic oscillations (HF QPOs) that appear in the X-ray fluxes of low-mass X-ray binaries remain an unexplained phenomenon. Among other ideas, it has been suggested that a non-linear resonance between two oscillation modes in an accretion disc orbiting either a black hole or a neutron star plays a role in exciting the observed modulation. Several possible resonances have been discussed. A particular model assumes resonances in which the disc-oscillation modes have the eigenfrequencies equal to the radial and vertical epicyclic frequencies of geodesic orbital motion. This model has been discussed for black hole microquasar sources as well as for a group of neutron star sources. Assuming several neutron (strange) star equations of state and Hartle-Thorne geometry of rotating stars, we briefly compare the frequencies expected from the model to those observed. Our comparison implies that the inferred neutron star radius RNS is larger than the related radius of the marginally stable circular orbit rms for nuclear matter equations of state and spin frequencies up to 800 Hz. For the same range of spin and a strange star (MIT) equation of state, the inferrred radius is RNS ˜ rms. The “Paczyński modulation” mechanism considered within the model requires that RNS < rms. However, we find this condition to be fulfilled only for the strange matter equation of state, masses below 1 M⊙, and spin frequencies above 800 Hz. This result most likely falsifies the postulation of the neutron star 3:2 resonant eigenfrequencies being equal to the frequencies of geodesic radial and vertical epicyclic modes. We suggest that the 3:2 epicyclic modes could stay among the possible choices only if a fairly non-geodesic accretion flow is assumed, or if a different modulation mechanism operates.

A frequency domain linearized Navier-Stokes method including acoustic damping by eddy viscosity using RANS

NASA Astrophysics Data System (ADS)

Holmberg, Andreas; Kierkegaard, Axel; Weng, Chenyang

2015-06-01

In this paper, a method for including damping of acoustic energy in regions of strong turbulence is derived for a linearized Navier-Stokes method in the frequency domain. The proposed method is validated and analyzed in 2D only, although the formulation is fully presented in 3D. The result is applied in a study of the linear interaction between the acoustic and the hydrodynamic field in a 2D T-junction, subject to grazing flow at Mach 0.1. Part of the acoustic energy at the upstream edge of the junction is shed as harmonically oscillating disturbances, which are conveyed across the shear layer over the junction, where they interact with the acoustic field. As the acoustic waves travel in regions of strong shear, there is a need to include the interaction between the background turbulence and the acoustic field. For this purpose, the oscillation of the background turbulence Reynold's stress, due to the acoustic field, is modeled using an eddy Newtonian model assumption. The time averaged flow is first solved for using RANS along with a k-ε turbulence model. The spatially varying turbulent eddy viscosity is then added to the spatially invariant kinematic viscosity in the acoustic set of equations. The response of the 2D T-junction to an incident acoustic field is analyzed via a plane wave scattering matrix model, and the result is compared to experimental data for a T-junction of rectangular ducts. A strong improvement in the agreement between calculation and experimental data is found when the modification proposed in this paper is implemented. Discrepancies remaining are likely due to inaccuracies in the selected turbulence model, which is known to produce large errors e.g. for flows with significant rotation, which the grazing flow across the T-junction certainly is. A natural next step is therefore to test the proposed methodology together with more sophisticated turbulence models.

Characterizing Feedback Control Mechanisms in Nonlinear Microbial Models of Soil Organic Matter Decomposition by Stability Analysis

NASA Astrophysics Data System (ADS)

Georgiou, K.; Tang, J.; Riley, W. J.; Torn, M. S.

2014-12-01

Soil organic matter (SOM) decomposition is regulated by biotic and abiotic processes. Feedback interactions between such processes may act to dampen oscillatory responses to perturbations from equilibrium. Indeed, although biological oscillations have been observed in small-scale laboratory incubations, the overlying behavior at the plot-scale exhibits a relatively stable response to disturbances in input rates and temperature. Recent studies have demonstrated the ability of microbial models to capture nonlinear feedbacks in SOM decomposition that linear Century-type models are unable to reproduce, such as soil priming in response to increased carbon input. However, these microbial models often exhibit strong oscillatory behavior that is deemed unrealistic. The inherently nonlinear dynamics of SOM decomposition have important implications for global climate-carbon and carbon-concentration feedbacks. It is therefore imperative to represent these dynamics in Earth System Models (ESMs) by introducing sub-models that accurately represent microbial and abiotic processes. In the present study we explore, both analytically and numerically, four microbe-enabled model structures of varying levels of complexity. The most complex model combines microbial physiology, a non-linear mineral sorption isotherm, and enzyme dynamics. Based on detailed stability analysis of the nonlinear dynamics, we calculate the system modes as functions of model parameters. This dependence provides insight into the source of state oscillations. We find that feedback mechanisms that emerge from careful representation of enzyme and mineral interactions, with parameter values in a prescribed range, are critical for both maintaining system stability and capturing realistic responses to disturbances. Corroborating and expanding upon the results of recent studies, we explain the emergence of oscillatory responses and discuss the appropriate microbe-enabled model structure for inclusion in ESMs.

B-periodic oscillations in the Hall-resistance induced by a dc-current-bias under combined microwave-excitation and dc-current bias in the GaAs/AlGaAs 2D system.

PubMed

Liu, Han-Chun; Reichl, C; Wegscheider, W; Mani, R G

2018-05-18

We report the observation of dc-current-bias-induced B-periodic Hall resistance oscillations and Hall plateaus in the GaAs/AlGaAs 2D system under combined microwave radiation- and dc bias excitation at liquid helium temperatures. The Hall resistance oscillations and plateaus appear together with concomitant oscillations also in the diagonal magnetoresistance. The periods of Hall and diagonal resistance oscillations are nearly identical, and source power (P) dependent measurements demonstrate sub-linear relationship of the oscillation amplitude with P over the span 0 < P ≤ 20 mW.

NEW MODEL AND MEASUREMENT PRINCIPLE OF FLOWING AND HEAT TRANSFER CHARACTERISTICS OF REGENERATOR

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Y. Y.; Graduate University of the Chinese Academy of Sciences, Beijing, 100049; Luo, E. C.

2008-03-16

Regenerators play key role in oscillating-flow cryocoolers or thermoacoustic heat engine systems. However, their flowing and heat transfer mechanism is still not well understood. The complexities of the oscillating flow regenerator make traditional method of heat transfer research become difficult or helpless. In this paper, a model for porous media regenerator was given based on the linear thermoacoustic theory. Then the correlations for characteristic parameters were obtained by deducing universal expressions for thermoacoustic viscous function F{sub v} and thermal function F{sub T}. A simple acoustical method and experimental system to get F{sub v} and F{sub T} via measurements of isothermalmore » regenerators were presented. Some measurements of packed stainless screen regenerators were performed, and preliminary experimental results for flow and convective coefficients were derived, which showing flowing friction factor is approximately within 132/Re to 173/Re.« less

A microscopic derivation of nuclear collective rotation-vibration model and its application to nuclei

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gulshani, P., E-mail: matlap@bell.net

We derive a microscopic version of the successful phenomenological hydrodynamic model of Bohr-Davydov-Faessler-Greiner for collective rotation-vibration motion of an axially symmetric deformed nucleus. The derivation is not limited to small oscillation amplitude. The nuclear Schrodinger equation is canonically transformed to collective co-ordinates, which is then linearized using a constrained variational method. The associated constraints are imposed on the wavefunction rather than on the particle co-ordinates. The approach yields three self-consistent, time-reversal invariant, cranking-type Schrodinger equations for the rotation-vibration and intrinsic motions, and a self-consistency equation. For harmonic oscillator mean-field potentials, these equations are solved in closed forms for excitation energy,more » cut-off angular momentum, and other nuclear properties for the ground-state rotational band in some deformed nuclei. The results are compared with measured data.« less

Dynamical systems for modeling the evolution of the magnetic field of stars and Earth

NASA Astrophysics Data System (ADS)

Popova, H.

2016-02-01

The cycles of solar magnetic activity are connected with a solar dynamo that operates in the convective zone. Solar dynamo mechanism is based on the combined action of the differential rotation and the alpha-effect. Application of these concepts allows us to get an oscillating solution as a wave of the toroidal field propagating from middle latitudes to the equator. We investigated the dynamo model with the meridional circulation by the low-mode approach. This approach is based on an assumption that the solar magnetic field can be described by non-linear dynamical systems with a relatively small number of parameters. Such non-linear dynamical systems are based on the equations of dynamo models. With this method dynamical systems have been built for media which contains the meridional flow and thickness of the convection zone of the star. It was shown the possibility of coexistence of quiasi-biennial and 22-year cycle. We obtained the different regimes (oscillations, vacillations, dynamo-bursts) depending on the value of the dynamo-number, the meridional circulation, and thickness of the convection zone. We discuss the features of these regimes and compare them with the observed features of evolution of the solar and geo magnetic fields. We built theoretical paleomagnetic time scale and butterfly-diagrams for the helicity and toroidal magnetic field for different regimes.

Dynamical systems for modeling evolution of the magnetic field of the Sun, stars and planets

NASA Astrophysics Data System (ADS)

Popova, E.

2016-12-01

The magnetic activity of the Sun, stars and planets are connected with a dynamo process based on the combined action of the differential rotation and the alpha-effect. Application of this concept allows us to get different types of solutions which can describe the magnetic activity of celestial bodies. We investigated the dynamo model with the meridional circulation by the low-mode approach. This approach is based on an assumption that the magnetic field can be described by non-linear dynamical systems with a relatively small number of parameters. Such non-linear dynamical systems are based on the equations of dynamo models. With this method dynamical systems have been built for media which contains the meridional flow and thickness of the spherical shell where dynamo process operates. It was shown the possibility of coexistence of quiasi-biennial oscillations, 22-year cycle, and grand minima of magnetic activity which is consistent with the observational data for the solar activity. We obtained different regimes (oscillations, vacillations, dynamo-bursts) depending on a value of the dynamo-number, the meridional circulation, and thickness of the spherical shell. We discuss features of these regimes and compare them with the observed features of the magnetic fields of the Sun, stars and Earth. We built theoretical paleomagnetic time scale and butterfly-diagrams for the helicity and toroidal magnetic field for different regimes.

Linear dynamical modes as new variables for data-driven ENSO forecast

NASA Astrophysics Data System (ADS)

Gavrilov, Andrey; Seleznev, Aleksei; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander; Kurths, Juergen

2018-05-01

A new data-driven model for analysis and prediction of spatially distributed time series is proposed. The model is based on a linear dynamical mode (LDM) decomposition of the observed data which is derived from a recently developed nonlinear dimensionality reduction approach. The key point of this approach is its ability to take into account simple dynamical properties of the observed system by means of revealing the system's dominant time scales. The LDMs are used as new variables for empirical construction of a nonlinear stochastic evolution operator. The method is applied to the sea surface temperature anomaly field in the tropical belt where the El Nino Southern Oscillation (ENSO) is the main mode of variability. The advantage of LDMs versus traditionally used empirical orthogonal function decomposition is demonstrated for this data. Specifically, it is shown that the new model has a competitive ENSO forecast skill in comparison with the other existing ENSO models.

Pulse-coupled mixed-mode oscillators: Cluster states and extreme noise sensitivity

NASA Astrophysics Data System (ADS)

Karamchandani, Avinash J.; Graham, James N.; Riecke, Hermann

2018-04-01

Motivated by rhythms in the olfactory system of the brain, we investigate the synchronization of all-to-all pulse-coupled neuronal oscillators exhibiting various types of mixed-mode oscillations (MMOs) composed of sub-threshold oscillations (STOs) and action potentials ("spikes"). We focus particularly on the impact of the delay in the interaction. In the weak-coupling regime, we reduce the system to a Kuramoto-type equation with non-sinusoidal phase coupling and the associated Fokker-Planck equation. Its linear stability analysis identifies the appearance of various cluster states. Their type depends sensitively on the delay and the width of the pulses. Interestingly, long delays do not imply slow population rhythms, and the number of emerging clusters only loosely depends on the number of STOs. Direct simulations of the oscillator equations reveal that for quantitative agreement of the weak-coupling theory the coupling strength and the noise have to be extremely small. Even moderate noise leads to significant skipping of STO cycles, which can enhance the diffusion coefficient in the Fokker-Planck equation by two orders of magnitude. Introducing an effective diffusion coefficient extends the range of agreement significantly. Numerical simulations of the Fokker-Planck equation reveal bistability and solutions with oscillatory order parameters that result from nonlinear mode interactions. These are confirmed in simulations of the full spiking model.

Nonlinear oscillatory rarefied gas flow inside a rectangular cavity

NASA Astrophysics Data System (ADS)

Wang, Peng; Zhu, Lianhua; Su, Wei; Wu, Lei; Zhang, Yonghao

2018-04-01

The nonlinear oscillation of rarefied gas flow inside a two-dimensional rectangular cavity is investigated on the basis of the Shakhov kinetic equation. The gas dynamics, heat transfer, and damping force are studied numerically via the discrete unified gas-kinetic scheme for a wide range of parameters, including gas rarefaction, cavity aspect ratio, and oscillation frequency. Contrary to the linear oscillation where the velocity, temperature, and heat flux are symmetrical and oscillate with the same frequency as the oscillating lid, flow properties in nonlinear oscillatory cases turn out to be asymmetrical, and second-harmonic oscillation of the temperature field is observed. As a consequence, the amplitude of the shear stress near the top-right corner of the cavity could be several times larger than that at the top-left corner, while the temperature at the top-right corner could be significantly higher than the wall temperature in nearly the whole oscillation period. For the linear oscillation with the frequency over a critical value, and for the nonlinear oscillation, the heat transfer from the hot to cold region dominates inside the cavity, which is contrary to the anti-Fourier heat transfer in a low-speed rarefied lid-driven cavity flow. The damping force exerted on the oscillating lid is studied in detail, and the scaling laws are developed to describe the dependency of the resonance and antiresonance frequencies (corresponding to the damping force at a local maximum and minimum, respectively) on the reciprocal aspect ratio from the near hydrodynamic to highly rarefied regimes. These findings could be useful in the design of the micro-electro-mechanical devices operating in the nonlinear-flow regime.

1-kW monolithic narrow linewidth linear-polarized fiber laser at 1030 nm

NASA Astrophysics Data System (ADS)

Xu, Yang; Fang, Qiang; Cui, Xuelong; Hou, Bowen; Fu, Shijie; Xie, Zhaoxin; Shi, Wei

2018-02-01

We demonstrate an all-fiberized, linear-polarized, narrow spectral linewidth laser system with kilowatts-level output power at 1030 nm in master oscillator-power amplifier (MOPA) configuration. The laser system consists of a linear-polarized, narrow linewidth ( 28 GHz) fiber laser oscillator and two stages of linear-polarized fiber amplifiers. A 925 W linear-polarized fiber laser with a polarization extinction ratio (PER) of 15.2 dB and a spectral width of 60 GHz at the central wavelength of 1030.1 nm is achieved. Owing to the setting of the appropriate parameters for the laser, no indication of Stimulate Brillouin Scattering (SBS) is observed in the system. Moreover, thanks to the excellent quantum efficiency of the laser and the thightly coiling of the active fiber in the main amplifier, the mode instability (MI) is successfully avoided. As a result, the near diffraction-limited beam quality (M2<1.3) is achieved.

Structural, linear and nonlinear optical properties of co-doped ZnO thin films

NASA Astrophysics Data System (ADS)

Shaaban, E. R.; El-Hagary, M.; Moustafa, El Sayed; Hassan, H. Shokry; Ismail, Yasser A. M.; Emam-Ismail, M.; Ali, A. S.

2016-01-01

Different compositions of Co-doped zinc oxide [(Zn(1- x)Co x O) ( x = 0, 0.02, 0.04, 0.06, 0.08 and 0.10)] thin films were evaporated onto highly clean glass substrates by thermal evaporation technique using a modified source. The structural properties investigated by X-ray diffraction revealed hexagonal wurtzite ZnO-type structure. The crystallite size of the films was found to decrease with increasing Co content. The optical characterization of the films has been carried out using spectral transmittance and reflectance obtained in the wavelength range from 300 to 2500 nm. The refractive index has been found to increase with increasing Co content. It was further found that optical energy gap decreases from 3.28 to 3.03 eV with increasing Co content from x = 0 to x = 0.10, respectively. The dispersion of refractive index has been analyzed in terms of Wemple-DiDomenico (WDD) single-oscillator model. The oscillator parameters, the single-oscillator energy ( E o), the dispersion energy ( E d), and the static refractive index ( n 0), were determined. The nonlinear refractive index of the Zn(1- x)Co x O thin films was calculated and revealed well correlation with the linear refractive index and WDD parameters which in turn depend on the density and molar volume of the system.

Some problems of control of dynamical conditions of technological vibrating machines

NASA Astrophysics Data System (ADS)

Kuznetsov, N. K.; Lapshin, V. L.; Eliseev, A. V.

2017-10-01

The possibility of control of dynamical condition of the shakers that are designed for vibration treatment of parts interacting with granular media is discussed. The aim of this article is to develop the methodological basis of technology of creation of mathematical models of shake tables and the development of principles of formation of vibrational fields, estimation of their parameters and control of the structure vibration fields. Approaches to build mathematical models that take into account unilateral constraints, the relationships between elements, with the vibrating surface are developed. Methods intended to construct mathematical model of linear mechanical oscillation systems are used. Small oscillations about the position of static equilibrium are performed. The original method of correction of vibration fields by introduction of the oscillating system additional ties to the structure are proposed. Additional ties are implemented in the form of a mass-inertial device for changing the inertial parameters of the working body of the vibration table by moving the mass-inertial elements. The concept of monitoring the dynamic state of the vibration table based on the original measuring devices is proposed. Estimation for possible changes in dynamic properties is produced. The article is of interest for specialists in the field of creation of vibration technology machines and equipment.

Nonlinear multivariate and time series analysis by neural network methods

NASA Astrophysics Data System (ADS)

Hsieh, William W.

2004-03-01

Methods in multivariate statistical analysis are essential for working with large amounts of geophysical data, data from observational arrays, from satellites, or from numerical model output. In classical multivariate statistical analysis, there is a hierarchy of methods, starting with linear regression at the base, followed by principal component analysis (PCA) and finally canonical correlation analysis (CCA). A multivariate time series method, the singular spectrum analysis (SSA), has been a fruitful extension of the PCA technique. The common drawback of these classical methods is that only linear structures can be correctly extracted from the data. Since the late 1980s, neural network methods have become popular for performing nonlinear regression and classification. More recently, neural network methods have been extended to perform nonlinear PCA (NLPCA), nonlinear CCA (NLCCA), and nonlinear SSA (NLSSA). This paper presents a unified view of the NLPCA, NLCCA, and NLSSA techniques and their applications to various data sets of the atmosphere and the ocean (especially for the El Niño-Southern Oscillation and the stratospheric quasi-biennial oscillation). These data sets reveal that the linear methods are often too simplistic to describe real-world systems, with a tendency to scatter a single oscillatory phenomenon into numerous unphysical modes or higher harmonics, which can be largely alleviated in the new nonlinear paradigm.

Development of a nearshore oscillating surge wave energy converter with variable geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tom, N. M.; Lawson, M. J.; Yu, Y. H.

This paper presents an analysis of a novel wave energy converter concept that combines an oscillating surge wave energy converter (OSWEC) with control surfaces. The control surfaces allow for a variable device geometry that enables the hydrodynamic properties to be adapted with respect to structural loading, absorption range and power-take-off capability. The device geometry is adjusted on a sea state-to-sea state time scale and combined with wave-to-wave manipulation of the power take-off (PTO) to provide greater control over the capture efficiency, capacity factor, and design loads. This work begins with a sensitivity study of the hydrodynamic coefficients with respect tomore » device width, support structure thickness, and geometry. A linear frequency domain analysis is used to evaluate device performance in terms of absorbed power, foundation loads, and PTO torque. Previous OSWEC studies included nonlinear hydrodynamics, in response a nonlinear model that includes a quadratic viscous damping torque that was linearized via the Lorentz linearization. Inclusion of the quadratic viscous torque led to construction of an optimization problem that incorporated motion and PTO constraints. Results from this study found that, when transitioning from moderate-to-large sea states the novel OSWEC was capable of reducing structural loads while providing a near constant power output.« less

The electric field standing wave effect in infrared transflection spectroscopy

NASA Astrophysics Data System (ADS)

Mayerhöfer, Thomas G.; Popp, Jürgen

2018-02-01

We show that an electric field standing wave effect is responsible for the oscillations and the non-linear dependence of the absorbance on the layer thickness in thin layers on a reflective surface. This effect is connected to the occurrence of interference inside these layers. Consequently, the absorptance undergoes a maximum electric field intensity enhancement at spectral positions close to those where corresponding non-absorbing layers on a metal show minima in the reflectance. The effect leads to changes of peak maxima ratios with layer thickness and shows the same periodicity as oscillations in the peak positions. These peculiarities are fully based on and described by Maxwell's equations but cannot be understood and described if the strongly simplifying model centered on reflectance absorbance is employed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Das, Anirban; Dighe, Amol; Sen, Manibrata, E-mail: anirbandas@theory.tifr.res.in, E-mail: amol@theory.tifr.res.in, E-mail: manibrata@theory.tifr.res.in

Neutrino self-interactions are known to lead to non-linear collective flavor oscillations in a core-collapse supernova. We point out new possible effects of non-standard self-interactions (NSSI) of neutrinos on flavor conversions in a two-flavor framework. We show that, for a single-energy neutrino-antineutrino ensemble, a flavor instability is generated even in normal hierarchy for large enough NSSI. Using a toy model for the neutrino spectra, we show that flavor-preserving NSSI lead to pinching of spectral swaps, while flavor-violating NSSI cause swaps to develop away from a spectral crossing or even in the absence of a spectral crossing. Consequently, NSSI could give risemore » to collective oscillations and spectral splits even during neutronization burst, for both hierarchies.« less

Filtering of non-linear instabilities

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1978-01-01

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown that these problems can be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate filtering can reduce the intensity of these oscillations and possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and nonconservation differencing. The entire spectrum of filtered equations retains a three point character as well as second order spatial accuracy. Burgers equation was considered as a model.

Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators

NASA Astrophysics Data System (ADS)

Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, A.; Rubin, J. E.

2016-06-01

Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts. Our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.

The role of shock induced trailing-edge separation in limit cycle oscillations

NASA Technical Reports Server (NTRS)

Cunningham, Atlee M., Jr.

1989-01-01

The potential role of shock induced trailing edge separation (SITES) in limit cycle oscillations (LCO) was established. It was shown that the flip-flop characteristics of transition to and from SITES as well as its hysteresis could couple with wing modes with torsional motion and low damping. This connection led to the formulation of a very simple nonlinear math model using the linear equations of motion with a nonlinear step forcing function with hysteresis. A finite difference solution with time was developed and calculations were made for the F-111 TACT were used to determine the step forcing function due to SITES transition. Since no data were available for the hysteresis, a parameter study was conducted allowing the hysteresis effect to vary. Very small hysteresis effects, which were within expected bounds, were required to obtain reasonable response levels that essentially agreed with flight test results. Also in agreement with wind tunnel tests, LCO calculations for the 1/6 scale F-111 model showed that the model should have not experienced LCO.

The role of passive avian head stabilization in flapping flight

PubMed Central

Pete, Ashley E.; Kress, Daniel; Dimitrov, Marina A.; Lentink, David

2015-01-01

Birds improve vision by stabilizing head position relative to their surroundings, while their body is forced up and down during flapping flight. Stabilization is facilitated by compensatory motion of the sophisticated avian head–neck system. While relative head motion has been studied in stationary and walking birds, little is known about how birds accomplish head stabilization during flapping flight. To unravel this, we approximate the avian neck with a linear mass–spring–damper system for vertical displacements, analogous to proven head stabilization models for walking humans. We corroborate the model's dimensionless natural frequency and damping ratios from high-speed video recordings of whooper swans (Cygnus cygnus) flying over a lake. The data show that flap-induced body oscillations can be passively attenuated through the neck. We find that the passive model robustly attenuates large body oscillations, even in response to head mass and gust perturbations. Our proof of principle shows that bird-inspired drones with flapping wings could record better images with a swan-inspired passive camera suspension. PMID:26311316

Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators

DOE PAGES

Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; ...

2016-02-27

Artificial perceptions of light called phosphenes were motivated by earlier studies. We analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolutionmore » and stability of planar fronts. Moreover, our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.« less

Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.

Artificial perceptions of light called phosphenes were motivated by earlier studies. We analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolutionmore » and stability of planar fronts. Moreover, our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.« less

Improving Streamflow Forecasts Using Predefined Sea Surface Temperature

NASA Astrophysics Data System (ADS)

Kalra, A.; Ahmad, S.

2011-12-01

With the increasing evidence of climate variability, water resources managers in the western United States are faced with greater challenges of developing long range streamflow forecast. This is further aggravated by the increases in climate extremes such as floods and drought caused by climate variability. Over the years, climatologists have identified several modes of climatic variability and their relationship with streamflow. These climate modes have the potential of being used as predictor in models for improving the streamflow lead time. With this as the motivation, the current research focuses on increasing the streamflow lead time using predefine climate indices. A data driven model i.e. Support Vector Machine (SVM) based on the statistical learning theory is used to predict annual streamflow volume 3-year in advance. The SVM model is a learning system that uses a hypothesis space of linear functions in a Kernel induced higher dimensional feature space, and is trained with a learning algorithm from the optimization theory. Annual oceanic-atmospheric indices, comprising of Pacific Decadal Oscillation (PDO), North Atlantic Oscillation (NAO), Atlantic Multidecadal Oscillation (AMO), El Niño-Southern Oscillations (ENSO), and a new Sea Surface Temperature (SST) data set of "Hondo" Region for a period of 1906-2005 are used to generate annual streamflow volumes. The SVM model is applied to three gages i.e. Cisco, Green River, and Lees Ferry in the Upper Colorado River Basin in the western United States. Based on the performance measures the model shows very good forecasts, and the forecast are in good agreement with measured streamflow volumes. Previous research has identified NAO and ENSO as main drivers for extending streamflow forecast lead-time in the UCRB. Inclusion of "Hondo Region" SST information further improve the model's forecasting ability. The overall results of this study revealed that the annual streamflow of the UCRB is significantly influenced by predefine climate modes and the proposed SVM modeling technique incorporating oceanic-atmospheric oscillations is expected to be useful to water managers in the long-term management of the water resources within the UCRB.

Heat-driven spin torques in antiferromagnets

NASA Astrophysics Data System (ADS)

Białek, Marcin; Bréchet, Sylvain; Ansermet, Jean-Philippe

2018-04-01

Heat-driven magnetization damping, which is a linear function of a temperature gradient, is predicted in antiferromagnets by considering the sublattice dynamics subjected to a heat-driven spin torque. This points to the possibility of achieving spin torque oscillator behavior. The model is based on the magnetic Seebeck effect acting on sublattices which are exchange coupled. The heat-driven spin torque is estimated and the feasibility of detecting this effect is discussed.

Dynamical relationship between wind speed magnitude and meridional temperature contrast: Application to an interannual oscillation in Venusian middle atmosphere GCM

NASA Astrophysics Data System (ADS)

Yamamoto, Masaru; Takahashi, Masaaki

2018-03-01

We derive simple dynamical relationships between wind speed magnitude and meridional temperature contrast. The relationship explains scatter plot distributions of time series of three variables (maximum zonal wind speed UMAX, meridional wind speed VMAX, and equator-pole temperature contrast dTMAX), which are obtained from a Venus general circulation model with equatorial Kelvin-wave forcing. Along with VMAX and dTMAX, UMAX likely increases with the phase velocity and amplitude of a forced wave. In the scatter diagram of UMAX versus dTMAX, points are plotted along a linear equation obtained from a thermal-wind relationship in the cloud layer. In the scatter diagram of VMAX versus UMAX, the apparent slope is somewhat steep in the high UMAX regime, compared with the low UMAX regime. The scatter plot distributions are qualitatively consistent with a quadratic equation obtained from a diagnostic equation of the stream function above the cloud top. The plotted points in the scatter diagrams form a linear cluster for weak wave forcing, whereas they form a small cluster for strong wave forcing. An interannual oscillation of the general circulation forming the linear cluster in the scatter diagram is apparent in the experiment of weak 5.5-day wave forcing. Although a pair of equatorial Kelvin and high-latitude Rossby waves with a same period (Kelvin-Rossby wave) produces equatorward heat and momentum fluxes in the region below 60 km, the equatorial wave does not contribute to the long-period oscillation. The interannual fluctuation of the high-latitude jet core leading to the time variation of UMAX is produced by growth and decay of a polar mixed Rossby-gravity wave with a 14-day period.

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmic flows and cosmic web from luminous red galaxies

NASA Astrophysics Data System (ADS)

Ata, Metin; Kitaura, Francisco-Shu; Chuang, Chia-Hsun; Rodríguez-Torres, Sergio; Angulo, Raul E.; Ferraro, Simone; Gil-Marín, Hector; McDonald, Patrick; Hernández Monteagudo, Carlos; Müller, Volker; Yepes, Gustavo; Autefage, Mathieu; Baumgarten, Falk; Beutler, Florian; Brownstein, Joel R.; Burden, Angela; Eisenstein, Daniel J.; Guo, Hong; Ho, Shirley; McBride, Cameron; Neyrinck, Mark; Olmstead, Matthew D.; Padmanabhan, Nikhil; Percival, Will J.; Prada, Francisco; Rossi, Graziano; Sánchez, Ariel G.; Schlegel, David; Schneider, Donald P.; Seo, Hee-Jong; Streblyanska, Alina; Tinker, Jeremy; Tojeiro, Rita; Vargas-Magana, Mariana

2017-06-01

We present a Bayesian phase-space reconstruction of the cosmic large-scale matter density and velocity fields from the Sloan Digital Sky Survey-III Baryon Oscillations Spectroscopic Survey Data Release 12 CMASS galaxy clustering catalogue. We rely on a given Λ cold dark matter cosmology, a mesh resolution in the range of 6-10 h-1 Mpc, and a lognormal-Poisson model with a redshift-dependent non-linear bias. The bias parameters are derived from the data and a general renormalized perturbation theory approach. We use combined Gibbs and Hamiltonian sampling, implemented in the argo code, to iteratively reconstruct the dark matter density field and the coherent peculiar velocities of individual galaxies, correcting hereby for coherent redshift space distortions. Our tests relying on accurate N-body-based mock galaxy catalogues show unbiased real space power spectra of the non-linear density field up to k ˜ 0.2 h Mpc-1, and vanishing quadrupoles down to r ˜ 20 h-1 Mpc. We also demonstrate that the non-linear cosmic web can be obtained from the tidal field tensor based on the Gaussian component of the reconstructed density field. We find that the reconstructed velocities have a statistical correlation coefficient compared to the true velocities of each individual light-cone mock galaxy of r ˜ 0.68 including about 10 per cent of satellite galaxies with virial motions (about r = 0.75 without satellites). The power spectra of the velocity divergence agree well with theoretical predictions up to k ˜ 0.2 h Mpc-1. This work will be especially useful to improve, for example, baryon acoustic oscillation reconstructions, kinematic Sunyaev-Zeldovich, integrated Sachs-Wolfe measurements or environmental studies.

Effects of aging in catastrophe on the steady state and dynamics of a microtubule population

NASA Astrophysics Data System (ADS)

Jemseena, V.; Gopalakrishnan, Manoj

2015-05-01

Several independent observations have suggested that the catastrophe transition in microtubules is not a first-order process, as is usually assumed. Recent in vitro observations by Gardner et al. [M. K. Gardner et al., Cell 147, 1092 (2011), 10.1016/j.cell.2011.10.037] showed that microtubule catastrophe takes place via multiple steps and the frequency increases with the age of the filament. Here we investigate, via numerical simulations and mathematical calculations, some of the consequences of the age dependence of catastrophe on the dynamics of microtubules as a function of the aging rate, for two different models of aging: exponential growth, but saturating asymptotically, and purely linear growth. The boundary demarcating the steady-state and non-steady-state regimes in the dynamics is derived analytically in both cases. Numerical simulations, supported by analytical calculations in the linear model, show that aging leads to nonexponential length distributions in steady state. More importantly, oscillations ensue in microtubule length and velocity. The regularity of oscillations, as characterized by the negative dip in the autocorrelation function, is reduced by increasing the frequency of rescue events. Our study shows that the age dependence of catastrophe could function as an intrinsic mechanism to generate oscillatory dynamics in a microtubule population, distinct from hitherto identified ones.

Demonstration of nonlinear effects in acoustic landmine experiments using a clamped-plate soil oscillator

NASA Astrophysics Data System (ADS)

Korman, Murray S.; Bond, Emilia

2005-09-01

Current nonlinear experiments involving the detection of plastic landmines using acoustic-to-seismic coupling have been developed from Sabatier's (linear) and Donskoy's (nonlinear) earlier methods. A laboratory apparatus called the soil-plate oscillator has been developed at the National Center for Physical Acoustics, and later at the U.S. Naval Academy, to model acoustic mine detection. The apparatus consists of a thick-walled cylinder filled with sifted homogeneous soil resting on a thin elastic plate that is clamped to the bottom of the column. It represents a good simplified physical model for VS 1.6 and VS 2.2 inert anti-tank plastic buried landmines. Using a loudspeaker (located over the soil) that is driven by a swept sinusoid, tuning curve experiments are performed. The vibration amplitude versus frequency is measured on a swept spectrum analyzer using an accelerometer located on the soil-air interface or under the plate. The backbone curve shows a linear decrease in peak frequency versus increasing amplitude. A two-tone test experiment is performed using two loudspeakers generating acoustic frequencies (closely spaced on either side of resonance, typically ~100 Hz). A rich vibration spectrum of combination frequency tones (along with the primaries) is observed which is characteristic of actual nonlinear detection schemes.

Algebraic motion of vertically displacing plasmas

NASA Astrophysics Data System (ADS)

Bhattacharjee, Amitava; Pfefferle, David; Hirvijoki, Eero

2017-10-01

The vertical displacement of tokamak plasmas is modelled during the non-linear phase by a free-moving current-carrying rod coupled to a set of fixed conducting wires and a cylindrical conducting shell. The models capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the vacuum vessel. The plasma is assumed not to vary during the VDE such that it behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented from coming in contact with the wall due to steep effective potential barriers by the eddy currents, and will hence oscillate at Alfvénic frequencies about a given force-free position. In addition to damping oscillations, resistivity allows for the column to drift towards the vessel on slow flux penetration timescales. The initial exponential motion of the plasma, i.e. the resistive vertical instability, is succeeded by a non-linear sinking behaviour, that is shown analytically to be algebraic and decelerative. The acceleration of the plasma column often observed in experiments is thus conjectured to originate from an early sharing of toroidal current between the core, the halo plasma and the wall or from the thermal quench dynamics precipitating loss of plasma current

Structure of resonances and formation of stationary points in symmetrical chains of bilinear oscillators

NASA Astrophysics Data System (ADS)

Dyskin, Arcady V.; Pasternak, Elena; Shufrin, Igor

2014-12-01

Dynamics of strongly nonlinear systems can in many cases be modelled by bilinear oscillators, which are the oscillators whose springs have different stiffnesses in compression and tension. This underpins the analysis of a wide range of phenomena, from oscillations of fragmented structures, connections and mooring lines to deformation of geological media. Single bilinear oscillators were studied previously and the presence of multiple resonances both super- and sub-harmonic was found. Less attention was paid to systems of multiple bilinear oscillators that describe many natural and engineering processes such as for example the behaviour of fragmented solids. Here we fill this gap concentrating on the simplest case - 1D symmetrical chains of bilinear oscillators. We show that the presence and structure of resonances in a symmetric chain of bilinear oscillators with fixed ends depends upon the number of oscillating masses. Two elementary chains act as the basic ones: a single mass bilinear chain (a mass connected to the fixed points by two bilinear springs) that behaves as a linear oscillator with a single resonance and a two mass chain that is a coupled bilinear oscillator (two masses connected by three bilinear springs). The latter has multiple resonances. We demonstrate that longer chains either do not have resonances or get decomposed, in the resonance, into either the single mass or two mass elementary chains with stationary masses in between. The resonance frequencies are inherited from the basic chains of decomposition. We show that if the number of masses is odd the chain can be decomposed into the single mass bilinear chains separated by stationary masses. It then inherits the resonances of the single mass bilinear chain. The chains with the number of masses minus 2 divisible by 3 can be decomposed into the two mass bilinear chains separated by stationary masses and inherit the resonances of the two mass chains. The chains whose lengths satisfy both criteria (such as chains with 5, 11, 17 … masses) allow both types of resonances.

0.5 V 5.8 GHz highly linear current-reuse voltage-controlled oscillator with back-gate tuning technique

NASA Astrophysics Data System (ADS)

Ikeda, Sho; Lee, Sang-Yeop; Ito, Hiroyuki; Ishihara, Noboru; Masu, Kazuya

2015-04-01

In this paper, we present a voltage-controlled oscillator (VCO), which achieves highly linear frequency tuning under a low supply voltage of 0.5 V. To obtain the linear frequency tuning of a VCO, the high linearity of the threshold voltage of a varactor versus its back-gate voltage is utilized. This enables the linear capacitance tuning of the varactor; thus, a highly linear VCO can be achieved. In addition, to decrease the power consumption of the VCO, a current-reuse structure is employed as a cross-coupled pair. The proposed VCO was fabricated using a 65 nm Si complementary metal oxide semiconductor (CMOS) process. It shows the ratio of the maximum VCO gain (KVCO) to the minimum one to be 1.28. The dc power consumption is 0.33 mW at a supply voltage of 0.5 V. The measured phase noise at 10 MHz offset is -123 dBc/Hz at an output frequency of 5.8 GHz.

On coherent oscillations of a string.

NASA Technical Reports Server (NTRS)

Liu, C. H.

1972-01-01

Vibrations of an elastic string when the separation between the ends varies randomly are studied. The emphasis is on the evolution of the coherent, or ordered, oscillations of the string. Using a perturbation technique borrowed from quantum field theory and the modified Kryloff-Bogoliuboff method, the 'multiple scattering' effect of the random separation between the ends on the linear and nonlinear coherent oscillations are investigated. It is found that due to the random interactions the coherent fundamental oscillation as well as the harmonies are damped. Their frequencies are also modified.

Surface Oscillations of a Free-Falling Droplet of an Ideal Fluid

NASA Astrophysics Data System (ADS)

Kistovich, A. V.; Chashechkin, Yu. D.

2018-03-01

According to observations, drops freely falling in the air under the action of gravity are deformed and oscillate in a wide range of frequencies and scales. A technique for calculating surface axisymmetric oscillations of a deformed droplet in the linear approximation under the assumption that the amplitude and wavelength are small when compared to the droplet diameter is proposed. The basic form of an axisymmetric droplet is chosen from observations. The calculation results for surface oscillations agree with recorded data on the varying shape of water droplets falling in the air.

Circadian Rhythms in Cyanobacteria

PubMed Central

Golden, Susan S.

2015-01-01

SUMMARY Life on earth is subject to daily and predictable fluctuations in light intensity, temperature, and humidity created by rotation of the earth. Circadian rhythms, generated by a circadian clock, control temporal programs of cellular physiology to facilitate adaptation to daily environmental changes. Circadian rhythms are nearly ubiquitous and are found in both prokaryotic and eukaryotic organisms. Here we introduce the molecular mechanism of the circadian clock in the model cyanobacterium Synechococcus elongatus PCC 7942. We review the current understanding of the cyanobacterial clock, emphasizing recent work that has generated a more comprehensive understanding of how the circadian oscillator becomes synchronized with the external environment and how information from the oscillator is transmitted to generate rhythms of biological activity. These results have changed how we think about the clock, shifting away from a linear model to one in which the clock is viewed as an interactive network of multifunctional components that are integrated into the context of the cell in order to pace and reset the oscillator. We conclude with a discussion of how this basic timekeeping mechanism differs in other cyanobacterial species and how information gleaned from work in cyanobacteria can be translated to understanding rhythmic phenomena in other prokaryotic systems. PMID:26335718

Wave propagation in a strongly nonlinear locally resonant granular crystal

NASA Astrophysics Data System (ADS)

Vorotnikov, K.; Starosvetsky, Y.; Theocharis, G.; Kevrekidis, P. G.

2018-02-01

In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact, containing linear resonators. The relevant model is presented and examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results. The generic dynamics of the system involves a degradation of the well-known traveling pulse of the standard Hertzian chain of elastic beads. Nevertheless, the present system is richer, in that as the primary pulse decays, secondary ones emerge and eventually interfere with it creating modulated wavetrains. Remarkably, upon suitable choices of parameters, this interference "distills" a weakly nonlocal solitary wave (a "nanopteron"). This motivates the consideration of such nonlinear structures through a separate Fourier space technique, whose results suggest the existence of such entities not only with a single-side tail, but also with periodic tails on both ends. These tails are found to oscillate with the intrinsic oscillation frequency of the out-of-phase motion between the outer hollow bead and its internal linear attachment.

REVIEWS OF TOPICAL PROBLEMS: Free oscillations of the sun and the giant planets

NASA Astrophysics Data System (ADS)

Vorontsov, S. V.; Zharkov, V. N.

1981-08-01

The current state of research on the free oscillations of the sun is reviewed. Observational data on oscillations with periods from 5 to 160 min published through the end of 1980 are described. The interpretation of these data in connection with research on the internal structure of the sun is discussed. A theory of the free oscillations in the linear adiabatic approximation is described; differential rotation is taken into account. The principles for classifying the theoretical normal modes are discussed. The problem of the excitation of the solar oscillations is outlined. The theoretical normal-mode spectra of Jupiter and Saturn are discussed.

Fluid-structure interaction of a rolling restrained body of revolution at high angles of attack

NASA Astrophysics Data System (ADS)

Degani, D.; Ishay, M.; Gottlieb, O.

2017-03-01

The current work investigates numerically rolling instabilities of a free-to-roll slender rigid-body of revolution placed in a wind tunnel at a high angle of attack. The resistance to the roll moment is represented by a linear torsion spring and equivalent linear damping representing friction in the bearings of a simulated wind tunnel model. The body is subjected to a three-dimensional, compressible, laminar flow. The full Navier-Stokes equations are solved using the second-order implicit finite difference Beam-Warming scheme, adapted to a curvilinear coordinate system, whereas the coupled structural second order equation of motion for roll is solved by a fourth-order Runge-Kutta method. The body consists of a 3.5-diameter tangent ogive forebody with a 7.0-diameter long cylindrical afterbody extending aft of the nose-body junction to x/D = 10.5. We describe in detail the investigation of three angles of attack 20°, 40°, and 65°, at a Reynolds number of 30 000 (based on body diameter) and a Mach number of 0.2. Three distinct configurations are investigated as follows: a fixed body, a free-to-roll body with a weak torsion spring, and a free-to-roll body with a strong torsion spring. For each angle of attack the free-to-roll configuration portrays a distinct and different behavior pattern, including bi-stable limit-cycle oscillations. The bifurcation structure incorporates both large and small amplitude periodic roll oscillations where the latter lose their periodicity with increasing stiffness of the restraining spring culminating with distinct quasiperiodic oscillations. We note that removal of an applied upstream disturbance for a restrained body does not change the magnitude or complexity of the oscillations or of the flow patterns along the body. Depending on structure characteristics and flow conditions even a small rolling moment coefficient at the relatively low angle of attack of 20° may lead to large amplitude resonant roll oscillations.

A time-domain digitally controlled oscillator composed of a free running ring oscillator and flying-adder

NASA Astrophysics Data System (ADS)

Wei, Liu; Wei, Li; Peng, Ren; Qinglong, Lin; Shengdong, Zhang; Yangyuan, Wang

2009-09-01

A time-domain digitally controlled oscillator (DCO) is proposed. The DCO is composed of a free-running ring oscillator (FRO) and a two lap-selectors integrated flying-adder (FA). With a coiled cell array which allows uniform loading capacitances of the delay cells, the FRO produces 32 outputs with consistent tap spacing for the FA as reference clocks. The FA uses the outputs from the FRO to generate the output of the DCO according to the control number, resulting in a linear dependence of the output period, instead of the frequency on the digital controlling word input. Thus the proposed DCO ensures a good conversion linearity in a time-domain, and is suitable for time-domain all-digital phase locked loop applications. The DCO was implemented in a standard 0.13 μm digital logic CMOS process. The measurement results show that the DCO has a linear and monotonic tuning curve with gain variation of less than 10%, and a very low root mean square period jitter of 9.3 ps in the output clocks. The DCO works well at supply voltages ranging from 0.6 to 1.2 V, and consumes 4 mW of power with 500 MHz frequency output at 1.2 V supply voltage.

How a small noise generates large-amplitude oscillations of volcanic plug and provides high seismicity

NASA Astrophysics Data System (ADS)

Alexandrov, Dmitri V.; Bashkirtseva, Irina A.; Ryashko, Lev B.

2015-04-01

A non-linear behavior of dynamic model of the magma-plug system under the action of N-shaped friction force and stochastic disturbances is studied. It is shown that the deterministic dynamics essentially depends on the mutual arrangement of an equilibrium point and the friction force branches. Variations of this arrangement imply bifurcations, birth and disappearance of stable limit cycles, changes of the stability of equilibria, system transformations between mono- and bistable regimes. A slope of the right increasing branch of the friction function is responsible for the formation of such regimes. In a bistable zone, the noise generates transitions between small and large amplitude stochastic oscillations. In a monostable zone with single stable equilibrium, a new dynamic phenomenon of noise-induced generation of large amplitude stochastic oscillations in the plug rate and pressure is revealed. A beat-type dynamics of the plug displacement under the influence of stochastic forcing is studied as well.

Rotational dynamics of bases in the gene coding interferon alpha 17 (IFNA17).

PubMed

Krasnobaeva, L A; Yakushevich, L V

2015-02-01

In the present work, rotational oscillations of nitrogenous bases in the DNA with the sequence of the gene coding interferon alpha 17 (IFNA17), are investigated. As a mathematical model simulating oscillations of the bases, we use a system of two coupled nonlinear partial differential equations that takes into account effects of dissipation, action of external fields and dependence of the equation coefficients on the sequence of bases. We apply the methods of the theory of oscillations to solve the equations in the linear approach and to construct the dispersive curves determining the dependence of the frequency of the plane waves (ω) on the wave vector (q). In the nonlinear case, the solutions in the form of kink are considered, and the main characteristics of the kink: the rest energy (E0), the rest mass (m0), the size (d) and sound velocity (C0), are calculated. With the help of the energetic method, the kink velocity (υ), the path (S), and the lifetime (τ) are also obtained.

Bubble oscillation and inertial cavitation in viscoelastic fluids.

PubMed

Jiménez-Fernández, J; Crespo, A

2005-08-01

Non-linear acoustic oscillations of gas bubbles immersed in viscoelastic fluids are theoretically studied. The problem is formulated by considering a constitutive equation of differential type with an interpolated time derivative. With the aid of this rheological model, fluid elasticity, shear thinning viscosity and extensional viscosity effects may be taken into account. Bubble radius evolution in time is analyzed and it is found that the amplitude of the bubble oscillations grows drastically as the Deborah number (the ratio between the relaxation time of the fluid and the characteristic time of the flow) increases, so that, even for moderate values of the external pressure amplitude, the behavior may become chaotic. The quantitative influence of the rheological fluid properties on the pressure thresholds for inertial cavitation is investigated. Pressure thresholds values in terms of the Deborah number for systems of interest in ultrasonic biomedical applications, are provided. It is found that these critical pressure amplitudes are clearly reduced as the Deborah number is increased.

Analysis of spontaneous oscillations for a three-state power-stroke model.

PubMed

Washio, Takumi; Hisada, Toshiaki; Shintani, Seine A; Higuchi, Hideo

2017-02-01

Our study considers the mechanism of the spontaneous oscillations of molecular motors that are driven by the power stroke principle by applying linear stability analysis around the stationary solution. By representing the coupling equation of microscopic molecular motor dynamics and mesoscopic sarcomeric dynamics by a rank-1 updated matrix system, we derived the analytical representations of the eigenmodes of the Jacobian matrix that cause the oscillation. Based on these analytical representations, we successfully derived the essential conditions for the oscillation in terms of the rate constants of the power stroke and the reversal stroke transitions of the molecular motor. Unlike the two-state model, in which the dependence of the detachment rates on the motor coordinates or the applied forces on the motors plays a key role for the oscillation, our three-state power stroke model demonstrates that the dependence of the rate constants of the power and reversal strokes on the strains in the elastic elements in the motor molecules plays a key role, where these rate constants are rationally determined from the free energy available for the power stroke, the stiffness of the elastic element in the molecular motor, and the working stroke size. By applying the experimentally confirmed values to the free energy, the stiffness, and the working stroke size, our numerical model reproduces well the experimentally observed oscillatory behavior. Furthermore, our analysis shows that two eigenmodes with real positive eigenvalues characterize the oscillatory behavior, where the eigenmode with the larger eigenvalue indicates the transient of the system of the quick sarcomeric lengthening induced by the collective reversal strokes, and the smaller eigenvalue correlates with the speed of sarcomeric shortening, which is much slower than lengthening. Applying the perturbation analyses with primal physical parameters, we find that these two real eigenvalues occur on two branches derived from a merge point of a pair of complex-conjugate eigenvalues generated by Hopf bifurcation.

Quantum Drude oscillator model of atoms and molecules: Many-body polarization and dispersion interactions for atomistic simulation

NASA Astrophysics Data System (ADS)

Jones, Andrew P.; Crain, Jason; Sokhan, Vlad P.; Whitfield, Troy W.; Martyna, Glenn J.

2013-04-01

Treating both many-body polarization and dispersion interactions is now recognized as a key element in achieving the level of atomistic modeling required to reveal novel physics in complex systems. The quantum Drude oscillator (QDO), a Gaussian-based, coarse grained electronic structure model, captures both many-body polarization and dispersion and has linear scale computational complexity with system size, hence it is a leading candidate next-generation simulation method. Here, we investigate the extent to which the QDO treatment reproduces the desired long-range atomic and molecular properties. We present closed form expressions for leading order polarizabilities and dispersion coefficients and derive invariant (parameter-free) scaling relationships among multipole polarizability and many-body dispersion coefficients that arise due to the Gaussian nature of the model. We show that these “combining rules” hold to within a few percent for noble gas atoms, alkali metals, and simple (first-row hydride) molecules such as water; this is consistent with the surprising success that models with underlying Gaussian statistics often exhibit in physics. We present a diagrammatic Jastrow-type perturbation theory tailored to the QDO model that serves to illustrate the rich types of responses that the QDO approach engenders. QDO models for neon, argon, krypton, and xenon, designed to reproduce gas phase properties, are constructed and their condensed phase properties explored via linear scale diffusion Monte Carlo (DMC) and path integral molecular dynamics (PIMD) simulations. Good agreement with experimental data for structure, cohesive energy, and bulk modulus is found, demonstrating a degree of transferability that cannot be achieved using current empirical models or fully ab initio descriptions.

Rigorous Model Reduction for a Damped-Forced Nonlinear Beam Model: An Infinite-Dimensional Analysis

NASA Astrophysics Data System (ADS)

Kogelbauer, Florian; Haller, George

2018-06-01

We use invariant manifold results on Banach spaces to conclude the existence of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces of the linearized beam equation. Reduction in the governing PDE to SSMs provides an explicit low-dimensional model which captures the correct asymptotics of the full, infinite-dimensional dynamics. Our approach is general enough to admit extensions to other types of continuum vibrations. The model-reduction procedure we employ also gives guidelines for a mathematically self-consistent modeling of damping in PDEs describing structural vibrations.

Stall flutter experiment in a transonic oscillating linear cascade

NASA Technical Reports Server (NTRS)

Boldman, D. R.; Buggele, A. E.; Michalson, G. M.

1981-01-01

Two dimensional biconvex airfoils were oscillated at reduced frequencies up to 0.5 based on semi-chord and a free stream Mach number of 0.80 to simulate transonic stall flutter in rotors. Steady-state periodicity was confirmed through end-wall pressure measurements, exit flow traverses, and flow visualization. The initial flow visualization results from flutter tests indicated that the oscillating shock on the airfoils lagged the airfoil motion by as much as 80 deg. These initial data exhibited an appreciable amount of scatter; however, a linear fit of the results indicated that the greatest shock phase lag occurred at a positive interblade phase angle. Photographs of the steady-state and unsteady flow fields reveal some of the features of the lambda shock wave on the suction surface of the airfoils.

The human oculomotor response to simultaneous visual and physical movements at two different frequencies

NASA Technical Reports Server (NTRS)

Wall, C.; Assad, A.; Aharon, G.; Dimitri, P. S.; Harris, L. R.

2001-01-01

In order to investigate interactions in the visual and vestibular systems' oculomotor response to linear movement, we developed a two-frequency stimulation technique. Thirteen subjects lay on their backs and were oscillated sinusoidally along their z-axes at between 0.31 and 0.81 Hz. During the oscillation subjects viewed a large, high-contrast, visual pattern oscillating in the same direction as the physical motion but at a different, non-harmonically related frequency. The evoked eye movements were measured by video-oculography and spectrally analysed. We found significant signal level at the sum and difference frequencies as well as at other frequencies not present in either stimulus. The emergence of new frequencies indicates non-linear processing consistent with an agreement-detector system that have previously proposed.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin method for the Biot’s consolidation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Random mechanics: Nonlinear vibrations, turbulences, seisms, swells, fatigue

NASA Astrophysics Data System (ADS)

Kree, P.; Soize, C.

The random modeling of physical phenomena, together with probabilistic methods for the numerical calculation of random mechanical forces, are analytically explored. Attention is given to theoretical examinations such as probabilistic concepts, linear filtering techniques, and trajectory statistics. Applications of the methods to structures experiencing atmospheric turbulence, the quantification of turbulence, and the dynamic responses of the structures are considered. A probabilistic approach is taken to study the effects of earthquakes on structures and to the forces exerted by ocean waves on marine structures. Theoretical analyses by means of vector spaces and stochastic modeling are reviewed, as are Markovian formulations of Gaussian processes and the definition of stochastic differential equations. Finally, random vibrations with a variable number of links and linear oscillators undergoing the square of Gaussian processes are investigated.

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

NASA Astrophysics Data System (ADS)

Stankiewicz, Witold; Morzyński, Marek; Kotecki, Krzysztof; Noack, Bernd R.

2017-04-01

We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier-Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier-Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limit-cycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.

Multiscale characterization and prediction of monsoon rainfall in India using Hilbert-Huang transform and time-dependent intrinsic correlation analysis

NASA Astrophysics Data System (ADS)

Adarsh, S.; Reddy, M. Janga

2017-07-01

In this paper, the Hilbert-Huang transform (HHT) approach is used for the multiscale characterization of All India Summer Monsoon Rainfall (AISMR) time series and monsoon rainfall time series from five homogeneous regions in India. The study employs the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) for multiscale decomposition of monsoon rainfall in India and uses the Normalized Hilbert Transform and Direct Quadrature (NHT-DQ) scheme for the time-frequency characterization. The cross-correlation analysis between orthogonal modes of All India monthly monsoon rainfall time series and that of five climate indices such as Quasi Biennial Oscillation (QBO), El Niño Southern Oscillation (ENSO), Sunspot Number (SN), Atlantic Multi Decadal Oscillation (AMO), and Equatorial Indian Ocean Oscillation (EQUINOO) in the time domain showed that the links of different climate indices with monsoon rainfall are expressed well only for few low-frequency modes and for the trend component. Furthermore, this paper investigated the hydro-climatic teleconnection of ISMR in multiple time scales using the HHT-based running correlation analysis technique called time-dependent intrinsic correlation (TDIC). The results showed that both the strength and nature of association between different climate indices and ISMR vary with time scale. Stemming from this finding, a methodology employing Multivariate extension of EMD and Stepwise Linear Regression (MEMD-SLR) is proposed for prediction of monsoon rainfall in India. The proposed MEMD-SLR method clearly exhibited superior performance over the IMD operational forecast, M5 Model Tree (MT), and multiple linear regression methods in ISMR predictions and displayed excellent predictive skill during 1989-2012 including the four extreme events that have occurred during this period.

Quantum Theories of Self-Localization

NASA Astrophysics Data System (ADS)

Bernstein, Lisa Joan

In the classical dynamics of coupled oscillator systems, nonlinearity leads to the existence of stable solutions in which energy remains localized for all time. Here the quantum-mechanical counterpart of classical self-localization is investigated in the context of two model systems. For these quantum models, the terms corresponding to classical nonlinearities modify a subset of the stationary quantum states to be particularly suited to the creation of nonstationary wavepackets that localize energy for long times. The first model considered here is the Quantized Discrete Self-Trapping model (QDST), a system of anharmonic oscillators with linear dispersive coupling used to model local modes of vibration in polyatomic molecules. A simple formula is derived for a particular symmetry class of QDST systems which gives an analytic connection between quantum self-localization and classical local modes. This formula is also shown to be useful in the interpretation of the vibrational spectra of some molecules. The second model studied is the Frohlich/Einstein Dimer (FED), a two-site system of anharmonically coupled oscillators based on the Frohlich Hamiltonian and motivated by the theory of Davydov solitons in biological protein. The Born-Oppenheimer perturbation method is used to obtain approximate stationary state wavefunctions with error estimates for the FED at the first excited level. A second approach is used to reduce the first excited level FED eigenvalue problem to a system of ordinary differential equations. A simple theory of low-energy self-localization in the FED is discussed. The quantum theories of self-localization in the intrinsic QDST model and the extrinsic FED model are compared.

Renormalization Group for nonlinear oscillators in the absence of linear restoring force

NASA Astrophysics Data System (ADS)

Sarkar, A.; Bhattacharjee, J. K.

2010-09-01

Perturbative Renormalization Group (RG) has been very useful in probing periodic orbits in two-dimensional dynamical systems (Sarkar A., Bhattacharjee J. K., Chakraborty S. and Banerjee D., arXiv:1005.2858v1 (2010)). The method relies on finding a linear center, around which perturbation analysis is done. However it is not obvious as to how systems devoid of any linear terms may be approached using this method. We propose here how RG can be done even in the absence of linear terms. We successfully apply the method to extract correct results for a variant of the second-order Riccati equation. In this variant the periodic orbit disappears as a parameter is varied. Our RG captures this disappearance correctly. We have also applied the technique successfully on the force-free Van der Pol-Duffing oscillator.

Potential Factors Affecting Survival Differ by Run-Timing and Location: Linear Mixed-Effects Models of Pacific Salmonids (Oncorhynchus spp.) in the Klamath River, California

PubMed Central

Quiñones, Rebecca M.; Holyoak, Marcel; Johnson, Michael L.; Moyle, Peter B.

2014-01-01

Understanding factors influencing survival of Pacific salmonids (Oncorhynchus spp.) is essential to species conservation, because drivers of mortality can vary over multiple spatial and temporal scales. Although recent studies have evaluated the effects of climate, habitat quality, or resource management (e.g., hatchery operations) on salmonid recruitment and survival, a failure to look at multiple factors simultaneously leaves open questions about the relative importance of different factors. We analyzed the relationship between ten factors and survival (1980–2007) of four populations of salmonids with distinct life histories from two adjacent watersheds (Salmon and Scott rivers) in the Klamath River basin, California. The factors were ocean abundance, ocean harvest, hatchery releases, hatchery returns, Pacific Decadal Oscillation, North Pacific Gyre Oscillation, El Niño Southern Oscillation, snow depth, flow, and watershed disturbance. Permutation tests and linear mixed-effects models tested effects of factors on survival of each taxon. Potential factors affecting survival differed among taxa and between locations. Fall Chinook salmon O. tshawytscha survival trends appeared to be driven partially or entirely by hatchery practices. Trends in three taxa (Salmon River spring Chinook salmon, Scott River fall Chinook salmon; Salmon River summer steelhead trout O. mykiss) were also likely driven by factors subject to climatic forcing (ocean abundance, summer flow). Our findings underscore the importance of multiple factors in simultaneously driving population trends in widespread species such as anadromous salmonids. They also show that the suite of factors may differ among different taxa in the same location as well as among populations of the same taxa in different watersheds. In the Klamath basin, hatchery practices need to be reevaluated to protect wild salmonids. PMID:24866173

Self-Synchronized Phenomena Generated in Rotor-Type Oscillators: On the Influence of Coupling Condition between Oscillators

NASA Astrophysics Data System (ADS)

Bonkobara, Yasuhiro; Mori, Hiroki; Kondou, Takahiro; Ayabe, Takashi

Self-synchronized phenomena generated in rotor-type oscillators mounted on a straight-line spring-mass system are investigated experimentally and analytically. In the present study, we examine the occurrence region and pattern of self-synchronization in two types of coupled oscillators: rigidly coupled oscillators and elastically coupled oscillators. It is clarified that the existence regions of stable solutions are governed mainly by the linear natural frequency of each spring-mass system. The results of numerical analysis confirm that the self-synchronized solutions of the elastically coupled oscillators correspond to those of the rigidly coupled oscillators. In addition, the results obtained in the present study are compared with the previously reported results for a metronome system and a moving apparatus and the different properties of the phenomena generated in the rotor-type oscillators and the pendulum-type oscillators are shown in terms of the construction of branches of self-synchronized solution and the stability.

The Global Warming Hiatus Tied to the North Atlantic Oscillation and Its Prediction

NASA Astrophysics Data System (ADS)

Li, J.; Sun, C.

2015-12-01

The twentieth century Northern Hemisphere mean surface temperature (NHT) is characterized by a multidecadal warming-cooling-warming pattern followed by a flat trend since about 2000 (recent warming hiatus). Here we demonstrate that the multidcadal variability in NHT including the recent warming hiatus is tied to the North Atlantic Oscillation (NAO) and the NAO is implicated as a useful predictor of NHT multidecadal variability. Observational analysis shows that the NAO leads both the detrended NHT and oceanic Atlantic Multidecadal Oscillation (AMO) by 15-20 years. Theoretical analysis illuminates that the NAO precedes NHT multidecadal variability through its delayed effect on the AMO due to the large thermal inertia associated with slow oceanic processes. The CCSM4 model is employed to investigate possible physical mechanisms. The positive NAO forces the strengthening of the Atlantic meridional overturning circulation (AMOC) and induces a basin-wide uniform sea surface temperature (SST) warming that corresponds to the AMO. The SST field exhibits a delayed response to the preceding enhanced AMOC, and shows a pattern similar to the North Atlantic tripole (NAT), with SST warming in the northern North Atlantic and cooling in the southern part. This SST pattern (negative NAT phase) may lead to an atmospheric response that resembles the negative NAO phase, and subsequently the oscillation proceeds, but in the opposite sense. Based on these mechanisms, a simple delayed oscillator model is established to explain the quasi-periodic multidecadal variability of the NAO. The magnitude of the NAO forcing of the AMOC/AMO and the time delay of the AMOC/AMO feedback are two key parameters of the delayed oscillator. For a given set of parameters, the quasi 60-year cycle of the NAO can be well predicted. This delayed oscillator model is useful for understanding of the oscillatory mechanism of the NAO, which has potential for decadal predictions as well as the interpretation of proxy data records. An NAO-based linear model is therefore established to predict the NHT, which gives an excellent hindcast for NHT in 1971-2011 with the recent flat trend well predicted. NHT in 2012-2027 is predicted to fall slightly over the next decades, due to the recent NAO decadal weakening that temporarily offsets the anthropogenically induced warming.

CHARACTERIZING INTERMITTENCY OF 4-Hz QUASI-PERIODIC OSCILLATION IN XTE J1550–564 USING HILBERT–HUANG TRANSFORM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Su, Yi-Hao; Chou, Yi; Hu, Chin-Ping

We present time-frequency analysis results based on the Hilbert–Huang transform (HHT) for the evolution of a 4-Hz low-frequency quasi-periodic oscillation (LFQPO) around the black hole X-ray binary XTE J1550–564. The origin of LFQPOs is still debated. To understand the cause of the peak broadening, we utilized a recently developed time-frequency analysis, HHT, for tracking the evolution of the 4-Hz LFQPO from XTE J1550–564. By adaptively decomposing the ∼4-Hz oscillatory component from the light curve and acquiring its instantaneous frequency, the Hilbert spectrum illustrates that the LFQPO is composed of a series of intermittent oscillations appearing occasionally between 3 and 5more » Hz. We further characterized this intermittency by computing the confidence limits of the instantaneous amplitudes of the intermittent oscillations, and constructed both the distributions of the QPO’s high- and low-amplitude durations, which are the time intervals with and without significant ∼4-Hz oscillations, respectively. The mean high-amplitude duration is 1.45 s and 90% of the oscillation segments have lifetimes below 3.1 s. The mean low-amplitude duration is 0.42 s and 90% of these segments are shorter than 0.73 s. In addition, these intermittent oscillations exhibit a correlation between the oscillation’s rms amplitude and mean count rate. This correlation could be analogous to the linear rms-flux relation found in the 4-Hz LFQPO through Fourier analysis. We conclude that the LFQPO peak in the power spectrum is broadened owing to intermittent oscillations with varying frequencies, which could be explained by using the Lense–Thirring precession model.« less

Design and analysis of a shock absorber with variable moment of inertia for passive vehicle suspensions

NASA Astrophysics Data System (ADS)

Xu, Tongyi; Liang, Ming; Li, Chuan; Yang, Shuai

2015-10-01

A two-terminal mass (TTM) based vibration absorber with variable moment of inertia (VMI) for passive vehicle suspension is proposed. The VMI of the system is achieved by the motion of sliders embedded in a hydraulic driven flywheel. The moment of inertia increases in reaction to strong vertical vehicle oscillations and decreases for weak vertical oscillations. The hydraulic mechanism of the system converts the relative linear motion between the two terminals of the suspension into rotating motion of the flywheel. In the case of stronger vehicle vertical oscillation, the sliders inside the flywheel move away from the center of the flywheel because of the centrifugal force, hence yielding higher moment of inertia. The opposite is true in the case of weaker vehicle oscillation. As such, the moment of inertia adjusts itself adaptively in response to the road conditions. The performance of the proposed TTM-VMI absorber has been analyzed via dynamics modeling and simulation and further examined by experiments. In comparison to its counterpart with constant moment of inertia, the proposed VMI system offers faster response, better road handling and safety, improved ride comfort, and reduced suspension deflection except in the case of sinusoidal excitations.

El Nino-southern oscillation: A coupled response to the greenhouse effect?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, De-Zheng

The purpose of this article to elucidate the link between the El Nino-Southern Oscillation (ENSO) and radiative forcing (of which the greenhouse effect is a major part). A unified theory for the tropical Pacific climate is developed by considering the response of the coupled ocean-atmosphere to a changing radiative forcing. The hypothesis is that both the zonal surface sea temperature (SST) gradients and ENSO are a coupled response to the strong radiative heating or the tropical warmth. Owing to ocean-atmosphere interaction, the stronger the radiative heating, the larger the zonal SST gradients. When the SST gradients exceed a critical value,more » however, the ocean-atmosphere interaction in the cold-tongue region is too strong for the coupled system to hold steady. Consequently, the coupled system enters an oscillatory state. These coupled dynamics are examined in a simple mathematical model whose behavior is consistent with the hypothesis. With a linear temperature profile throughout the depth of subsurface ocean, the model predicts that both the magnitude and period of the oscillation increase with increases in radiative forcing or the greenhouse effect. The increase in the magnitude of the oscillation largely comes from an enhancement of the magnitude of the cold anomalies, while the increase in the period mostly comes from a prolonged duration of the warm events. With a profile in which the lapse rate decreases with depth, the sensitivity is more moderate. The simplicity of the model prevents a quantitative simulation of the sensitivity of ENSO to increases in the greenhouse effect, but qualitatively the model results support the empirical interpretation of the prolonged duration of the 1990-1995 ENSO event. 5 refs., 7 figs.« less

Fast fMRI can detect oscillatory neural activity in humans.

PubMed

Lewis, Laura D; Setsompop, Kawin; Rosen, Bruce R; Polimeni, Jonathan R

2016-10-25

Oscillatory neural dynamics play an important role in the coordination of large-scale brain networks. High-level cognitive processes depend on dynamics evolving over hundreds of milliseconds, so measuring neural activity in this frequency range is important for cognitive neuroscience. However, current noninvasive neuroimaging methods are not able to precisely localize oscillatory neural activity above 0.2 Hz. Electroencephalography and magnetoencephalography have limited spatial resolution, whereas fMRI has limited temporal resolution because it measures vascular responses rather than directly recording neural activity. We hypothesized that the recent development of fast fMRI techniques, combined with the extra sensitivity afforded by ultra-high-field systems, could enable precise localization of neural oscillations. We tested whether fMRI can detect neural oscillations using human visual cortex as a model system. We detected small oscillatory fMRI signals in response to stimuli oscillating at up to 0.75 Hz within single scan sessions, and these responses were an order of magnitude larger than predicted by canonical linear models. Simultaneous EEG-fMRI and simulations based on a biophysical model of the hemodynamic response to neuronal activity suggested that the blood oxygen level-dependent response becomes faster for rapidly varying stimuli, enabling the detection of higher frequencies than expected. Accounting for phase delays across voxels further improved detection, demonstrating that identifying vascular delays will be of increasing importance with higher-frequency activity. These results challenge the assumption that the hemodynamic response is slow, and demonstrate that fMRI has the potential to map neural oscillations directly throughout the brain.

Non-linear Relationship between BOLD Activation and Amplitude of Beta Oscillations in the Supplementary Motor Area during Rhythmic Finger Tapping and Internal Timing.

PubMed

Gompf, Florian; Pflug, Anja; Laufs, Helmut; Kell, Christian A

2017-01-01

Functional imaging studies using BOLD contrasts have consistently reported activation of the supplementary motor area (SMA) both during motor and internal timing tasks. Opposing findings, however, have been shown for the modulation of beta oscillations in the SMA. While movement suppresses beta oscillations in the SMA, motor and non-motor tasks that rely on internal timing increase the amplitude of beta oscillations in the SMA. These independent observations suggest that the relationship between beta oscillations and BOLD activation is more complex than previously thought. Here we set out to investigate this rapport by examining beta oscillations in the SMA during movement with varying degrees of internal timing demands. In a simultaneous EEG-fMRI experiment, 20 healthy right-handed subjects performed an auditory-paced finger-tapping task. Internal timing was operationalized by including conditions with taps on every fourth auditory beat, which necessitates generation of a slow internal rhythm, while tapping to every auditory beat reflected simple auditory-motor synchronization. In the SMA, BOLD activity increased and power in both the low and the high beta band decreased expectedly during each condition compared to baseline. Internal timing was associated with a reduced desynchronization of low beta oscillations compared to conditions without internal timing demands. In parallel with this relative beta power increase, internal timing activated the SMA more strongly in terms of BOLD. This documents a task-dependent non-linear relationship between BOLD and beta-oscillations in the SMA. We discuss different roles of beta synchronization and desynchronization in active processing within the same cortical region.

Response mechanisms of attached premixed flames subjected to harmonic forcing

NASA Astrophysics Data System (ADS)

Shreekrishna

The persistent thrust for a cleaner, greener environment has prompted air pollution regulations to be enforced with increased stringency by environmental protection bodies all over the world. This has prompted gas turbine manufacturers to move from nonpremixed combustion to lean, premixed combustion. These lean premixed combustors operate quite fuel-lean compared to the stochiometric, in order to minimize CO and NOx productions, and are very susceptible to oscillations in any of the upstream flow variables. These oscillations cause the heat release rate of the flame to oscillate, which can engage one or more acoustic modes of the combustor or gas turbine components, and under certain conditions, lead to limit cycle oscillations. This phenomenon, called thermoacoustic instabilities, is characterized by very high pressure oscillations and increased heat fluxes at system walls, and can cause significant problems in the routine operability of these combustors, not to mention the occasional hardware damages that could occur, all of which cumulatively cost several millions of dollars. In a bid towards understanding this flow-flame interaction, this research works studies the heat release response of premixed flames to oscillations in reactant equivalence ratio, reactant velocity and pressure, under conditions where the flame preheat zone is convectively compact to these disturbances, using the G-equation. The heat release response is quantified by means of the flame transfer function and together with combustor acoustics, forms a critical component of the analytical models that can predict combustor dynamics. To this end, low excitation amplitude (linear) and high excitation amplitude (nonlinear) responses of the flame are studied in this work. The linear heat release response of lean, premixed flames are seen to be dominated by responses to velocity and equivalence ratio fluctuations at low frequencies, and to pressure fluctuations at high frequencies which are in the vicinity of typical screech frequencies in gas turbine combustors. The nonlinear response problem is exclusively studied in the case of equivalence ratio coupling. Various nonlinearity mechanisms are identified, amongst which the crossover mechanisms, viz., stoichiometric and flammability crossovers, are seen to be responsible in causing saturation in the overall heat release magnitude of the flame. The response physics remain the same across various preheat temperatures and reactant pressures. Finally, comparisons between the chemiluminescence transfer function obtained experimentally and the heat release transfer functions obtained from the reduced order model (ROM) are performed for lean, CH4/Air swirl-stabilized, axisymmetric V-flames. While the comparison between the phases of the experimental and theoretical transfer functions are encouraging, their magnitudes show disagreement at lower Strouhal number gains show disagreement.

A GPS Phase-Locked Loop Performance Metric Based on the Phase Discriminator Output

PubMed Central

Stevanovic, Stefan; Pervan, Boris

2018-01-01

We propose a novel GPS phase-lock loop (PLL) performance metric based on the standard deviation of tracking error (defined as the discriminator’s estimate of the true phase error), and explain its advantages over the popular phase jitter metric using theory, numerical simulation, and experimental results. We derive an augmented GPS phase-lock loop (PLL) linear model, which includes the effect of coherent averaging, to be used in conjunction with this proposed metric. The augmented linear model allows more accurate calculation of tracking error standard deviation in the presence of additive white Gaussian noise (AWGN) as compared to traditional linear models. The standard deviation of tracking error, with a threshold corresponding to half of the arctangent discriminator pull-in region, is shown to be a more reliable/robust measure of PLL performance under interference conditions than the phase jitter metric. In addition, the augmented linear model is shown to be valid up until this threshold, which facilitates efficient performance prediction, so that time-consuming direct simulations and costly experimental testing can be reserved for PLL designs that are much more likely to be successful. The effect of varying receiver reference oscillator quality on the tracking error metric is also considered. PMID:29351250

Aeroelastic coupling of geometrically nonlinear structures and linear unsteady aerodynamics: Two formulations

NASA Astrophysics Data System (ADS)

Demasi, L.; Livne, E.

2009-07-01

Two different time domain formulations of integrating commonly used frequency-domain unsteady aerodynamic models based on a modal approach with full order finite element models for structures with geometric nonlinearities are presented. Both approaches are tailored to flight vehicle configurations where geometric stiffness effects are important but where deformations are moderate, flow is attached, and linear unsteady aerodynamic modeling is adequate, such as low aspect ratio wings or joined-wing and strut-braced wings at small to moderate angles of attack. Results obtained using the two approaches are compared using both planar and non-planar wing configurations. Sub-critical and post-flutter speeds are considered. It is demonstrated that the two methods lead to the same steady solution for the sub-critical case after the transients subside. It is also shown that the two methods predict the amplitude and frequency of limit cycle oscillation (when present) with the same accuracy.

On the analytical modeling of the nonlinear vibrations of pretensioned space structures

NASA Technical Reports Server (NTRS)

Housner, J. M.; Belvin, W. K.

1983-01-01

Pretensioned structures are receiving considerable attention as candidate large space structures. A typical example is a hoop-column antenna. The large number of preloaded members requires efficient analytical methods for concept validation and design. Validation through analyses is especially important since ground testing may be limited due to gravity effects and structural size. The present investigation has the objective to present an examination of the analytical modeling of pretensioned members undergoing nonlinear vibrations. Two approximate nonlinear analysis are developed to model general structural arrangements which include beam-columns and pretensioned cables attached to a common nucleus, such as may occur at a joint of a pretensioned structure. Attention is given to structures undergoing nonlinear steady-state oscillations due to sinusoidal excitation forces. Three analyses, linear, quasi-linear, and nonlinear are conducted and applied to study the response of a relatively simple cable stiffened structure.

Topical Meeting on Optical Bistability Held at Rochester, New York on 15-17 June 1983.

DTIC Science & Technology

1983-01-01

distortion of their initial directions of polarization : both of the beams are linearly polarized , with their electric vectors either (i)parallel to...New Zealand. ChSAM aIB ct Multistability, self-oscillation, and chaos in a model for polarization I Chas mnd Optlcal Bltabillty: Blfuraton...second circularly polarized pumping beam has been observed, transition sequence arises that is consistent with recent observ- Sense of response

Shock wave oscillation driven by turbulent boundary layer fluctuations

NASA Technical Reports Server (NTRS)

Plotkin, K. J.

1972-01-01

Pressure fluctuations due to the interaction of a shock wave with a turbulent boundary layer were investigated. A simple model is proposed in which the shock wave is convected from its mean position by velocity fluctuations in the turbulent boundary layer. Displacement of the shock is assumed limited by a linear restoring mechanism. Predictions of peak root mean square pressure fluctuation and spectral density are in excellent agreement with available experimental data.

Pressure-coupled combustion response model for solid propellants based on Zeldovich-Novozhilov approach

NASA Technical Reports Server (NTRS)

Harstad, K. G.; Strand, L. D.

1987-01-01

An exact analytical solution is given to the problem of long-time propellant thermal response to a specified pressure oscillation. Coupling to the gas phase is made using the quasisteady Zeldovich-Novozhilov approximation. Explicit linear and lowest order (quadratic) nonlinear expressions for propellant response are obtained from the implicit nonlinear solutions. Using these expressions, response curves are presented for an ammonium perchlorate composite propellant and HMX monopropellant.

Constraints on running vacuum model with H ( z ) and f σ{sub 8}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Geng, Chao-Qiang; Lee, Chung-Chi; Yin, Lu, E-mail: geng@phys.nthu.edu.tw, E-mail: lee.chungchi16@gmail.com, E-mail: yinlumail@foxmail.com

We examine the running vacuum model with Λ ( H ) = 3 ν H {sup 2} + Λ{sub 0}, where ν is the model parameter and Λ{sub 0} is the cosmological constant. From the data of the cosmic microwave background radiation, weak lensing and baryon acoustic oscillation along with the time dependent Hubble parameter H ( z ) and weighted linear growth f ( z )σ{sub 8}( z ) measurements, we find that ν=(1.37{sup +0.72}{sub −0.95})× 10{sup −4} with the best fitted χ{sup 2} value slightly smaller than that in the ΛCDM model.

On the modeling of the bottom particles segregation with non-linear diffusion equations: application to the marine sand ripples

NASA Astrophysics Data System (ADS)

Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander

2015-04-01

The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.

Continuous and discontinuous transitions to synchronization.

PubMed

Wang, Chaoqing; Garnier, Nicolas B

2016-11-01

We describe how the transition to synchronization in a system of globally coupled Stuart-Landau oscillators changes from continuous to discontinuous when the nature of the coupling is moved from diffusive to reactive. We explain this drastic qualitative change as resulting from the co-existence of a particular synchronized macrostate together with the trivial incoherent macrostate, in a range of parameter values for which the latter is linearly stable. In contrast to the paradigmatic Kuramoto model, this particular state observed at the synchronization transition contains a finite, non-vanishing number of synchronized oscillators, which results in a discontinuous transition. We consider successively two situations where either a fully synchronized state or a partially synchronized state exists at the transition. Thermodynamic limit and finite size effects are briefly discussed, as well as connections with recently observed discontinuous transitions.

Concepts for radically increasing the numerical convergence rate of the Euler equations

NASA Technical Reports Server (NTRS)

Nixon, David; Tzuoo, Keh-Lih; Caruso, Steven C.; Farshchi, Mohammad; Klopfer, Goetz H.; Ayoub, Alfred

1987-01-01

Integral equation and finite difference methods have been developed for solving transonic flow problems using linearized forms of the transonic small disturbance and Euler equations. A key element is the use of a strained coordinate system in which the shock remains fixed. Additional criteria are developed to determine the free parameters in the coordinate straining; these free parameters are functions of the shock location. An integral equation analysis showed that the shock is located by ensuring that no expansion shocks exist in the solution. The expansion shock appears as oscillations in the solution near the sonic line, and the correct shock location is determined by removing these oscillations. A second objective was to study the ability of the Euler equation to model separated flow.

Sound wave resonances in micro-electro-mechanical systems devices vibrating at high frequencies according to the kinetic theory of gases

NASA Astrophysics Data System (ADS)

Desvillettes, Laurent; Lorenzani, Silvia

2012-09-01

The mechanism leading to gas damping in micro-electro-mechanical systems (MEMS) devices vibrating at high frequencies is investigated by using the linearized Boltzmann equation based on simplified kinetic models and diffuse reflection boundary conditions. Above a certain frequency of oscillation, the sound waves propagating through the gas are trapped in the gaps between the moving elements and the fixed boundaries of the microdevice. In particular, we found a scaling law, valid for all Knudsen numbers Kn (defined as the ratio between the gas mean free path and a characteristic length of the gas flow), that predicts a resonant response of the system. This response enables a minimization of the damping force exerted by the gas on the oscillating wall of the microdevice.

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.

Analysis of Zenith Tropospheric Delay above Europe based on long time series derived from the EPN data

NASA Astrophysics Data System (ADS)

Baldysz, Zofia; Nykiel, Grzegorz; Figurski, Mariusz; Szafranek, Karolina; Kroszczynski, Krzysztof; Araszkiewicz, Andrzej

2015-04-01

In recent years, the GNSS system began to play an increasingly important role in the research related to the climate monitoring. Based on the GPS system, which has the longest operational capability in comparison with other systems, and a common computational strategy applied to all observations, long and homogeneous ZTD (Zenith Tropospheric Delay) time series were derived. This paper presents results of analysis of 16-year ZTD time series obtained from the EPN (EUREF Permanent Network) reprocessing performed by the Military University of Technology. To maintain the uniformity of data, analyzed period of time (1998-2013) is exactly the same for all stations - observations carried out before 1998 were removed from time series and observations processed using different strategy were recalculated according to the MUT LAC approach. For all 16-year time series (59 stations) Lomb-Scargle periodograms were created to obtain information about the oscillations in ZTD time series. Due to strong annual oscillations which disturb the character of oscillations with smaller amplitude and thus hinder their investigation, Lomb-Scargle periodograms for time series with the deleted annual oscillations were created in order to verify presence of semi-annual, ter-annual and quarto-annual oscillations. Linear trend and seasonal components were estimated using LSE (Least Square Estimation) and Mann-Kendall trend test were used to confirm the presence of linear trend designated by LSE method. In order to verify the effect of the length of time series on the estimated size of the linear trend, comparison between two different length of ZTD time series was performed. To carry out a comparative analysis, 30 stations which have been operating since 1996 were selected. For these stations two periods of time were analyzed: shortened 16-year (1998-2013) and full 18-year (1996-2013). For some stations an additional two years of observations have significant impact on changing the size of linear trend - only for 4 stations the size of linear trend was exactly the same for two periods of time. In one case, the nature of the trend has changed from negative (16-year time series) for positive (18-year time series). The average value of a linear trends for 16-year time series is 1,5 mm/decade, but their spatial distribution is not uniform. The average value of linear trends for all 18-year time series is 2,0 mm/decade, with better spatial distribution and smaller discrepancies.

Water-absorbing capacitor system for measuring relative humidity

NASA Technical Reports Server (NTRS)

Laue, Eric G. (Inventor)

1987-01-01

A method and apparatus using a known water-absorbent polymer as a capacitor which is operated at a dc voltage for measuring relative humidity is presented. When formed as a layer between porous electrically-conductive electrodes and operated in an RC oscillator circuit, the oscillator frequency varies inversely with the partial pressure of the moisture to be measured. In a preferred embodiment, the capacitor is formed from Nafion and is operated at a low dc voltage with a resistor as an RC circuit in an RC oscillator. At the low voltage, the leakage current is proper for oscillation over a satisfactory range. The frequency of oscillation varies in an essentially linear fashion with relative humidity which is represented by the moisture being absorbed into the Nafion. The oscillation frequency is detected by a frequency detector.

Beta Peak Frequencies at Rest Correlate with Endogenous GABA+/Cr Concentrations in Sensorimotor Cortex Areas

PubMed Central

Baumgarten, Thomas J.; Oeltzschner, Georg; Hoogenboom, Nienke; Wittsack, Hans-Jörg; Schnitzler, Alfons; Lange, Joachim

2016-01-01

Neuronal oscillatory activity in the beta band (15–30 Hz) is a prominent signal within the human sensorimotor cortex. Computational modeling and pharmacological modulation studies suggest an influence of GABAergic interneurons on the generation of beta band oscillations. Accordingly, studies in humans have demonstrated a correlation between GABA concentrations and power of beta band oscillations. It remains unclear, however, if GABA concentrations also influence beta peak frequencies and whether this influence is present in the sensorimotor cortex at rest and without pharmacological modulation. In the present study, we investigated the relation between endogenous GABA concentration (measured by magnetic resonance spectroscopy) and beta oscillations (measured by magnetoencephalography) at rest in humans. GABA concentrations and beta band oscillations were measured for left and right sensorimotor and occipital cortex areas. A significant positive linear correlation between GABA concentration and beta peak frequency was found for the left sensorimotor cortex, whereas no significant correlations were found for the right sensorimotor and the occipital cortex. The results show a novel connection between endogenous GABA concentration and beta peak frequency at rest. This finding supports previous results that demonstrated a connection between oscillatory beta activity and pharmacologically modulated GABA concentration in the sensorimotor cortex. Furthermore, the results demonstrate that for a predominantly right-handed sample, the correlation between beta band oscillations and endogenous GABA concentrations is evident only in the left sensorimotor cortex. PMID:27258089

Numerical investigation of multi-beam laser heterodyne measurement with ultra-precision for linear expansion coefficient of metal based on oscillating mirror modulation

NASA Astrophysics Data System (ADS)

Li, Yan-Chao; Wang, Chun-Hui; Qu, Yang; Gao, Long; Cong, Hai-Fang; Yang, Yan-Ling; Gao, Jie; Wang, Ao-You

2011-01-01

This paper proposes a novel method of multi-beam laser heterodyne measurement for metal linear expansion coefficient. Based on the Doppler effect and heterodyne technology, the information is loaded of length variation to the frequency difference of the multi-beam laser heterodyne signal by the frequency modulation of the oscillating mirror, this method can obtain many values of length variation caused by temperature variation after the multi-beam laser heterodyne signal demodulation simultaneously. Processing these values by weighted-average, it can obtain length variation accurately, and eventually obtain the value of linear expansion coefficient of metal by the calculation. This novel method is used to simulate measurement for linear expansion coefficient of metal rod under different temperatures by MATLAB, the obtained result shows that the relative measurement error of this method is just 0.4%.

An Agile Beam Transmit Array Using Coupled Oscillator Phase Control

NASA Technical Reports Server (NTRS)

Pogorzelski, Ronald S.; Scaramastra, Rocco P.; Huang, John; Beckon, Robert J.; Petree, Steve M.; Chavez, Cosme

1993-01-01

A few years ago York and colleagues suggested that injection locking of voltage controlled oscillators could be used to implement beam steering in a phased array [I]. The scheme makes use of the fact that when an oscillator is injection locked to an external signal, the phase difference between the output of the oscillator and the injection signal is governed by the difference between the injection frequency and the free running frequency of the oscillator (the frequency to which the oscillator is tuned). Thus, if voltage controlled oscillators (VCOs) are used, this phase difference is controlled by an applied voltage. Now, if a set of such oscillators are coupled to nearest neighbors, they can be made to mutually injection lock and oscillate as an ensemble. If they are all tuned to the same frequency, they will all oscillate in phase. Thus, if the outputs are connected to radiating elements forming a linear array, the antenna will radiate normal to the line of elements. Scanning is accomplished by antisymmetrically detuning the end oscillators in the array by application of a pair of appropriate voltages to their tuning ports. This results in a linear phase progression across the array which is just the phasing required to scan the beam. The scan angle is determined by the degree of detuning. We have constructed a seven element one dimensional agile beam array at S-band based on the above principle. Although, a few such arrays have been built in the past, this array possesses two unique features. First, the VCO MMICs have buffer amplifiers which isolate the output from the tuning circuit, and second, the oscillators are weakly coupled to each other at their resonant circuits rather than their outputs. This results in a convenient isolation between the oscillator array design and the radiating aperture design. An important parameter in the design is the so called coupling phase which determines the phase shift of the signals passing from one oscillator to its neighbors. Using this array, we have been able to verify the theoretical predictions concerning the effect of this phase on both the locking range and ensemble frequency of the array. However, the scan range achieved fell somewhat short of the theoretical value because of the amplitude variation of the oscillator outputs with tuning.

Optimal entrainment of circadian clocks in the presence of noise

NASA Astrophysics Data System (ADS)

Monti, Michele; Lubensky, David K.; ten Wolde, Pieter Rein

2018-03-01

Circadian clocks are biochemical oscillators that allow organisms to estimate the time of the day. These oscillators are inherently noisy due to the discrete nature of the reactants and the stochastic character of their interactions. To keep these oscillators in sync with the daily day-night rhythm in the presence of noise, circadian clocks must be coupled to the dark-light cycle. In this paper, we study the entrainment of phase oscillators as a function of the intrinsic noise in the system. Using stochastic simulations, we compute the optimal coupling strength, intrinsic frequency, and shape of the phase-response curve, that maximize the mutual information between the phase of the clock and time. We show that the optimal coupling strength and intrinsic frequency increase with the noise, but that the shape of the phase-response curve varies nonmonotonically with the noise: in the low-noise regime, it features a dead zone that increases in width as the noise increases, while in the high-noise regime, the width decreases with the noise. These results arise from a tradeoff between maximizing stability—noise suppression—and maximizing linearity of the input-output, i.e., time-phase, relation. We also show that three analytic approximations—the linear-noise approximation, the phase-averaging method, and linear-response theory—accurately describe different regimes of the coupling strength and the noise.

Oscillating-Linear-Drive Vacuum Compressor for CO2

NASA Technical Reports Server (NTRS)

Izenson, Michael G.; Shimko, Martin

2005-01-01

A vacuum compressor has been designed to compress CO2 from approximately equal to 1 psia (approximately equal to 6.9 kPa absolute pressure) to approximately equal to 75 psia (approximately equal to 0.52 MPa), to be insensitive to moisture, to have a long operational life, and to be lightweight, compact, and efficient. The compressor consists mainly of (1) a compression head that includes hydraulic diaphragms, a gas-compression diaphragm, and check valves; and (2) oscillating linear drive that includes a linear motor and a drive spring, through which compression force is applied to the hydraulic diaphragms. The motor is driven at the resonance vibrational frequency of the motor/spring/compression-head system, the compression head acting as a damper that takes energy out of the oscillation. The net effect of the oscillation is to cause cyclic expansion and contraction of the gas-compression diaphragm, and, hence, of the volume bounded by this diaphragm. One-way check valves admit gas into this volume from the low-pressure side during expansion and allow the gas to flow out to the high-pressure side during contraction. Fatigue data and the results of diaphragm stress calculations have been interpreted as signifying that the compressor can be expected to have an operational life of greater than 30 years with a confidence level of 99.9 percent.

Fluid-structure coupling for an oscillating hydrofoil

NASA Astrophysics Data System (ADS)

Münch, C.; Ausoni, P.; Braun, O.; Farhat, M.; Avellan, F.

2010-08-01

Fluid-structure investigations in hydraulic machines using coupled simulations are particularly time-consuming. In this study, an alternative method is presented that linearizes the hydrodynamic load of a rigid, oscillating hydrofoil. The hydrofoil, which is surrounded by incompressible, turbulent flow, is modeled with forced and free pitching motions, where the mean incidence angle is 0° with a maximum angle amplitude of 2°. Unsteady simulations of the flow, performed with ANSYS CFX, are presented and validated with experiments which were carried out in the EPFL High-Speed Cavitation Tunnel. First, forced motion is investigated for reduced frequencies ranging from 0.02 to 100. The hydrodynamic load is modeled as a simple combination of inertia, damping and stiffness effects. As expected, the potential flow analysis showed the added moment of inertia is constant, while the fluid damping and the fluid stiffness coefficients depend on the reduced frequency of the oscillation motion. Behavioral patterns were observed and two cases were identified depending on if vortices did or did not develop in the hydrofoil wake. Using the coefficients identified in the forced motion case, the time history of the profile incidence is then predicted analytically for the free motion case and excellent agreement is found for the results from coupled fluid-structure simulations. The model is validated and may be extended to more complex cases, such as blade grids in hydraulic machinery.

Regularized linearization for quantum nonlinear optical cavities: application to degenerate optical parametric oscillators.

PubMed

Navarrete-Benlloch, Carlos; Roldán, Eugenio; Chang, Yue; Shi, Tao

2014-10-06

Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods. Apart from its operational value, we believe that our work is valuable also from a fundamental point of view, especially in connection to the question of how far linearized or Gaussian theories can be pushed to describe nonlinear dissipative systems which have access to non-Gaussian states.

Introduction to the Treatment of Non-Linear Effects Using a Gravitational Pendulum

ERIC Educational Resources Information Center

Weltner, Klaus; Esperidiao, Antonio Sergio C.; Miranda, Paulo

2004-01-01

We show that the treatment of pendulum movement, other than the linear approximation,may be an instructive experimentally based introduction to the physics of non-linear effects. Firstly the natural frequency of a gravitational pendulum is measured as function of its amplitude. Secondly forced oscillations of a gravitational pendulum are…

A modified homotopy perturbation method and the axial secular frequencies of a non-linear ion trap.

PubMed

Doroudi, Alireza

2012-01-01

In this paper, a modified version of the homotopy perturbation method, which has been applied to non-linear oscillations by V. Marinca, is used for calculation of axial secular frequencies of a non-linear ion trap with hexapole and octopole superpositions. The axial equation of ion motion in a rapidly oscillating field of an ion trap can be transformed to a Duffing-like equation. With only octopole superposition the resulted non-linear equation is symmetric; however, in the presence of hexapole and octopole superpositions, it is asymmetric. This modified homotopy perturbation method is used for solving the resulting non-linear equations. As a result, the ion secular frequencies as a function of non-linear field parameters are obtained. The calculated secular frequencies are compared with the results of the homotopy perturbation method and the exact results. With only hexapole superposition, the results of this paper and the homotopy perturbation method are the same and with hexapole and octopole superpositions, the results of this paper are much more closer to the exact results compared with the results of the homotopy perturbation method.

Optimal control of parametric oscillations of compressed flexible bars

NASA Astrophysics Data System (ADS)

Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.

2018-05-01

In this paper the problem of damping of the linear systems oscillations with piece-wise constant control is solved. The motion of bar construction is reduced to the form described by Hill's differential equation using the Bubnov-Galerkin method. To calculate switching moments of the one-side control the method of sequential linear programming is used. The elements of the fundamental matrix of the Hill's equation are approximated by trigonometric series. Examples of the optimal control of the systems for various initial conditions and different number of control stages have been calculated. The corresponding phase trajectories and transient processes are represented.

Stability of two-mode internal resonance in a nonlinear oscillator

NASA Astrophysics Data System (ADS)

Zanette, Damián H.

2018-05-01

We analyze the stability of synchronized periodic motion for two coupled oscillators, representing two interacting oscillation modes in a nonlinear vibrating beam. The main oscillation mode is governed by the forced Duffing equation, while the other mode is linear. By means of the multiple-scale approach, the system is studied in two situations: an open-loop configuration, where the excitation is an external force, and a closed-loop configuration, where the system is fed back with an excitation obtained from the oscillation itself. The latter is relevant to the functioning of time-keeping micromechanical devices. While the accessible amplitudes and frequencies of stationary oscillations are identical in the two situations, their stability properties are substantially different. Emphasis is put on resonant oscillations, where energy transfer between the two coupled modes is maximized and, consequently, the strong interdependence between frequency and amplitude caused by nonlinearity is largely suppressed.

Detecting, anticipating, and predicting critical transitions in spatially extended systems.

PubMed

Kwasniok, Frank

2018-03-01

A data-driven linear framework for detecting, anticipating, and predicting incipient bifurcations in spatially extended systems based on principal oscillation pattern (POP) analysis is discussed. The dynamics are assumed to be governed by a system of linear stochastic differential equations which is estimated from the data. The principal modes of the system together with corresponding decay or growth rates and oscillation frequencies are extracted as the eigenvectors and eigenvalues of the system matrix. The method can be applied to stationary datasets to identify the least stable modes and assess the proximity to instability; it can also be applied to nonstationary datasets using a sliding window approach to track the changing eigenvalues and eigenvectors of the system. As a further step, a genuinely nonstationary POP analysis is introduced. Here, the system matrix of the linear stochastic model is time-dependent, allowing for extrapolation and prediction of instabilities beyond the learning data window. The methods are demonstrated and explored using the one-dimensional Swift-Hohenberg equation as an example, focusing on the dynamics of stochastic fluctuations around the homogeneous stable state prior to the first bifurcation. The POP-based techniques are able to extract and track the least stable eigenvalues and eigenvectors of the system; the nonstationary POP analysis successfully predicts the timing of the first instability and the unstable mode well beyond the learning data window.

Detecting, anticipating, and predicting critical transitions in spatially extended systems

NASA Astrophysics Data System (ADS)

Kwasniok, Frank

2018-03-01

A data-driven linear framework for detecting, anticipating, and predicting incipient bifurcations in spatially extended systems based on principal oscillation pattern (POP) analysis is discussed. The dynamics are assumed to be governed by a system of linear stochastic differential equations which is estimated from the data. The principal modes of the system together with corresponding decay or growth rates and oscillation frequencies are extracted as the eigenvectors and eigenvalues of the system matrix. The method can be applied to stationary datasets to identify the least stable modes and assess the proximity to instability; it can also be applied to nonstationary datasets using a sliding window approach to track the changing eigenvalues and eigenvectors of the system. As a further step, a genuinely nonstationary POP analysis is introduced. Here, the system matrix of the linear stochastic model is time-dependent, allowing for extrapolation and prediction of instabilities beyond the learning data window. The methods are demonstrated and explored using the one-dimensional Swift-Hohenberg equation as an example, focusing on the dynamics of stochastic fluctuations around the homogeneous stable state prior to the first bifurcation. The POP-based techniques are able to extract and track the least stable eigenvalues and eigenvectors of the system; the nonstationary POP analysis successfully predicts the timing of the first instability and the unstable mode well beyond the learning data window.

An advanced panel method for analysis of arbitrary configurations in unsteady subsonic flow

NASA Technical Reports Server (NTRS)

Dusto, A. R.; Epton, M. A.

1980-01-01

An advanced method is presented for solving the linear integral equations for subsonic unsteady flow in three dimensions. The method is applicable to flows about arbitrary, nonplanar boundary surfaces undergoing small amplitude harmonic oscillations about their steady mean locations. The problem is formulated with a wake model wherein unsteady vorticity can be convected by the steady mean component of flow. The geometric location of the unsteady source and doublet distributions can be located on the actual surfaces of thick bodies in their steady mean locations. The method is an outgrowth of a recently developed steady flow panel method and employs the linear source and quadratic doublet splines of that method.

Loop Shaping Control Design for a Supersonic Propulsion System Model Using Quantitative Feedback Theory (QFT) Specifications and Bounds

NASA Technical Reports Server (NTRS)

Connolly, Joseph W.; Kopasakis, George

2010-01-01

This paper covers the propulsion system component modeling and controls development of an integrated mixed compression inlet and turbojet engine that will be used for an overall vehicle Aero-Propulso-Servo-Elastic (APSE) model. Using previously created nonlinear component-level propulsion system models, a linear integrated propulsion system model and loop shaping control design have been developed. The design includes both inlet normal shock position control and jet engine rotor speed control for a potential supersonic commercial transport. A preliminary investigation of the impacts of the aero-elastic effects on the incoming flow field to the propulsion system are discussed, however, the focus here is on developing a methodology for the propulsion controls design that prevents unstart in the inlet and minimizes the thrust oscillation experienced by the vehicle. Quantitative Feedback Theory (QFT) specifications and bounds, and aspects of classical loop shaping are used in the control design process. Model uncertainty is incorporated in the design to address possible error in the system identification mapping of the nonlinear component models into the integrated linear model.

Reaction wheel low-speed compensation using a dither signal

NASA Astrophysics Data System (ADS)

Stetson, John B., Jr.

1993-08-01

A method for improving low-speed reaction wheel performance on a three-axis controlled spacecraft is presented. The method combines a constant amplitude offset with an unbiased, oscillating dither to harmonically linearize rolling solid friction dynamics. The complete, nonlinear rolling solid friction dynamics using an analytic modification to the experimentally verified Dahl solid friction model were analyzed using the dual-input describing function method to assess the benefits of dither compensation. The modified analytic solid friction model was experimentally verified with a small dc servomotor actuated reaction wheel assembly. Using dither compensation abrupt static friction disturbances are eliminated and near linear behavior through zero rate can be achieved. Simulated vehicle response to a wheel rate reversal shows that when the dither and offset compensation is used, elastic modes are not significantly excited, and the uncompensated attitude error reduces by 34:1.

Non-linear Relationship between BOLD Activation and Amplitude of Beta Oscillations in the Supplementary Motor Area during Rhythmic Finger Tapping and Internal Timing

PubMed Central

Gompf, Florian; Pflug, Anja; Laufs, Helmut; Kell, Christian A.

2017-01-01

Functional imaging studies using BOLD contrasts have consistently reported activation of the supplementary motor area (SMA) both during motor and internal timing tasks. Opposing findings, however, have been shown for the modulation of beta oscillations in the SMA. While movement suppresses beta oscillations in the SMA, motor and non-motor tasks that rely on internal timing increase the amplitude of beta oscillations in the SMA. These independent observations suggest that the relationship between beta oscillations and BOLD activation is more complex than previously thought. Here we set out to investigate this rapport by examining beta oscillations in the SMA during movement with varying degrees of internal timing demands. In a simultaneous EEG-fMRI experiment, 20 healthy right-handed subjects performed an auditory-paced finger-tapping task. Internal timing was operationalized by including conditions with taps on every fourth auditory beat, which necessitates generation of a slow internal rhythm, while tapping to every auditory beat reflected simple auditory-motor synchronization. In the SMA, BOLD activity increased and power in both the low and the high beta band decreased expectedly during each condition compared to baseline. Internal timing was associated with a reduced desynchronization of low beta oscillations compared to conditions without internal timing demands. In parallel with this relative beta power increase, internal timing activated the SMA more strongly in terms of BOLD. This documents a task-dependent non-linear relationship between BOLD and beta-oscillations in the SMA. We discuss different roles of beta synchronization and desynchronization in active processing within the same cortical region. PMID:29249950

Interactive coupling of electronic and optical man-made devices to biological systems

NASA Astrophysics Data System (ADS)

Ozden, Ilker

Fireflies blink synchronously, lasers are "mode-locked" for amplification, cardiac pacemaker cells maintain a steady heartbeat, and crickets chirps get in step. These are examples of coupled oscillators. Coupled non-linear limit-cycle oscillator models are used extensively to provide information about the collective behavior of many physical and biological systems. Depending on the system parameters, namely, the coupling coefficient and the time delay in the coupling, these coupled limit-cycle oscillator exhibit several interesting phenomena; they either synchronize to a common frequency, or oscillate completely independent of each other, or drag each other to a standstill i.e., show "amplitude death". Many neuronal systems exhibit synchronized limit-cycle oscillations in network of electrically coupled cells. The inferior olivary (IO) neuron is an example of such a system. The inferior olive has been widely studied by neuroscientists as it exhibits spontaneous oscillations in its membrane potential, typically in the range of 1--10 Hz. Located in the medulla, the inferior olive is believed to form the neural basis for precise timing and learning in motor circuits by making strong synaptic connections onto Purkinjee cells in the cerebellum. In this thesis work, we report on work, which focuses on the implementation and study of coupling of a biological circuit, which is the inferior olivary system, with a man-made electronic oscillator, the so-called Chua's circuit. We were able to study the interaction between the two oscillators over a wide range coupling conditions. With increasing coupling strength, the oscillators become phase-locked, or synchronized, but with a phase relationship which is either in- or out-of-phase depending on the detailed adjustment in the coupling. Finally, the coupled system reaches the conditions for amplitude death, a rather fundamental result given that the interaction has taken place between purely biological and man-made circuit elements.

Entanglement dynamics in short- and long-range harmonic oscillators

NASA Astrophysics Data System (ADS)

Nezhadhaghighi, M. Ghasemi; Rajabpour, M. A.

2014-11-01

We study the time evolution of the entanglement entropy in the short- and long-range-coupled harmonic oscillators that have well-defined continuum limit field theories. We first introduce a method to calculate the entanglement evolution in generic coupled harmonic oscillators after quantum quench. Then we study the entanglement evolution after quantum quench in harmonic systems in which the couplings decay effectively as 1 /rd +α with the distance r . After quenching the mass from a nonzero value to zero we calculate numerically the time evolution of von Neumann and Rényi entropies. We show that for 1 <α <2 we have a linear growth of entanglement and then saturation independent of the initial state. For 0 <α <1 depending on the initial state we can have logarithmic growth or just fluctuation of entanglement. We also calculate the mutual information dynamics of two separated individual harmonic oscillators. Our findings suggest that in our system there is no particular connection between having a linear growth of entanglement after quantum quench and having a maximum group velocity or generalized Lieb-Robinson bound.

Impact of a Stochastic Parameterization Scheme on El Nino-Southern Oscillation in the Community Climate System Model

NASA Astrophysics Data System (ADS)

Christensen, H. M.; Berner, J.; Sardeshmukh, P. D.

2017-12-01

Stochastic parameterizations have been used for more than a decade in atmospheric models. They provide a way to represent model uncertainty through representing the variability of unresolved sub-grid processes, and have been shown to have a beneficial effect on the spread and mean state for medium- and extended-range forecasts. There is increasing evidence that stochastic parameterization of unresolved processes can improve the bias in mean and variability, e.g. by introducing a noise-induced drift (nonlinear rectification), and by changing the residence time and structure of flow regimes. We present results showing the impact of including the Stochastically Perturbed Parameterization Tendencies scheme (SPPT) in coupled runs of the National Center for Atmospheric Research (NCAR) Community Atmosphere Model, version 4 (CAM4) with historical forcing. SPPT results in a significant improvement in the representation of the El Nino-Southern Oscillation in CAM4, improving the power spectrum, as well as both the inter- and intra-annual variability of tropical pacific sea surface temperatures. We use a Linear Inverse Modelling framework to gain insight into the mechanisms by which SPPT has improved ENSO-variability.

Fourier functional analysis for unsteady aerodynamic modeling

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Chin, Suei

1991-01-01

A method based on Fourier analysis is developed to analyze the force and moment data obtained in large amplitude forced oscillation tests at high angles of attack. The aerodynamic models for normal force, lift, drag, and pitching moment coefficients are built up from a set of aerodynamic responses to harmonic motions at different frequencies. Based on the aerodynamic models of harmonic data, the indicial responses are formed. The final expressions for the models involve time integrals of the indicial type advocated by Tobak and Schiff. Results from linear two- and three-dimensional unsteady aerodynamic theories as well as test data for a 70-degree delta wing are used to verify the models. It is shown that the present modeling method is accurate in producing the aerodynamic responses to harmonic motions and the ramp type motions. The model also produces correct trend for a 70-degree delta wing in harmonic motion with different mean angles-of-attack. However, the current model cannot be used to extrapolate data to higher angles-of-attack than that of the harmonic motions which form the aerodynamic model. For linear ramp motions, a special method is used to calculate the corresponding frequency and phase angle at a given time. The calculated results from modeling show a higher lift peak for linear ramp motion than for harmonic ramp motion. The current model also shows reasonably good results for the lift responses at different angles of attack.

Towards classical spectrum generating algebras for f-deformations

NASA Astrophysics Data System (ADS)

Kullock, Ricardo; Latini, Danilo

2016-01-01

In this paper we revise the classical analog of f-oscillators, a generalization of q-oscillators given in Man'ko et al. (1997) [8], in the framework of classical spectrum generating algebras (SGA) introduced in Kuru and Negro (2008) [9]. We write down the deformed Poisson algebra characterizing the entire family of non-linear oscillators and construct its general solution algebraically. The latter, covering the full range of f-deformations, shows an energy dependence both in the amplitude and the frequency of the motion.

Transverse Motion of a Particle with an Oscillating Charge and Variable Mass in a Magnetic Field

NASA Astrophysics Data System (ADS)

Alisultanov, Z. Z.; Ragimkhanov, G. B.

2018-03-01

The problem of motion of a particle with an oscillating electric charge and variable mass in an uniform magnetic field has been solved. Three laws of mass variation have been considered: linear growth, oscillations, and stepwise growth. Analytical expressions for the particle velocity at different time dependences of the particle mass are obtained. It is established that simultaneous consideration of changes in the mass and charge leads to a significant change in the particle trajectory.

Explosive axion production from saxion

NASA Astrophysics Data System (ADS)

Ema, Yohei; Nakayama, Kazunori

2018-01-01

The dynamics of saxion in a supersymmetric axion model and its effect on the axion production is studied in detail. We find that the axion production is very efficient when the saxion oscillation amplitude is much larger than the Peccei-Quinn scale, due to a spike-like behavior of the effective axion mass. We also consider the axino production and several cosmological consequences. The possibility of detection of gravitational waves from the non-linear dynamics of the saxion and axion is discussed.

Theta oscillations promote temporal sequence learning.

PubMed

Crivelli-Decker, Jordan; Hsieh, Liang-Tien; Clarke, Alex; Ranganath, Charan

2018-05-17

Many theoretical models suggest that neural oscillations play a role in learning or retrieval of temporal sequences, but the extent to which oscillations support sequence representation remains unclear. To address this question, we used scalp electroencephalography (EEG) to examine oscillatory activity over learning of different object sequences. Participants made semantic decisions on each object as they were presented in a continuous stream. For three "Consistent" sequences, the order of the objects was always fixed. Activity during Consistent sequences was compared to "Random" sequences that consisted of the same objects presented in a different order on each repetition. Over the course of learning, participants made faster semantic decisions to objects in Consistent, as compared to objects in Random sequences. Thus, participants were able to use sequence knowledge to predict upcoming items in Consistent sequences. EEG analyses revealed decreased oscillatory power in the theta (4-7 Hz) band at frontal sites following decisions about objects in Consistent sequences, as compared with objects in Random sequences. The theta power difference between Consistent and Random only emerged in the second half of the task, as participants were more effectively able to predict items in Consistent sequences. Moreover, we found increases in parieto-occipital alpha (10-13 Hz) and beta (14-28 Hz) power during the pre-response period for objects in Consistent sequences, relative to objects in Random sequences. Linear mixed effects modeling revealed that single trial theta oscillations were related to reaction time for future objects in a sequence, whereas beta and alpha oscillations were only predictive of reaction time on the current trial. These results indicate that theta and alpha/beta activity preferentially relate to future and current events, respectively. More generally our findings highlight the importance of band-specific neural oscillations in the learning of temporal order information. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

A theoretical and experimental investigation of the linear and nonlinear impulse responses from a magnetoplasma column

NASA Technical Reports Server (NTRS)

Grody, N. C.

1973-01-01

Linear and nonlinear responses of a magnetoplasma resulting from inhomogeneity in the background plasma density are studied. The plasma response to an impulse electric field was measured and the results are compared with the theory of an inhomogeneous cold plasma. Impulse responses were recorded for the different plasma densities, static magnetic fields, and neutral pressures and generally appeared as modulated, damped oscillations. The frequency spectra of the waveforms consisted of two separated resonance peaks. For weak excitation, the results correlate with the linear theory of a cold, inhomogeneous, cylindrical magnetoplasma. The damping mechanism is identified with that of phase mixing due to inhomogeneity in plasma density. With increasing excitation voltage, the nonlinear impulse responses display stronger damping and a small increase in the frequency of oscillation.

Stabilization of business cycles of finance agents using nonlinear optimal control

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

2017-11-01

Stabilization of the business cycles of interconnected finance agents is performed with the use of a new nonlinear optimal control method. First, the dynamics of the interacting finance agents and of the associated business cycles is described by a modeled of coupled nonlinear oscillators. Next, this dynamic model undergoes approximate linearization round a temporary operating point which is defined by the present value of the system's state vector and the last value of the control inputs vector that was exerted on it. The linearization procedure is based on Taylor series expansion of the dynamic model and on the computation of Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms in the Taylor series expansion is considered as a disturbance which is compensated by the robustness of the control loop. Next, for the linearized model of the interacting finance agents, an H-infinity feedback controller is designed. The computation of the feedback control gain requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. Through Lyapunov stability analysis it is proven that the control scheme satisfies an H-infinity tracking performance criterion, which signifies elevated robustness against modelling uncertainty and external perturbations. Moreover, under moderate conditions the global asymptotic stability features of the control loop are proven.

Anomalous Damping of a Microelectromechanical Oscillator in Superfluid ^{3}He-B.

PubMed

Zheng, P; Jiang, W G; Barquist, C S; Lee, Y; Chan, H B

2016-11-04

The mechanical resonance properties of a microelectromechanical oscillator with a gap of 1.25  μm was studied in superfluid ^{3}He-B at various pressures. The oscillator was driven in the linear damping regime where the damping coefficient is independent of the oscillator velocity. The quality factor of the oscillator remains low (Q≈80) down to 0.1T_{c}, 4 orders of magnitude less than the intrinsic quality factor measured in vacuum at 4 K. In addition to the Boltzmann temperature dependent contribution to the damping, a damping proportional to temperature was found to dominate at low temperatures. We propose a multiple scattering mechanism of the surface Andreev bound states to be a possible cause for the anomalous damping.

Determination of Longitudinal Stability and Control Characteristics from Free-Flight Model Tests with Results at Transonic Speeds for Three Airplane Configurations

NASA Technical Reports Server (NTRS)

Gillis, Clarence L; Mitchell, Jesse L

1957-01-01

A test technique and data analysis method has been developed for determining the longitudinal aerodynamic characteristics from free-flight tests of rocket-propelled models. The technique makes use of accelerometers and an angle-of-attack indicator to permit instantaneous measurements of lift, drag, and pitching moments. The data, obtained during transient oscillations resulting from control-surface disturbances, are analyzed by essentially nonlinear direct methods (such as cross plots of the variation of lift coefficient with angle of attack) and by linear indirect methods by using the equations of motion for a transient oscillation. The analysis procedure has been set forth in some detail and the feasibility of the method has been demonstrated by data measured through the transonic speed range on several airplane configurations. It was shown that the flight conditions and dynamic similitude factors for the tests described were reasonably close to typical full-scale airplane conditions.

Flutter Analysis of the Thermal Protection Layer on the NASA HIAD

NASA Technical Reports Server (NTRS)

Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

2013-01-01

A combination of classical plate theory and a supersonic aerodynamic model is used to study the aeroelastic flutter behavior of a proposed thermal protection system (TPS) for the NASA HIAD. The analysis pertains to the rectangular configurations currently being tested in a NASA wind-tunnel facility, and may explain why oscillations of the articles could be observed. An analysis using a linear flat plate model indicated that flutter was possible well within the supersonic flow regime of the wind tunnel tests. A more complex nonlinear analysis of the TPS, taking into account any material curvature present due to the restraint system or substructure, indicated that significantly greater aerodynamic forcing is required for the onset of flutter. Chaotic and periodic limit cycle oscillations (LCOs) of the TPS are possible depending on how the curvature is imposed. When the pressure from the base substructure on the bottom of the TPS is used as the source of curvature, the flutter boundary increases rapidly and chaotic behavior is eliminated.

H-mode transitions and limit cycle oscillations from mean field transport equations

DOE PAGES

Staebler, Gary M.; Groebner, Richard J.

2014-11-28

The mean field toroidal and parallel momentum transport equations will be shown to admit both onestep transitions to suppressed transport (L/H) and limit cycle oscillations (LCO). Both types of transitions are driven by the suppression of turbulence by the mean field ExB velocity shear. Using experimental data to evaluate the coefficients of a reduced transport model, the observed frequency of the LCO can be matched. The increase in the H-mode power threshold above and below a minimum density agrees with the trends in the model. Both leading and lagging phase relations between the turbulent density fluctuation amplitude and the ExBmore » velocity shear can occur depending on the evolution of the linear growth rate of the turbulence. As a result, the transport solutions match the initial phase of the L/H transition where the poloidal and ExB velocities are observed to change, and the density fluctuations drop, faster than the diamagnetic velocity.« less

Study on the influence of supplying compressed air channels and evicting channels on pneumatical oscillation systems for vibromooshing

NASA Astrophysics Data System (ADS)

Glăvan, D. O.; Radu, I.; Babanatsas, T.; Babanatis Merce, R. M.; Kiss, I.; Gaspar, M. C.

2018-01-01

The paper presents a pneumatic system with two oscillating masses. The system is composed of a cylinder (framework) with mass m1, which has a piston with mass m2 inside. The cylinder (framework system) has one supplying channel for compressed air and one evicting channel for each work chamber (left and right of the piston). Functionality of the piston position comparatively with the cylinder (framework) is possible through the supplying or evicting of compressed air. The variable force that keeps the movement depends on variation of the pressure that is changing depending on the piston position according to the cylinder (framework) and to the section form that is supplying and evicting channels with compressed air. The paper presents the physical model/pattern, the mathematical model/pattern (differential equations) and numerical solution of the differential equations in hypothesis with the section form of supplying and evicting channels with compressed air is rectangular (variation linear) or circular (variation nonlinear).

Dynamical Causal Modeling from a Quantum Dynamical Perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Demiralp, Emre; Demiralp, Metin

Recent research suggests that any set of first order linear vector ODEs can be converted to a set of specific vector ODEs adhering to what we have called ''Quantum Harmonical Form (QHF)''. QHF has been developed using a virtual quantum multi harmonic oscillator system where mass and force constants are considered to be time variant and the Hamiltonian is defined as a conic structure over positions and momenta to conserve the Hermiticity. As described in previous works, the conversion to QHF requires the matrix coefficient of the first set of ODEs to be a normal matrix. In this paper, thismore » limitation is circumvented using a space extension approach expanding the potential applicability of this method. Overall, conversion to QHF allows the investigation of a set of ODEs using mathematical tools available to the investigation of the physical concepts underlying quantum harmonic oscillators. The utility of QHF in the context of dynamical systems and dynamical causal modeling in behavioral and cognitive neuroscience is briefly discussed.« less

An adjoint-based sensitivity analysis of thermoacoustic network models

NASA Astrophysics Data System (ADS)

Sogaro, Francesca; Morgans, Aimee; Schmid, Peter

2017-11-01

Thermoacoustic instability is a phenomenon that occurs in numerous combustion systems, from rockets to land-based gas turbines. The acoustic oscillations of these systems are of significant importance as they can result in severe vibrations, thrust oscillations, thermal stresses and mechanical loads that lead to fatigue or even failure. In this work we use a low-order network model representation of a combustor system where linear acoustics are solved together with the appropriate boundary conditions, area change jump conditions, acoustic dampers and an appropriate flame transfer function. Special emphasis is directed towards the interaction between acoustically driven instabilities and flame-intrinsic modes. Adjoint methods are used to perform a sensitivity analysis of the spectral properties of the system to changes in the parameters involved. An exchange of modal identity between acoustic and intrinsic modes will be demonstrated and analyzed. The results provide insight into the interplay between various mode types and build a quantitative foundation for the design of combustors.

Phase shifting two coupled circadian pacemakers - Implications for jet lag

NASA Technical Reports Server (NTRS)

Gander, P. H.; Kronauer, R. E.; Graeber, R. C.

1985-01-01

Two Van der Pol oscillators with reciprocal linear velocity coupling are utilized to model the response of the human circadian timing system to abrupt displacements of the environmental time cues (zeitgebers). The core temperature rhythm and sleep-wake cycle simulated by the model are examined. The relationship between the masking of circadian rhythms by environmental variables and behavioral and physiological events and the rates of resynchronization is studied. The effects of zeitgeber phase shifts and zeitgeber strength on the resynchronization rates are analyzed. The influence of intrinsic pacemakers periods and coupling strength on resynchronization are investigated. The simulated data reveal that: resynchronization after a time zone shift depends on the magnitude of the shift; the time of day of the shift has little influence on resynchronization; the strength of zeitgebers affects the rate and direction of the resynchronization; the intrinsic pacemaker periods have a significant effect on resynchronization; and increasing the coupling between the oscillators results in an increase in the rate of resynchronization. The model data are compared to transmeridian flight studies data and similar resynchronization patterns are observed.

Rogue waves driven by polarization instabilities in a long ring fiber oscillator

NASA Astrophysics Data System (ADS)

Kolpakov, S. A.; Kbashi, Hani; Sergeyev, Sergey

2017-05-01

We present an experimental and theoretical results of a study of a complex nonlinear polarization dynamics in a passively self-mode-locked erbium-doped fiber oscillator implemented in a ring configuration and operating near lasing threshold. The theoretical model consists of seven coupled non-linear equations and takes into account both orthogonal states of polarizations in the fiber. The experiment confirmed the existence of seven eigenfrequencies, predicted by the model due to polarization instability near lasing threshold. By adjusting the state of polarization of the pump and in-cavity birefringence we changed some eigenfrequencies from being different (non-degenerate state) to matching (degenerate state). The non-degenerate states of oscillator lead to the L-shaped probability distribution function and true rogue wave regime with a positive dominant Lyapunov exponent value between 1.4 and 2.6. Small detuning from partially degenerate case also leads to L-shaped probability distribution function with the tail trespassing eight standard deviations threshold, giving periodic patterns of pulses along with positive dominant Lyapunov exponent of a filtered signal between 0.6 and 3.2. The partial degeneration, in turn, guides to quasi-symmetric distribution and the value of dominant Lyapunov exponent of 42 which is a typical value for systems with a source of the strongly nonhomogeneous external noise.

Parametric survey of longitudinal prominence oscillation simulations

NASA Astrophysics Data System (ADS)

Zhang, Q. M.; Chen, P. F.; Xia, C.; Keppens, R.; Ji, H. S.

2013-06-01

Context. Longitudinal filament oscillations recently attracted increasing attention, while the restoring force and the damping mechanisms are still elusive. Aims: We intend to investigate the underlying physics for coherent longitudinal oscillations of the entire filament body, including their triggering mechanism, dominant restoring force, and damping mechanisms. Methods: With the MPI-AMRVAC code, we carried out radiative hydrodynamic numerical simulations of the longitudinal prominence oscillations. We modeled two types of perturbations of the prominence, impulsive heating at one leg of the loop and an impulsive momentum deposition, which cause the prominence to oscillate. We studied the resulting oscillations for a large parameter scan, including the chromospheric heating duration, initial velocity of the prominence, and field line geometry. Results: We found that both microflare-sized impulsive heating at one leg of the loop and a suddenly imposed velocity perturbation can propel the prominence to oscillate along the magnetic dip. Our extensive parameter survey resulted in a scaling law that shows that the period of the oscillation, which weakly depends on the length and height of the prominence and on the amplitude of the perturbations, scales with √R/g⊙, where R represents the curvature radius of the dip, and g⊙ is the gravitational acceleration of the Sun. This is consistent with the linear theory of a pendulum, which implies that the field-aligned component of gravity is the main restoring force for the prominence longitudinal oscillations, as confirmed by the force analysis. However, the gas pressure gradient becomes significant for short prominences. The oscillation damps with time in the presence of non-adiabatic processes. Radiative cooling is the dominant factor leading to damping. A scaling law for the damping timescale is derived, i.e., τ~ l1.63 D0.66w-1.21v0-0.30, showing strong dependence on the prominence length l, the geometry of the magnetic dip (characterized by the depth D and the width w), and the velocity perturbation amplitude v0. The larger the amplitude, the faster the oscillation damps. We also found that mass drainage significantly reduces the damping timescale when the perturbation is too strong.

Temperature responsive transmitter

NASA Technical Reports Server (NTRS)

Kleinberg, Leonard L. (Inventor)

1987-01-01

A temperature responsive transmitter is provided in which frequency varies linearly with temperature. The transmitter includes two identically biased transistors connected in parallel. A capacitor, which reflects into the common bases to generate negative resistance effectively in parallel with the capacitor, is connected to the common emitters. A crystal is effectively in parallel with the capacitor and the negative resistance. Oscillations occur if the magnitude of the absolute value of the negative resistance is less than the positive resistive impedance of the capacitor and the inductance of the crystal. The crystal has a large linear temperature coefficient and a resonant frequency which is substantially less than the gain-bandwidth product of the transistors to ensure that the crystal primarily determines the frequency of oscillation. A high-Q tank circuit having an inductor and a capacitor is connected to the common collectors to increase the collector current flow which in turn enhances the radiation of the oscillator frequency by the inductor.

QPO observations related to neutron star equations of state

NASA Astrophysics Data System (ADS)

Stuchlik, Zdenek; Urbanec, Martin; Török, Gabriel; Bakala, Pavel; Cermak, Petr

We apply a genetic algorithm method for selection of neutron star models relating them to the resonant models of the twin peak quasiperiodic oscillations observed in the X-ray neutron star binary systems. It was suggested that pairs of kilo-hertz peaks in the X-ray Fourier power density spectra of some neutron stars reflect a non-linear resonance between two modes of accretion disk oscillations. We investigate this concept for a specific neutron star source. Each neutron star model is characterized by the equation of state (EOS), rotation frequency Ω and central energy density ρc . These determine the spacetime structure governing geodesic motion and position dependent radial and vertical epicyclic oscillations related to the stable circular geodesics. Particular kinds of resonances (KR) between the oscillations with epicyclic frequencies, or the frequencies derived from them, can take place at special positions assigned ambiguously to the spacetime structure. The pairs of resonant eigenfrequencies relevant to those positions are therefore fully given by KR,ρc , Ω, EOS and can be compared to the observationally determined pairs of eigenfrequencies in order to eliminate the unsatisfactory sets (KR,ρc , Ω, EOS). For the elimination we use the advanced genetic algorithm. Genetic algorithm comes out from the method of natural selection when subjects with the best adaptation to assigned conditions have most chances to survive. The chosen genetic algorithm with sexual reproduction contains one chromosome with restricted lifetime, uniform crossing and genes of type 3/3/5. For encryption of physical description (KR,ρ, Ω, EOS) into chromosome we used Gray code. As a fitness function we use correspondence between the observed and calculated pairs of eigenfrequencies.

Design and experimental validation of linear and nonlinear vehicle steering control strategies

NASA Astrophysics Data System (ADS)

Menhour, Lghani; Lechner, Daniel; Charara, Ali

2012-06-01

This paper proposes the design of three control laws dedicated to vehicle steering control, two based on robust linear control strategies and one based on nonlinear control strategies, and presents a comparison between them. The two robust linear control laws (indirect and direct methods) are built around M linear bicycle models, each of these control laws is composed of two M proportional integral derivative (PID) controllers: one M PID controller to control the lateral deviation and the other M PID controller to control the vehicle yaw angle. The indirect control law method is designed using an oscillation method and a nonlinear optimisation subject to H ∞ constraint. The direct control law method is designed using a linear matrix inequality optimisation in order to achieve H ∞ performances. The nonlinear control method used for the correction of the lateral deviation is based on a continuous first-order sliding-mode controller. The different methods are designed using a linear bicycle vehicle model with variant parameters, but the aim is to simulate the nonlinear vehicle behaviour under high dynamic demands with a four-wheel vehicle model. These steering vehicle controls are validated experimentally using the data acquired using a laboratory vehicle, Peugeot 307, developed by National Institute for Transport and Safety Research - Department of Accident Mechanism Analysis Laboratory's (INRETS-MA) and their performance results are compared. Moreover, an unknown input sliding-mode observer is introduced to estimate the road bank angle.

Dynamic localization in optical and Zeeman lattices in the presence of spin-orbit coupling

NASA Astrophysics Data System (ADS)

Kartashov, Yaroslav V.; Konotop, Vladimir V.; Zezyulin, Dmitry A.; Torner, Lluis

2016-12-01

The dynamic localization of a two-level atom in a periodic potential under the action of spin-orbit coupling and a weak harmonically varying linear force is studied. We consider optical and Zeeman potentials that are either in phase or out of phase in two spinor components, respectively. The expectation value for the position of the atom after one oscillation period of the linear force is recovered in authentic resonances or in pseudoresonances. The frequencies of the linear force corresponding to authentic resonances are determined by the band structure of the periodic potential and are affected by the spin-orbit coupling. The width or dispersion of the wave packet in authentic resonances is usually minimal. The frequencies corresponding to pseudoresonances do not depend on the type of potential and on the strength of the spin-orbit coupling, while the evolution of excitations at the corresponding frequencies is usually accompanied by significant dispersion. Pseudoresonances are determined by the initial phase of the linear force and by the quasimomentum of the wave packet. Due to the spinor nature of the system, the motion of the atom is accompanied by periodic, but not harmonic, spin oscillations. Under the action of spin-orbit coupling the oscillations of the wave packet can be nearly completely suppressed in optical lattices. Dynamic localization in Zeeman lattices is characterized by doubling of the resonant oscillation periods due to band crossing at the boundary of the Brillouin zone. We also show that higher harmonics in the Fourier expansion of the energy band lead to effective dispersion, which can be strong enough to prevent dynamic localization of the Bloch wave packet.

Fourier series expansion for nonlinear Hamiltonian oscillators.

PubMed

Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac

2010-06-01

The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.

CAVITY EXCITATION CIRCUIT

DOEpatents

Franck, J.V.

1959-10-20

An electronic oscillator is described for energizing a resonant cavity and to a system for stabilizing the operatin g frequency of the oscillator at the particular frequency necessary to establish a particular preferred field configuration or mode in the cavity, in this instance a linear accelerator. A freely rnnning oscillator has an output coupled to a resonant cavity wherein a field may be built up at any one of several adjacent frequencies. A pickup loop in the cavity is suitably shielded and positioned in the cavity so that only energy at the panticular desired frequency is fed back to stabilize the oscillator. A phase and gain control is in cluded in the feedback line.

Anatomical and functional assemblies of brain BOLD oscillations

PubMed Central

Baria, Alexis T.; Baliki, Marwan N.; Parrish, Todd; Apkarian, A. Vania

2011-01-01

Brain oscillatory activity has long been thought to have spatial properties, the details of which are unresolved. Here we examine spatial organizational rules for the human brain oscillatory activity as measured by blood oxygen level-dependent (BOLD). Resting state BOLD signal was transformed into frequency space (Welch’s method), averaged across subjects, and its spatial distribution studied as a function of four frequency bands, spanning the full bandwidth of BOLD. The brain showed anatomically constrained distribution of power for each frequency band. This result was replicated on a repository dataset of 195 subjects. Next, we examined larger-scale organization by parceling the neocortex into regions approximating Brodmann Areas (BAs). This indicated that BAs of simple function/connectivity (unimodal), vs. complex properties (transmodal), are dominated by low frequency BOLD oscillations, and within the visual ventral stream we observe a graded shift of power to higher frequency bands for BAs further removed from the primary visual cortex (increased complexity), linking frequency properties of BOLD to hodology. Additionally, BOLD oscillation properties for the default mode network demonstrated that it is composed of distinct frequency dependent regions. When the same analysis was performed on a visual-motor task, frequency-dependent global and voxel-wise shifts in BOLD oscillations could be detected at brain sites mostly outside those identified with general linear modeling. Thus, analysis of BOLD oscillations in full bandwidth uncovers novel brain organizational rules, linking anatomical structures and functional networks to characteristic BOLD oscillations. The approach also identifies changes in brain intrinsic properties in relation to responses to external inputs. PMID:21613505

Stability analysis of a time-periodic 2-dof MEMS structure

NASA Astrophysics Data System (ADS)

Kniffka, Till Jochen; Welte, Johannes; Ecker, Horst

2012-11-01

Microelectromechanical systems (MEMS) are becoming important for all kinds of industrial applications. Among them are filters in communication devices, due to the growing demand for efficient and accurate filtering of signals. In recent developments single degree of freedom (1-dof) oscillators, that are operated at a parametric resonances, are employed for such tasks. Typically vibration damping is low in such MEM systems. While parametric excitation (PE) is used so far to take advantage of a parametric resonance, this contribution suggests to also exploit parametric anti-resonances in order to improve the damping behavior of such systems. Modeling aspects of a 2-dof MEM system and first results of the analysis of the non-linear and the linearized system are the focus of this paper. In principle the investigated system is an oscillating mechanical system with two degrees of freedom x = [x1x2]T that can be described by Mx+Cx+K1x+K3(x2)x+Fes(x,V(t)) = 0. The system is inherently non-linear because of the cubic mechanical stiffness K3 of the structure, but also because of electrostatic forces (1+cos(ωt))Fes(x) that act on the system. Electrostatic forces are generated by comb drives and are proportional to the applied time-periodic voltage V(t). These drives also provide the means to introduce time-periodic coefficients, i.e. parametric excitation (1+cos(ωt)) with frequency ω. For a realistic MEM system the coefficients of the non-linear set of differential equations need to be scaled for efficient numerical treatment. The final mathematical model is a set of four non-linear time-periodic homogeneous differential equations of first order. Numerical results are obtained from two different methods. The linearized time-periodic (LTP) system is studied by calculating the Monodromy matrix of the system. The eigenvalues of this matrix decide on the stability of the LTP-system. To study the unabridged non-linear system, the bifurcation software ManLab is employed. Continuation analysis including stability evaluations are executed and show the frequency ranges for which the 2-dof system becomes unstable due to parametric resonances. Moreover, the existence of frequency intervals are shown where enhanced damping for the system is observed for this MEMS. The results from the stability studies are confirmed by simulation results.

Multi-scale Quantitative Precipitation Forecasting Using ...

EPA Pesticide Factsheets

Global sea surface temperature (SST) anomalies can affect terrestrial precipitation via ocean-atmosphere interaction known as climate teleconnection. Non-stationary and non-linear characteristics of the ocean-atmosphere system make the identification of the teleconnection signals difficult to be detected at a local scale as it could cause large uncertainties when using linear correlation analysis only. This paper explores the relationship between global SST and terrestrial precipitation with respect to long-term non-stationary teleconnection signals during 1981-2010 over three regions in North America and one in Central America. Empirical mode decomposition as well as wavelet analysis is utilized to extract the intrinsic trend and the dominant oscillation of the SST and precipitation time series in sequence. After finding possible associations between the dominant oscillation of seasonal precipitation and global SST through lagged correlation analysis, the statistically significant SST regions are extracted based on the correlation coefficient. With these characterized associations, individual contribution of these SST forcing regions linked to the related precipitation responses are further quantified through nonlinear modeling with the aid of extreme learning machine. Results indicate that the non-leading SST regions also contribute a salient portion to the terrestrial precipitation variability compared to some known leading SST regions. In some cases, these

Hub vortex helical instability as the origin of wake meandering in the lee of a model wind-turbine

NASA Astrophysics Data System (ADS)

Viola, Francesco; Iungo, Giacomo Valerio; Camarri, Simone; Porte-Agel, Fernando; Gallaire, Francois

2012-11-01

Wind tunnel measurements were performed for the wake produced by a three-bladed wind turbine immersed in uniform flow. These tests show the presence of a vorticity structure in the near wake region mainly oriented along the streamwise direction, which is denoted as hub vortex. The hub vortex is characterized by oscillations with frequencies lower than the one connected to the rotational velocity of the rotor, which are ascribed to wake meandering by previous works. This phenomenon consists in transversal oscillations of the wind turbine wake, which are excited by the shedding of vorticity structures from the rotor disc acting as a bluff body. In this work temporal and spatial linear stability analyses of a wind turbine wake are performed on a base flow obtained through time-averaged wind tunnel velocity measurements. This study shows that the low frequency spectral component detected experimentally is the result of a convective instability of the hub vortex, which is characterized by a counter-winding single-helix structure. Simultaneous hot-wire measurements confirm the presence of a helicoidal unstable mode of the hub vortex with a streamwise wavenumber roughly equal to the one predicted from the linear instability analysis.

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.

Higher-dimensional generalizations of the Watanabe–Strogatz transform for vector models of synchronization

NASA Astrophysics Data System (ADS)

Lohe, M. A.

2018-06-01

We generalize the Watanabe–Strogatz (WS) transform, which acts on the Kuramoto model in d  =  2 dimensions, to a higher-dimensional vector transform which operates on vector oscillator models of synchronization in any dimension , for the case of identical frequency matrices. These models have conserved quantities constructed from the cross ratios of inner products of the vector variables, which are invariant under the vector transform, and have trajectories which lie on the unit sphere S d‑1. Application of the vector transform leads to a partial integration of the equations of motion, leaving independent equations to be solved, for any number of nodes N. We discuss properties of complete synchronization and use the reduced equations to derive a stability condition for completely synchronized trajectories on S d‑1. We further generalize the vector transform to a mapping which acts in and in particular preserves the unit ball , and leaves invariant the cross ratios constructed from inner products of vectors in . This mapping can be used to partially integrate a system of vector oscillators with trajectories in , and for d  =  2 leads to an extension of the Kuramoto system to a system of oscillators with time-dependent amplitudes and trajectories in the unit disk. We find an inequivalent generalization of the Möbius map which also preserves but leaves invariant a different set of cross ratios, this time constructed from the vector norms. This leads to a different extension of the Kuramoto model with trajectories in the complex plane that can be partially integrated by means of fractional linear transformations.

Tunable optical nonreciprocity and a phonon-photon router in an optomechanical system with coupled mechanical and optical modes

NASA Astrophysics Data System (ADS)

Li, Guolong; Xiao, Xiao; Li, Yong; Wang, Xiaoguang

2018-02-01

We propose a multimode optomechanical system to realize tunable optical nonreciprocity that has the prospect of making an optical diode for information technology. The proposed model consists of two subsystems, each of which contains two optical cavities, injected with a classical field and a quantum signal via a 50:50 beam splitter, and a mechanical oscillator, coupled to both cavities via optomechanical coupling. Meanwhile two cavities and an oscillator in a subsystem are respectively coupled to their corresponding cavities and an oscillator in the other subsystem. Our scheme yields nonreciprocal effects at different frequencies with opposite directions, but each effective linear optomechanical coupling can be controlled by an independent classical one-frequency pump. With this setup one is able to apply quantum states with large fluctuations, which extends the scope of applicable quantum states, and exploit the independence of paths. Moreover, the optimal frequencies for nonreciprocal effects can be controlled by adjusting the relevant parameters. We also exhibit the path switching of two directions, from a mechanical input to two optical output channels, via tuning the signal frequency. In experiment, the considered scheme can be tuned to reach small damping rates of the oscillators relative to those of the cavities, which is more practical and requires less power than in previous schemes.

The influence of Reynolds numbers on resistance properties of jet pumps

DOE Office of Scientific and Technical Information (OSTI.GOV)

Geng, Q.; Graduate University of Chinese Academy of Sciences, Beijing 100049; Zhou, G.

2014-01-29

Jet pumps are widely used in thermoacoustic Stirling heat engines and pulse tube cryocoolers to eliminate the effect of Gedeon streaming. The resistance properties of jet pumps are principally influenced by their structures and flow regimes which are always characterized by Reynolds numbers. In this paper, the jet pump of which cross section contracts abruptly is selected as our research subject. Based on linear thermoacoustic theory, a CFD model is built and the oscillating flow of the working gas is simulated and analyzed with different Reynolds numbers in the jet pump. According to the calculations, the influence of different structuresmore » and Reynolds numbers on the resistance properties of the jet pump are analyzed and presented. The results show that Reynolds numbers have a great influence on the resistance properties of jet pumps and some empirical formulas which are widely used are unsuitable for oscillating flow with small Reynolds numbers. This paper provides a more comprehensive understanding on resistance properties of jet pumps with oscillating flow and is significant for the design of jet pumps in practical thermoacoustic engines and refrigerators.« less

Temperature compensation and temperature sensation in the circadian clock

PubMed Central

Kidd, Philip B.; Young, Michael W.; Siggia, Eric D.

2015-01-01

All known circadian clocks have an endogenous period that is remarkably insensitive to temperature, a property known as temperature compensation, while at the same time being readily entrained by a diurnal temperature oscillation. Although temperature compensation and entrainment are defining features of circadian clocks, their mechanisms remain poorly understood. Most models presume that multiple steps in the circadian cycle are temperature-dependent, thus facilitating temperature entrainment, but then insist that the effect of changes around the cycle sums to zero to enforce temperature compensation. An alternative theory proposes that the circadian oscillator evolved from an adaptive temperature sensor: a gene circuit that responds only to temperature changes. This theory implies that temperature changes should linearly rescale the amplitudes of clock component oscillations but leave phase relationships and shapes unchanged. We show using timeless luciferase reporter measurements and Western blots against TIMELESS protein that this prediction is satisfied by the Drosophila circadian clock. We also review evidence for pathways that couple temperature to the circadian clock, and show previously unidentified evidence for coupling between the Drosophila clock and the heat-shock pathway. PMID:26578788

The dynamics of scarlet fever epidemics in England and Wales in the 19th century.

PubMed Central

Duncan, C. J.; Duncan, S. R.; Scott, S.

1996-01-01

There was a marked rise in scarlet fever mortality in England and Wales in the mid-nineteenth century and spectral analysis of the registration details, 1847-80, shows that the interepidemic interval was 5-6 years, but after 1880 the endemic level fell and the fatal epidemics disappeared. The dynamics of the scarlet fever epidemics can be represented by a linearized mathematical model and because the system is lightly damped, it could be driven by an oscillation in susceptibility. Epidemics were significantly correlated with dry conditions in spring/summer (P < 0.001), suggesting that these produced a low amplitude oscillation in susceptibility which drove the system. Epidemics also correlated (P < 0.001) with an oscillation in wheat prices but at a lag of 3 years, suggesting that malnutrition during pregnancy caused increased susceptibility in the subsequent children which interacted synergistically with seasonal dry conditions. Scarlet fever mortality was sharply reduced after 1880 in parallel with falling wheat prices suggesting that the remarkable period of high scarlet fever mortality (1840-80) was dependent on poor nutritive levels during that time. PMID:8972674

The dynamics of scarlet fever epidemics in England and Wales in the 19th century.

PubMed

Duncan, C J; Duncan, S R; Scott, S

1996-12-01

There was a marked rise in scarlet fever mortality in England and Wales in the mid-nineteenth century and spectral analysis of the registration details, 1847-80, shows that the interepidemic interval was 5-6 years, but after 1880 the endemic level fell and the fatal epidemics disappeared. The dynamics of the scarlet fever epidemics can be represented by a linearized mathematical model and because the system is lightly damped, it could be driven by an oscillation in susceptibility. Epidemics were significantly correlated with dry conditions in spring/summer (P < 0.001), suggesting that these produced a low amplitude oscillation in susceptibility which drove the system. Epidemics also correlated (P < 0.001) with an oscillation in wheat prices but at a lag of 3 years, suggesting that malnutrition during pregnancy caused increased susceptibility in the subsequent children which interacted synergistically with seasonal dry conditions. Scarlet fever mortality was sharply reduced after 1880 in parallel with falling wheat prices suggesting that the remarkable period of high scarlet fever mortality (1840-80) was dependent on poor nutritive levels during that time.

The influence of Reynolds numbers on resistance properties of jet pumps

NASA Astrophysics Data System (ADS)

Geng, Q.; Zhou, G.; Li, Q.

2014-01-01

Jet pumps are widely used in thermoacoustic Stirling heat engines and pulse tube cryocoolers to eliminate the effect of Gedeon streaming. The resistance properties of jet pumps are principally influenced by their structures and flow regimes which are always characterized by Reynolds numbers. In this paper, the jet pump of which cross section contracts abruptly is selected as our research subject. Based on linear thermoacoustic theory, a CFD model is built and the oscillating flow of the working gas is simulated and analyzed with different Reynolds numbers in the jet pump. According to the calculations, the influence of different structures and Reynolds numbers on the resistance properties of the jet pump are analyzed and presented. The results show that Reynolds numbers have a great influence on the resistance properties of jet pumps and some empirical formulas which are widely used are unsuitable for oscillating flow with small Reynolds numbers. This paper provides a more comprehensive understanding on resistance properties of jet pumps with oscillating flow and is significant for the design of jet pumps in practical thermoacoustic engines and refrigerators.

Resilient guaranteed cost control of a power system.

PubMed

Soliman, Hisham M; Soliman, Mostafa H; Hassan, Mohammad F

2014-05-01

With the development of power system interconnection, the low-frequency oscillation is becoming more and more prominent which may cause system separation and loss of energy to consumers. This paper presents an innovative robust control for power systems in which the operating conditions are changing continuously due to load changes. However, practical implementation of robust control can be fragile due to controller inaccuracies (tolerance of resistors used with operational amplifiers). A new design of resilient (non-fragile) robust control is given that takes into consideration both model and controller uncertainties by an iterative solution of a set of linear matrix inequalities (LMI). Both uncertainties are cast into a norm-bounded structure. A sufficient condition is derived to achieve the desired settling time for damping power system oscillations in face of plant and controller uncertainties. Furthermore, an improved controller design, resilient guaranteed cost controller, is derived to achieve oscillations damping in a guaranteed cost manner. The effectiveness of the algorithm is shown for a single machine infinite bus system, and then, it is extended to multi-area power system.

Modeling cross-hole slug tests in an unconfined aquifer

DOE PAGES

Malama, Bwalya; Kuhlman, Kristopher L.; Brauchler, Ralf; ...

2016-06-28

Cross-hole slug test date are analyzed with an extended version of a recently published unconfined aquifer model accounting for waterable effects using the linearized kinematic condition. The use of cross-hole slug test data to characterize aquifer heterogeneity and source/observation well oscillation parameters is evaluated. The data were collected in a series of multi-well and multi-level pneumatic slug tests conducted at a site in Widen, Switzerland. Furthermore, the tests involved source and observation well pairs separated by distances of up to 4 m, and instrumented with pressure transducers to monitor aquifer response in discrete intervals.

Acoustic manipulation of oscillating spherical bodies: Emergence of axial negative acoustic radiation force

NASA Astrophysics Data System (ADS)

Rajabi, Majid; Mojahed, Alireza

2016-11-01

In this paper, emergence of negative axial acoustic radiation force on a rigid oscillating spherical body is investigated for acoustic manipulation purposes. The problem of plane acoustic wave scattering from an oscillating spherical body submerged in an ideal acoustic fluid medium is solved. For the case of oscillating direction collinear with the wave propagation wave number vector (desired path), it has been shown that the acoustic radiation force, as a result of nonlinear acoustic wave interaction with bodies can be expressed as a linear function of incident wave field and the oscillation properties of the oscillator (i.e., amplitude and phase of oscillation). The negative (i.e., pulling effects) and positive (i.e., pushing effects) radiation force situations are divided in oscillation complex plane with a specific frequency-dependant straight line. This characteristic line defines the radiation force cancellation state. In order to investigate the stability of the mentioned manipulation strategy, the case of misaligned oscillation of sphere with the wave propagation direction is studied. The proposed methodology may suggest a novel concept of single-beam acoustic handling techniques based on smart carriers.

Wave transience in a compressible atmosphere. I - Transient internal wave, mean-flow interaction. II - Transient equatorial waves in the quasi-biennial oscillation

NASA Technical Reports Server (NTRS)

Dunkerton, T. J.

1981-01-01

Analytical and numerical solutions are obtained in an approximate quasi-linear model, to describe the way in which vertically propagating waves give rise to mean flow accelerations in an atmosphere due to the effects of wave transience. These effects in turn result from compressibility and vertical group velocity feedback, and culminate in the spontaneous formation and descent of regions of strong mean wind shear. The numerical solutions display mean flow accelerations due to Kelvin waves in the equatorial stratosphere, with wave absorption altering the transience mechanism in such significant respects as causing the upper atmospheric mean flow acceleration to be very sensitive to the precise magnitude and distribution of the damping mechanisms. The numerical simulations of transient equatorial waves in the quasi-biennial oscillation are also considered.

Nonlinear oscillation of a rigid body over high- Tc superconductors supported by electro-magnetic forces

NASA Astrophysics Data System (ADS)

Sugiura, T.; Ogawa, S.; Ura, H.

2005-10-01

Characteristics of high- Tc superconducting levitation systems are no contact support and stable levitation without control. They can be applied to supporting mechanisms in machines, such as linear-drives and magnetically levitated trains. But small damping due to noncontact support and nonlinearity in the magnetic force can easily cause complicated phenomena of nonlinear dynamics. This research deals with nonlinear oscillation of a rigid bar supported at its both ends by electro-magnetic forces between superconductors and permanent magnets as a simple modeling of the above application. Deriving the equation of motion, we discussed an effect of nonlinearity in the magnetic force on dynamics of the levitated body: occurrence of combination resonance in the asymmetrical system. Numerical analyses and experiments were also carried out, and their results confirmed the above theoretical prediction.

Fermi surfaces in Kondo insulators

NASA Astrophysics Data System (ADS)

Liu, Hsu; Hartstein, Máté; Wallace, Gregory J.; Davies, Alexander J.; Ciomaga Hatnean, Monica; Johannes, Michelle D.; Shitsevalova, Natalya; Balakrishnan, Geetha; Sebastian, Suchitra E.

2018-04-01

We report magnetic quantum oscillations measured using torque magnetisation in the Kondo insulator YbB12 and discuss the potential origin of the underlying Fermi surface. Observed quantum oscillations as well as complementary quantities such as a finite linear specific heat capacity in YbB12 exhibit similarities with the Kondo insulator SmB6, yet also crucial differences. Small heavy Fermi sections are observed in YbB12 with similarities to the neighbouring heavy fermion semimetallic Fermi surface, in contrast to large light Fermi surface sections in SmB6 which are more similar to the conduction electron Fermi surface. A rich spectrum of theoretical models is suggested to explain the origin across different Kondo insulating families of a bulk Fermi surface potentially from novel itinerant quasiparticles that couple to magnetic fields, yet do not couple to weak DC electric fields.

Stochastic resonance in a fractional oscillator driven by multiplicative quadratic noise

NASA Astrophysics Data System (ADS)

Ren, Ruibin; Luo, Maokang; Deng, Ke

2017-02-01

Stochastic resonance of a fractional oscillator subject to an external periodic field as well as to multiplicative and additive noise is investigated. The fluctuations of the eigenfrequency are modeled as the quadratic function of the trichotomous noise. Applying the moment equation method and Shapiro-Loginov formula, we obtain the exact expression of the complex susceptibility and related stability criteria. Theoretical analysis and numerical simulations indicate that the spectral amplification (SPA) depends non-monotonicly both on the external driving frequency and the parameters of the quadratic noise. In addition, the investigations into fractional stochastic systems have suggested that both the noise parameters and the memory effect can induce the phenomenon of stochastic multi-resonance (SMR), which is previously reported and believed to be absent in the case of the multiplicative noise with only a linear term.

Source model of volcanic tremor: two-phase flow instability in a pipe-valve system

NASA Astrophysics Data System (ADS)

Fujita, E.

2003-12-01

Volcanic tremor at a shallow depth beneath the volcano is inferred to link to hydrothermal activities powered by heat supply from magma. In this study, we developed numerical simulations of the instabilities of the water-steam two-phase flow in a pipe-valve system and considered the source mechanism of volcanic tremor. The experiments of two-phase flow by Veziroglu and Lee [1968] revealed the two kinds of oscillating modes, density wave oscillation with the period of a few seconds and pressure drop oscillation with the period of dozens of seconds. These modes were mainly controlled by the pressure difference between inlet and outlet, flux rate of fluid and heat supply rate. Especially, the former mode appears when the flux rate is small and the latter does when the pressure difference and heat supply rate are larger. We performed some preliminary numerical simulation of these oscillations in water-steam flow in a cylindrical conduit. As an example, we assume the flow in conduit of 4 m length with the valves at inlet and outlet with the conditions of non-slip at the wall. As initial conditions, the inlet and outlet pressures are fixed to be 1.2E5 Pa and 1.0E5 Pa, respectively, water temperature of 370 K, heat supply of 1.0E6 - 2.0E7W/m3. The friction except the valve area is assumed to be 1000kg/m3. After the heating condition becomes stable, we shut the valve at the outlet and detect the significant oscillation. In case of the heat supply of 1.1E7W/m3, density drop oscillation with the period of 0.16s has appeared. In this model, the oscillation originates from the density change due to vaporization, and its information arrives at the outlet with the velocity of two-phase flow. The cycle of heating and boiling controls the interval of the tremor occurrence and the period is determined by the length of the pipe and the flow velocity. The shut of valve physically corresponds to geometrical narrowing, choking, and non-linear effect of flow and/or surrounding medium.

The Matrix Pencil and its Applications to Speech Processing

DTIC Science & Technology

2007-03-01

Elementary Linear Algebra ” 8th edition, pp. 278, 2000 John Wiley & Sons, Inc., New York [37] Wai C. Chu, “Speech Coding Algorithms”, New Jeresy: John...Ben; Daniel, James W.; “Applied Linear Algebra ”, pp. 342-345, 1988 Prentice Hall, Englewood Cliffs, NJ [35] Haykin, Simon “Applied Linear Adaptive...ABSTRACT Matrix Pencils facilitate the study of differential equations resulting from oscillating systems. Certain problems in linear ordinary