Limit-cycle oscillators subject to a delayed feedback
Erneux, T.; Grasman, J.
2008-01-01
The coexistence of two stable limit cycles exhibiting different periods is examined for a nonlinear oscillator subject to a delayed feedback. For the case of a weakly nonlinear oscillator, we discuss the validity of a previously determined phase equation. For the case of a strongly nonlinear oscilla
Synchronization of Limit Cycle Oscillators by Telegraph Noise
Goldobin, Denis S.
2014-01-01
We study the influence of telegraph noise on synchrony of limit cycle oscillators. Adopting the phase description for these oscillators, we derive the explicit expression for the Lyapunov exponent. We show that either for weak noise or frequent switching the Lyapunov exponent is negative, and the phase model gives adequate analytical results. In some systems moderate noise can desynchronize oscillations, and we demonstrate this for the Van der Pol--Duffing system.
On controlling networks of limit-cycle oscillators
Skardal, Per Sebastian; Arenas, Alex
2016-09-01
The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications ranging from the power grid to cardiac excitation. Here, we study the control of network-coupled limit cycle oscillators, extending the previous work that focused on phase oscillators. Based on stabilizing a target fixed point, our method aims to attain complete frequency synchronization, i.e., consensus, by applying control to as few oscillators as possible. We develop two types of controls. The first type directs oscillators towards larger amplitudes, while the second does not. We present numerical examples of both control types and comment on the potential failures of the method.
Collective dynamics of delay-coupled limit cycle oscillators
Abhijit Sen; Ramana Dodla; George L Johnston
2005-04-01
Coupled limit cycle oscillators with instantaneous mutual coupling offer a useful but idealized mathematical paradigm for the study of collective behavior in a wide variety of biological, physical and chemical systems. In most real-life systems however the interaction is not instantaneous but is delayed due to finite propagation times of signals, reaction times of chemicals, individual neuron firing periods in neural networks etc. We present a brief overview of the effect of time-delayed coupling on the collective dynamics of such coupled systems. Simple model equations describing two oscillators with a discrete time-delayed coupling as well as those describing linear arrays of a large number of oscillators with time-delayed global or local couplings are studied. Analytic and numerical results pertaining to time delay induced changes in the onset and stability of amplitude death and phase-locked states are discussed. A number of recent experimental and theoretical studies reveal interesting new directions of research in this field and suggest exciting future areas of exploration and applications.
Piecewise-linearized methods for oscillators with limit cycles
Ramos, J.I. [Room I-320-D, E.T.S. Ingenieros Industriales, Universidad de Malaga, Plaza El Ejido, s/n 29013 Malaga (Spain)] e-mail: jirs@lcc.uma.es
2006-03-01
A piecewise linearization method based on the linearization of nonlinear ordinary differential equations in small intervals, that provides piecewise analytical solutions in each interval and smooth solutions everywhere, is developed for the study of the limit cycles of smooth and non-smooth, conservative and non-conservative, nonlinear oscillators. It is shown that this method provides nonlinear maps for the displacement and velocity which depend on the previous values through the nonlinearity and its partial derivatives with respect to time, displacement and velocity, and yields non-standard finite difference formulae. It is also shown by means of five examples that the piecewise linearization method presented here is more robust and yields more accurate (in terms of displacement, energy and frequency) solutions than the harmonic balance procedure, the method of slowly varying amplitude and phase, and other non-standard finite difference equations.
Suppression and revival of oscillation in indirectly coupled limit cycle oscillators
Sharma, P.R.; Kamal, N.K.; Verma, U.K. [Department of Physics, Central University of Rajasthan, Ajmer 305 817, Rajasthan (India); Suresh, K. [Department of Physics, Anjalai Ammal-Engineering College, Koyilvenni 614 403, Tamil Nadu (India); Thamilmaran, K. [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu (India); Shrimali, M.D., E-mail: shrimali@curaj.ac.in [Department of Physics, Central University of Rajasthan, Ajmer 305 817, Rajasthan (India)
2016-09-16
Highlights: • The phenomena of suppression and revival of oscillations are studied in indirectly coupled nonlinear oscillators. • The decay parameter and a feedback factor play a crucial role in emergent dynamical behavior of oscillators. • The critical curves for different dynamical regions are obtained analytically using linear stability analysis. • Electronic circuit experiments demonstrate these emergent dynamical states. - Abstract: We study the phenomena of suppression and revival of oscillations in a system of limit cycle oscillators coupled indirectly via a dynamic local environment. The dynamics of the environment is assumed to decay exponentially with time. We show that for appropriate coupling strength, the decay parameter of the environment plays a crucial role in the emergent dynamics such as amplitude death (AD) and oscillation death (OD). We also show that introducing a feedback factor in the diffusion term revives the oscillations in this system. The critical curves for the regions of different emergent states as a function of coupling strength, decay parameter of the environment and feedback factor in the coupling are obtained analytically using linear stability analysis. These results are found to be consistent with the numerics and are also observed experimentally.
Alemela, Panduranga Reddy; Roman Casado, Juan; Tarband Veeraraghavan, Santos Kumar; Kok, Jim
2013-01-01
In this work comprehensive experimental and numerical studies incorporating the most relevant physical mechanisms causing limit cycle pressure and combustion rate oscillations (LCO) in a laboratory scale combustor will be discussed. The strong interaction between the aerodynamics-combustion-acoustic
Time Delay Effects on Coupled Limit Cycle Oscillators at Hopf Bifurcation
Reddy, D V R; Johnston, G L
1998-01-01
We present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple model consisting of just two oscillators with a time delayed coupling, the bifurcation diagram obtained by numerical and analytical solutions shows significant changes in the stability boundaries of the amplitude death, phase locked and incoherent regions. A novel result is the occurrence of amplitude death even in the absence of a frequency mismatch between the two oscillators. Similar results are obtained for an array of N oscillators with a delayed mean field coupling and the regions of such amplitude death in the parameter space of the coupling strength and time delay are quantified. Some general analytic results for the N tending to infinity (thermodynamic) limit are also obtained and the implications of the time delay effects for physical applications are discussed.
A theoretical study of limit cycle oscillations of plenum air cushions
Hinchey, M. J.; Sullivan, P. A.
1981-11-01
Air cushion vehicles (ACV) are prone to the occurrence of dynamic instabilities which frequently appear as stable finite amplitude oscillations. The aim of this work is to ascertain if the non-linearities characteristics of ACV dynamics generate limit cycle oscillations for cushion systems operating at conditions for which a linear theory predicts instability. The types of non-linearity that can occur are discussed, and an analysis is presented for a single cell flexible skirted plenum chamber constrained to move in pure heave only. Two cushion feed cases are considered: a plenum box supply and a duct. The results obtained by a Galerkin/describing function analysis are compared with those generated by a full numerical simulation. For the plenum box supply system, it is shown that the limit cycles can be suppressed by using a piston to introduce high frequency small amplitude volume oscillations into the plenum chamber.
Robust Nonlinear Regulation of Limit Cycle Oscillations in UAVs Using Synthetic Jet Actuators
Natalie Ramos Pedroza; William MacKunis; Golubev, Vladimir V.
2014-01-01
In this paper, a synthetic jet actuators (SJA)-based nonlinear robust controller is developed, which is capable of completely suppressing limit cycle oscillations (LCO) in UAV systems with parametric uncertainty in the SJA dynamics and unmodeled external disturbances. Specifically, the control law compensates for uncertainty in an input gain matrix, which results from the unknown airflow dynamics generated by the SJA. Challenges in the control design include compensation for input-multiplicat...
黄思训; 项杰; 韩威
2004-01-01
The troposphere and ocean mixed layer were considered as two components of a dynamic system operated by solar radiation as the constant source of energy, where upon an air-sea coupling selfexited coupling oscillation model was based with the aid of a locally averaged thermodynamic climate model, resulting mathematically in a closed self-governed dynamic system, a so-called El Nino-Southern Oscillation (ENSO) system. With the limit cycle solution of the system. It is shown that the essential physics of the coupled system can be described by the ENSO system. Compared with the observations, the theoretical limit cycle orbit matches the observed phase loop qualitatively. The ENSO system provides a useful theoretical framework for study of interannual variation of the tropical climate system.
Suppression of limit cycle oscillations using the nonlinear tuned vibration absorber
Habib, G.; Kerschen, G.
2015-01-01
The objective of this study is to mitigate, or even completely eliminate, the limit cycle oscillations in mechanical systems using a passive nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA). An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is not imposed a priori, as it is the case for most existing nonlinear absorbers. The NLTVA parameters are determined analytically using stability and bifurcation analyses, and the resulting design is validated using numerical continuation. The proposed developments are illustrated using a Van der Pol–Duffing primary system. PMID:27547085
One-dimensional modelling of limit-cycle oscillation and H-mode power scaling
Wu, Xingquan; Xu, Guosheng; Wan, Baonian; Rasmussen, Jens Juul; Naulin, Volker; Nielsen, Anders Henry
2015-05-01
To understand the connection between the dynamics of microscopic turbulence and the macroscale power scaling in the L-I-H transition in magnetically confined plasmas, a new time-dependent, one-dimensional (in radius) model has been developed. The model investigates the radial force balance equation at the edge region of the plasma and applies the quenching effect of turbulence via the E × B flow shear rate exceeding the shear suppression threshold. By slightly ramping up the heating power, the spatio-temporal evolution of turbulence intensity, density and pressure profiles, poloidal flow and E × B flow self-consistently displays the L-H transition with an intermediate phase (I-phase) characterized by limit-cycle oscillations. Since the poloidal flow is partially damped to the neoclassical flow in the edge region, the numerical results reveal two different oscillation relationships between the E × B flow and the turbulence intensity depending on which oscillation of the diamagnetic flow or poloidal flow is dominant. Specifically, by including the effects of boundary conditions of density and temperature, the model results in a linear dependence of the H-mode access power on the density and magnetic field. These results imply that the microscopic turbulence dynamics and the macroscale power scaling for the L-H transition are strongly connected.
Amplitude and Frequency Control: Stability of Limit Cycles in Phase-Shift and Twin-T Oscillators
J. P. Dada
2008-01-01
Full Text Available We show a technique for external direct current (DC control of the amplitudes of limit cycles both in the Phase-shift and Twin-T oscillators. We have found that amplitudes of the oscillator output voltage depend on the DC control voltage. By varying the total impedance of each oscillator oscillatory network, frequencies of oscillations are controlled using potentiometers. The main advantage of the proposed circuits is that both the amplitude and frequency of the waveforms generated can be independently controlled. Analytical, numerical, and experimental methods are used to determine the boundaries of the states of the oscillators. Equilibrium points, stable limit cycles, and divergent states are found. Analytical results are compared with the numerical and experimental solutions, and a good agreement is obtained.
Control of Limit Cycle Oscillations of a Two-Dimensional Aeroelastic System
M. Ghommem
2010-01-01
Full Text Available Linear and nonlinear static feedback controls are implemented on a nonlinear aeroelastic system that consists of a rigid airfoil supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. The normal form is used to investigate the Hopf bifurcation that occurs as the freestream velocity is increased and to analytically predict the amplitude and frequency of the ensuing limit cycle oscillations (LCO. It is shown that linear control can be used to delay the flutter onset and reduce the LCO amplitude. Yet, its required gains remain a function of the speed. On the other hand, nonlinear control can be effciently implemented to convert any subcritical Hopf bifurcation into a supercritical one and to significantly reduce the LCO amplitude.
Robust Nonlinear Regulation of Limit Cycle Oscillations in UAVs Using Synthetic Jet Actuators
Natalie Ramos Pedroza
2014-09-01
Full Text Available In this paper, a synthetic jet actuators (SJA-based nonlinear robust controller is developed, which is capable of completely suppressing limit cycle oscillations (LCO in UAV systems with parametric uncertainty in the SJA dynamics and unmodeled external disturbances. Specifically, the control law compensates for uncertainty in an input gain matrix, which results from the unknown airflow dynamics generated by the SJA. Challenges in the control design include compensation for input-multiplicative parametric uncertainty in the actuator dynamic model. The result was achieved via innovative algebraic manipulation in the error system development, along with a Lyapunov-based robust control law. A rigorous Lyapunov-based stability analysis is utilized to prove asymptotic LCO suppression, considering a detailed dynamic model of the pitching and plunging dynamics. Numerical simulation results are provided to demonstrate the robustness and practical performance of the proposed control law.
Theoretical analysis of saturation and limit cycles in short pulse FEL oscillators
Piovella, N.; Chaix, P.; Jaroszynski, D. [Commissariat a l`Energie Atomique, Bruyeres-le-Chatel (France)] [and others
1995-12-31
We derive a model for the non linear evolution of a short pulse oscillator from low signal up to saturation in the small gain regime. This system is controlled by only two independent parameters: cavity detuning and losses. Using a closure relation, this model reduces to a closed set of 5 non linear partial differential equations for the EM field and moments of the electron distribution. An analysis of the linearised system allows to define and calculate the eigenmodes characterising the small signal regime. An arbitrary solution of the complete nonlinear system can then be expanded in terms of these eigenmodes. This allows interpreting various observed nonlinear behaviours, including steady state saturation, limit cycles, and transition to chaos. The single mode approximation reduces to a Landau-Ginzburg equation. It allows to obtain gain, nonlinear frequency shift, and efficiency as functions of cavity detuning and cavity losses. A generalisation to two modes allows to obtain a simple description of the limit cycle behaviour, as a competition between these two modes. An analysis of the transitions to more complex dynamics is also given. Finally, the analytical results are compared to the experimental data from the FELIX experiment.
Kurebayashi, Wataru; Nakao, Hiroya
2015-01-01
The phase reduction method is a dimension reduction method for weakly driven limit-cycle oscillators, which has played an important role in the theoretical analysis of synchro- nization phenomena. Recently, we proposed a generalization of the phase reduction method [W. Kurebayashi et al., Phys. Rev. Lett. 111, 2013]. This generalized phase reduction method can robustly predict the dynamics of strongly driven oscillators, for which the conventional phase reduction method fails. In this generalized method, the external input to the oscillator should be properly decomposed into a slowly varying component and remaining weak fluctua- tions. In this paper, we propose a simple criterion for timescale decomposition of the external input, which gives accurate prediction of the phase dynamics and enables us to systematically apply the generalized phase reduction method to a general class of limit-cycle oscillators. The validity of the criterion is confirmed by numerical simulations.
Power harvesting by electromagnetic coupling from wind-induced limit cycle oscillations
Boccalero, G.; Olivieri, S.; Mazzino, A.; Boragno, C.
2017-09-01
Recent developments of low-power microprocessors open to new applications such as wireless sensor networks (WSN) with the consequent problem of autonomous powering. For this purpose, a possible strategy is represented by energy harvesting from wind or other flows exploiting fluid-structure interactions. In this work, we present an updated picture of a flutter-based device characterized by fully passive dynamics and a simple constructive layout, where limit cycle oscillations are undergone by an elastically bounded wing. In this case, the conversion from mechanical to electrical energy is performed by means of an electromagnetic coupling between a pair of coils and magnets. A centimetric-size prototype is shown to harvest energy from low wind velocities (between 2 and 4 m s-1), reaching a power peak of 14 mW, representing a valuable amount for applications related to WSN. A mathematical description of the nonlinear dynamics is then provided by a quasi-steady phenomenological model, revealing satisfactory agreement with the experimental framework within a certain parametric range and representing a useful tool for future optimizations.
Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations
Sandhu, Rimple; Poirel, Dominique; Pettit, Chris; Khalil, Mohammad; Sarkar, Abhijit
2016-07-01
A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid-structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib-Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.
Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations
Sandhu, Rimple [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Poirel, Dominique [Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario (Canada); Pettit, Chris [Department of Aerospace Engineering, United States Naval Academy, Annapolis, MD (United States); Khalil, Mohammad [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada)
2016-07-01
A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.
Limit-cycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery.
Layton, H E; Pitman, E B; Moore, L C
2000-02-01
A mathematical model was used to evaluate the potential effects of limit-cycle oscillations (LCO) on tubuloglomerular feedback (TGF) regulation of fluid and sodium delivery to the distal tubule. In accordance with linear systems theory, simulations of steady-state responses to infinitesimal perturbations in single-nephron glomerular filtration rate (SNGFR) show that TGF regulatory ability (assessed as TGF compensation) increases with TGF gain magnitude gamma when gamma is less than the critical value gamma(c), the value at which LCO emerge in tubular fluid flow and NaCl concentration at the macula densa. When gamma > gamma(c) and LCO are present, TGF compensation is reduced for both infinitesimal and finite perturbations in SNGFR, relative to the compensation that could be achieved in the absence of LCO. Maximal TGF compensation occurs when gamma approximately gamma(c). Even in the absence of perturbations, LCO increase time-averaged sodium delivery to the distal tubule, while fluid delivery is little changed. These effects of LCO are consequences of nonlinear elements in the TGF system. Because increased distal sodium delivery may increase the rate of sodium excretion, these simulations suggest that LCO enhance sodium excretion.
Numerical simulation of transonic limit cycle oscillations using high-order low-diffusion schemes
Wang, Baoyuan; Zha, Ge-Cheng
2010-05-01
This paper simulates the NLR7301 airfoil limit cycle oscillation (LCO) caused by fluid-structure interaction (FSI) using Reynolds averaged Navier-Stokes equations (RANS) coupled with Spalart-Allmaras (S-A) one-equation turbulence model. A low diffusion E-CUSP (LDE) scheme with 5th order weighted essentially nonoscillatory scheme (WENO) is employed to calculate the inviscid fluxes. A fully conservative 4th order central differencing is used for the viscous terms. A fully coupled fluid-structural interaction model is employed. For the case computed in this paper, the predicted LCO frequency, amplitudes, averaged lift and moment, all agree excellently with the experiment performed by Schewe et al. The solutions appear to have bifurcation and are dependent on the initial fields or initial perturbation. The developed computational fluid dynamics (CFD)/computational structure dynamics (CSD) simulation is able to capture the LCO with very small amplitudes measured in the experiment. This is attributed to the high order low diffusion schemes, fully coupled FSI model, and the turbulence model used. This research appears to be the first time that a numerical simulation of LCO matches the experiment. The simulation confirms several observations of the experiment.
Krediet, H.J.
2012-01-01
Thermo-acoustic analysis is crucial for a successful development of new gas turbine combustion systems. In this context, it becomes more and more necessary to predict the limit cycle pressure amplitude of thermo-acoustic combustion instabilities to figure out if they are within the critical design l
Krediet, H.J.
2012-01-01
Thermo-acoustic analysis is crucial for a successful development of new gas turbine combustion systems. In this context, it becomes more and more necessary to predict the limit cycle pressure amplitude of thermo-acoustic combustion instabilities to figure out if they are within the critical design l
Jewett, M. E.; Kronauer, R. E.; Brown, E. N. (Principal Investigator)
1998-01-01
In 1990, Kronauer proposed a mathematical model of the effects of light on the human circadian pacemaker. Although this model predicted many general features of the response of the human circadian pacemaker to light exposure, additional data now available enable us to refine the original model. We first refined the original model by incorporating the results of a dose response curve to light into the model's predicted relationship between light intensity and the strength of the drive onto the pacemaker. Data from three bright light phase resetting experiments were then used to refine the amplitude recovery characteristics of the model. Finally, the model was tested and further refined using data from an extensive phase resetting experiment in which a 3-cycle bright light stimulus was presented against a background of dim light. In order to describe the results of the four resetting experiments, the following major refinements to the original model were necessary: (i) the relationship between light intensity (I) and drive onto the pacemaker was reduced from I1/3 to I0.23 for light levels between 150 and 10,000 lux; (ii) the van der Pol oscillator from the original model was replaced with a higher-order limit cycle oscillator so that amplitude recovery is slower near the singularity and faster near the limit cycle; (iii) a direct effect of light on circadian period (tau x) was incorporated into the model such that as I increases, tau x decreases, which is in accordance with "Aschoff's rule". This refined model generates the following testable predictions: it should be difficult to enhance normal circadian amplitude via bright light; near the critical point of a type 0 phase response curve (PRC) the slope should be steeper than it is in a type 1 PRC; and circadian period measured during forced desynchrony should be directly affected by ambient light intensity.
A universal order parameter for synchrony in networks of limit cycle oscillators
Schröder, Malte; Timme, Marc; Witthaut, Dirk
2017-07-01
We analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of the introduced order parameters capture all transitions from incoherence over phase locking to full synchrony for arbitrary, finite networks. We then introduce an alternative, universal order parameter that accurately tracks the degree of partial phase locking and synchronization, adapting the traditional definition to account for the network topology and its influence on the phase coherence of the oscillators. We rigorously prove that this order parameter is strictly monotonously increasing with the coupling strength in the phase locked state, directly reflecting the dynamic stability of the network. Furthermore, it indicates the onset of full phase locking by a diverging slope at the critical coupling strength. The order parameter may find applications across systems where different types of synchrony are possible, including biological networks and power grids.
Gang Chen
2012-01-01
Full Text Available It is not easy for the system identification-based reduced-order model (ROM and even eigenmode based reduced-order model to predict the limit cycle oscillation generated by the nonlinear unsteady aerodynamics. Most of these traditional ROMs are sensitive to the flow parameter variation. In order to deal with this problem, a support vector machine- (SVM- based ROM was investigated and the general construction framework was proposed. The two-DOF aeroelastic system for the NACA 64A010 airfoil in transonic flow was then demonstrated for the new SVM-based ROM. The simulation results show that the new ROM can capture the LCO behavior of the nonlinear aeroelastic system with good accuracy and high efficiency. The robustness and computational efficiency of the SVM-based ROM would provide a promising tool for real-time flight simulation including nonlinear aeroelastic effects.
Phase reduction of weakly perturbed limit cycle oscillations in time-delay systems
Novičenko, V.; Pyragas, K.
2012-06-01
The phase reduction method is applied to a general class of weakly perturbed time-delay systems exhibiting periodic oscillations. The adjoint equation with an appropriate initial condition for the infinitesimal phase response curve of a time-delay system is derived. The method is demonstrated numerically for the Mackey-Glass equation as well as for a chaotic Rössler system subject to a delayed feedback control (DFC). We show that the profile of the phase response curve of a periodic orbit stabilized by the DFC algorithm does not depend on the control matrix. This property is universal and holds for any dynamical system subject to the DFC.
Zalian, Cyrus
2016-01-01
Context. The Blazhko effect, in RR Lyrae type stars, is a century old mystery. Dozens of theory exists, but none have been able to entirely reproduce the observational facts associated to this modulation phenomenon. Existing theory all rely on the usual continuous modelization of the star. Aims. We present a new paradigm which will not only explain the Blazhko effect, but at the same time, will give us alternative explanations to the red limit of the instability strip, the synchronization of layers, the mode selection and the existence of a limit cycle for radially pulsating stars. Methods. We describe the RR Lyrae type pulsating stars as a system of coupled nonlinear oscillators. Considering a spatial discretisation of the star, supposing a spherical symmetry, we develop the equation of motion and energy up to the third order in the radial and adiabatic case. Then, we include the influence of the ionization region as a relaxation oscillator by including elements from synchronisation theory. Results. This dis...
Bartels, Robert E.; Funk, Christie; Scott, Robert C.
2015-01-01
Research focus in recent years has been given to the design of aircraft that provide significant reductions in emissions, noise and fuel usage. Increases in fuel efficiency have also generally been attended by overall increased wing flexibility. The truss-braced wing (TBW) configuration has been forwarded as one that increases fuel efficiency. The Boeing company recently tested the Subsonic Ultra Green Aircraft Research (SUGAR) Truss-Braced Wing (TBW) wind-tunnel model in the NASA Langley Research Center Transonic Dynamics Tunnel (TDT). This test resulted in a wealth of accelerometer data. Other publications have presented details of the construction of that model, the test itself, and a few of the results of the test. This paper aims to provide a much more detailed look at what the accelerometer data says about the onset of aeroelastic instability, usually known as flutter onset. Every flight vehicle has a location in the flight envelope of flutter onset, and the TBW vehicle is not different. For the TBW model test, the flutter onset generally occurred at the conditions that the Boeing company analysis said it should. What was not known until the test is that, over a large area of the Mach number dynamic pressure map, the model displayed wing/engine nacelle aeroelastic limit cycle oscillation (LCO). This paper dissects that LCO data in order to provide additional insights into the aeroelastic behavior of the model.
Multiple Limit Cycles in an Immune System
Xun-cheng Huang; Le-min Zhu; Minaya Villasana
2008-01-01
The nonlinear oscillatory phenomenon has been observed in the system of immune response, which corresponds to the limit cycles in the mathematical models. We prove that the system simulating an immune response studied by Huang has at least three limit cycles in the system. The conditions for the multiple limit cycles are useful in analyzing the nonlinear oscillation in immune response.
Carnot cycle for an oscillator
Arnaud, Jacques; Chusseau, Laurent; Philippe, Fabrice
2002-09-01
In 1824 Carnot established that the efficiency of cyclic engines operating between a hot bath at absolute temperature Thot and a bath at a lower temperature Tcold cannot exceed 1 - Tcold/Thot. We show that linear oscillators alternately in contact with hot and cold baths obey this principle in the quantum as well as classical regime. The expression of the work performed is derived from a simple prescription. Reversible and non-reversible cycles are illustrated. The paper begins with historical considerations and is essentially self-contained.
Limit cycle behaviour in FELIX
Jaroszynski, D. A.; Bakker, R. J.; Oepts, D.; van der Meer, A. F. G.; van Amersfoort, P. W.
1993-07-01
The free electron laser for infrared experiments (FELIX) operates at wavelengths up to λ = 110 μm. A radio-frequency linear accelerator is used to produce electron micropulses with a duration of about 3 ps. With N = 38 undulator periods, this puts FELIX well into the regime where the slippage length, Nλ, exceeds the electron micropulse length, and prominent short pulse effects are expected. One of these effects, stable limit cycle oscillations of the pulse energy, has not been detected experimentally before. Such oscillations occur when the saturated optical pulses move away from the electron pulses, due to the changing balance between lethargy and desynchronism, while new subpulses grow periodically. In FELIX, limit cycle behaviour is clearly demonstrated. The observations are in agreement with numerical simulations of the pulse propagation, and the oscillation period is given by a simple formula containing the slippage length and the desynchronism between optical and electron pulses. We also show how lethargic behaviour can be used to reduce the optical bandwidth of the FEL and to store optical energy in the optical cavity without saturation limiting the energy stored.
ZHOU Ming-gang; HUANG Qi-bai; WANG Yong; XU Zhi-sheng
2007-01-01
This paper presents the research on the laws of systematic-parameter dependent variation in the vibration amplitude of drum-brake limit cycle oscillations (LCO). We established a two-degree non-linear dynamic model to describe the low-frequency vibration of the drum brake, applied the centre manifold theory to simplify the system, and obtained the LCO amplitude by calculating the normal form of the simplified system at the Hopf bifurcation point. It is indicated that when the friction coefficient is smaller than the friction coefficient at the bifurcation point, the amplitude decreases; whereas with a friction coefficient larger than the friction coefficient of bifurcation point, LCO occurs. The results suggest that it is applicable to suppress the LCO amplitude by changing systematic parameters, and thus improve the safety and ride comfort when applying brake. These findings can be applied to guiding the design of drum brakes.
Understanding Oscillations of the Geological Carbon Cycle
Bachan, A.; Payne, J.; Saltzman, M.; Thomas, E.; Kump, L. R.
2015-12-01
The geological cycling of carbon ties together the sedimentary reservoirs with Earth's biosphere and climate. Perturbations to this coupled system are recorded in the carbon isotopic composition of marine limestones (δ13Ccarb). In the past decade numerous intervals of large-amplitude oscillations in δ13Ccarbhave been identified, with a variety of explanations proposed for individual events. Yet, when data spanning the past ~1 Ga are viewed as a whole, it is clear that large-scale oscillations are a common feature of the carbon isotopic record. The ubiquity of oscillations suggests that they may share a single origin rather than having many disparate causes. Here we present a simple two-box model of the geological carbon cycle exhibiting such oscillations: the Carbon-Cycle Oscillator. Analogous to a damped mass-spring system, the burial fluxes of carbonate and phosphate in the model act like friction, whereas P supply and Corg burial act like the restoring force of the spring. When the sensitivities of P supply and Corg burial to the sizes of the C and P reservoirs, respectively, increase above a critical threshold, the model exhibits oscillations upon perturbation. We suggest that intervals with large oscillations in bulk ocean-atmosphere δ13C are characterized by a greater sensitivity of the C:P burial-ratio and ALK:P weathering-ratio to the state of the ocean-atmosphere carbon pool. In addition, moderating of the slope of that dependence in general can account for the observed decrease in the amplitude of oscillations over the past billion years. We hypothesize that factors with a unidirectional trajectory during Earth history (e.g. increased oxygenation of the deep ocean, and evolution of pelagic calcifiers) led to a decrease in the Earth System's gain and increase in its resilience over geologic time, even in the face of continuing perturbations from the solid Earth and extraterrestrial realms.
Limit cycles in quantum systems
Niemann, Patrick
2015-04-27
In this thesis we investigate Limit Cycles in Quantum Systems. Limit cycles are a renormalization group (RG) topology. When degrees of freedom are integrated out, the coupling constants flow periodically in a closed curve. The presence of limit cycles is restricted by the necessary condition of discrete scale invariance. A signature of discrete scale invariance and limit cycles is log-periodic behavior. The first part of this thesis is concerned with the study of limit cycles with the similarity renormalization group (SRG). Limit cycles are mainly investigated within conventional renormalization group frameworks, where degrees of freedom, which are larger than a given cutoff, are integrated out. In contrast, in the SRG potentials are unitarily transformed and thereby obtain a band-diagonal structure. The width of the band structure can be regarded as an effective cutoff. We investigate the appearance of limit cycles in the SRG evolution. Our aim is to extract signatures as well as the scaling factor of the limit cycle. We consider the 1/R{sup 2}-potential in a two-body system and a three-body system with large scattering lengths. Both systems display a limit cycle. Besides the frequently used kinetic energy generator we apply the exponential and the inverse generator. In the second part of this thesis, Limit Cycles at Finite Density, we examine the pole structure of the scattering amplitude for distinguishable fermions at zero temperature in the medium. Unequal masses and a filled Fermi sphere for each fermion species are considered. We focus on negative scattering lengths and the unitary limit. The properties of the three-body spectrum in the medium and implications for the phase structure of ultracold Fermi gases are discussed.
Wen Hua ZHANG; Jiu Li LUO
2004-01-01
The thermokinetic behavior of the B-Z reaction system was influenced by both the chemical reaction-heat conduction coupling and the temperature undulation due to temperature controlling of heat compensation type. Quantitative research indicated that this kind of temperature fluctuation will lead to limit cycle degeneration and the periodic or quasi-periodic response behavior of the focus near a supercritical Hopf bifurcation.
Limit cycle vibrations in turbomachinery
Ryan, S. G.
1991-01-01
The focus is on an examination of rotordynamic systems which are simultaneously susceptible to limit cycle instability and subharmonic response. Characteristics of each phenomenon are determined as well as their interrelationship. A normalized, single mass rotor model is examined as well as a complex model of the high pressure fuel turbopump and the Space Shuttle Main Engine. Entrainment of limit cycle instability by subharmonic response is demonstrated for both models. The nonuniqueness of the solution is also demonstrated.
Backaction limits on self-sustained optomechanical oscillations
Poot, M; Bagheri, M; Pernice, W H P; Tang, H X
2012-01-01
The maximum amplitude of mechanical oscillators coupled to optical cavities are studied both analytically and numerically. The optical backaction on the resonator enables self-sustained oscillations whose limit cycle is set by the dynamic range of the cavity. The maximum attainable amplitude and the phonon generation quantum efficiency of the backaction process are studied for both unresolved and resolved cavities. Quantum efficiencies far exceeding one are found in the resolved sideband regime where the amplitude is low. On the other hand the maximum amplitude is found in the unresolved system. Finally, the role of mechanical nonlinearities is addressed.
Limit cycle dynamics in swimming systems
Finkel, Cyndee; von Ellenrieder, Karl
2013-11-01
An experimental apparatus was constructed to model basic features expected in the flow about a freely swimming fish. A D-shaped cylinder is used to represent the body and an oscillating foil, the tail. The swimming system is suspended in a constant freestream flow. A closed loop PI controller is used to maintain a set point, stream-wise location. The system is released from multiple downstream and upstream locations and permitted to swim to the set point. The Strouhal number measured when the swimming system achieves a constant forward swimming speed is compared to values observed in nature. The results suggest that self-regulation passively selects the Strouhal number and that no other external sensory input is necessary for this to happen. This self-regulation is a result of a limit cycle process that stems from nonlinear periodic oscillations. Phase plane analyses are used to examine the synchronous conditions due to the coupling of the foil and wake vortices. It is shown that the phase locking indices depend on the Strouhal number and approach a frequency locking ratio of about 0 . 5 . The results suggest that Strouhal number selection in steady forward natural swimming is the result of a limit cycle process and not actively controlled by an organism.
Jacobs, Henry O
2012-01-01
Steady swimming can be characterized as both periodic and stable. These characteristics are the very definition of limit cycles, and so we ask "Can we view swimming as a limit cycle?" In this paper we will find that the answer is "yes". We will define a class of dissipative systems which correspond to the passive dynamics of a body immersed in a Navier-Stokes fluid (i.e. the dynamics of a dead fish). Upon performing reduction by symmetry we will find a hyperbolically stable fixed point which corresponds to the stability of a dead fish in stagnant water. Given a periodic force on the shape of the body we will invoke the persistence theorem to assert the existence of a loop which approximately satisfies the exact equations of motion. If we lift this loop with a phase reconstruction formula we will find that the lifted loops are not loops, but stable trajectories which represent regular periodic motion reminiscent of swimming.
Limit Cycles Sparked by Mutation in the Repeated Prisoner's Dilemma
Toupo, Danielle F P; Strogatz, Steven H
2015-01-01
We explore a replicator-mutator model of the repeated Prisoner's Dilemma involving three strategies: always cooperate (ALLC), always defect (ALLD), and tit-for-tat (TFT). The dynamics resulting from single unidirectional mutations are considered, with detailed results presented for the mutations TFT $\\rightarrow$ ALLC and ALLD $\\rightarrow$ ALLC. For certain combinations of parameters, given by the mutation rate $\\mu$ and the complexity cost $c$ of playing tit-for-tat, we find that the population settles into limit cycle oscillations, with the relative abundance of ALLC, ALLD, and TFT cycling periodically. Surprisingly, these oscillations can occur for unidirectional mutations between any two strategies. In each case, the limit cycles are created and destroyed by supercritical Hopf and homoclinic bifurcations, organized by a Bogdanov-Takens bifurcation. Our results suggest that stable oscillations are a robust aspect of a world of ALLC, ALLD, and costly TFT; the existence of cycles does not depend on the deta...
游波; 岑理相
2015-01-01
Understanding the non-Markovian dynamics of dissipative processes induced by memory effects of the environment is a fundamental subject of open quantum systems. Because of the complexity of open quantum systems, e.g., the multiple energy scales involving that of the system, the environment, and their mutual coupling, it is generally a challenging task to characterize the relationship among the parameters of the system dynamics and the reservoir spectra. For the two-level spontaneous emission model within structured environments, it was shown in a recent literature (Opt. Lett. 38, 3650) that a functional relation could be established between the asymptotically non-decaying population and the spectral density of the reservoir as the system undergoes a long-time evolution. It hence renders a distinct perspective to look into the character of long-lived quantum coherence in the corresponding non-Markovian process. This article is devoted to further investigate the phenomena of limit cycle oscillations possibly occurring in such non-Markovian dissipative systems in a long-time evolution. For a two-level system subjected to an environment with Ohmic class spectra, due to the presence of a unique bound-state mode of the system, the evolution trajectory of the given initial states will converge to a limit cycle in the Bloch space. The dependence of the radius and the location of the limit cycle on the spectral density function of the reservoir are manifested by virtue of the described functional relation. For the model subjected to a photonic crystal environment with multiple bands, our studies reveal that, owing to the presence of two or more bound states, the evolution trajectory of the system will converge to a toric curve of a paraboloid in the Bloch space and the phenomena of periodic or quasi-periodic oscillations could exhibit. While the equation of the parabolic curve is fully determined by the initial values of the state vector in the Bloch space, our results
Limit-Cycle Dynamics with Reduced Sensitivity to Perturbations (Postprint)
2015-01-01
described mathematically as a limit cycle, are funda- mental components in complex systems such as biolog - ical oscillators and technological...perturbations can negatively impact the stability of a high-frequency oscillator. Here we demonstrate that nonlinear dynamics, which usually degrades system...parts of the complex refractive index variation with car- rier density, while A and B describe coupling terms that depend on the steady-state bias current
Limit-cycle dynamics with reduced sensitivity to perturbations.
Simpson, Thomas B; Liu, Jia-Ming; AlMulla, Mohammad; Usechak, Nicholas G; Kovanis, Vassilios
2014-01-17
Limit-cycle oscillators are used to model a broad range of periodic nonlinear phenomena. Using the optically injected semiconductor laser as a paradigmatic example, we demonstrate that at specific operating points, the period-one oscillation frequency is simultaneously insensitive to multiple perturbation sources. In our system these include the temperature fluctuations experienced by the master and slave lasers as well as fluctuations in the bias current applied to the slave laser. Tuning of the oscillation frequency then depends only on the injected optical field amplitude. Experimental measurements are in detailed quantitative agreement with numerical modeling. These special operating points should prove valuable for developing ultrastable nonlinear oscillators, such as a narrow-linewidth, frequency-tunable photonic microwave oscillator.
Bifurcation of limit cycles near equivariant compound cycles
2007-01-01
In this paper we study some equivariant systems on the plane. We first give some criteria for the outer or inner stability of compound cycles of these systems. Then we investigate the number of limit cycles which appear near a compound cycle of a Hamiltonian equivariant system under equivariant perturbations. In the last part of the paper we present an application of our general theory to show that a Z3 equivariant system can have 13 limit cycles.
Trapping Phenomenon Attenuates Tipping Points for Limit Cycles
Medeiros, Everton S; Baptista, Murilo S; Feudel, Ulrike
2016-01-01
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical behavior. While tipping in a fold bifurcation of an equilibrium is well understood, much less is known about tipping of oscillations (limit cycles) though this dynamics are the typical response of many natural systems to a periodic external forcing, like e.g. seasonal forcing in ecology and climate sciences. We provide a detailed analysis of tipping phenomena in periodically forced systems and show that, when limit cycles are considered, a transient structure, so-called channel, plays a fundamental role in the transition. Specifically, we demonstrate that trajectories crossing such channel conserve, for a characteristic time, the twisting behavior of the stable limit cycle destroyed in the fold bifurcation of cycles. As a consequence, this channel acts like a ghost of the limit...
Toward efficient aeroelastic energy harvesting through limit cycle shaping
Kirschmeier, Benjamin; Bryant, Matthew
2016-04-01
Increasing demand to harvest energy from renewable resources has caused significant research interest in unsteady aerodynamic and hydrodynamic phenomena. Apart from the traditional horizontal axis wind turbines, there has been significant growth in the study of bio-inspired oscillating wings for energy harvesting. These systems are being built to harvest electricity for wireless devices, as well as for large scale mega-watt power generation. Such systems can be driven by aeroelastic flutter phenomena which, beyond a critical wind speed, will cause the system to enter into limitcycle oscillations. When the airfoil enters large amplitude, high frequency motion, leading and trailing edge vortices form and, when properly synchronized with the airfoil kinematics, enhance the energy extraction efficiency of the device. A reduced order dynamic stall model is employed on a nonlinear aeroelastic structural model to investigate whether the parameters of a fully passive aeroelastic device can be tuned to produce limit cycle oscillations at desired kinematics. This process is done through an optimization technique to find the necessary structural parameters to achieve desired structural forces and moments corresponding to a target limit cycle. Structural nonlinearities are explored to determine the essential nonlinearities such that the system's limit cycle closely matches the desired kinematic trajectory. The results from this process demonstrate that it is possible to tune system parameters such that a desired limit cycle trajectory can be achieved. The simulations also demonstrate that the high efficiencies predicted by previous computational aerodynamics studies can be achieved in fully passive aeroelastic devices.
An Intracellular Calcium Oscillations Model Including Mitochondrial Calcium Cycling
SHI Xiao-Min; LIU Zeng-Rong
2005-01-01
@@ Calcium is a ubiquitous second messenger. Mitochondria contributes significantly to intracellular Ca2+ dynamics.The experiment of Kaftan et al. [J. Biol. Chem. 275(2000) 25465] demonstrated that inhibiting mitochondrial Ca2+ uptake can reduce the frequency of cytosolic Ca2+ concentration oscillations of gonadotropes. By considering the mitochondrial Ca2+ cycling we develop a three-variable model of intracellular Ca2+ oscillations based on the models of Atri et al. [Biophys. J. 65 (1993) 1727] and Falcke et al. [Biophys. J. 77 (1999) 37]. The model reproduces the fact that mitochondrial Ca2+ cycling increases the frequency of cytosolic Ca2+ oscillations, which accords with Kaftan's results. Moreover the model predicts that when the mitochondria overload with Ca2+, the cytosolic Ca2+ oscillations vanish, which may trigger apoptosis.
Asymptotic Limit of a Singularly Perturbed Stationary Diffusion Equation: The Case of a Limit Cycle
Ge, Hao
2010-01-01
A limit cycle for a nonlinear ordinary differential equation has a sustained, stationary oscillation in time; Any non-trivial stationary stochastic process also exhibits stationary oscillations in time, though with randomness and a stationary probability density. A reconciliation of these two views of oscillatory dynamics has been elusive, although it becomes increasingly important in the biochemical modeling of cellular dynamics, where stochatic models based on the chemical master equation and the deterministic model based on the Law of Mass Action are routinely compared. Using a singularly perturbed stationary diffusion equation as a model for the chemical master equation with sufficiently large volume, $\\epsilon \\leftrightarrow 1/V$, we show that its stationary solution $u(\\vx)$ exhibits a clear separation of the exponentially and algebraic small contributions: $u(\\vx)=C_{\\epsilon}(\\vx) e^{-\\phi(\\vx)/\\epsilon}$, in which $\\phi(x)\\ge 0$ and $=0$ on the entire stable limit cycle. On the limit cycle, $C_0(\\vx...
Strong feedback limit of the Goodwin circadian oscillator
Woller, Aurore; Gonze, Didier; Erneux, Thomas
2013-03-01
The three-variable Goodwin model constitutes a prototypical oscillator based on a negative feedback loop. It was used as a minimal model for circadian oscillations. Other core models for circadian clocks are variants of the Goodwin model. The Goodwin oscillator also appears in many studies of coupled oscillator networks because of its relative simplicity compared to other biophysical models involving a large number of variables and parameters. Because the synchronization properties of Goodwin oscillators still remain difficult to explore mathematically, further simplifications of the Goodwin model have been sought. In this paper, we investigate the strong negative feedback limit of Goodwin equations by using asymptotic techniques. We find that Goodwin oscillations approach a sequence of decaying exponentials that can be described in terms of a single-variable leaky integrated-and-fire model.
Limit cycles can reduce the width of the habitable zone
Haqq-Misra, Jacob; Batalha, Natasha E; Harman, Chester E; Kasting, James F
2016-01-01
The liquid water habitable zone (HZ) describes the orbital distance at which a terrestrial planet can maintain above-freezing conditions through regulation by the carbonate-silicate cycle. Recent calculations have suggested that planets in the outer regions of the habitable zone cannot maintain stable, warm climates, but rather should oscillate between long, globally glaciated states and shorter periods of climatic warmth. Such conditions, similar to 'Snowball Earth' episodes experienced on Earth, would be inimical to the development of complex land life, including intelligent life. Here, we build upon previous studies with an updated an energy balance climate model to calculate this 'limit cycle' region of the habitable zone where such cycling would occur. We argue that an abiotic Earth would have a greater CO$_2$ partial pressure than today because plants and other biota help to enhance the storage of CO$_2$ in soil. When we tune our abiotic model accordingly, we find that limit cycles can occur but that pr...
Desipramine restricts estral cycle oscillations in swimming.
Contreras, C M; Martínez-Mota, L; Saavedra, M
1998-10-01
1. Desipramine (DMI) is a tricyclic antidepressant which reduces the immobility in rats forced to swim; however, it is unknown whether estral cycle phases impinge on DMI actions on immobility in daily swimming tests during several weeks. 2. In female wistar rats, vaginal smears taken before testing defined four estral phases. Afterwards, the authors assessed the latency for the first period of immobility in five-min forced swim tests practiced on 21-day DMI (DMI group), 21-day washout saline given after a 21-day DMI treatment (washout-saline group), or non-treated rats (control group). 3. We observed a longer latency for the first period of immobility in proestrus-estrus from the control and washout-saline groups. The 21-day treatment with DMI (2.1 mg/kg i.p., once a day) significantly (p estral cycle phase. 4. It is concluded that proestrus-estrus relates to increased struggling behavior. DMI enhances struggling behavior independently of hormonal state.
Regions of Attraction for Hybrid Limit Cycles of Walking Robots
Manchester, Ian R; Levashov, Michael; Tedrake, Russ
2010-01-01
This paper illustrates the application of recent research in region-of-attraction analysis for nonlinear hybrid limit cycles. Three example systems are analyzed in detail: the van der Pol oscillator, the "rimless wheel", and the "compass gait", the latter two being simplified models of underactuated walking robots. The method used involves decomposition of the dynamics about the target cycle into tangential and transverse components, and a search for a Lyapunov function in the transverse dynamics using sum-of-squares analysis (semidefinite programming). Each example illuminates different aspects of the procedure, including optimization of transversal surfaces, the handling of impact maps, optimization of the Lyapunov function, and orbitally-stabilizing control design.
Rong, Zhen; Deng, Xueying; Ma, Baofeng; Wang, Bing
2016-01-01
...° swept wing configuration undergoing a limit cycle oscillation using a synchronous measurement and control technique of wing rock/particle image velocimetry/dynamic pressure associated with the time...
Synthesis of Oscillators Using Limit Variables and NAM Expansion
Ahmed M. Soliman
2011-01-01
Full Text Available A systematic synthesis procedure for generating second-order grounded passive element canonic oscillators is given. The synthesis procedure is based on using nodal admittance matrix (NAM expansion with the bracket method as well as using the infinity parameters. The resulting derived oscillators include circuits using various types of current conveyors. Two classes of oscillators are considered in this paper, and they have the advantages of having independent control on the condition of oscillation and on the frequency of oscillation by varying two different grounded resistors. The two classes of oscillators considered can be easily compensated for the parasitic element effects introduced by the current conveyors. This paper is considered to be continuation to the recently published paper on oscillators using NAM expansion D. G. Haigh et al. (2006. This is the first paper in the literature which uses limit-variables called infinity-variables D. G. Haigh et al. (2005 in the synthesis of oscillator circuits. Simulation results demonstrating the practicality of some of the generated circuits are included.
Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators
Villanueva, L. G.; Kenig, E.; Karabalin, R. B.; Matheny, M. H.; Lifshitz, Ron; Cross, M. C.; Roukes, M. L.
2013-01-01
In its most basic form an oscillator consists of a resonator driven on resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic regime. Contrary to this conventional paradigm, in this Letter we show that by operating the oscillator at special points in the resonator’s anharmonic regime we can overcome fundamental limitations of oscillator performance due to thermodynamic noise as well as practical limitations due to noise from the sustaining circuit. We develop a comprehensive model that accounts for the major contributions to the phase noise of the nonlinear oscillator. Using a nano-electromechanical system based oscillator, we experimentally verify the existence of a special region in the operational parameter space that enables suppressing the most significant contributions to the oscillator’s phase noise, as predicted by our model. PMID:23679770
Limit cycle walking on a regularized ground
Jacobs, Henry O
2012-01-01
The singular nature of contact problems, such as walking, makes them difficult to analyze mathematically. In this paper we will "regularize" the contact problem of walking by approximating the ground with a smooth repulsive potential energy and a smooth dissipative friction force. Using this model we are able to prove the existence of a limit cycle for a periodically perturbed system which consists of three masses connected by springs. In particular, this limit cycle exists in a symmetry reduced phase. In the unreduced phase space, the motion of the masses resembles walking.
Limit Cycles Can Reduce the Width of the Habitable Zone
Haqq-Misra, Jacob; Kopparapu, Ravi Kumar; Batalha, Natasha E.; Harman, Chester E.; Kasting, James F.
2016-08-01
The liquid water habitable zone (HZ) describes the orbital distance at which a terrestrial planet can maintain above-freezing conditions through regulation by the carbonate-silicate cycle. Recent calculations have suggested that planets in the outer regions of the HZ cannot maintain stable, warm climates, but rather should oscillate between long, globally glaciated states and shorter periods of climatic warmth. Such conditions, similar to “Snowball Earth” episodes experienced on Earth, would be inimical to the development of complex land life, including intelligent life. Here, we build on previous studies with an updated energy balance climate model to calculate this “limit cycle” region of the HZ where such cycling would occur. We argue that an abiotic Earth would have a greater CO2 partial pressure than today because plants and other biota help to enhance the storage of CO2 in soil. When we tune our abiotic model accordingly, we find that limit cycles can occur but that previous calculations have overestimated their importance. For G stars like the Sun, limit cycles occur only for planets with CO2 outgassing rates less than that on modern Earth. For K- and M-star planets, limit cycles should not occur; however, M-star planets may be inhospitable to life for other reasons. Planets orbiting late G-type and early K-type stars retain the greatest potential for maintaining warm, stable conditions. Our results suggest that host star type, planetary volcanic activity, and seafloor weathering are all important factors in determining whether planets will be prone to limit cycling.
Theory for Diffusion-Limited Oscillating Chemical Reactions
Bussemaker, H J
1997-01-01
A kinetic description of lattice-gas automaton models for reaction-diffusion systems is presented. It provides corrections to the mean-field rate equations in the diffusion-limited regime. When applied to the two-species Maginu model, the theory gives an excellent quantitative prediction of the effect of slow diffusion on the periodic oscillations of the average concentrations in a spatially homogeneous state.
Physiology of Saccharomyces cerevisiae during cell cycle oscillations.
Duboc, P; Marison, I; von Stockar, U
1996-10-18
Synchronized populations of Saccharomyces cerevisiae CBS 426 are characterized by autonomous oscillations of process variables. CO2 evolution rate, O2 uptake rate and heat production rate varied by a factor of 2 for a continuous culture grown at a dilution rate of 0.10 h-1. Elemental analysis showed that the carbon mass fraction of biomass did not change. Since the reactor is not at steady state, the elemental and energy balances were calculated on cumulated quantities, i.e. the integral of the reaction rates. It was possible to show that carbon, degree of reduction and energy balances matched. Application of simple mass balance principles for non-steady state systems indicated that oscillations were basically characterized by changes in biomass production rate. In addition, the amount of intermediates, e.g. ethanol or acetate, produced or consumed was negligible. Growth rate was low during the S-phase (0.075 h-1) and high during the G2, M and G1 phases (0.125 h-1) for a constant dilution rate of 0.10 h-1. However, nitrogen, ash, sulfur and potassium content showed systematic increases during the S-phase (bud initiation). Cell component analyses showed that changes in cellular fractions during oscillations (storage carbohydrate content decreased during the S-phase) were due to changes in production rates, particularly for protein and carbohydrates. Nevertheless, using the data evaluation techniques for dynamic systems presented here, it was shown that storage carbohydrates are not consumed during the S-phase. Only the synthesis rate of the different cell components changed depending on position in cell cycle. The growth process may be divided into two phenomena: the formation of new cells during mitosis with a low yield, and size increase of new born cells with high yield. Both kinetic and stoichiometric coefficients varied with the position in the oscillation: the results showed that biomass structure changed and that specific growth rate, as well as biomass yield
Characterizing Observed Limit Cycles in the Cassini Main Engine Guidance Control System
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
Cross-spectrum Measurement of Thermal-noise Limited Oscillators
Hati, Archita; Howe, David A
2015-01-01
Cross-spectrum analysis is a commonly-used technique for the detection of phase and amplitude noise of a signal in the presence of interfering noise. It extracts the desired correlated noise from two time series in the presence of uncorrelated interfering noise. Recently, we demonstrated that the phase-inversion (anti-correlation) effect due to AM noise leakage can cause complete or partial collapse of the cross-spectral function. In this paper, we discuss the newly discovered effect of anti-correlated thermal noise that originates from the common-mode power divider (splitter), an essential component in a cross-spectrum noise measurement system. We studied this effect for different power splitters and discuss its influence on the measurement of thermal-noise limited oscillators. An oscillator whose thermal noise is primarily set by the 50 ohm source resistance is referred to as a thermally-limited oscillator. We provide theory, simulation and experimental results. In addition, we expand this study to reveal h...
A direct experimental limit on neutron -- mirror neutron oscillations
Ban, G; Naviliat-Cuncic, O; Bodek, K; Kistryn, S; Kuzniak, M; Zejma, J; Khomutov, N; Knowles, P; Rebetez, M; Weis, A; Plonka, C; Rogel, G; Quéméner, G; Rebreyend, D; Roccia, S; Tur, M; Daum, M; Henneck, R; Heule, S; Kasprzak, M; Kirch, K; Knecht, A; Mtchedlishvili, A; Zsigmond, G
2007-01-01
In case a mirror world with a copy of our ordinary particle spectrum would exist, the neutron n and its degenerate partner, the mirror neutron ${\\rm n'}$, could potentially mix and undergo ${\\rm nn'}$ oscillations. The interaction of an ordinary magnetic field with the ordinary neutron would lift the degeneracy between the mirror partners, diminish the ${\\rm n'}$-amplitude in the n-wavefunction and, thus, suppress its observability. We report an experimental comparison of ultracold neutron storage in a trap with and without superimposed magnetic field. No influence of the magnetic field is found and a limit on the oscillation time $\\tau_{\\rm nn'} > 103$ s (95% C.L.) is derived.
Synchronized Cycles: An allosteric model of the cyanobacterial circadian oscillator
Lubensky, David; van Zon, J. S.; Altena, P.; Ten Wolde, P. R.
2007-03-01
In a remarkable experiment, Nakajima et al. [Science, 2005] showed that the 3 cyanobacterial clock proteins KaiA, KaiB, and KaiC are sufficient to generate circadian phosphorylation of KaiC in vitro. This system is thus a rare example of a functioning biochemical circuit that can be reconstituted in the test tube. Theoretically, it presents the further challenge that the only reactions driven out of equilibrium are those associated with KaiC phosphorylation and dephosphorylation. Here, we present a model of the Kai system. At its heart is the assumption, motivated by classical models of allostery, that each KaiC hexamer to tends to be phosphorylated in a cyclic manner. For macroscopic oscillations to be possible, however, the cycles of the different hexamers must be synchronized. We propose a novel synchronisation mechanism that allows us to reproduce a wide range of published data, including temperature compensation of the oscillation period, and to make nontrivial predictions about the effects of varying the concentrations of the Kai proteins.
Lie transform Hamiltonian perturbation theory for limit cycle systems
Shah, Tirth; Chakraborty, Sagar
2016-01-01
Usage of a Hamiltonian perturbation theory for nonconservative system is counterintuitive and in general, a technical impossibility by definition. However, the dual (time independent) Hamiltonian formalism for nonconservative systems have opened the door for using various Hamiltonian (and hence, Lagrangian) perturbation theories for investigating the dynamics of such systems. Following the recent extension of the canonical perturbation theory that brings Li\\'enard systems possessing limit cycles under its scope, here we show that the Lie transform Hamiltonian perturbation theory can also be generalized to find perturbative solutions for similar systems. The Lie transform perturbation theories are comparatively easier while seeking higher order corrections in the perturbative series for the solutions and they are also numerically implementable using any symbolic algebra package. For the sake of concreteness, we have illustrated the methodology using the important example of the van der Pol oscillator. While th...
Oscillatory decay of the survival probability of activated diffusion across a limit cycle
Duc, K Dao; Holcman, D
2013-01-01
Activated escape of a Brownian particle from the domain of attraction of a stable focus over a limit cycle exhibits non-Kramers behavior: it is non-Poissonian. When the attractor is moved closer to the boundary oscillations can be discerned in the survival probability. We show that these oscillations are due to complex-valued higher order eigenvalues of the Fokker-Planck operator, which we compute explicitly in the limit of small noise. We also show that in this limit the period of the oscillations is the winding number of the activated stochastic process. These peak probability oscillations are not related to stochastic resonance and should be detectable in planar dynamical systems with the topology described here.
Periodic Orbits and Invariant Tori from a Semistable Limit Cycle in the Fast Dynamics
无
2006-01-01
Some global behavior for a slowly varying oscillator was investigated. Based on a series of transformations and the theory of periodic orbits and integral manifold, the bifurcations of subharmonic solutions and invariant tori generated from a semistable limit cycle in the fast dynamics were discussed.
ON THE LIMIT CYCLES OF PLANAR AUTONOMOUS SYSTEMS
无
2001-01-01
The authors investigate the global properties of general autonomous systems on the plane and establish criteria for the nonexistence, existence and uniqueness of limit cycles. As application examples, the limit cycles for some polynomial systems are studied.
Hierarchy of Distinguished Limits and Drifts for Oscillating Flows
Vladimirov, Vladimir A
2015-01-01
Lagrangian motions of fluid particles in a general velocity field oscillating in time are studied with the use of the two-timing method. Our aims are: (i) to calculate systematically the most general and practically usable asymptotic solutions without making any assumptions either physical or leading to simplifying the calculations; (ii) to classify various drift motions and find their limits of applicability; (iii) to introduce a logical order into the area under consideration; (iv) to open the gate for application of the same ideas to the studying of more complex systems. Our approach to study a drift is rather unusual: instead of solving the ODE for trajectories we consider a hyperbolic PDE for a scalar lagrangian field $a(\\vx,t)$, the trajectories represent characteristics curves for this PDE. It leads us to purely eulerian description of lagrangian motion, that greatly simplifies the calculations. There are two small scaling parameters in the problem: a dimensionless external frequency and a ratio of two...
Limit Cycles near Stationary Points in the Lorenz System
YANG Shi-Pu; ZHU Ke-Qin; ZHOU Xiao-Zhou
2005-01-01
@@ The limit cycles in the Lorenz system near the stationary points are analysed numerically. A plane in phase space of the linear Lorenz system is used to locate suitable initial points of trajectories near the limit cycles. The numerical results show a stable and an unstable limit cycle near the stationary point. The stable limit cycle is smaller than the unstable one and has not been previously reported in the literature. In addition, all the limit cycles in the Lorenz system are theoretically proven not to be planar.
Castillo D, R.; Ortiz V, J. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico); Calleros M, G. [CFE, CNLV, Alto Lucero, Veracruz (Mexico)]. e-mail: rcd@nuclear.inin.mx
2003-07-01
The boiling water reactors (BWRs) are designed for usually to operate in a stable-lineal regime. In a limit cycle the behavior of the one system is no lineal-stable. In a BWR, instabilities of nuclear- thermohydraulics nature can take the reactor to a limit cycle. The limit cycles should to be avoided since the oscillations of power can cause thermal fatigue to the fuel and/or shroud. In this work the employment of the delays method is analyzed for its application in the detection of limit cycles in a nuclear power plant. The foundations of the method and it application to power signals to different operation conditions are presented. The analyzed signals are: to steady state, nuclear-thermohydraulic instability, a non linear transitory and, finally, failure of a controller plant . Among the main results it was found that the delays method can be applied to detect limit cycles in the power monitors of the BWR reactors. It was also found that the first zero of the autocorrelation function is an appropriate approach to select the delay in the detection of limit cycles, for the analyzed cases. (Author)
Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators
Villanueva, L. G.; Kenig, E.; Karabalin, R. B.; Matheny, M. H.; Lifshitz, R; Cross, M. C.; Roukes, M. L.
2013-01-01
Self-sustained oscillators are ubiquitous and essential for metrology, communications, time reference, and geolocation. In its most basic form an oscillator consists of a resonator driven on-resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic, regime. Contrary ...
Buchli, Jonas; Righetti, Ludovic; Ijspeert, Auke Jan
2006-12-01
Periodic behavior is key to life and is observed in multiple instances and at multiple time scales in our metabolism, our natural environment, and our engineered environment. A natural way of modeling or generating periodic behavior is done by using oscillators, i.e., dynamical systems that exhibit limit cycle behavior. While there is extensive literature on methods to analyze such dynamical systems, much less work has been done on methods to synthesize an oscillator to exhibit some specific desired characteristics. The goal of this article is twofold: (1) to provide a framework for characterizing and designing oscillators and (2) to review how classes of well-known oscillators can be understood and related to this framework. The basis of the framework is to characterize oscillators in terms of their fundamental temporal and spatial behavior and in terms of properties that these two behaviors can be designed to exhibit. This focus on fundamental properties is important because it allows us to systematically compare a large variety of oscillators that might at first sight appear very different from each other. We identify several specifications that are useful for design, such as frequency-locking behavior, phase-locking behavior, and specific output signal shape. We also identify two classes of design methods by which these specifications can be met, namely offline methods and online methods. By relating these specifications to our framework and by presenting several examples of how oscillators have been designed in the literature, this article provides a useful methodology and toolbox for designing oscillators for a wide range of purposes. In particular, the focus on synthesis of limit cycle dynamical systems should be useful both for engineering and for computational modeling of physical or biological phenomena.
High-frequency oscillations in human and monkey neocortex during the wake-sleep cycle.
Le Van Quyen, Michel; Muller, Lyle E; Telenczuk, Bartosz; Halgren, Eric; Cash, Sydney; Hatsopoulos, Nicholas G; Dehghani, Nima; Destexhe, Alain
2016-08-16
Beta (β)- and gamma (γ)-oscillations are present in different cortical areas and are thought to be inhibition-driven, but it is not known if these properties also apply to γ-oscillations in humans. Here, we analyze such oscillations in high-density microelectrode array recordings in human and monkey during the wake-sleep cycle. In these recordings, units were classified as excitatory and inhibitory cells. We find that γ-oscillations in human and β-oscillations in monkey are characterized by a strong implication of inhibitory neurons, both in terms of their firing rate and their phasic firing with the oscillation cycle. The β- and γ-waves systematically propagate across the array, with similar velocities, during both wake and sleep. However, only in slow-wave sleep (SWS) β- and γ-oscillations are associated with highly coherent and functional interactions across several millimeters of the neocortex. This interaction is specifically pronounced between inhibitory cells. These results suggest that inhibitory cells are dominantly involved in the genesis of β- and γ-oscillations, as well as in the organization of their large-scale coherence in the awake and sleeping brain. The highest oscillation coherence found during SWS suggests that fast oscillations implement a highly coherent reactivation of wake patterns that may support memory consolidation during SWS.
Changing Credit Limits, Changing Business Cycles
Jensen, Henrik; Ravn, Søren Hove; Santoro, Emiliano
In the last decades, capital markets across the industrialized world have undergone massive deregulation, involving increases in the loan-to-value (LTV) ratios of households and firms. We study the business-cycle implications of this phenomenon in a dynamic general equilibrium model with multiple...... poses a serious challenge for regulatory and macroprudential policies....
Phase-amplitude reduction of transient dynamics far from attractors for limit-cycling systems
Shirasaka, Sho; Kurebayashi, Wataru; Nakao, Hiroya
2017-02-01
Phase reduction framework for limit-cycling systems based on isochrons has been used as a powerful tool for analyzing the rhythmic phenomena. Recently, the notion of isostables, which complements the isochrons by characterizing amplitudes of the system state, i.e., deviations from the limit-cycle attractor, has been introduced to describe the transient dynamics around the limit cycle [Wilson and Moehlis, Phys. Rev. E 94, 052213 (2016)]. In this study, we introduce a framework for a reduced phase-amplitude description of transient dynamics of stable limit-cycling systems. In contrast to the preceding study, the isostables are treated in a fully consistent way with the Koopman operator analysis, which enables us to avoid discontinuities of the isostables and to apply the framework to system states far from the limit cycle. We also propose a new, convenient bi-orthogonalization method to obtain the response functions of the amplitudes, which can be interpreted as an extension of the adjoint covariant Lyapunov vector to transient dynamics in limit-cycling systems. We illustrate the utility of the proposed reduction framework by estimating the optimal injection timing of external input that efficiently suppresses deviations of the system state from the limit cycle in a model of a biochemical oscillator.
Transcription of ftsZ oscillates during the cell cycle of Escherichia coli.
Garrido, T; Sánchez, M; Palacios, P; Aldea, M; Vicente, M
1993-10-01
The FtsZ protein is a key element controlling cell division in Escherichia coli. A powerful transcription titration assay was used to quantify the ftsZ mRNA present in synchronously dividing cells. The ftsZ mRNA levels oscillate during the cell cycle reaching a maximum at about the time DNA replication initiates. This cell cycle dependency is specifically due to the two proximal ftsZ promoters. A strain was constructed in which expression of ftsZ could be modulated by an exogenous inducer. In this strain cell size and cell division frequency were sensitive to the cellular FtsZ contents, demonstrating the rate-limiting role of this protein in cell division. Transcriptional activity of the ftsZ promoters was found to be independent of DnaA, indicating that DNA replication and cell division may be independently controlled at the time when new rounds of DNA replication are initiated. This suggests a parallelism between the prokaryotic cell cycle signals and the START point of eukaryotic cell cycles.
Numerical Analysis of Conductor Galloping Limitation by Oscillation Frequency Detuning
I. I. Serguey
2009-01-01
Full Text Available A numerical method has been developed for calculation of conductor oscillations at the moment of galloping that takes account of pendulum oscillation dampers in the form of eccentric loads. The method is recommended for a numerical analysis of various schemes pertaining to arrangement of horizontal pendulums in the span and their parameters including angles of their initial setting. The obtained results can be used for designing and operation of aerial power lines.
On the number of limit cycles in double homoclinic bifurcations
韩茂安; 陈健
2000-01-01
Let L be a double homoclinic loop of a Hamiltonian system on the plane. We obtain a condition under which L generates at most two large limit cycles by perturbations. We also give conditions for the existence of at most five or six limit cycles which appear near L under perturbations.
The Limits of Schumpeter's Business Cycles
Andersen, Esben Sloth
2006-01-01
Schumpeter designed Business Cycles as his major work, but it has never received much attention. The problem is partly related to its complex treatment of the theory of waveform economic evolution and the related study of the statistics and history of 150 years of capitalist evolution, but the book...... that problem in Capitalism, Socialism and Democracy, but we have to return to the works of his youth to understand his conception of the coevolutionary processes of socio-economic life....... also makes a deliberate analytical delimitation: the emphasis on economic evolution and the placement of institutional change as an external factor. This definition of the task did not allow Schumpeter to make a full-blown study of the history of capitalist evolution. To some extent, he overcame...
Volcanic CO2 Emissions and Glacial Cycles: Coupled Oscillations
Burley, J. M.; Huybers, P. J.; Katz, R. F.
2016-12-01
Following the mid-Pleistocene transition, the dominant period of glacial cycles changed from 40 ka to 100 ka. It is broadly accepted that the 40 ka glacial cycles were driven by cyclical changes in obliquity. However, this forcing does not explain the 100 ka glacial cycles. Mechanisms proposed for 100 ka cycles include isostatic bed depression and proglacial lakes destabilising the Laurentide ice sheet, non-linear responses to orbital eccentricity, and Antarctic ice sheets influencing deep-ocean stratification. None of these are universally accepted. Here we investigate the hypothesis that variations in volcanic CO2 emissions can cause 100 ka glacial cycles. Any proposed mechanism for 100 ka glacial cycles must give the Earth's climate system a memory of 10^4 - 10^5years. This timescale is difficult to achieve for surface processes, however it is possible for the solid Earth. Recent work suggests volcanic CO2 emissions change in response to glacial cycles [1] and that there could be a 50 ka delay in that response [2]. Such a lagged response could drive glacial cycles from 40 ka cycles to an integer multiple of the forcing period. Under what conditions could the climate system admit such a response? To address this, we use a simplified climate model modified from Huybers and Tziperman [3]. Our version comprises three component models for energy balance, ice sheet growth and atmospheric CO2 concentration. The model is driven by insolation alone with other components varying according to a system of coupled, differential equations. The model is run for 500 ka to produce several glacial cycles and the resulting changes in global ice volume and atmospheric CO2 concentration.We obtain a switch from 40 ka to 100 ka cycles as the volcanic CO2 response to glacial cycles is increased. These 100 ka cycles are phase-locked to obliquity, lasting 80 or 120 ka. Whilst the MOR response required (in this model) is larger than plausible estimates based on [2], it illustrates the
Limiting Phase Trajectories and Resonance Energy Transfer in a System of Two Coupled Oscillators
L. I. Manevitch
2010-01-01
Full Text Available We study a problem of energy exchange in a system of two coupled oscillators subject to 1 : 1 resonance. Our results exploit the concept of limiting phase trajectories (LPTs. The LPT, associated with full energy transfer, is, in certain sense, an alternative to nonlinear normal modes characterized by conservation of energy. We consider two benchmark examples. As a first example, we construct an LPT and examine the convergence to stationary oscillations for a Duffing oscillator subjected to resonance harmonic excitation. As a second example, we treat resonance oscillations in a system of two nonlinearly coupled oscillators. We demonstrate the reduction of the equations of motion to an equation of a single oscillator. It is shown that the most intense energy exchange and beating arise when motion of the equivalent oscillator is close to an LPT. Damped beating and the convergence to rest in a system with dissipation are demonstrated.
Stall Flutter Control of a Smart Blade Section Undergoing Asymmetric Limit Oscillations
Nailu Li
2016-01-01
Full Text Available Stall flutter is an aeroelastic phenomenon resulting in unwanted oscillatory loads on the blade, such as wind turbine blade, helicopter rotor blade, and other flexible wing blades. Although the stall flutter and related aeroelastic control have been studied theoretically and experimentally, microtab control of asymmetric limit cycle oscillations (LCOs in stall flutter cases has not been generally investigated. This paper presents an aeroservoelastic model to study the microtab control of the blade section undergoing moderate stall flutter and deep stall flutter separately. The effects of different dynamic stall conditions and the consequent asymmetric LCOs for both stall cases are simulated and analyzed. Then, for the design of the stall flutter controller, the potential sensor signal for the stall flutter, the microtab control capability of the stall flutter, and the control algorithm for the stall flutter are studied. The improvement and the superiority of the proposed adaptive stall flutter controller are shown by comparison with a simple stall flutter controller.
Analysis of Types of Oscillations in Goodwin's Model of Business Cycle
Antonova, A. O.; Reznik, S. N.; Todorov, M. D.
2010-11-01
Types of solutions of the Goodwin business cycle model with the fixed investment time lag have been numerically studied. It is shown that the long-periodic Goodwin's oscillations are excited by the independent investment A in case A exceeds a threshold. If A falls below the threshold, then there are only sawtooth oscillations with a period equal to the investment time lag. Near the threshold, the time behavior of the income is irregular.
On the limit cycles of a quintic planar vector field
2007-01-01
This paper concerns the number and distributions of limit cycles in a Z2-equivariant quintic planar vector field.25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation.It can be concluded that H（5）≥25=52, where H（5）is the Hilbert number for quintic polynomial systems.The results obtained are useful to study the weakened 16th Hilbert problem.
On the limit cycles of a quintic planar vector field
Yu-hai WU; Li-xin TIAN; Mao-an HAN
2007-01-01
This paper concerns the number and distributions of limit cycles in a Z2-equivariant quintic planar vector field. 25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation. It can be concluded that H(5) ≥ 25 ＝ 52,where H(5) is the Hilbert number for quintic polynomial systems. The results obtained are useful to study the weakened 16th Hilbert problem.
Bifurcation of limit cycles from quartic isochronous systems
Linping Peng
2014-04-01
Full Text Available This article concerns the bifurcation of limit cycles for a quartic system with an isochronous center. By using the averaging theory, it shows that under any small quartic homogeneous perturbations, at most two limit cycles bifurcate from the period annulus of the considered system, and this upper bound can be reached. In addition, we study a family of perturbed isochronous systems and prove that there are at most three limit cycles bifurcating from the period annulus of the unperturbed one, and the upper bound is sharp.
Damped driven coupled oscillators: entanglement, decoherence and the classical limit
Mancilla, R D Guerrero; Rey-Gonzalez, R R; Fonseca-Romero, K M [Grupo de Optica e Informacion Cuantica, Departamento de Fisica, Universidad Nacional de Colombia, Bogota (Colombia)], E-mail: rdguerrerom@unal.edu.co, E-mail: rrreyg@unal.edu.co, E-mail: kmfonsecar@unal.edu.co
2009-03-13
We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, comprising a first subsystem (a harmonic oscillator) coupled to a driven and damped second subsystem (another harmonic oscillator). We choose initial states whose dynamics is confined to a couple of two-level systems, and show that the maximum value of entanglement between the two subsystems, as measured by concurrence, depends on the dissipation rate to the coupling-constant ratio and the initial state. While in a related model the entropy of the first subsystem (a two-level system) never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model.
Neutron-antineutron oscillations beyond the quasi-free limit
Davis, E David
2016-01-01
Prompted by plans to conduct a new neutron oscillation experiment at the European Spallation Source (ESS), we consider issues associated with the magnetic field that must be present, some of which are potentially exacerbated by the significantly larger length $l$ contemplated for the neutron propagation region. To this end, we introduce a stochastic model of the residual magnetic field within the propagation region which draws on features of magnetic profiles measured during the last free neutron oscillation experiment [conducted at the Institut Laue-Langevin (ILL) in the 1990's]. We average over both fluctuations in the magnetic field sampled by neutrons, and representative spectra of neutron speeds. We find that deviations from the quasi-free result for the antineutron probability do not depend quadratically on $l$ (as a naive perturbative estimate would suggest) but increase only linearly with $l$. As regards the large spikes in the magnetic field which can be expected at, for example, joints in the magnet...
Limit Cycle Prediction Based on Evolutionary Multiobjective Formulation
M. Katebi
2009-01-01
In the second part, SIDF is extended to the class of nonlinear multiinput multioutput (MIMO systems containing separable nonlinear elements of any general form. In both cases linearized harmonic balance equations are derived and the search for a limit cycle is formulated as a multiobjective problem. Multiobjective genetic algorithm (MOGA is utilized to search the space of parameters of theoretically possible limit cycle operations. Case studies are presented to demonstrate the effectiveness of the proposed approach.
Alien limit cycles in Liénard equations
Coll, B.; Dumortier, F.; Prohens, R.
This paper aims at providing an example of a family of polynomial Liénard equations exhibiting an alien limit cycle. This limit cycle is perturbed from a 2-saddle cycle in the boundary of an annulus of periodic orbits given by a Hamiltonian vector field. The Hamiltonian represents a truncated pendulum of degree 4. In comparison to a former polynomial example, not only the equations are simpler but a lot of tedious calculations can be avoided, making the example also interesting with respect to simplicity in treatment.
Neutron-antineutron oscillations beyond the quasifree limit
Davis, E. David; Young, Albert R.
2017-02-01
Prompted by plans for a free neutron oscillation experiment at the European Spallation Source (ESS), we consider issues associated with the magnetic fields that must be present. To this end, we introduce a stochastic model of the residual magnetic field within the propagation region which draws on features of magnetic profiles measured during the last free oscillation experiment at the Institut Laue-Langevin (ILL). A perturbative analysis, which relates the antineutron probability to the power spectral density of the magnetic field sampled, suggests that deviations from the quasifree result will increase quadratically with the length l of the propagation region. However, with inclusion of averaging over representative spectra of neutron speeds, departures from the quasifree result are found to be approximately linear in l . As regards the large spikes in the magnetic field at, for example, joints in the magnetic shielding of the propagation region (despite compensating currents and magnetic idealization of the shield), we demonstrate that their effect scales as l /D3 /2, where D is the diameter of the cylindrical magnetic shielding, and identify conditions under which they can be neglected. We also establish that any large magnetic field encountered after the propagation region is exited will not diminish the probability for antineutron detection. For the range of values of l of most interest to the ESS experiment, it should suffice to improve on the level of magnetic suppression achieved at the ILL by a factor of 2.
On the limiting behavior of a harmonic oscillator with random external disturbance
G. L. Kulinich
1995-01-01
Full Text Available This paper deals with the limiting behavior of a harmonic oscillator under the external random disturbance that is a process of the white noise type. Influence of noises is investigated in resonance and non-resonance cases.
Pulse-transmission Oscillators: Autonomous Boolean Models and the Yeast Cell Cycle
Sevim, Volkan; Gong, Xinwei; Socolar, Joshua
2010-03-01
Models of oscillatory gene expression typically involve a constitutively expressed or positively autoregulated gene which is repressed by a negative feedback loop. In Boolean representations of such systems, which include the repressilator and relaxation oscillators, dynamical stability stems from the impossibility of satisfying all of the Boolean rules at once. We consider a different class of networks, in which oscillations are due to the transmission of a pulse of gene activation around a ring. Using autonomous Boolean modeling methods, we show how the circulating pulse can be stabilized by decoration of the ring with certain feedback and feed-forward motifs. We then discuss the relation of these models to ODE models of transcriptional networks, emphasizing the role of explicit time delays. Finally, we show that a network recently proposed as a generator of cell cycle oscillations in yeast contains the motifs required to support stable transmission oscillations.
Combustion oscillation study in a kerosene fueled rocket-based combined-cycle engine combustor
Huang, Zhi-Wei; He, Guo-Qiang; Qin, Fei; Xue, Rui; Wei, Xiang-Geng; Shi, Lei
2016-12-01
This study reports the combustion oscillation features in a three-dimensional (3D) rocket-based combined-cycle (RBCC) engine combustor under flight Mach number (Mflight) 3.0 conditions both experimentally and numerically. Experiment is performed on a direct-connect ground test facility, which measures the wall pressure along the flow-path. High-speed imaging of the flame luminosity and schlieren is carried out at exit of the primary rocket. Compressible reactive large eddy simulation (LES) with reduced chemical kinetics of a surrogate model for kerosene is performed to further understand the combustion oscillation mechanisms in the combustor. LES results are validated with experimental data by the time-averaged and root mean square (RMS) pressure values, and show acceptable agreement. Effects of the primary rocket jet on pressure oscillation in the combustor are analyzed. Relation of the high speed rocket jet oscillation, which is thought to among the most probable sources of combustion oscillation, with the RBCC combustor is recognized. Results reveal that the unsteady over-expanded rocket jet has significant impacts on the combustion oscillation feature of the RBCC combustor, which is different from a thermo-acoustics type oscillation. The rocket jet/air inflow physical interactions under different rocket jet expansion degrees are experimentally studied.
The Torsional Oscillation and the Timing of the Solar Cycle: Is it Maximum Yet?
Howe, R.; Christensen-Dalsgaard, J.; Hill, F.;
2013-01-01
After the late start to Cycle 24 there are some indications that activity may have peaked as early as late 2011 and that the polar-field reversal has already occurred in the North. We use helioseismic measurements of the migrating zonal flow pattern known as the torsional oscillation to estimate...
Stabilizing Ferroresonance Oscillations in Voltage Transformers Using Limiter Circuit
Hamid Radmanesh
2012-12-01
Full Text Available This paper employs the multiple scales method and chaos theory for analyzing chaotic behavior of the voltage transformer (VT with linear core loss model. It is shown that ferroresonance phenomenon in VTs can be classified as chaotic dynamics, including a sequence of bifurcations such as period doubling bifurcation (PDB, saddle node bifurcation (SNB, Hopf Bifurcation (HB and chaos. Bifurcation diagrams and phase plane diagrams are drawn using a continuation method for linear core loss model and lyapunov exponents are obtained using the multiple scales method. At first an overview of the subject in the literature is provided. Then, ferroresonance phenomenon is introduced and its various types in a VT are simulated. Finally the effects of ferroresonance suppression circuit on stabilizing these oscillations are studied. The proposed approach is implemented using MATLAB, and simulation results are presented. The results show connecting the ferroresonance suppression circuit to the system configuration, causes great controlling effect on ferroresonance overvoltage.
de Winter, Lenneke; Schepers, Lutz W; Cuaresma, Maria; Barbosa, Maria J; Martens, Dirk E; Wijffels, René H
2014-10-10
The circadian clock schedules processes in microalgae cells at suitable times in the day/night cycle. To gain knowledge about these biological time schedules, Neochloris oleoabundans was grown under constant light conditions and nitrogen limitation. Under these constant conditions, the only variable was the circadian clock. The results were compared to previous work done under nitrogen-replete conditions, in order to determine the effect of N-limitation on circadian rhythms in the cell cycle and biomass composition of N. oleoabundans. The circadian clock was not affected by nitrogen-limitation, and cell division was timed in the natural night, despite of constant light conditions. However, because of nitrogen-limitation, not the entire population was able to divide every day. Two subpopulations were observed, which divided alternately every other day. This caused oscillations in biomass yield and composition. Starch and total fatty acids (TFA) were accumulated during the day. Also, fatty acid composition changed during the cell cycle. Neutral lipids were built up during the day, especially in cells that were arrested in their cell cycle (G2 and G3). These findings give insight in the influence of circadian rhythms on the cell cycle and biomass composition.
Rapid Amazonian Moisture Oscillations Correlated with Dansgaard-Oeschger Cycles
Wang, X.; Auler, A. S.; Edwards, R.; Cheng, H.; Ito, E.; Dorale, J. A.
2007-12-01
Terrestrial paleoclimate records on abrupt climate events from the tropics, e.g. Dansgaard-Oeschger (D-O) oscillations, are still rare, in particular, from Amazonia, which contains the largest tropical rainforest in the world. We have obtained a high-resolution oxygen isotopic record of cave calcite from Caverna Paraíso (PAR, 04o04'S, 55o27'W), Amazonia, Brazil. The chronology was determined by 69 U-Th ages from 4 stalagmites. Tests for equilibrium conditions show that their oxygen isotopic variations are primarily caused by climate change. We thus interpret the Paraíso record, spanning the last 50 thousand years, in terms of meteoric precipitation changes at this equatorial location. The oxygen isotopic profile shows significant abrupt millennial-scale variations during Marine Isotope Stage (MIS) 3, with amplitudes as large as 2 per mil. Using independent age scales, we compare the record to contemporaneous records from caves in eastern China and high-latitude ice cores. During MIS 3, the PAR calcite oxygen isotopic profile correlates remarkably with the Hulu Cave record (Wang Y.J. et al., 2001, Science), indicating that precipitation histories at the two sites are asynchronous, similar to our previous observations from northeastern and southern Brazil speleothems (Wang X.F. et al., 2004, Nature; Wang X.F. et al., 2006, Quat. Sci. Rev.). During MIS 3, Paraíso precipitation also broadly anti-correlates with Greenland D-O events (NGRIP members, 2004, Nature) and positively correlates with Antarctic warm events (EPICA community members, 2006, Nature). Our record adds further support to the idea that abrupt climate events have a worldwide distribution during MIS 3 (Voelker et al., 2002, Quat. Sci. Rev.). The observed correlations between the records support an oceanic meridional overturning circulation mechanism for driving the abrupt millennial-scale events of the last glacial period, coupled with strong air-sea feedbacks from the tropics. In combination with
Robust synchronization of coupled circadian and cell cycle oscillators in single mammalian cells.
Bieler, Jonathan; Cannavo, Rosamaria; Gustafson, Kyle; Gobet, Cedric; Gatfield, David; Naef, Felix
2014-07-15
Circadian cycles and cell cycles are two fundamental periodic processes with a period in the range of 1 day. Consequently, coupling between such cycles can lead to synchronization. Here, we estimated the mutual interactions between the two oscillators by time-lapse imaging of single mammalian NIH3T3 fibroblasts during several days. The analysis of thousands of circadian cycles in dividing cells clearly indicated that both oscillators tick in a 1:1 mode-locked state, with cell divisions occurring tightly 5 h before the peak in circadian Rev-Erbα-YFP reporter expression. In principle, such synchrony may be caused by either unidirectional or bidirectional coupling. While gating of cell division by the circadian cycle has been most studied, our data combined with stochastic modeling unambiguously show that the reverse coupling is predominant in NIH3T3 cells. Moreover, temperature, genetic, and pharmacological perturbations showed that the two interacting cellular oscillators adopt a synchronized state that is highly robust over a wide range of parameters. These findings have implications for circadian function in proliferative tissues, including epidermis, immune cells, and cancer.
Mixed-layer water oscillations in tropical Pacific for ENSO cycle
无
2007-01-01
The main modes of interannal variabilities of thermocline and sea surface wind stress in the tropical Pacific and their interactions are investigated, which show the following results. (1) The thermocline anomalies in the tropical Pacific have a zonal dipole pattern with 160°W as its axis and a meridional seesaw pattern with 6-8°N as its transverse axis. The meridional oscillation has a phase lag of about 90° to the zonal oscillation, both oscillations get together to form the El Ni(n)o/La Ni(n)a cycle, which behaves as a mixed layer water oscillates anticlockwise within the tropical Pacific basin between equator and 12°N. (2) There are two main patterns of wind stress anomalies in the tropical Pacific, of which the first component caused by trade wind anomaly is characterized by the zonal wind stress anomalies and its corresponding divergences field in the equatorial Pacific, and the abnormal cross-equatorial flow wind stress and its corresponding divergence field, which has a sign opposite to that of the equatorial region, in the off-equator of the tropical North Pacific, and the second component represents the wind stress anomalies and corresponding divergences caused by the ITCZ anomaly. (3) The trade winds anomaly plays a decisive role in the strength and phase transition of the ENSO cycle, which results in the sea level tilting, provides an initial potential energy to the mixed layer water oscillation, and causes the opposite thermocline displacement between the west side and east side of the equator and also between the equator and 12°N of the North Pacific basin, therefore determines the amplitude and route for ENSO cycle. The ITCZ anomaly has some effects on the phase transition. (4) The thermal anomaly of the tropical western Pacific causes the wind stress anomaly and extends eastward along the equator accompanied with the mixed layer water oscillation in the equatorial Pacific, which causes the trade winds anomaly and produces the anomalous wind
More on the renormalization group limit cycle in QCD
Evgeny Epelbaum; Hans-Werner Hammer; Ulf-G. Meissner; Andreas Nogga
2006-02-26
We present a detailed study of the recently conjectured infrared renormalization group limit cycle in QCD using chiral effective field theory. We show that small increases in the up and down quark masses, corresponding to a pion mass around 200 MeV, can move QCD to the critical renormalization group trajectory for an infrared limit cycle in the three-nucleon system. At the critical values of the quark masses, the binding energies of the deuteron and its spin-singlet partner are tuned to zero and the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. At next-to-leading order in the chiral counting, we find three parameter sets where this effect occurs. For one of them, we study the structure of the three-nucleon system using both chiral and contact effective field theories in detail. Furthermore, we calculate the influence of the limit cycle on scattering observables.
Ge, Hao; Qian, Hong
2012-06-01
Landscape is one of the key notions in literature on biological processes and physics of complex systems with both deterministic and stochastic dynamics. The large deviation theory (LDT) provides a possible mathematical basis for the scientists' intuition. In terms of Freidlin-Wentzell's LDT, we discuss explicitly two issues in singularly perturbed stationary diffusion processes arisen from nonlinear differential equations: (1) For a process whose corresponding ordinary differential equation has a stable limit cycle, the stationary solution exhibits a clear separation of time scales: an exponential terms and an algebraic prefactor. The large deviation rate function attains its minimum zero on the entire stable limit cycle, while the leading term of the prefactor is inversely proportional to the velocity of the non-uniform periodic oscillation on the cycle. (2) For dynamics with multiple stable fixed points and saddles, there is in general a breakdown of detailed balance among the corresponding attractors. Two landscapes, a local and a global, arise in LDT, and a Markov jumping process with cycle flux emerges in the low-noise limit. A local landscape is pertinent to the transition rates between neighboring stable fixed points; and the global landscape defines a nonequilibrium steady state. There would be nondifferentiable points in the latter for a stationary dynamics with cycle flux. LDT serving as the mathematical foundation for emergent landscapes deserves further investigations.
Transcriptome changes and cAMP oscillations in an archaeal cell cycle
Soppa Jörg
2007-06-01
Full Text Available Abstract Background The cell cycle of all organisms includes mass increase by a factor of two, replication of the genetic material, segregation of the genome to different parts of the cell, and cell division into two daughter cells. It is tightly regulated and typically includes cell cycle-specific oscillations of the levels of transcripts, proteins, protein modifications, and signaling molecules. Until now cell cycle-specific transcriptome changes have been described for four eukaryotic species ranging from yeast to human, but only for two prokaryotic species. Similarly, oscillations of small signaling molecules have been identified in very few eukaryotic species, but not in any prokaryote. Results A synchronization procedure for the archaeon Halobacterium salinarum was optimized, so that nearly 100% of all cells divide in a time interval that is 1/4th of the generation time of exponentially growing cells. The method was used to characterize cell cycle-dependent transcriptome changes using a genome-wide DNA microarray. The transcript levels of 87 genes were found to be cell cycle-regulated, corresponding to 3% of all genes. They could be clustered into seven groups with different transcript level profiles. Cluster-specific sequence motifs were detected around the start of the genes that are predicted to be involved in cell cycle-specific transcriptional regulation. Notably, many cell cycle genes that have oscillating transcript levels in eukaryotes are not regulated on the transcriptional level in H. salinarum. Synchronized cultures were also used to identify putative small signaling molecules. H. salinarum was found to contain a basal cAMP concentration of 200 μM, considerably higher than that of yeast. The cAMP concentration is shortly induced directly prior to and after cell division, and thus cAMP probably is an important signal for cell cycle progression. Conclusion The analysis of cell cycle-specific transcriptome changes of H. salinarum
The optimal performance of a quantum refrigeration cycle working with harmonic oscillators
Lin Bi Hong; Hua Ben
2003-01-01
The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here ...
Synchronized Helicity Oscillations: A Link Between Planetary Tides and the Solar Cycle?
Stefani, F.; Giesecke, A.; Weber, N.; Weier, T.
2016-10-01
Recent years have seen an increased interest in the question of whether the gravitational action of planets could have an influence on the solar dynamo. Without discussing the observational validity of the claimed correlations, we examine which possible physical mechanism might link the weak planetary forces with solar dynamo action. We focus on the helicity oscillations that were recently found in simulations of the current-driven, kink-type Tayler instability, which is characterized by an m=1 azimuthal dependence. We show how these helicity oscillations may be resonantly excited by some m=2 perturbations that reflect a tidal oscillation. Specifically, we speculate that the tidal oscillation of 11.07 years induced by the Venus-Earth-Jupiter system may lead to a 1:1 resonant excitation of the oscillation of the α-effect. Finally, we recover a 22.14-year cycle of the solar dynamo in the framework of a reduced zero-dimensional α-Ω dynamo model.
Synchronized helicity oscillations: a link between planetary tides and the solar cycle?
Stefani, F; Weber, N; Weier, T
2015-01-01
Recent years have seen an increased interest in the question whether the gravitational action of planets could have an influence on the solar dynamo. Without discussing the observational validity of the claimed correlations, we ask for a possible physical mechanism which might link the weak planetary forces with solar dynamo action. We focus on the helicity oscillations which were recently found in simulations of the current-driven, kink-type Tayler instability which is characterized by an m=1 azimuthal dependence. We show how these helicity oscillations can be resonantly excited by some m=2 perturbation that reflects a tidal oscillation. Specifically, we speculate that the 11.07 years tidal oscillation induced by the Venus-Earth-Jupiter system may lead to a 1:1 resonant excitation of the oscillation of the alpha effect. Finally, in the framework of a reduced, zero-dimensional alpha-Omega dynamo model we recover a 22.14 years cycle of the solar dynamo.
Synchronized Helicity Oscillations: A Link Between Planetary Tides and the Solar Cycle?
Stefani, F.; Giesecke, A.; Weber, N.; Weier, T.
2016-09-01
Recent years have seen an increased interest in the question of whether the gravitational action of planets could have an influence on the solar dynamo. Without discussing the observational validity of the claimed correlations, we examine which possible physical mechanism might link the weak planetary forces with solar dynamo action. We focus on the helicity oscillations that were recently found in simulations of the current-driven, kink-type Tayler instability, which is characterized by an m=1 azimuthal dependence. We show how these helicity oscillations may be resonantly excited by some m=2 perturbations that reflect a tidal oscillation. Specifically, we speculate that the tidal oscillation of 11.07 years induced by the Venus-Earth-Jupiter system may lead to a 1:1 resonant excitation of the oscillation of the α-effect. Finally, we recover a 22.14-year cycle of the solar dynamo in the framework of a reduced zero-dimensional α- Ω dynamo model.
Unstable, self-limiting thermochemical temperature oscillations in Macrozamia cycads.
Roemer, Robert B; Terry, L Irene; Walter, Gimme H
2008-06-01
Field measurements and laboratory experiments on the Australian cycads Macrozamia lucida and Macrozamia macleayi demonstrate that their cones' diel peak thermogenic temperature increase varies systematically with cone stage, with single thermogenic temperature peaks occurring daily for up to 2 weeks and reaching 12 degrees C above ambient at midstage. The initiation, magnitude and timing of those peaks are strongly modulated by ambient temperature; the period between successive thermogenic temperature peaks is not circadian, and light is neither necessary nor sufficient to initiate a thermogenic event. A mathematical analysis is developed that provides a unified explanation of the experimental results. It describes these unstable, self-limiting thermogenic events in terms of conservation of energy and a first-order chemical reaction rate model that includes an Arrhenius equation dependence of the cone's metabolic heating rate on the cone temperature.
Basins of attraction changes by amplitude constraining of oscillators with limited power supply
Souza, S.L.T. de [Instituto de Fisica, Universidade de Sao Paulo, CP 66318, 05315-970 Sao Paulo, SP (Brazil); Caldas, I.L. [Instituto de Fisica, Universidade de Sao Paulo, CP 66318, 05315-970 Sao Paulo, SP (Brazil); Viana, R.L. [Departamento de Fisica, Universidade Federal do Parana, CP 19081, 81531-990 Curitiba, Parana (Brazil)] e-mail: viana@fisica.ufpr.br; Balthazar, J.M. [Departamento de Estatistica, Matematica Aplicada e Computacional, Instituto de Geociencias e Ciencias Exatas, Universidade Estadual Paulista, CP 178, 13500-230 Rio Claro, SP (Brazil); Brasil, R.M.L.R.F. [Departamento de Engenharia Estrutural e de Fundacoes, Escola Politecnica, Universidade de Sao Paulo, 05424-930 Sao Paulo, SP (Brazil)
2005-11-01
We investigate the dynamics of a Duffing oscillator driven by a limited power supply, such that the source of forcing is considered to be another oscillator, coupled to the first one. The resulting dynamics come from the interaction between both systems. Moreover, the Duffing oscillator is subjected to collisions with a rigid wall (amplitude constraint). Newtonian laws of impact are combined with the equations of motion of the two coupled oscillators. Their solutions in phase space display periodic (and chaotic) attractors, whose amplitudes, especially when they are too large, can be controlled by choosing the wall position in suitable ways. Moreover, their basins of attraction are significantly modified, with effects on the final state system sensitivity.
Performances and limits of a parallel oscillator for electrochemical quartz crystal microbalances.
Ehahoun, Hervé; Gabrielli, Claude; Keddam, Michel; Perrot, Hubert; Rousseau, Philippe
2002-03-01
This paper describes a driving circuit for an electrochemical quartz crystal microbalance (EQCM) adapted to a wide range of applications. The oscillator is a Miller-type parallel oscillator using an operational transconductance amplifier (OTA). A theoretical study of the oscillating circuit led to the analytical expression of the microbalance frequency as well as to an overestimation of the error on the mass measurement. The reliability of the EQCM was then experimentally verified through electrochemical copper deposition and dissolution. The limit of operation of the EQCM was also investigated, both analytically and experimentally. This work shows that parallel oscillators using few electronic components allow a very reliable EQCM to be obtained for mass measurements on metallic films, even if they are highly damped.
Does the potential for chaos constrain the embryonic cell-cycle oscillator?
R Scott McIsaac
2011-07-01
Full Text Available Although many of the core components of the embryonic cell-cycle network have been elucidated, the question of how embryos achieve robust, synchronous cellular divisions post-fertilization remains unexplored. What are the different schemes that could be implemented by the embryo to achieve synchronization? By extending a cell-cycle model previously developed for embryos of the frog Xenopus laevis to include the spatial dimensions of the embryo, we establish a novel role for the rapid, fertilization-initiated calcium wave that triggers cell-cycle oscillations. Specifically, in our simulations a fast calcium wave results in synchronized cell cycles, while a slow wave results in full-blown spatio-temporal chaos. We show that such chaos would ultimately lead to an unpredictable patchwork of cell divisions across the embryo. Given this potential for chaos, our results indicate a novel design principle whereby the fast calcium-wave trigger following embryo fertilization synchronizes cell divisions.
Stability and Limit Oscillations of a Control Event-Based Sampling Criterion
M. De la Sen
2012-01-01
Full Text Available This paper investigates the presence of limit oscillations in an adaptive sampling system. The basic sampling criterion operates in the sense that each next sampling occurs when the absolute difference of the signal amplitude with respect to its currently sampled signal equalizes a prescribed threshold amplitude. The sampling criterion is extended involving a prescribed set of amplitudes. The limit oscillations might be interpreted through the equivalence of the adaptive sampling and hold device with a nonlinear one consisting of a relay with multiple hysteresis whose parameterization is, in general, dependent on the initial conditions of the dynamic system. The performed study is performed on the time domain.
Self-Ordered Limit Cycles, Chaos, and Phase Slippage with a Superfluid inside an Optical Resonator
Piazza, Francesco; Ritsch, Helmut
2015-10-01
We study dynamical phases of a driven Bose-Einstein condensate coupled to the light field of a high-Q optical cavity. For high field seeking atoms at red detuning the system is known to show a transition from a spatially homogeneous steady state to a self-ordered regular lattice exhibiting superradiant scattering into the cavity. For blue atom pump detuning the particles are repelled from the maxima of the light-induced optical potential suppressing scattering. We show that this generates a new dynamical instability of the self-ordered phase, leading to the appearance of self-ordered stable limit cycles characterized by large amplitude self-sustained oscillations of both the condensate density and cavity field. The limit cycles evolve into chaotic behavior by period doubling. Large amplitude oscillations of the condensate are accompanied by phase slippage through soliton nucleation at a rate that increases in the chaotic regime. Different from a superfluid in a closed setup, this driven dissipative superfluid is not destroyed by the proliferation of solitons since kinetic energy is removed through cavity losses.
Limit Cycle Analysis in a Class of Hybrid Systems
Antonio Favela-Contreras
2016-01-01
Full Text Available Hybrid systems are those that inherently combine discrete and continuous dynamics. This paper considers the hybrid system model to be an extension of the discrete automata associating a continuous evolution with each discrete state. This model is called the hybrid automaton. In this work, we achieve a mathematical formulation of the steady state and we show a way to obtain the initial conditions region to reach a specific limit cycle for a class of uncoupled and coupled continuous-linear hybrid systems. The continuous-linear term is used in the sense of the system theory and, in this sense, continuous-linear hybrid automata will be defined. Thus, some properties and theorems that govern the hybrid automata dynamic behavior to evaluate a limit cycle existence have been established; this content is explained under a theoretical framework.
Limit cycles, bifurcations, and accuracy of the milling process
Mann, B. P.; Bayly, P. V.; Davies, M. A.; Halley, J. E.
2004-10-01
Time finite element analysis (TFEA) is used to determine the accuracy, stability, and limit cycle behavior of the milling process. Predictions are compared to traditional Euler simulation and experiments. The TFEA method forms an approximate solution by dividing the time in the cut into a finite number of elements. The approximate solution is then matched with the exact solution for free vibration to obtain a discrete linear map. Stability is then determined from the characteristic multipliers of the map. Map fixed points correspond to stable periodic solutions which are used to evaluate surface location error. Bifurcations and limit cycle behavior are predicted from a non-linear TFEA formulation. Experimental cutting tests are used to confirm theoretical predictions.
Particle manipulation beyond the diffraction limit using structured super-oscillating light beams
Singh, Brijesh Kumar; Roichman, Yael; Arie, Ady
2016-01-01
The diffraction limited resolution of light focused by a lens was derived in 1873 by Ernst Abbe. Later in 1952, a method to reach sub-diffraction light spots was proposed by modulating the wavefront of the focused beam. In a related development, super-oscillating functions, i.e. band limited functions that locally oscillate faster than their highest Fourier component, were introduced and experimentally applied for super-resolution microscopy. Up till now, only simple Gaussian-like sub-diffraction spots were used. Here we show that the amplitude and phase profile of these sub-diffraction spots can be arbitrarily controlled. In particular we utilize Hermite-Gauss, Laguerre-Gauss and Airy functions to structure super-oscillating beams with sub-diffraction lobes. These structured beams are then used for high resolution trapping and manipulation of nanometer-sized particles. The trapping potential provides unprecedented localization accuracy and stiffness, significantly exceeding those provided by standard diffrac...
Mitsui, Takahito; Aihara, Kazuyuki
2015-01-01
Glacial-interglacial cycles are large variations in continental ice mass and greenhouse gases, which have dominated climate variability over the Quaternary. The dominant periodicity of the cycles is $\\sim $40 kyr before the so-called middle Pleistocene transition between $\\sim$1.2 and $\\sim$0.7 Myr ago, and it is $\\sim $100 kyr after the transition. In this paper, the dynamics of glacial-interglacial cycles are investigated using a phase oscillator model forced by the time-varying incoming solar radiation (insolation). We analyze the bifurcations of the system and show that strange nonchaotic attractors appear through nonsmooth saddle-node bifurcations of tori. The bifurcation analysis indicates that mode-locking is likely to occur for the 41 kyr glacial cycles but not likely for the 100 kyr glacial cycles. The sequence of mode-locked 41 kyr cycles is robust to small parameter changes. However, the sequence of 100 kyr glacial cycles can be sensitive to parameter changes when the system has a strange nonchaoti...
From quiescence to proliferation : Cdk oscillations drive the mammalian cell cycle
Claude eGérard
2012-11-01
Full Text Available We recently proposed a detailed model describing the dynamics of the network of cyclin-dependent kinases (Cdks driving the mammalian cell cycle [Gérard, C. and Goldbeter, A. (2009. Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle. Proc. Natl. Acad. Sci. USA 106, 21643-21648]. The model contains four modules, each centered around one cyclin/Cdk complex. Cyclin D/Cdk4-6 and cyclin E/Cdk2 promote progression in G1 and elicit the G1/S transition, respectively; cyclin A/Cdk2 ensures progression in S and the transition S/G2, while the activity of cyclin B/Cdk1 brings about the G2/M transition. This model shows that in the presence of sufficient amounts of growth factor the Cdk network is capable of temporal self-organization in the form of sustained oscillations, which correspond to the ordered, sequential activation of the various cyclin/Cdk complexes that control the successive phases of the cell cycle. The results suggest that the switch from cellular quiescence to cell proliferation corresponds to the transition from a stable steady state to sustained oscillations in the Cdk network. The transition depends on a finely tuned balance between factors that promote or hinder progression in the cell cycle. We show that the transition from quiescence to proliferation can occur in multiple ways that alter this balance. By resorting to bifurcation diagrams, we analyze the mechanism of oscillations in the Cdk network. Finally, we show that the complexity of the detailed model can be greatly reduced, without losing its key dynamical properties, by considering a skeleton model for the Cdk network. Using such a skeleton model for the mammalian cell cycle we show that positive feedback loops enhance the amplitude and the robustness of Cdk oscillations with respect to molecular noise. We compare the relative merits of the detailed and skeleton versions of the model for the Cdk network driving the mammalian cell cycle.
Modeling two-oscillator circadian systems entrained by two environmental cycles.
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.
Limits on the oscillation plus decay model using published MINOS neutrino and antineutrino data
Gomes, Abner Leonel Gadelha; Gomes, Ricardo Avelino [Universidade Federal de Goias (UFGO), Goiania (Brazil). Instituto de Fisica; Peres, Orlando Goulart [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Instituto de Fisica Gleb Wataghin
2013-07-01
Full text: The neutrino oscillation model is the theoretical model that explains the so called anomalous neutrino phenomena. Models such as neutrino decay and decoherence failed to explain the neutrino experimental results. Nevertheless, it was proposed that the oscillation model could be the dominant model with the possibility to add alternative models to it and determine limits for the parameters of the additional models. In this phenomenological work we considered the neutrino oscillation plus decay model and used the published data from the MINOS experiment. MINOS is a long-baseline neutrino experiment with two magnetized detectors (the Near Detector at Fermilab, 1 km from the target and depth of 225 meters of water equivalent (mwe), and the Far Detector at Soudan, MN, 735 km from the target and depth of 2100 mwe) exposed to the NuMI (Neutrinos at the Main Injector) beam. We used recent results from neutrino and antineutrino configurations of the NuMI beam and fitted by a 2-flavor oscillation model - transition from ν{sub μ} (ν{sub -}bar{sub μ}) to ν{sub τ} (ν{sub -}bar{sub τ}). We show the best fit and allowed region found for neutrino and antineutrino data, reproducing the published results. We then combined the data and under the oscillation plus decay framework calculated 1D and 2D allowed regions to determine limits for the decay parameter. (author)
Coupled Oscillator Model of the Business Cycle withFluctuating Goods Markets
Ikeda, Y.; Aoyama, H.; Fujiwara, Y.; Iyetomi, H.; Ogimoto, K.; Souma, W.; Yoshikawa, H.
The sectoral synchronization observed for the Japanese business cycle in the Indices of Industrial Production data is an example of synchronization. The stability of this synchronization under a shock, e.g., fluctuation of supply or demand, is a matter of interest in physics and economics. We consider an economic system made up of industry sectors and goods markets in order to analyze the sectoral synchronization observed for the Japanese business cycle. A coupled oscillator model that exhibits synchronization is developed based on the Kuramoto model with inertia by adding goods markets, and analytic solutions of the stationary state and the coupling strength are obtained. We simulate the effects on synchronization of a sectoral shock for systems with different price elasticities and the coupling strengths. Synchronization is reproduced as an equilibrium solution in a nearest neighbor graph. Analysis of the order parameters shows that the synchronization is stable for a finite elasticity, whereas the synchronization is broken and the oscillators behave like a giant oscillator with a certain frequency additional to the common frequency for zero elasticity.
Adaptive robust control of chaotic oscillations in power system with excitation limits
Wei Du-Qu; Luo Xiao-Shu
2007-01-01
With system parameters falling into a certain area, power system with excitation limits experiences complicated chaotic oscillations which threaten the secure and stable operation of power system. In this paper, to control these unwanted chaotic oscillations, a straightforward adaptive chaos controller based on Lyapunov asymptotical stability theory is designed. Since the presented controller does not need to change the controlled system structure and not to use any information of system except the system state variables, the designed controller is simple and desirable.Simulation results show that the proposed control law is very effective. This work is helpful to maintain the power system's security operation.
Few-cycle, Broadband, Mid-infrared Optical Parametric Oscillator Pumped by a 20-fs Ti:sapphire Laser
Kumar, Suddapalli Chaitanya; Ideguchi, Takuro; Yan, Ming; Holzner, Simon; Hänsch, Theodor W; Picqué, Nathalie; Ebrahim-Zadeh, Majid
2014-01-01
We report a few-cycle, broadband, singly-resonant optical parametric oscillator (OPO) for the mid-infrared based on MgO-doped periodically-poled LiNbO3 (MgO:PPLN), synchronously pumped by a 20-fs Ti:sapphire laser. By using crystal interaction lengths as short as 250 um, and careful dispersion management of input pump pulses and the OPO resonator, near-transform-limited, few-cycle idler pulses tunable across the mid-infrared have been generated, with as few as 3.7 optical cycles at 2682 nm. The OPO can be continuously tuned over 2179-3732 nm by cavity delay tuning, providing up to 33 mW of output power at 3723 nm. The idler spectra exhibit stable broadband profiles with bandwidths spaning over 422 nm (FWHM) recorded at 3732 nm. We investigate the effect of crystal length on spectral bandwidth and pulse duration at a fixed wavelength, confirming near-transform-limited idler pulses for all grating interaction lengths. By locking the repetition frequency of the pump laser to a radio-frequency reference, and with...
Air pollution at a hotspot location in Delhi: Detecting trends, seasonal cycles and oscillations
Kandlikar, Milind
This paper uses spectral methods to analyze changes in air quality at a single monitoring site in Delhi since 2000. Power spectral density calculations of daily concentration data for particulate matter (PM10), carbon monoxide (CO), oxides of nitrogen (NO x) and oxides of sulfur (SO x) reveal the presence of trends and periodic oscillations for all the pollutants. Singular Spectrum Analysis (SSA) is used to decompose daily data into statistically significant non-linear trends, seasonal cycles and other oscillations. Periods of sharp reductions were observed for both SO x and CO concentrations in 2001 and 2002, respectively. NO x concentration trends show a sustained rise from 2000 to 2004, followed by small decline thereafter. PM10 concentration trends remain essentially unchanged over the time period. All pollutants also show strong annual and biannual cycles. The observed trends in CO and NO x likely relate changes in Delhi's vehicular traffic emissions. The sharp drop in both the trend and amplitude of the seasonal cycle of CO coincides with the switch to Compressed Natural Gas (CNG) as a fuel for Delhi's public transport fleet. Observed changes in SO x and PM10 concentrations were most likely caused by sources unrelated to vehicular traffic.
Double-Paddle Oscillators as Probes of Quantum Turbulence in the Zero Temperature Limit
Schmoranzer, David; Jackson, Martin; Zemma, Elisa; Luzuriaga, Javier
2016-11-01
We present a technical report on our tests of a double-paddle oscillator as a detector of quantum turbulence in superfluid 4 He at low temperatures ranging from 20 to 1100 mK. The device, known to operate well in the two-fluid regime (Zemma and Luzuriaga in J Low Temp Phys 166:171-181, 2012), is also capable of detecting quantum turbulence in the zero temperature limit. The oscillator demonstrated Lorentzian responses with quality factors of order 10^5 in vacuum, and displayed negative-Duffing resonances in liquid, even at moderate drives. In superfluid He-II at low temperatures, its sensitivity was adversely affected by acoustic damping at higher harmonics. While it successfully created and detected the quantum turbulence, its overall performance does not compare favourably with other oscillators such as tuning forks.
The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
Quintela, T. S.; Fabris, J. C.; Nogueira, J. A.
2016-09-01
In this work, we explicitly solve the problem of the harmonic oscillator in the classical limit of a minimal-length scenario. We show that (i) the motion equation of the oscillator is not linear anymore because the presence of a minimal length introduces an anarmonic term and (ii) its motion is described by a Jacobi sine elliptic function. Therefore, the motion is periodic with the same amplitude and with the new period depending on the minimal length. This result (the change in the period of oscillation) is very important since it enables us to find in a quite simple way the most relevant effect of the presence of a minimal length and consequently traces of the Planck-scale physics. We show applications of our results in spectroscopy and gravity.
Ferber, Torben
2012-09-15
OPERA, the oscillation project with emulsion-tracking apparatus, is a long-baseline neutrino oscillation experiment. It combines an almost pure, high-energy {nu}{sub {mu}} beam produced at the SPS accelerator at CERN, Switzerland, with the OPERA neutrino detector located at a distance of about 730 km in the LNGS underground laboratory in Italy. By using a lead/photo emulsion target, {nu}{sub {tau}} charged current (CC) interactions of {nu}{sub {tau}} from {nu}{sub {mu}} {yields} {nu}{sub {tau}} oscillations can be observed on an event-by-event basis with very low background rates. Within this thesis, a {nu}{sub {mu}}{yields}{nu}{sub {mu}} disappearance search is described that uses a flux normalization. independent measurement of the CC event fraction as a function of the hadronic energy as measured by the electronic detectors of OPERA. This allows to derive limits on {nu}{sub {mu}}{yields}{nu}{sub {mu}} oscillations, complementary to the main {nu}{sub {tau}} appearance analysis. For maximal mixing, vertical stroke {Delta}m{sup 2}{sub 23} vertical stroke >4.4 x 10{sup -3} eV{sup 2} is excluded at 90% C.L. by the disappearance analysis. This thesis represents the first application of this method, including systematic uncertainties, in a long-baseline neutrino oscillation experiment.
Limit Cycle Behaviour of the Bump-on-Tail Instability
Janssen, P. A. E. M.; Juul Rasmussen, Jens
1981-01-01
The nonlinear dynamics of the bump‐on‐tail instability is considered. The eigenmodes have discrete k because of finite periodic boundary conditions. Increasing a critical parameter (the number density) above its neutral stable value by a small fractional amount Δ2, one mode becomes unstable....... The nonlinear dynamics of the unstable mode is determined by means of the multiple time scale method. Usually, limit cycle behavior is found. A short comparison with quasi‐linear theory is given, and the results are compared with experiment....
Limit cycles and Hopf bifurcations in a Kolmogorov type system
Simona Muratori
1989-04-01
Full Text Available The paper is devoted to the study of a class of Kolmogorov type systems which can be used to represent the dynamic behaviour of prey and predators. The model is an extension of the classical prey-predator model since it allows intra-specific competition for the predator's species. The analysis shows that the system can only have Kolmogorov's two modes of behaviour: a globally stable equilibrium or a globally stable limit cycle. Moreover, the transition from one of these two modes to the other is a non-catastrophic Hopf bifurcation which can be specified analytically.
The seasonal cycle of interhemispheric oscillations in mass field of the global atmosphere
LU ChuHan; GUAN ZhaoYong; MEI ShiLong; QIN YuJing
2008-01-01
Using the daily and monthly data of surface air pressure, meridional wind, radiation and water vapor from NCEP/NCAR reanalysis for the period of 1979--2006, we have examined the seasonal variations of the interhemispheric oscillations (IHO) in mass field of the global atmosphere. Our results have dem-onstrated that IHO as observed in surface air pressure field shows the distinct seasonal cycle. This seasonal cycle has an interhemispheric seesaw structure with comparable annual ranges of surface air pressure in the Southern and Northern Hemispheres. Mass of water vapor changes out-of-phase be-tween the Southern and Northern Hemispheres, showing clearly a seasonal cycle with its annual range almost equivalent to annual range of the IHO seasonal cycle. Amazingly, the cross-equatorial flow is found to be induced by annual changes in water vapor mass as a response of the atmosphere to sea-sonal cycle of forcing from hemispheric net surface short- and long-wave radiations. The IHO season-ality exhibits its larger variations in magnitude in mid-latitudes other than in other regions of the globe. Additionally, our results also show that the global air mass is redistributed seasonally not only between the Northern and Southern Hemispheres but also between land and sea. This land-sea air mass redis-tribution induces a zonal pattern of surface air pressure in the Northern Hemisphere but the meridional pattern in the Southern Hemisphere.
Celine eFeillet
2015-05-01
Full Text Available Uncontrolled cell proliferation is one of the key features leading to cancer. Seminal works in chronobiology have revealed that disruption of the circadian timing system in mice, either by surgical, genetic or environmental manipulation, increased tumor development. In humans, shift work is a risk factor for cancer. Based on these observations, the link between the circadian clock and cell cycle has become intuitive. But despite identification of molecular connections between the two processes, the influence of the clock on the dynamics of the cell cycle has never been formally observed. Recently, two studies combining single live cell imaging with computational methods have shed light on robust coupling between clock and cell cycle oscillators. We recapitulate here these novel findings and integrate them with earlier results in both healthy and cancerous cells. Moreover, we propose that the cell cycle may be synchronized or slowed down through coupling with the circadian clock, which results in reduced tumour growth. More than ever, systems biology has become instrumental to understand the dynamic interaction between the circadian clock and cell cycle, which is critical in cellular coordination and for diseases such as cancer.
Feillet, Celine; van der Horst, Gijsbertus T J; Levi, Francis; Rand, David A; Delaunay, Franck
2015-01-01
Uncontrolled cell proliferation is one of the key features leading to cancer. Seminal works in chronobiology have revealed that disruption of the circadian timing system in mice, either by surgical, genetic, or environmental manipulation, increased tumor development. In humans, shift work is a risk factor for cancer. Based on these observations, the link between the circadian clock and cell cycle has become intuitive. But despite identification of molecular connections between the two processes, the influence of the clock on the dynamics of the cell cycle has never been formally observed. Recently, two studies combining single live cell imaging with computational methods have shed light on robust coupling between clock and cell cycle oscillators. We recapitulate here these novel findings and integrate them with earlier results in both healthy and cancerous cells. Moreover, we propose that the cell cycle may be synchronized or slowed down through coupling with the circadian clock, which results in reduced tumor growth. More than ever, systems biology has become instrumental to understand the dynamic interaction between the circadian clock and cell cycle, which is critical in cellular coordination and for diseases such as cancer.
Restoration of oscillation in network of oscillators in presence of direct and indirect interactions
Majhi, Soumen; Bera, Bidesh K. [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108 (India); Bhowmick, Sourav K. [Department of Electronics, Asutosh College, Kolkata-700026 (India); Ghosh, Dibakar, E-mail: diba.ghosh@gmail.com [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108 (India)
2016-10-23
The suppression of oscillations in coupled systems may lead to several unwanted situations, which requires a suitable treatment to overcome the suppression. In this paper, we show that the environmental coupling in the presence of direct interaction, which can suppress oscillation even in a network of identical oscillators, can be modified by introducing a feedback factor in the coupling scheme in order to restore the oscillation. We inspect how the introduction of the feedback factor helps to resurrect oscillation from various kinds of death states. We numerically verify the resurrection of oscillations for two paradigmatic limit cycle systems, namely Landau–Stuart and Van der Pol oscillators and also in generic chaotic Lorenz oscillator. We also study the effect of parameter mismatch in the process of restoring oscillation for coupled oscillators. - Highlights: • Amplitude death is observed using direct and indirect coupling. • Revival of oscillation using feedback parameter is discussed. • Restoration of oscillation is observed in limit cycle and chaotic systems.
An Optimal Model Identification For Oscillatory Dynamics With a Stable Limit Cycle
Protas, Bartosz; Morzynski, Marek
2012-01-01
We propose a general parameter-free model identification technique for a broad class of problems characterized by oscillatory dynamics with a stable limit cycle using measurement data. The model is cast in the form of an autonomous descriptor system with an evolution equation for the dominant oscillation and with manifolds for the low- and high-frequency components. The descriptor system comprises the Landau equation, the mean-field model for a Hopf bifurcation, and more general Galerkin {models} of fluid flow as special cases. We {develop} and validate a variational data assimilation approach which allows us to identify the system by making assumptions only on the smoothness of the propagator. The proposed model identification technique is illustrated using transient vortex shedding in a wake flow as an example problem. It is demonstrated that this approach can be used to systematically refine existing models, so that they describe more accurately available data. The article is written for practitioners work...
Canard explosion of limit cycles in templator models of self-replication mechanisms
Brøns, Morten
2011-01-01
Templators are differential equation models for self-replicating chemical systems. Beutel and Peacock-López [J. Chem. Phys. 126, 125104 (2007)]10.1063/1.2716396 have numerically analyzed a model for a cross-catalytic self-replicating system and found two cases of canard explosion, that is......, a substantial change of amplitude of a limit cycle over a very short parameter interval. We show how the model can be reduced to a two-dimensional system and how canard theory for slow-fast equations can be applied to yield analytic information about the canard explosion. In particular, simple expressions...... for the parameter value where the canard explosion occurs are obtained. The connection to mixed-mode oscillations also observed in the model is briefly discussed. © 2011 American Institute of Physics....
Cyclic di-GMP acts as a cell cycle oscillator to drive chromosome replication.
Lori, C; Ozaki, S; Steiner, S; Böhm, R; Abel, S; Dubey, B N; Schirmer, T; Hiller, S; Jenal, U
2015-07-01
Fundamental to all living organisms is the capacity to coordinate cell division and cell differentiation to generate appropriate numbers of specialized cells. Whereas eukaryotes use cyclins and cyclin-dependent kinases to balance division with cell fate decisions, equivalent regulatory systems have not been described in bacteria. Moreover, the mechanisms used by bacteria to tune division in line with developmental programs are poorly understood. Here we show that Caulobacter crescentus, a bacterium with an asymmetric division cycle, uses oscillating levels of the second messenger cyclic diguanylate (c-di-GMP) to drive its cell cycle. We demonstrate that c-di-GMP directly binds to the essential cell cycle kinase CckA to inhibit kinase activity and stimulate phosphatase activity. An upshift of c-di-GMP during the G1-S transition switches CckA from the kinase to the phosphatase mode, thereby allowing replication initiation and cell cycle progression. Finally, we show that during division, c-di-GMP imposes spatial control on CckA to install the replication asymmetry of future daughter cells. These studies reveal c-di-GMP to be a cyclin-like molecule in bacteria that coordinates chromosome replication with cell morphogenesis in Caulobacter. The observation that c-di-GMP-mediated control is conserved in the plant pathogen Agrobacterium tumefaciens suggests a general mechanism through which this global regulator of bacterial virulence and persistence coordinates behaviour and cell proliferation.
On the number of limit cycles for perturbed pendulum equations
Gasull, A.; Geyer, A.; Mañosas, F.
2016-08-01
We consider perturbed pendulum-like equations on the cylinder of the form x ¨ + sin (x) = ε∑s=0mQn,s (x)x˙s where Qn,s are trigonometric polynomials of degree n, and study the number of limit cycles that bifurcate from the periodic orbits of the unperturbed case ε = 0 in terms of m and n. Our first result gives upper bounds on the number of zeros of its associated first order Melnikov function, in both the oscillatory and the rotary regions. These upper bounds are obtained expressing the corresponding Abelian integrals in terms of polynomials and the complete elliptic functions of first and second kind. Some further results give sharp bounds on the number of zeros of these integrals by identifying subfamilies which are shown to be Chebyshev systems.
InP Gunn Diodes with Current Limiting Contact for High Efficiency Gunn Oscillators
Kim, Mi-Ra; Rhee, Jin-Koo; Lee, Chang-Woo; Chae, Yeon-Sik; Choi, Jae-Hyun; Kim, Wan-Joo
We fabricated and examined current limiting effect for InP Gunn diodes with stable depletion layer mode operation of diodes for high efficiency Gunn oscillators. Current limiting at the cathode was achieved by a shallow Schottky barrier at the interface. We discussed fabrication procedure, the results for negative differential resistance and rf tests for InP Gunn diodes. It was shown that the fabricated Gunn diodes have the output power of 10.22dBm at a frequency of 90.13GHz. Its input voltage and corresponding current were 8.55V and 252mA, respectively.
Entrainability of cell cycle oscillator models with exponential growth of cell mass.
Nakao, Mitsuyuki; Enkhkhudulmur, Tsog-Erdene; Katayama, Norihiro; Karashima, Akihiro
2014-01-01
Among various aspects of cell cycle, understanding synchronization mechanism of cell cycle is important because of the following reasons. (1)Cycles of cell assembly should synchronize to form an organ. (2) Synchronizing cell cycles are required to experimental analysis of regulatory mechanisms of cell cycles. (3) Cell cycle has a distinct phase relationship with the other biological rhythms such as circadian rhythm. However, forced as well as mutual entrainment mechanisms are not clearly known. In this study, we investigated entrainability of cell cycle models of yeast cell under the periodic forcing to both of the cell mass and molecular dynamics. Dynamics of models under study involve the cell mass growing exponentially. In our result, they are shown to allow only a limited frequency range for being entrained by the periodic forcing. In contrast, models with linear growth are shown to be entrained in a wider frequency range. It is concluded that if the cell mass is included in the cell cycle regulation, its entrainability is sensitive to a shape of growth curve assumed in the model.
BIFURCATION OF LIMIT CYCLES FROM A DOUBLE HOMOCLINIC LOOP WITH A ROUGH SADDLE
HAN MAOAN; BI PING
2004-01-01
This paper concerns with the bifurcation of limit cycles from a double bomoclinic loop under multiple parameter perturbations for general planar systems. The existence conditions of 4 homoclinic bifurcation curves and small and large limit cycles are especially investigated.
ON THE NUMBER OF LIMIT CYCLES OF A CUBIC SYSTEM NEAR A CUSPIDAL LOOP
无
2010-01-01
In this paper, we investigate the limit cycle bifurcations in a cubic near-Hamiltonian system by perturbing a cuspidal loop and prove that 5 limit cycles can appear in a neighborhood of the cuspidal loop.
无
2011-01-01
Using qualitative analysis, we study perturbed Hamiltonian systems with different n-th order polynomial as perturbation terms. By numerical simulation, we show that these perturbed systems have the same distribution of limit cycles. Our results imply that these perturbed systems are equivalent in the sense of distribution of limit cycles. This is useful for studying limit cycles of perturbed systems.
CENTER CONDITIONS AND BIFURCATION OF LIMIT CYCLES FOR A CLASS OF FIFTH DEGREE SYSTEMS
HuangWentao; LiuYirong
2004-01-01
The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated. Two recursive formulas to compute singular quantities at infinity and at the origin are given. The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles. Two fifth degree systems are constructed. One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity. The other perturbs six limit cycles at the origin.
Mouse hair cycle expression dynamics modeled as coupled mesenchymal and epithelial oscillators.
Ryan Tasseff
2014-11-01
Full Text Available The hair cycle is a dynamic process where follicles repeatedly move through phases of growth, retraction, and relative quiescence. This process is an example of temporal and spatial biological complexity. Understanding of the hair cycle and its regulation would shed light on many other complex systems relevant to biological and medical research. Currently, a systematic characterization of gene expression and summarization within the context of a mathematical model is not yet available. Given the cyclic nature of the hair cycle, we felt it was important to consider a subset of genes with periodic expression. To this end, we combined several mathematical approaches with high-throughput, whole mouse skin, mRNA expression data to characterize aspects of the dynamics and the possible cell populations corresponding to potentially periodic patterns. In particular two gene clusters, demonstrating properties of out-of-phase synchronized expression, were identified. A mean field, phase coupled oscillator model was shown to quantitatively recapitulate the synchronization observed in the data. Furthermore, we found only one configuration of positive-negative coupling to be dynamically stable, which provided insight on general features of the regulation. Subsequent bifurcation analysis was able to identify and describe alternate states based on perturbation of system parameters. A 2-population mixture model and cell type enrichment was used to associate the two gene clusters to features of background mesenchymal populations and rapidly expanding follicular epithelial cells. Distinct timing and localization of expression was also shown by RNA and protein imaging for representative genes. Taken together, the evidence suggests that synchronization between expanding epithelial and background mesenchymal cells may be maintained, in part, by inhibitory regulation, and potential mediators of this regulation were identified. Furthermore, the model suggests that
Mouse Hair Cycle Expression Dynamics Modeled as Coupled Mesenchymal and Epithelial Oscillators
Tasseff, Ryan; Bheda-Malge, Anjali; DiColandrea, Teresa; Bascom, Charles C.; Isfort, Robert J.; Gelinas, Richard
2014-01-01
The hair cycle is a dynamic process where follicles repeatedly move through phases of growth, retraction, and relative quiescence. This process is an example of temporal and spatial biological complexity. Understanding of the hair cycle and its regulation would shed light on many other complex systems relevant to biological and medical research. Currently, a systematic characterization of gene expression and summarization within the context of a mathematical model is not yet available. Given the cyclic nature of the hair cycle, we felt it was important to consider a subset of genes with periodic expression. To this end, we combined several mathematical approaches with high-throughput, whole mouse skin, mRNA expression data to characterize aspects of the dynamics and the possible cell populations corresponding to potentially periodic patterns. In particular two gene clusters, demonstrating properties of out-of-phase synchronized expression, were identified. A mean field, phase coupled oscillator model was shown to quantitatively recapitulate the synchronization observed in the data. Furthermore, we found only one configuration of positive-negative coupling to be dynamically stable, which provided insight on general features of the regulation. Subsequent bifurcation analysis was able to identify and describe alternate states based on perturbation of system parameters. A 2-population mixture model and cell type enrichment was used to associate the two gene clusters to features of background mesenchymal populations and rapidly expanding follicular epithelial cells. Distinct timing and localization of expression was also shown by RNA and protein imaging for representative genes. Taken together, the evidence suggests that synchronization between expanding epithelial and background mesenchymal cells may be maintained, in part, by inhibitory regulation, and potential mediators of this regulation were identified. Furthermore, the model suggests that impairing this negative
Two-timing Hypothesis, Distinguished Limits, Drifts, and Vibrodiffusion for Oscillating Flows
Vladimirov, Vladimir A
2015-01-01
In this paper we develop and use the two-timing method for a systematic study of a scalar advection caused by a general oscillating velocity field. Mathematically, we study and classify the multiplicity of distinguished limits and asymptotic solutions produced in the two-timing framework. Our calculations go far beyond the usual ones, performed by the two-timing method. We do not use any additional assumptions, hence our study can be seen as a test for the validity and sufficiency of the two-timing hypothesis. Physically, we derive the averaged equations in their maximum generality (and up to high orders in small parameters) and obtain qualitatively new results. Our results are: (i) the dimensionless advection equation contains \\emph{two independent dimensionless small parameters}: the ratio of two time-scales and the spatial amplitudes of oscillations; (ii) we identify a sequence of \\emph{distinguished limit solutions} which correspond to the successive degenerations of a \\emph{drift velocity}; (iii) for a g...
Albert Miklos Barth
2014-08-01
Full Text Available GABAA receptors containing δ subunits (δ-GABAARs are GABA-gated ion channels with extra- and perisynaptic localization, strong sensitivity to neurosteroids (NS, and a high degree of plasticity. In selective brain regions they are expressed on specific principal cells and interneurons (INs, and generate a tonic conductance that controls neuronal excitability and oscillations. Plasticity of δ-GABAARs in principal cells has been described during states of altered NS synthesis including acute stress, puberty, ovarian cycle, pregnancy and the postpartum period, with direct consequences on neuronal excitability and network dynamics. The defining network events implicated in cognitive function, memory formation and encoding are γ oscillations (30-120 Hz, a well-timed loop of excitation and inhibition between principal cells and PV-expressing INs (PV+INs. The δ-GABAARs of INs can modify γ oscillations, and a lower expression of δ-GABAARs on INs during pregnancy alters γ frequency recorded in vitro. The ovarian cycle is another physiological event with large fluctuations in NS levels and δ-GABAARs. Stages of the cycle are paralleled by swings in memory performance, cognitive function, and mood in both humans and rodents. Here we show δ-GABAARs changes during the mouse ovarian cycle in hippocampal cell types, with enhanced expression during diestrus in principal cells and specific INs. The plasticity of δ-GABAARs on PV-INs decreases the magnitude of γ oscillations continuously recorded in area CA1 throughout several days in vivo during diestrus and increases it during estrus. Such recurring changes in γ magnitude were not observed in non-cycling wild-type (WT females, cycling females lacking δ-GABAARs only on PV-INs (PV-Gabrd-/-, and in male mice during a time course equivalent to the ovarian cycle. Our findings may explain the impaired memory and cognitive performance experienced by women with premenstrual syndrome (PMS or premenstrual
A limit on exotic nu(mu) - nu(tau) oscillations derived from results of the OPERA experiment
Loverre, P F
2014-01-01
The OPERA experiment searching for nu(mu)- nu(tau) oscillations in the CERN to Gran Sasso nu(mu) beam, has detected so far three candidates of nu(tau) charged current interactions. All three events are attributed by the authors to the standard nu(mu)-nu(tau) oscillation at the atmospheric $Dm^2$. It is then possible to constrain the number of additional interactions, which could e.g. result from non-standard oscillations involving more than 3 neutrino mass states. In this paper, a 90 percent CL upper limit of 5.5 events is set on the number of additional nu(tau) interactions. This limit is then converted into limits on exotic nu(mu)-nu(tau) oscillations.
Parameter Limits for Neutrino Oscillation with Decoherence in KamLAND
Gomes, G Balieiro; de Holanda, P C; Oliveira, R L N
2016-01-01
In the framework of quantum open systems we analyze data from KamLAND by using a model that considers neutrino oscillation in a three-family approximation with the inclusion of the decoherence effect. Using a $\\chi^2$ test we find new limits for the decoherence parameter which we call $\\gamma$, considering the most recent data by KamLAND. Assuming an energy dependence of the type $ \\gamma = \\gamma_0 \\left( E/E_0 \\right) ^n$, in 95 \\% C.L. the limits found are $3.7 \\times 10^{-27} GeV$ for $ n=-1$, $6.8 \\times 10^{-22} GeV$ for $ n=0$, and $1.5 \\times 10^{-16} GeV$ for $ n=1 $ on the energy dependence.
Babu, K S
2016-01-01
We point out that if the baryon number violating neutron-antineutron oscillation is discovered, it would impose strong limits on the departure from Einstein's equivalence principle at a level of one part in $10^{19}$. If this departure owes its origin to the existence of long-range forces coupled to baryon number $B$ (or $B-L$), it would imply very stringent constraints on the strength of gauge bosons coupling to baryon number current. For instance, if the force mediating baryon number has strength $\\alpha_B$ and its range is larger than a megaparsec, we find the limit to be $\\alpha_B \\leq 2\\times 10^{-57}$, which is much stronger than all other existing bounds. For smaller range for the force, we get slightly weaker, but still stringent bounds by considering the potential of the Earth and the Sun.
A Constant Energy-Per-Cycle Ring Oscillator Over a Wide Frequency Range for Wireless Sensor Nodes.
Lee, Inhee; Sylvester, Dennis; Blaauw, David
2016-03-01
This paper presents an energy-efficient oscillator for wireless sensor nodes (WSNs). It avoids short-circuit current by minimizing the time spent in the input voltage range from Vthn to [Vdd - |Vthp|]. A current-feeding scheme with gate voltage control enables the oscillator to operate over a wide frequency range. A test chip is fabricated in a 0.18 μm CMOS process. The measurements show that the proposed oscillator achieves a constant energy-per-cycle (EpC) of 0.8 pJ/cycle over the 21-60 MHz frequency range and is more efficient than a conventional current-starved ring oscillator (CSRO) below 300 kHz at 1.8 V supply voltage. As an application example, the proposed oscillator is implemented in a switched-capacitor DC-DC converter. The converter is 11%-56% more efficient for load power values ranging from 583 pW to 2.9 nW than a converter using a conventional CSRO.
Limit on B$^{0}_{s}$ oscillation using a jet charge method
Buskulic, Damir; De Bonis, I; Décamp, D; Ghez, P; Goy, C; Lees, J P; Lucotte, A; Minard, M N; Odier, P; Pietrzyk, B; Ariztizabal, F; Chmeissani, M; Crespo, J M; Efthymiopoulos, I; Fernández, E; Fernández-Bosman, M; Gaitan, V; Garrido, L; Martínez, M; Orteu, S; Pacheco, A; Padilla, C; Palla, Fabrizio; Pascual, A; Perlas, J A; Sánchez, F; Teubert, F; Colaleo, A; Creanza, D; De Palma, M; Farilla, A; Gelao, G; Girone, M; Iaselli, Giuseppe; Maggi, G; Maggi, M; Marinelli, N; Natali, S; Nuzzo, S; Ranieri, A; Raso, G; Romano, F; Ruggieri, F; Selvaggi, G; Silvestris, L; Tempesta, P; Zito, G; Huang, X; Lin, J; Ouyang, Q; Wang, T; Xie, Y; Xu, R; Xue, S; Zhang, J; Zhang, L; Zhao, W; Bonvicini, G; Cassel, David G; Cattaneo, M; Comas, P; Coyle, P; Drevermann, H; Engelhardt, A; Forty, Roger W; Frank, M; Hagelberg, R; Harvey, J; Jacobsen, R; Janot, P; Jost, B; Knobloch, J; Lehraus, Ivan; Markou, C; Martin, E B; Mato, P; Mattison, T S; Meinhard, H; Minten, Adolf G; Miquel, R; Moffeit, K; Oest, T; Palazzi, P; Pater, J R; Pusztaszeri, J F; Ranjard, F; Rensing, P E; Rolandi, Luigi; Schlatter, W D; Schmelling, M; Schneider, O; Tejessy, W; Tomalin, I R; Venturi, A; Wachsmuth, H W; Wiedenmann, W; Wildish, T; Witzeling, W; Wotschack, J; Ajaltouni, Ziad J; Bardadin-Otwinowska, Maria; Barrès, A; Boyer, C; Falvard, A; Gay, P; Guicheney, C; Henrard, P; Jousset, J; Michel, B; Monteil, S; Montret, J C; Pallin, D; Perret, P; Podlyski, F; Proriol, J; Rossignol, J M; Saadi, F; Fearnley, Tom; Hansen, J B; Hansen, J D; Hansen, J R; Hansen, P H; Nilsson, B S; Kyriakis, A; Simopoulou, Errietta; Siotis, I; Vayaki, Anna; Zachariadou, K; Blondel, A; Bonneaud, G R; Brient, J C; Bourdon, P; Passalacqua, L; Rougé, A; Rumpf, M; Tanaka, R; Valassi, Andrea; Verderi, M; Videau, H L; Candlin, D J; Parsons, M I; Focardi, E; Parrini, G; Corden, M; Delfino, M C; Georgiopoulos, C H; Jaffe, D E; Antonelli, A; Bencivenni, G; Bologna, G; Bossi, F; Campana, P; Capon, G; Chiarella, V; Felici, G; Laurelli, P; Mannocchi, G; Murtas, F; Murtas, G P; Pepé-Altarelli, M; Dorris, S J; Halley, A W; ten Have, I; Knowles, I G; Lynch, J G; Morton, W T; O'Shea, V; Raine, C; Reeves, P; Scarr, J M; Smith, K; Smith, M G; Thompson, A S; Thomson, F; Thorn, S; Turnbull, R M; Becker, U; Braun, O; Geweniger, C; Graefe, G; Hanke, P; Hepp, V; Kluge, E E; Putzer, A; Rensch, B; Schmidt, M; Sommer, J; Stenzel, H; Tittel, K; Werner, S; Wunsch, M; Beuselinck, R; Binnie, David M; Cameron, W; Colling, D J; Dornan, Peter J; Konstantinidis, N P; Moneta, L; Moutoussi, A; Nash, J; San Martin, G; Sedgbeer, J K; Stacey, A M; Dissertori, G; Girtler, P; Kneringer, E; Kuhn, D; Rudolph, G; Bowdery, C K; Brodbeck, T J; Colrain, P; Crawford, G; Finch, A J; Foster, F; Hughes, G; Sloan, Terence; Whelan, E P; Williams, M I; Galla, A; Greene, A M; Kleinknecht, K; Quast, G; Raab, J; Renk, B; Sander, H G; Wanke, R; Zeitnitz, C; Aubert, Jean-Jacques; Bencheikh, A M; Benchouk, C; Bonissent, A; Bujosa, G; Calvet, D; Carr, J; Diaconu, C A; Etienne, F; Thulasidas, M; Nicod, D; Payre, P; Rousseau, D; Talby, M; Abt, I; Assmann, R W; Bauer, C; Blum, Walter; Brown, D; Dietl, H; Dydak, Friedrich; Ganis, G; Gotzhein, C; Jakobs, K; Kroha, H; Lütjens, G; Lutz, Gerhard; Männer, W; Moser, H G; Richter, R H; Rosado-Schlosser, A; Schwarz, A; Settles, Ronald; Seywerd, H C J; Stierlin, U; Saint-Denis, R; Wolf, G; Alemany, R; Boucrot, J; Callot, O; Cordier, A; Courault, F; Davier, M; Duflot, L; Grivaz, J F; Heusse, P; Jacquet, M; Kim, D W; Le Diberder, F R; Lefrançois, J; Lutz, A M; Musolino, G; Nikolic, I A; Park, H J; Park, I C; Schune, M H; Simion, S; Veillet, J J; Videau, I; Abbaneo, D; Azzurri, P; Bagliesi, G; Batignani, G; Bettarini, S; Bozzi, C; Calderini, G; Carpinelli, M; Ciocci, M A; Ciulli, V; Dell'Orso, R; Fantechi, R; Ferrante, I; Foà, L; Forti, F; Giassi, A; Giorgi, M A; Gregorio, A; Ligabue, F; Lusiani, A; Marrocchesi, P S; Messineo, A; Rizzo, G; Sanguinetti, G; Sciabà, A; Spagnolo, P; Steinberger, Jack; Tenchini, Roberto; Tonelli, G; Triggiani, G; Vannini, C; Verdini, P G; Walsh, J; Betteridge, A P; Blair, G A; Bryant, L M; Cerutti, F; Gao, Y; Green, M G; Johnson, D L; Medcalf, T; Mir, L M; Perrodo, P; Strong, J A; Bertin, V; Botterill, David R; Clifft, R W; Edgecock, T R; Haywood, S; Edwards, M; Maley, P; Norton, P R; Thompson, J C; Bloch-Devaux, B; Colas, P; Duarte, H; Emery, S; Kozanecki, Witold; Lançon, E; Lemaire, M C; Locci, E; Marx, B; Pérez, P; Rander, J; Renardy, J F; Rosowsky, A; Roussarie, A; Schuller, J P; Schwindling, J; Si Mohand, D; Trabelsi, A; Vallage, B; Johnson, R P; Kim, H Y; Litke, A M; McNeil, M A; Taylor, G; Beddall, A; Booth, C N; Boswell, R; Cartwright, S L; Combley, F; Dawson, I; Köksal, A; Letho, M; Newton, W M; Rankin, C; Thompson, L F; Böhrer, A; Brandt, S; Cowan, G D; Feigl, E; Grupen, Claus; Lutters, G; Minguet-Rodríguez, J A; Rivera, F; Saraiva, P; Smolik, L; Stephan, F; Apollonio, M; Bosisio, L; Della Marina, R; Giannini, G; Gobbo, B; Ragusa, F; Rothberg, J E; Wasserbaech, S R; Armstrong, S R; Bellantoni, L; Elmer, P; Feng, Z; Ferguson, D P S; Gao, Y S; González, S; Grahl, J; Harton, J L; Hayes, O J; Hu, H; McNamara, P A; Nachtman, J M; Orejudos, W; Pan, Y B; Saadi, Y; Schmitt, M; Scott, I J; Sharma, V; Turk, J; Walsh, A M; Wu Sau Lan; Wu, X; Yamartino, J M; Zheng, M; Zobernig, G
1995-01-01
A lower limit is set on the B_{s}^{0} meson oscillation parameter \\Delta m_{s} using data collected from 1991 to 1994 by the ALEPH detector. Events with a high transverse momentum lepton and a reconstructed secondary vertex are used. The high transverse momentum leptons are produced mainly by b hadron decays, and the sign of the lepton indicates the particle/antiparticle final state in decays of neutral B mesons. The initial state is determined by a jet charge technique using both sides of the event. A maximum likelihood method is used to set a lower limit of \\, \\Delta m_{s}. The 95\\% confidence level lower limit on \\Delta m_s ranges between 5.2 and 6.5(\\hbar/c^{2})~ps^{-1} when the fraction of b quarks from Z^0 decays that form B_{s}^{0} mesons is varied from 8\\% to 16\\%. Assuming that the B_{s}^{0} fraction is 12\\%, the lower limit would be \\Delta m_{s} > 6.1(\\hbar/c^{2})~ps^{-1} at 95\\% confidence level. For x_s = \\Delta m_s \\, \\tau_{B_s}, this limit also gives x_s > 8.8 using the B_{s}^{0} lifetime of \\ta...
Ventilator auto-cycling from cardiogenic oscillations: case report and review of literature.
Noujeim, Carlos; Bouakl, Imad; El-Khatib, Mohamad; Bou-Khalil, Pierre
2013-09-01
Brain death is the total loss of all brain and brain stem functions, and its diagnosis is often confirmed by an apnoea test, which relies on disconnecting the patient from the ventilator. Auto-triggering or auto-cycling is defined as a ventilator being triggered in the absence of patient effort, intrinsic respiratory drive or inspiratory muscle activity. Ventilator auto-triggering could delay the diagnosis of brain death leading to unnecessary admission for the patient and false hopes of recovery for the family. We report a case of ventilator auto-triggering associated with cardiogenic oscillations in a female patient. We confirmed the finding of ventilator auto-triggering by changing the patient's position and reassessing the triggering thresholds. Brain death was then confirmed by apnoea test. This case is presented to arouse the awareness of the medical staff and nurses to this phenomenon, which can mimic an intrinsic respiratory effort in patients allegedly diagnosed with brain death. Along with this case report, we review the English language publications for similar cases. © 2013 British Association of Critical Care Nurses.
Diurnal Oscillations in Liver Mass and Cell Size Accompany Ribosome Assembly Cycles.
Sinturel, Flore; Gerber, Alan; Mauvoisin, Daniel; Wang, Jingkui; Gatfield, David; Stubblefield, Jeremy J; Green, Carla B; Gachon, Frédéric; Schibler, Ueli
2017-05-04
The liver plays a pivotal role in metabolism and xenobiotic detoxification, processes that must be particularly efficient when animals are active and feed. A major question is how the liver adapts to these diurnal changes in physiology. Here, we show that, in mice, liver mass, hepatocyte size, and protein levels follow a daily rhythm, whose amplitude depends on both feeding-fasting and light-dark cycles. Correlative evidence suggests that the daily oscillation in global protein accumulation depends on a similar fluctuation in ribosome number. Whereas rRNA genes are transcribed at similar rates throughout the day, some newly synthesized rRNAs are polyadenylated and degraded in the nucleus in a robustly diurnal fashion with a phase opposite to that of ribosomal protein synthesis. Based on studies with cultured fibroblasts, we propose that rRNAs not packaged into complete ribosomal subunits are polyadenylated by the poly(A) polymerase PAPD5 and degraded by the nuclear exosome. Copyright © 2017 Elsevier Inc. All rights reserved.
Electronic Zero-Point Oscillations in the Strong-Interaction Limit of Density Functional Theory.
Gori-Giorgi, Paola; Vignale, Giovanni; Seidl, Michael
2009-04-14
The exchange-correlation energy in Kohn-Sham density functional theory can be expressed exactly in terms of the change in the expectation of the electron-electron repulsion operator when, in the many-electron Hamiltonian, this same operator is multiplied by a real parameter λ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is kept fixed by a suitable local one-body potential. The strong-interaction limit of density functional theory, defined as the limit λ→∞, turns out to be like the opposite noninteracting Kohn-Sham limit (λ→0) mathematically simpler than the physical (λ = 1) case and can be used to build an approximate interpolation formula between λ→0 and λ→∞ for the exchange-correlation energy. Here we extend the systematic treatment of the λ→∞ limit [Phys. Rev. A 2007, 75, 042511] to the next leading term, describing zero-point oscillations of strictly correlated electrons, with numerical examples for small spherical atoms. We also propose an improved approximate functional for the zero-point term and a revised interpolation formula for the exchange-correlation energy satisfying more exact constraints.
Performance of a quantum heat engine cycle working with harmonic oscillator systems
2007-01-01
A cycle model of an irreversible heat engine working with harmonic systems is established in this paper. Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained. The general expressions for several important parameters, such as the work, efficiency, power output, and rate of entropy production are derived. By means of numerical analysis, the optimally operating regions and the optimal values of performance parameters of the cycle are determined under the condition of maximum power output. At last, some special cases, such as high temperature limit and frictionless case, are dis-cussed in brief.
Performance of a quantum heat engine cycle working with harmonic oscillator systems
WANG JianHui; HE JiZhou; MAO ZhiYuan
2007-01-01
A cycle model of an irreversible heat engine working with harmonic systems is established in this paper. Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained. The general expressions for several important parameters, such as the work, efficiency, power output, and rate of entropy production are derived. By means of numerical analysis, the optimally operating regions and the optimal values of performance parameters of the cycle are determined under the condition of maximum power output. At last, some special cases, such as high temperature limit and frictionless case, are discussed in brief.
Number and Location of Limit Cycles in a Class of Perturbed Polynomial Systems
Chen-xi Yang; Rui-qi Wang
2004-01-01
In this paper,we investigate the number,location and stability of limit cycles in a class of perturbed polynomial systems with (2n+1)or(2n+2)-degree by constructing detection function and using qualitative analysis.We show that there are at most n limit cycles in the perturbed polynomial system,which is similar to the result of Perko in [8] by using Melnikov method.For n=2,we establish the general conditions depending on polynomial's coeffcients for the bifurcation,location and stability of limit cycles.The bifurcation parameter value of limit cycles in [5] is also improved by us.When n =3 the suffcient and necessary conditions for the appearance of 3 limit cycles are given.Two numerical examples for the location and stability of limit cycles are used to demonstrate our theoretical results.
47 CFR 27.50 - Power limits and duty cycle.
2010-10-01
... bandwidth. For mobile and portable stations using time division duplex (TDD) technology, the duty cycle must... supporting frequency division duplex (FDD) mobile and portable operations are restricted to transmitting in... 2 watts per 5 megahertz or less average EIRP is prohibited. For WCS CPE using TDD technology,...
Wang, Hongfang; Follmer, L.R.; Chao-li, Liu
2000-01-01
The ??13C of soil carbonate in rhizoconcretions collected from a loess-paleosol sequence in the central United States indicates that growing-season C3/C4 plant ratio oscillated by 35% on a 900 ?? 200 yr time scale during the late Wisconsinan glaciation. The pattern appears in phase with advance and retreat of the southern margin of the Laurentide ice sheet, suggesting influence by paleo-El Nin??o-Southern Oscillation cycles. The ??13C of soil organic matter indicates that the annual average C3/C4 plant ratio oscillated only by 18%, with a periodicity of 450 ?? 100 yr, and closely matched the cyclic pattern of loess-paleosol layers. It suggests a periodic enhancement of the penetration of the Gulf of Mexico air over the region during this time.
James R. Chagdes; Jessica E. Huber; Meredith Saletta; Meghan Darling-White; Arvind Raman; Shirley Rietdyk; Howard N. Zelaznik; Jeffrey M. Haddad
2016-01-01
Background: Many disease-specific factors such as muscular weakness, increased muscle stiffness, varying postural strategies, and changes in postural reflexes have been shown to lead to postural instability and fall risk in people with Parkinson’s disease (PD). Recently, analytical techniques, inspired by the dynamical systems perspective on movement control and coordination, have been used to examine the mechanisms underlying the dynamics of postural declines and the emergence of postural instabilities in people with PD. Methods: A wavelet-based technique was used to identify limit cycle oscillations (LCOs) in the anterior–posterior (AP) postural sway of people with mild PD (n=10) compared to age-matched controls (n=10). Participants stood on a foam and on a rigid surface while completing a dual task (speaking). Results: There was no significant difference in the root mean square of center of pressure between groups. Three out of 10 participants with PD demonstrated LCOs on the foam surface, while none in the control group demonstrated LCOs. An inverted pendulum model of bipedal stance was used to demonstrate that LCOs occur due to disease-specific changes associated with PD:time-delay and neuromuscular feedback gain. Conclusion: Overall, the LCO analysis and mathematical model appear to capture the subtle postural instabilities associated with mild PD. In addition, these findings provide insights into the mechanisms that lead to the emergence of unstable posture in patients with PD.
Jenkins, Alejandro
2013-04-01
Physicists are very familiar with forced and parametric resonance, but usually not with self-oscillation, a property of certain dynamical systems that gives rise to a great variety of vibrations, both useful and destructive. In a self-oscillator, the driving force is controlled by the oscillation itself so that it acts in phase with the velocity, causing a negative damping that feeds energy into the vibration: no external rate needs to be adjusted to the resonant frequency. The famous collapse of the Tacoma Narrows bridge in 1940, often attributed by introductory physics texts to forced resonance, was actually a self-oscillation, as was the swaying of the London Millennium Footbridge in 2000. Clocks are self-oscillators, as are bowed and wind musical instruments. The heart is a “relaxation oscillator”, i.e., a non-sinusoidal self-oscillator whose period is determined by sudden, nonlinear switching at thresholds. We review the general criterion that determines whether a linear system can self-oscillate. We then describe the limiting cycles of the simplest nonlinear self-oscillators, as well as the ability of two or more coupled self-oscillators to become spontaneously synchronized (“entrained”). We characterize the operation of motors as self-oscillation and prove a theorem about their limit efficiency, of which Carnot’s theorem for heat engines appears as a special case. We briefly discuss how self-oscillation applies to servomechanisms, Cepheid variable stars, lasers, and the macroeconomic business cycle, among other applications. Our emphasis throughout is on the energetics of self-oscillation, often neglected by the literature on nonlinear dynamical systems.
Campante, T. L.; Chaplin, W. J.; Handberg, R.; Miglio, A.; Davies, G. R.; Elsworth, Y. P. [School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT (United Kingdom); Lund, M. N.; Arentoft, T.; Christensen-Dalsgaard, J.; Karoff, C.; Kjeldsen, H.; Lundkvist, M. [Stellar Astrophysics Centre (SAC), Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C (Denmark); Huber, D. [NASA Ames Research Center, MS 244-30, Moffett Field, CA 94035 (United States); Hekker, S. [Astronomical Institute, " Anton Pannekoek," University of Amsterdam, Amsterdam (Netherlands); García, R. A. [Laboratoire AIM, CEA/DSM-CNRS-Université Paris Diderot (France); IRFU/SAp, Centre de Saclay, F-91191 Gif-sur-Yvette Cedex (France); Corsaro, E. [Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven (Belgium); Basu, S. [Department of Astronomy, Yale University, New Haven, CT 06520 (United States); Bedding, T. R. [Sydney Institute for Astronomy, School of Physics, University of Sydney, Sydney (Australia); Gilliland, R. L. [Center for Exoplanets and Habitable Worlds, The Pennsylvania State University, University Park, PA 16802 (United States); Kawaler, S. D., E-mail: campante@bison.ph.bham.ac.uk [Department of Physics and Astronomy, Iowa State University, Ames, IA 50011 (United States); and others
2014-03-10
We present a novel method for estimating lower-limit surface gravities (log g) of Kepler targets whose data do not allow the detection of solar-like oscillations. The method is tested using an ensemble of solar-type stars observed in the context of the Kepler Asteroseismic Science Consortium. We then proceed to estimate lower-limit log g for a cohort of Kepler solar-type planet-candidate host stars with no detected oscillations. Limits on fundamental stellar properties, as provided by this work, are likely to be useful in the characterization of the corresponding candidate planetary systems. Furthermore, an important byproduct of the current work is the confirmation that amplitudes of solar-like oscillations are suppressed in stars with increased levels of surface magnetic activity.
Campante, T L; Lund, M N; Huber, D; Hekker, S; García, R A; Corsaro, E; Handberg, R; Miglio, A; Arentoft, T; Basu, S; Bedding, T R; Christensen-Dalsgaard, J; Davies, G R; Elsworth, Y P; Gilliland, R L; Karoff, C; Kawaler, S D; Kjeldsen, H; Lundkvist, M; Metcalfe, T S; Aguirre, V Silva; Stello, D
2014-01-01
We present a novel method for estimating lower-limit surface gravities log g of Kepler targets whose data do not allow the detection of solar-like oscillations. The method is tested using an ensemble of solar-type stars observed in the context of the Kepler Asteroseismic Science Consortium. We then proceed to estimate lower-limit log g for a cohort of Kepler solar-type planet-candidate host stars with no detected oscillations. Limits on fundamental stellar properties, as provided by this work, are likely to be useful in the characterization of the corresponding candidate planetary systems. Furthermore, an important byproduct of the current work is the confirmation that amplitudes of solar-like oscillations are suppressed in stars with increased levels of surface magnetic activity.
Effect of higher strain range cycling on near fatigue-limit fatigue life
Fukuoka, Chie; Nakagawa, Y.G. [Ishikawajima-Harima Heavy Industries Co. Ltd., Tokyo (Japan). Research Inst; Rosinski, S.T.
1999-04-01
The objective of this study is to clarify the effects of pre-cycling above the fatigue limit on near the fatigue-limit fatigue behaviors of SA508, low alloy steel for nuclear pressure vessels, correlating fatigue lifetime with microstructural changes in the bulk. It has been observed that dislocation cell structure is well developed in an as-received SA508 sample and the misorientation among cells increases with fatigue accumulation during fatigue tests. The cell to cell misorientation was measured and statistically quantified by the Selected Area electron beam Diffraction (SAD). It was shown that a fatigue crack started growing abruptly when the SAD value (the mean misorientation among cells) exceeded a critical angle, 4-5 degrees. Fatigue tests were performed for SA508 samples, first at a high total strain range (0.62%) to 10, 100, and 6000 cycles followed by cycling at near the fatigue-limit strain range (0.40%). The sample with pre-cycling for 100 and 6000 cycles failed while ones with pre-cycling for 10 cycles and without pre-cycling did not rupture till about 10{sup 6} cycles where the tests were terminated. Small surface cracks were found all samples pre-cycled at the high strain range but the cracks were arrested for a long time at the near fatigue limit cycling followed by an abrupt growth at the failure. It was found by the SAD that samples failed at the fatigue limit when the average misorientation among cells exceeds the critical angle regardless of pre-cycling histories. The SAD value changed even during cycling below the fatigue limit, and the change in SAD value was strongly influenced by the number of pre-cycling above the fatigue limit. These changes well agreed with fatigue lifetime of the samples. (author)
Uniqueness of Limit Cycle for the Quadratic Systems with Weak Saddle and Focus
Shen Qi ZHAO; Ping Guang ZHANG
2004-01-01
It is proved that the quadratic system with a weak saddle has at most one limit cycle, and that if this system has a separatrix cycle passing through the weak saddle, then the stability of the separatrix cycle is contrary to that of the singular point surrounded by it.
Swing-Leg Retraction for Limit Cycle Walkers Improves Disturbance Rejection
Hobbelen, D.G.E.; Wisse, M.
2008-01-01
Limit cycle walkers are bipeds that exhibit a stable cyclic gaitwithout requiring local controllability at all times during gait. A well-known example of limit cycle walking is McGeer’s “passive dynamic walking,” but the concept expands to actuated bipeds as involved in this study. One of the stabil
Closed orbits and limit cycles of second-order autonomous Birkhoff systems
陈向炜
2003-01-01
In this paper,the existence of periodic orbits and the non-existence of limit cycles for the second-order autonomous Birkhoff system are studied.Further the existence of algebraic limit cycles for a generalized second-order autonomous Birkhoff system is studied.
LIMIT CYCLES OF SOME Z3-EQUIVARIANT NEAR-HAMILTONIAN SYSTEMS OF DEGREES 3 AND 4
Hongyan Ma; Maoan Han; Christoph Lhotka
2009-01-01
This paper studies the number of limit cycles of some Z3-equivariant near-Hamiltonian systems of degrees 3 and 4, which arc a perturbation of a cubic Hamiltonian system. By the Melnikov function method, we obtain 5 and 6 limit cycles respectively.
Resurgence of oscillation in coupled oscillators under delayed cyclic interaction
Bera, Bidesh K.; Majhi, Soumen; Ghosh, Dibakar
2017-07-01
This paper investigates the emergence of amplitude death and revival of oscillations from the suppression states in a system of coupled dynamical units interacting through delayed cyclic mode. In order to resurrect the oscillation from amplitude death state, we introduce asymmetry and feedback parameter in the cyclic coupling forms as a result of which the death region shrinks due to higher asymmetry and lower feedback parameter values for coupled oscillatory systems. Some analytical conditions are derived for amplitude death and revival of oscillations in two coupled limit cycle oscillators and corresponding numerical simulations confirm the obtained theoretical results. We also report that the death state and revival of oscillations from quenched state are possible in the network of identical coupled oscillators. The proposed mechanism has also been examined using chaotic Lorenz oscillator.
Classification of attractors for systems of identical coupled Kuramoto oscillators
Engelbrecht, Jan R. [Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467 (United States); Mirollo, Renato [Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467 (United States)
2014-03-15
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For N≠3 oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
Classification of attractors for systems of identical coupled Kuramoto oscillators.
Engelbrecht, Jan R; Mirollo, Renato
2014-03-01
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For [Formula: see text] oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
Yong-xi Gao; Yu-hai Wu; Li-xin Tian
2008-01-01
This paper concerns with the number and distributions of limit cycles of a quintic subject to a seven-degree perturbation. With the aid of numeric integral computation provided by Mathematica 4.1, at least 45 limit cycles are found in the above system by applying the method of double homoclinic loops bifurcation,Hopf bifurcation and qualitative analysis. The four configurations of 45 limit cycles of the system are also shown.The results obtained are useful to the study of the weakened 16th Hilbert Problem.
Limit cycles from a cubic reversible system via the third-order averaging method
Linping Peng
2015-04-01
Full Text Available This article concerns the bifurcation of limit cycles from a cubic integrable and non-Hamiltonian system. By using the averaging theory of the first and second orders, we show that under any small cubic homogeneous perturbation, at most two limit cycles bifurcate from the period annulus of the unperturbed system, and this upper bound is sharp. By using the averaging theory of the third order, we show that two is also the maximal number of limit cycles emerging from the period annulus of the unperturbed system.
A. Kleidon
2013-07-01
Full Text Available The hydrologic cycle results from the combination of energy conversions and atmospheric transport, and the laws of thermodynamics set limits to both. Here, we apply thermodynamics to derive the limits of the strength of hydrologic cycling within the Earth system and about the properties and processes that shape these limits. We set up simple models to derive analytical expressions of the limits of evaporation and precipitation in relation to vertical and horizontal differences in solar radiative forcing. These limits result from a fundamental trade-off by which a greater evaporation rate reduces the temperature gradient and thus the driver for atmospheric motion that exchanges moistened air from the surface with the drier air aloft. The limits on hydrologic cycling thus reflect the strong interaction between the hydrologic flux, motion, and the driving gradient. Despite the simplicity of the models, they yield estimates for the limits of hydrologic cycling that are within the observed magnitude, suggesting that the global hydrologic cycle operates near its maximum strength. We close with a discussion of how thermodynamic limits can provide a better characterization of the interaction of vegetation and human activity with hydrologic cycling.
A. Kleidon
2013-03-01
Full Text Available The hydrologic cycle results from the combination of energy conversions and atmospheric transport, and the laws of thermodynamics set limits to both. Here, we apply thermodynamics to derive the limits of the strength of hydrologic cycling within the Earth system and the properties and processes that shape these limits. We set up simple models to derive analytical expressions of the limits of evaporation and precipitation in relation to vertical and horizontal differences in solar radiative forcing. These limits result from a fundamental trade-off by which a greater evaporation rate reduces the temperature gradient and thus the driver for atmospheric motion that exchanges moistened air from the surface with the drier air aloft. The limits on hydrologic cycling thus reflect the strong interaction between the hydrologic flux, motion, and the driving gradient. Despite the simplicity of the models, they yield estimates for the limits of hydrologic cycling that are within the observed magnitude, suggesting that the global hydrologic cycle operates near its maximum strength. We close with a discussion of how thermodynamic limits can provide a better characterization of the interaction of vegetation and human activity with hydrologic cycling.
Effect of Inclination Angle on Performance Limit of a Closed-End Oscillating Heat Pipe
T. Hudakorn
2008-01-01
Full Text Available This study presents the effect of inclination angle on the performance limit of a Closed-End Oscillating Heat Pipe (CEOHP. The study was divided into 2 corresponding parts. The first part was visual study. The CEOHP was made of Pyrex glass tube with the inner diameter of 1.0 mm, evaporator length of 50 mm and had 10 meandering turns. The lengths of the condenser, adiabatic and evaporator sections were equal. The working fluid was R123 with filling ratio at 50% of total volume of the tube. It was found from the experiment that the performance limit at the horizontal orientation was the initial dry-out because the insufficient condensed liquid film was supplied the evaporator section. At the range of inclination angle of 5-90°, the cause of performance limit was dry-out due to the flooding phenomena at the entrance of the evaporator section. The second part was quantitative study. The CEOHPs were made of copper tubes with 0.66, 1.06 and 2.03 mm inner diameters. The evaporator lengths of CEOHPs were 50, 100 and 150 mm and the number of meandering turns was 10. For each CEOHP, the lengths of evaporator, adiabatic and condenser sections were equal. The working fluids were R123, ethanol and water at a filling ratio of 50% of total volume of the tube. The experiments were conducted at the inclination angles of 0-90° with 10° increments. With the controlled vapor temperature of 60±5°C, it was found from the quantitative results that the critical heat flux decreases as the evaporator length increases and the critical heat flux increases with an increase in the inner diameter for all inclination angles. Moreover, this study establishes the correlation to predict the ratio of the critical heat flux at the inclination angle range of 10-90° and that at vertical position. The Standard Deviation (STD is ±13.8%.
Mayr, H. G.; Lee, J. N.
2014-12-01
Very large solar cycle (SC) variations are observed in the zonal winds and temperatures of the quasi-biennial oscillation (QBO). The effect is too large to be produced by the small SC variations of the solar flux in the lower stratosphere. Dynamical downward coupling must be involved, and we present a review of the mechanism that emerged from studies with the Numerical Spectral Model (NSM). In the NSM, the QBO is generated with parameterized gravity waves and planetary waves. For a SC period of 10 years, the applied heat source varies exponentially with altitude: 0.2% (surface), 2% (50 km), 20% (100 km and above). With that solar forcing, the model reproduces qualitatively the SC modulations of the QBO zonal winds around the equator and temperature variations extending to high latitudes. The QBO is spawned in the lower mesosphere by a hemispherically symmetric equatorial annual oscillation (EAO) of the zonal wind velocities. Though small in magnitude, the SC modulation of the EAO is large. Like the symmetric QBO, the EAO extends into the lower atmosphere under the influence of, and amplified by, wave mean flow interactions. The amplitude modulations of the QBO and EAO are in phase with the imposed SC heat source. Essentially, the EAO provides the pathway and pacemaker for the SC modulation of the QBO - and wave interactions amplify the oscillations as they propagate down into the lower atmosphere. Analysis of NCEP temperature and zonal wind data (1958 to 2006) produces the hemispherically symmetric equatorial annual oscillation (EAO), and it contains spectral signatures with periods around 11 years. Moving windows of 44 years show that below 20 km the 11-year modulation of the EAO is phase locked to the SC. The spectral features from the 48-year data record reveal modulation signatures of 9.6 and 12 years, which produce EAO variations that mimic in limited altitude regimes the varying maxima and minima of the 10.7 cm solar index. In the lower stratosphere, the 40
Multiple ranges of flow rate with bistability and limit cycles for Schlögl's mechanism in a CSTR
Escher, Claus; Ross, John
1983-10-01
Continuous flow stirred tank reactor (CSTR) conditions are imposed upon Schlögl's trimolecular reaction mechanism A+2X ⇄ 3X and X ⇄ B. A nonzero constant flow rate (=inverse residence time) rather than constant concentrations of A,B forces the system far away from equilibrium. This change in constraints leads to some surprisingly complex features; first the system has bistability for separate ranges of flow rates, under constraints of all other parameters being fixed including the concentration of the chemical species in the input. This phenomena occurs even if the input contains A alone. Secondly, there occur limit cycle oscillations, but in that case the input has to include B or X as well as A.
微生物生长模型的极限环%Limit Cycles in a Microbial Growth Model
Minaya Villasana; 黄迅成
2008-01-01
A general microbial growth model is discussed in this paper. The conditions for the existence of periodical solutions, and the estimation of the perimeter and relative position of the limit cycles are obtained. These results are useful in the further study of the oscillation of the microbial growth systems.%讨论了一个一般的微生物生长模型的极限环问题.证明了周期解的存在条件,并估计了有关极限环的周长和相对位置.本文的结果对深入研究微生物生长系统的震荡现象是非常有用的.
Hoppe, Ulf-Peter
2010-05-15
This report is a tutorial and overview over some of the complex dynamic phenomena in the polar and equatorial stratosphere, and the unexpected correlation that exists between these and the solar cycle. Sudden stratospheric warmings (stratwarms) occur in the polar stratosphere in winter, but not equally distributed between the two hemispheres. As a result, the ozone hole in the springtime polar stratosphere is much more severe in the Southern Hemisphere than in the Northern Hemisphere. The Quasi-Biennial Oscillation (QBO) is a dynamic phenomenon of the equatorial stratosphere. Through processes not fully understood, the phase of the QBO (easterly or westerly) influences the onset of stratwarms. In addition, a correlation between the stratospheric winter temperature over the poles and the solar cycle has been found, but only if the datapoints are ordered by the phase of the QBO. - The best explanations and figures from four recent textbooks are selected, and abstracts of most relevant publications from the six last years are collected, with the most relevant portions for these subjects highlighted. - In addition to being basic science, the understanding of these phenomena is important in the context of the ozone hole, the greenhouse effect, as well as anthropogenic and natural climate change. (author)
Restoration of oscillation in network of oscillators in presence of direct and indirect interactions
Majhi, Soumen; Bera, Bidesh K.; Bhowmick, Sourav K.; Ghosh, Dibakar
2016-10-01
The suppression of oscillations in coupled systems may lead to several unwanted situations, which requires a suitable treatment to overcome the suppression. In this paper, we show that the environmental coupling in the presence of direct interaction, which can suppress oscillation even in a network of identical oscillators, can be modified by introducing a feedback factor in the coupling scheme in order to restore the oscillation. We inspect how the introduction of the feedback factor helps to resurrect oscillation from various kinds of death states. We numerically verify the resurrection of oscillations for two paradigmatic limit cycle systems, namely Landau-Stuart and Van der Pol oscillators and also in generic chaotic Lorenz oscillator. We also study the effect of parameter mismatch in the process of restoring oscillation for coupled oscillators.
Effects of Black Hole Spin on the Limit-Cycle Behaviour of Accretion Disks
Li Xue; Ju-Fu Lu
2011-03-01
We present a spatially 1.5-dimensional, time-dependent numerical study of accretion disks around Kerr black holes. Our study focuses on the limit-cycle behavior of thermally unstable accretion disks. We find that maximal luminosity may be a more appropriate probe of black hole spin than the cycle duration and influence radius.
Limit Cycles and Bifurcation in Piecewise-Analytic Systems: 1. General Theory
Banks, S.P.; Khathur, Saadi. A.
1989-01-01
The existence of limit cycles and periodic doubling bifurcations in piecewise-linear and piecewise-analytic systems is studied. Some theoretical sufficient conditions are obtained directly in terms of the right hand sided of the system.
THE LIMIT CYCLES OF A KIND OF EXPLOITED PREDATOR-PREY SYSTEM
无
2006-01-01
In this paper, a kind of exploited predator-prey system is studied. By using the qualitative theory, we obtain some sufficient conditions for the existence and nonexistence of limit cycles of the system.
Autonomous Metabolic Oscillations Robustly Gate the Early and Late Cell Cycle
Papagiannakis, Alexandros; Niebel, Bastian; Wit, Ernst C.; Heinemann, Matthias
2017-01-01
Eukaryotic cell division is known to be controlled by the cyclin/cyclin dependent kinase (CDK) machinery. However, eukaryotes have evolved prior to CDKs, and cells can divide in the absence of major cyclin/CDK components. We hypothesized that an autonomous metabolic oscillator provides dynamic trigg
Autonomous Metabolic Oscillations Robustly Gate the Early and Late Cell Cycle
Papagiannakis, Alexandros; Niebel, Bastian; Wit, Ernst C; Heinemann, Matthias
2017-01-01
Eukaryotic cell division is known to be controlled by the cyclin/cyclin dependent kinase (CDK) machinery. However, eukaryotes have evolved prior to CDKs, and cells can divide in the absence of major cyclin/CDK components. We hypothesized that an autonomous metabolic oscillator provides dynamic
ANALYSIS OF LIMIT CYCLES TO A PERTURBED INTEGRABLE NON-HAMILTONIAN SYSTEM
无
2012-01-01
Bifurcation of limit cycles to a perturbed integrable non-Hamiltonian system is investigated using both qualitative analysis and numerical exploration.The investigation is based on detection functions which are particularly effective for the perturbed integrable non-Hamiltonian system.The study reveals that the system has 3 limit cycles.By the method of numerical simulation,the distributed orderliness of the 3 limitcycles is observed,and their nicety places are determined.The study also indicates that each ...
Limit cycles bifurcated from a center in a three dimensional system
Bo Sang
2016-04-01
Full Text Available Based on the pseudo-division algorithm, we introduce a method for computing focal values of a class of 3-dimensional autonomous systems. Using the $\\epsilon^1$-order focal values computation, we determine the number of limit cycles bifurcating from each component of the center variety (obtained by Mahdi et al. It is shown that at most four limit cycles can be bifurcated from the center with identical quadratic perturbations and that the bound is sharp.
The Same Distribution of Limit Cycles in a Hamiltonian System with Nine Seven-order Perturbed Terms
Tao Jiang; Zhi-yan Yang
2008-01-01
Using qualitative analysis and numerical simulation, we investigate the number and distribution of limit cycles for a cubic Hamiltonian system with nine different seven-order perturbed terms. It is showed that these perturbed systems have the same distribution of limit cycles. Furthermore, these systems have 13,11 and 9 limit cycles for some parameters, respectively. The accurate positions of the 13, 11 and 9 limit cycles are obtained by numerical exploration, respectively.Our results imply that these perturbed systems are equivalent in the sense of distribution of limit cycles.This is useful for studying limit cycles of perturbed systems.
Numerical investigation into the existence of limit cycles in two-dimensional predator�prey systems
Quay van der Hoff
2013-05-01
Full Text Available There has been a surge of interest in developing and analysing models of interacting species in ecosystems, with specific interest in investigating the existence of limit cycles in systems describing the dynamics of these species. The original Lotka–Volterra model does not possess any limit cycles. In recent years this model has been modified to take disturbances into consideration and allow populations to return to their original numbers. By introducing logistic growth and a Holling Type II functional response to the traditional Lotka–Volterra-type models, it has been proven analytically that a unique, stable limit cycle exists. These proofs make use of Dulac functions, Liénard equations and invariant regions, relying on theory developed by Poincaré, Poincaré-Bendixson, Dulac and Liénard, and are generally perceived as difficult. Computer algebra systems are ideally suited to apply numerical methods to confirm or refute the analytical findings with respect to the existence of limit cycles in non-linear systems. In this paper a class of predator–prey models of a Gause type is used as the vehicle to illustrate the use of a simple, yet novel numerical algorithm. This algorithm confirms graphically the existence of at least one limit cycle that has analytically been proven to exist. Furthermore, adapted versions of the proposed algorithm may be applied to dynamic systems where it is difficult, if not impossible, to prove analytically the existence of limit cycles.
Relationship between phases of quasi-decadal oscillations of total ozone and the 11-year solar cycle
Visheratin, K. N.
2012-02-01
Temporal variability of the relationship between the phases of quasi-decadal oscillations (QDOs) of total ozone (TO), measured at the Arosa station, and the Ri international sunspot number have been analyzed for the period of 1932-2009. Before the 1970s, the maximum phase of ozone QDOs lagged behind solar activity variations by about 2.5-2.8 years and later outstripped by about 1.5 years. We assumed that the TO QDOs in midlatitudes of the Northern Hemisphere were close to being in resonance with solar activity oscillations in the period from the mid-1960s to the mid-1970s and assessed the characteristic delay period of TO QDOs. The global distribution of phases and amplitudes of TO QDOs have been studied for the period from 1979 to 2008 based on satellite data. The maximum phase of TO QDOs first onsets in northern middle and high latitudes and coincides with the end of the growth phase of the 11-year solar cycle. In the tropics, the maximum oscillation phase lags behind by 0.5-1 year. The maximum phase lag near 40-50° S is about two years. The latitudinal variations of the phase of TO QDOs have been approximated.
The Large-Volume Limit of a Quantum Tetrahedron is a Quantum Harmonic Oscillator
Schliemann, John
2013-01-01
It is shown that the volume operator of a quantum tetrahedron is, in the sector of large eigenvalues, accurately described by a quantum harmonic oscillator. This result relies on the fact that (i) the volume operator couples only neighboring states of its standard basis, and (ii) its matrix elements show a unique maximum as a function of internal angular momentum quantum numbers. These quantum numbers, considered as a continuous variable, are the coordinate of the oscillator describing its quadratic potential, while the corresponding derivative defines a momentum operator. We also analyze the scaling properties of the oscillator parameters as a function of the size of the tetrahedron, and the role of different angular momentum coupling schemes.
CHEN Wen; ZHOU Qun
2012-01-01
The modulation of the relationship between the Arctic Oscillation (AO) and the East Asian winter climate by the 11-year solar cycle was investigated.During winters with high solar activity (HS),robust warming appeared in northern Asia in a positive AO phase. This result corresponded to an enhanced anticyclonic flow at 850 hPa over northeastern Asia and a weakened East Asian trough (EAT) at 500 hPa.However,during winters with low solar activity (LS),both the surface warming and the intensities of the anticyclonic flow and the EAT were much less in the presence of a positive AO phase.The possible atmospheric processes for this 11-year solar-cycle modulation may be attributed to the indirect influence that solar activity induces in the structural changes of AO.During HS winters,the sea level pressure oscillation associated with the AO became stronger,with the significant influence of AO extending to East Asia.In the meantime,the AO-related zonal-mean zonal winds tended to extend more into the stratosphere during HS winters,which implies a stronger coupling to the stratosphere.These trends may have led to an enhanced AO phase difference; thus the associated East Asian climate anomalies became larger and more significant.The situation tended to reverse during LS winters.Further analyses revealed that the relationship between the winter AO and surface-climate anomalies in the following spring is also modulated by the 11-year solar cycle,with significant signals appearing only during HS phases.Solar-cycle variation should be taken into consideration when the AO is used to predict winter and spring climate anomalies over East Asia.
Limits and Optimization of Power Input or Output of Actual Thermal Cycles
Emin Açıkkalp
2013-08-01
Full Text Available In classical thermodynamic, maximum power obtained from system (or minimum power supplied to system defined as availability (exergy, but availability term is only used for reversible systems. In reality, there is no reversible system, all systems are irreversible, because reversible cycles doesn’t include constrains like time or size and they operates in quasi-equilibrium state. Purpose of this study is to define limits of the all basic thermodynamic cycles and to provide finite-time exergy models for irreversible cycles and to obtain the maximum (or minimum available power for irreversible (finite-time exergy cycles. In this study, available power optimization and performance limits were defined all basic irreversible thermodynamic cycles, by using first and second law of thermodynamic. Finally, these results were evaluated in terms of cycles’ first and second law efficiency, COP, power output (or input and exergy destruction.
Abou-Jaoudé, Wassim; Chaves, Madalena; Gouzé, Jean-Luc
2014-12-01
A class of piecewise affine differential (PWA) models, initially proposed by Glass and Kauffman (in J Theor Biol 39:103-129, 1973), has been widely used for the modelling and the analysis of biological switch-like systems, such as genetic or neural networks. Its mathematical tractability facilitates the qualitative analysis of dynamical behaviors, in particular periodic phenomena which are of prime importance in biology. Notably, a discrete qualitative description of the dynamics, called the transition graph, can be directly associated to this class of PWA systems. Here we present a study of periodic behaviours (i.e. limit cycles) in a class of two-dimensional piecewise affine biological models. Using concavity and continuity properties of Poincaré maps, we derive structural principles linking the topology of the transition graph to the existence, number and stability of limit cycles. These results notably extend previous works on the investigation of structural principles to the case of unequal and regulated decay rates for the 2-dimensional case. Some numerical examples corresponding to minimal models of biological oscillators are treated to illustrate the use of these structural principles.
Le Yaouanc, A; Morénas, V; Oliver, L; Pène, O; Raynal, J C
2000-01-01
The detailed way in which duality between sum of exclusive states and the free quark model description operates in semileptonic total decay widths, is analysed. It is made very explicit by the use of the non relativistic harmonic oscillator quark model in the SV limit, and a simple interaction current with the lepton pair. In particular, the Voloshin sum rule is found to eliminate the mismatches of order $\\delta m/m_b^2$.
Modeling the effects of cell cycle M-phase transcriptional inhibition on circadian oscillation.
Bin Kang
2008-03-01
Full Text Available Circadian clocks are endogenous time-keeping systems that temporally organize biological processes. Gating of cell cycle events by a circadian clock is a universal observation that is currently considered a mechanism serving to protect DNA from diurnal exposure to ultraviolet radiation or other mutagens. In this study, we put forward another possibility: that such gating helps to insulate the circadian clock from perturbations induced by transcriptional inhibition during the M phase of the cell cycle. We introduced a periodic pulse of transcriptional inhibition into a previously published mammalian circadian model and simulated the behavior of the modified model under both constant darkness and light-dark cycle conditions. The simulation results under constant darkness indicated that periodic transcriptional inhibition could entrain/lock the circadian clock just as a light-dark cycle does. At equilibrium states, a transcriptional inhibition pulse of certain periods was always locked close to certain circadian phases where inhibition on Per and Bmal1 mRNA synthesis was most balanced. In a light-dark cycle condition, inhibitions imposed at different parts of a circadian period induced different degrees of perturbation to the circadian clock. When imposed at the middle- or late-night phase, the transcriptional inhibition cycle induced the least perturbations to the circadian clock. The late-night time window of least perturbation overlapped with the experimentally observed time window, where mitosis is most frequent. This supports our hypothesis that the circadian clock gates the cell cycle M phase to certain circadian phases to minimize perturbations induced by the latter. This study reveals the hidden effects of the cell division cycle on the circadian clock and, together with the current picture of genome stability maintenance by circadian gating of cell cycle, provides a more comprehensive understanding of the phenomenon of circading gating of
Modeling the effects of cell cycle M-phase transcriptional inhibition on circadian oscillation.
Kang, Bin; Li, Yuan-Yuan; Chang, Xiao; Liu, Lei; Li, Yi-Xue
2008-03-28
Circadian clocks are endogenous time-keeping systems that temporally organize biological processes. Gating of cell cycle events by a circadian clock is a universal observation that is currently considered a mechanism serving to protect DNA from diurnal exposure to ultraviolet radiation or other mutagens. In this study, we put forward another possibility: that such gating helps to insulate the circadian clock from perturbations induced by transcriptional inhibition during the M phase of the cell cycle. We introduced a periodic pulse of transcriptional inhibition into a previously published mammalian circadian model and simulated the behavior of the modified model under both constant darkness and light-dark cycle conditions. The simulation results under constant darkness indicated that periodic transcriptional inhibition could entrain/lock the circadian clock just as a light-dark cycle does. At equilibrium states, a transcriptional inhibition pulse of certain periods was always locked close to certain circadian phases where inhibition on Per and Bmal1 mRNA synthesis was most balanced. In a light-dark cycle condition, inhibitions imposed at different parts of a circadian period induced different degrees of perturbation to the circadian clock. When imposed at the middle- or late-night phase, the transcriptional inhibition cycle induced the least perturbations to the circadian clock. The late-night time window of least perturbation overlapped with the experimentally observed time window, where mitosis is most frequent. This supports our hypothesis that the circadian clock gates the cell cycle M phase to certain circadian phases to minimize perturbations induced by the latter. This study reveals the hidden effects of the cell division cycle on the circadian clock and, together with the current picture of genome stability maintenance by circadian gating of cell cycle, provides a more comprehensive understanding of the phenomenon of circading gating of cell cycle.
Dilixiati, Adila; Koyanagi, Satoru; Kusunose, Naoki; Matsunaga, Naoya; Ohdo, Shigehiro
2017-08-01
Maintenance of circadian rhythms is essential to many aspects of human health, including metabolism and neurological and psychiatric well-being. Chronic disruption of circadian clock function is implicated in increasing the risk of metabolic syndrome, cardiovascular events and development of cancers. However, there are little approaches to reinforce the function of circadian clock for prevention of these diseases. Essence of Chicken (EC) is a nutritional supplement that is traditionally made by extracting water soluble substances derived from cooking the whole chicken. In this study, we found that dietary supplementation with EC enhanced circadian oscillation of glucocorticoid secretion in mice, and this was accompanied by enhancement of circadian oscillation in the adrenal expression of steroidogenic acute regulatory (StAR) protein that mediates the rate-limiting step of glucocorticoid synthesis. Furthermore, EC facilitated re-entrainment of behavioral rhythm in mice when phase of the light-dark cycle was suddenly advanced. These results suggest that intake of EC has enhancement effect on circadian clock function in mice, which may contribute to sustain health and also offer new preventive strategies against circadian-related diseases. Copyright © 2017 The Authors. Production and hosting by Elsevier B.V. All rights reserved.
Adila Dilixiati
2017-08-01
Full Text Available Maintenance of circadian rhythms is essential to many aspects of human health, including metabolism and neurological and psychiatric well-being. Chronic disruption of circadian clock function is implicated in increasing the risk of metabolic syndrome, cardiovascular events and development of cancers. However, there are little approaches to reinforce the function of circadian clock for prevention of these diseases. Essence of Chicken (EC is a nutritional supplement that is traditionally made by extracting water soluble substances derived from cooking the whole chicken. In this study, we found that dietary supplementation with EC enhanced circadian oscillation of glucocorticoid secretion in mice, and this was accompanied by enhancement of circadian oscillation in the adrenal expression of steroidogenic acute regulatory (StAR protein that mediates the rate-limiting step of glucocorticoid synthesis. Furthermore, EC facilitated re-entrainment of behavioral rhythm in mice when phase of the light–dark cycle was suddenly advanced. These results suggest that intake of EC has enhancement effect on circadian clock function in mice, which may contribute to sustain health and also offer new preventive strategies against circadian-related diseases.
One-dimensional modelling of limit-cycle oscillation and H-mode power scaling
Wu, Xingquan; Xu, Guosheng; Wan, Baonian
2015-01-01
To understand the connection between the dynamics of microscopic turbulence and the macroscale power scaling in the L-I-H transition in magnetically confined plasmas, a new time-dependent, one-dimensional (in radius) model has been developed. The model investigates the radial force balance equati...
The Effect of Drive Signal Limiting on High Cycle Fatigue Life Analysis
Kihm, Frederic; Rizzi, Stephen A.
2014-01-01
It is common practice to assume a Gaussian distribution of both the input acceleration and the response when modeling random vibration tests. In the laboratory, however, shaker controllers often limit the drive signal to prevent high amplitude peaks. The high amplitudes may either be truncated at a given level (socalled brick wall limiting or abrupt clipping), or compressed (soft limiting), resulting in drive signals which are no longer Gaussian. The paper first introduces several methods for limiting a drive signal, including brick wall limiting and compression. The limited signal is then passed through a linear time-invariant system representing a device under test. High cycle fatigue life predictions are subsequently made using spectral fatigue and rainflow cycle counting schemes. The life predictions are compared with those obtained from unclipped input signals. Some guidelines are provided to help the test engineer decide how clipping should be applied under different test scenarios.
Limit cycle analysis of active disturbance rejection control system with two nonlinearities.
Wu, Dan; Chen, Ken
2014-07-01
Introduction of nonlinearities to active disturbance rejection control algorithm might have high control efficiency in some situations, but makes the systems with complex nonlinearity. Limit cycle is a typical phenomenon that can be observed in the nonlinear systems, usually causing failure or danger of the systems. This paper approaches the problem of the existence of limit cycles of a second-order fast tool servo system using active disturbance rejection control algorithm with two fal nonlinearities. A frequency domain approach is presented by using describing function technique and transfer function representation to characterize the nonlinear system. The derivations of the describing functions for fal nonlinearities and treatment of two nonlinearities connected in series are given to facilitate the limit cycles analysis. The effects of the parameters of both the nonlinearity and the controller on the limit cycles are presented, indicating that the limit cycles caused by the nonlinearities can be easily suppressed if the parameters are chosen carefully. Simulations in the time domain are performed to assess the prediction accuracy based on the describing function.
Cavity-mediated coupling of mechanical oscillators limited by quantum backaction
Spethmann, Nicolas; Schreppler, Sydney; Buchmann, Lukas; Stamper-Kurn, Dan M
2015-01-01
A complex quantum system can be constructed by coupling simple quantum elements to one another. For example, trapped-ion or superconducting quantum bits may be coupled by Coulomb interactions, mediated by the exchange of virtual photons. Alternatively quantum objects can be coupled by the exchange of real photons, particularly when driven within resonators that amplify interactions with a single electro-magnetic mode. However, in such an open system, the capacity of a coupling channel to convey quantum information or generate entanglement may be compromised. Here, we realize phase-coherent interactions between two spatially separated, near-ground-state mechanical oscillators within a driven optical cavity. We observe also the noise imparted by the optical coupling, which results in correlated mechanical fluctuations of the two oscillators. Achieving the quantum backaction dominated regime opens the door to numerous applications of cavity optomechanics with a complex mechanical system. Our results thereby illu...
On oscillation of a food-limited population model with time delay
Leonid Berezansky
2003-01-01
Full Text Available For a scalar nonlinear delay differential equation Ṅ(t = r(tN(t(K − N(h(t/(K + s(tN(g(t,r(t ≥ 0, h(t ≤ t, g(t ≤ t and some generalizations of this equation, we establish explicit oscillation and nonoscillation conditions. Coefficient r(t and delays are not assumed to be continuous.
The estimate of the amplitude of limit cycles of symmetric Liénard systems
Cao, Yuli; Liu, Changjian
2017-02-01
Symmetric Liénard system x ˙ = y - F (x) , y ˙ = - g (x) (i.e. F (x) and g (x) are odd functions) is studied. It is well known that under some hypotheses, this system has a unique limit cycle. We develop a method to give both the upper bound and lower bound of the amplitude, which is the maximal value of the x-coordinate, of the unique limit cycle. As an application, we consider van der Pol equation x ˙ = y - μ (x3 / 3 - x) , y ˙ = - x, where μ > 0. Denote by A (μ) the amplitude of its unique limit cycle, then for any μ, we show that A (μ) 2. Both the upper bound and the lower bound improve the existing ones.
On the limit cycle for the 1/r^2 potential in momentum space
Hammer, H W; Swingle, Brian G.
2006-01-01
The renormalization of the attractive 1/r^2 potential has recently been studied using a variety of regulators. In particular, it was shown that renormalization with a square well in position space allows multiple solutions for the depth of the square well, including, but not requiring a renormalization group limit cycle. Here, we consider the renormalization of the 1/r^2 potential in momentum space. We regulate the problem with a momentum cutoff and absorb the cutoff dependence using a momentum-independent counterterm potential. The strength of this counterterm is uniquely determined and runs on a limit cycle. We also calculate the bound state spectrum and scattering observables, emphasizing the manifestation of the limit cycle in these observables.
Onset of a Limit Cycle and Universal Three-Body Parameter in Efimov Physics
Horinouchi, Yusuke; Ueda, Masahito
2015-01-01
The Efimov effect is the only experimentally realized universal phenomenon that exhibits the renormalization-group limit cycle with the three-body parameter parametrizing a family of universality classes. Recent experiments in ultracold atoms have unexpectedly revealed that the three-body parameter itself is universal when measured in units of an effective range. By performing an exact functional renormalization-group analysis with various finite-range interaction potentials, we demonstrate that the onset of the renormalization-group flow into the limit cycle is universal, regardless of short-range details, which connects the missing link between the two universalities of the Efimov physics. A close connection between the topological property of the limit cycle and few-body physics is also suggested.
Limit cycles in a generalized Gause-type predator-prey system
无
2001-01-01
The qualitative behavior of solutions for a generalized Game-type predator-prey system was studied.A large number of biologcal and bioeconomic models are special cases of this system. The system was investigated in the region D = { ( x, y) | x > 0, y > 0} because of the biological meaning of the system. The authors derived some sufficient conditions for the boundedness of the solutions and the existence of limit cycles of the system, which ensure that the system has at least one limit cycle. The theory of limit sets of autonomous plane systems and the theorem of cycle field of Poincare-Bendixson are efficiently employed in the research. The main results and their consequences presented not only generalize some known results, but also improve some corresponding results of other authors.
Bifurcations of limit cycles in open and closed loop reverse flow reactors
Russo, Lucia; Crescitelli, Silvestro; Brasiello, Antonio
2013-10-01
The present work analyses the bifurcations of limit cycles in open and loop reverse flow reactors. The open loop system consists of a reactor where the flow direction is periodically forced whereas in the closed loop system, the flow inversion is dictated by a control law which activates when the temperature at the edge of catalytic bed falls below the set-point value. We performed the bifurcation analysis of the open loop system as the switch time is varied and we constructed the solution diagram through the application of continuation technique. Many Naimark-Sacker bifurcations leading to quasi-periodic regimes have been found on the limit cycles branches. Finally, we compared these limit cycles with those of the closed loop system where the flow inversion is dictated by a control system which acts if the temperature measured at the edge of reactor falls below a set-point value.
Long-term oscillations in the sleep/wake cycle of infants
Diambra, L.; Malta, C. P.; Capurro, A.
2009-11-01
The development of circadian sleep-wakefulness rhythm was investigated by a longitudinal study of six normal infants. We propose an entropy based measure for the sleep/wake cycle fragmentation. Our results confirm that the sleep/wake cycle fragmentation and the sleep/wake ratio decrease, while the circadian power increases during the maturation process of infants. In addition to these expected linear trends in the variables devised to quantify sleep consolidation, circadian power and sleep/wake ratio, we found that they present infradian rhythms in the monthly range.
Oscillator models of the solar cycle: Towards the development of inversion methods
Lopes, Ilídio; Nagy, Melinda; Petrovay, Kristof
2014-01-01
This article reviews some of the leading results obtained in solar dynamo physics by using temporal oscillator models as a tool to interpret observational data and dynamo model predictions. We discuss how solar observational data such as the sunspot number is used to infer the leading quantities responsible for the solar variability during the last few centuries. Moreover, we discuss the advantages and difficulties of using inversion methods (or backward methods) over forward methods to interpret the solar dynamo data. We argue that this approach could help us to have a better insight about the leading physical processes responsible for solar dynamo, in a similar manner as helioseismology has helped to achieve a better insight on the thermodynamic structure and flow dynamics in the Sun's interior.
Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations
Schubert, O; Langer, F; Urbanek, B; Lange, C; Huttner, U; Golde, D; Meier, T; Kira, M; Koch, S W; Huber, R
2016-01-01
Ultrafast charge transport in strongly biased semiconductors is at the heart of highspeed electronics, electro-optics, and fundamental solid-state physics. Intense light pulses in the terahertz (THz) spectral range have opened fascinating vistas: Since THz photon energies are far below typical electronic interband resonances, a stable electromagnetic waveform may serve as a precisely adjustable bias. Novel quantum phenomena have been anticipated for THz amplitudes reaching atomic field strengths. We exploit controlled THz waveforms with peak fields of 72 MV/cm to drive coherent interband polarization combined with dynamical Bloch oscillations in semiconducting gallium selenide. These dynamics entail the emission of phase-stable high-harmonic transients, covering the entire THz-to-visible spectral domain between 0.1 and 675 THz. Quantum interference of different ionization paths of accelerated charge carriers is controlled via the waveform of the driving field and explained by a quantum theory of inter- and in...
A Polycycle and Limit Cycles in a Non-Differentiable Predator-Prey Model
E Sáez; I Szántó
2007-05-01
For a non-differentiable predator-prey model, we establish conditions for the existence of a heteroclinic orbit which is part of one contractive polycycle and for some values of the parameters, we prove that the heteroclinic orbit is broken and generates a stable limit cycle. In addition, in the parameter space, we prove that there exists a curve such that the unique singularity in the realistic quadrant of the predator-prey model is a weak focus of order two and by Hopf bifurcations we can have at most two small amplitude limit cycles.
Feng LI; Yin Lai JIN
2011-01-01
In this paper,center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated.With the help of computer algebra system MATHEMATICA,the first 8 quasi Lyapunov constants are deduced.As a result,the necessary and sufficient conditions to have a center are obtained.The fact that there exist 8 small amplitude limit cycles created from the three-order nilpotent critical point is also proved.Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems.
Stability of limit cycles in a pluripotent stem cell dynamics model
Adimy, Mostafa [Laboratoire de Mathematiques Appliquees UMR 5142, Universite de Pau et des Pays de l' Adour, Avenue de l' universite, 64000 Pau (France)] e-mail: mostafa.adimy@univ-pau.fr; Crauste, Fabien [Laboratoire de Mathematiques Appliquees UMR 5142, Universite de Pau et des Pays de l' Adour, Avenue de l' universite, 64000 Pau (France)] e-mail: fabien.crauste@univ-pau.fr; Halanay, Andrei [Department of Mathematics 1, University Politehnica of Bucharest, Splaiul Independentei 313, RO-060042, Bucharest (Romania)] e-mail: halanay@vectron.mathem.pub.ro; Neamtu, Mihaela [Faculty of Economics, I.N. Pestalozzi 16, West University of Timisoara, RO-300115, Timisoara (Romania)] e-mail: mihaela.neamtu@fse.uvt.ro; Opris, Dumitru [Department of Applied Mathematics, Faculty of Mathematics, Bd. V. Parvan 4, West University of Timisoara, RO-300223, Timisoara (Romania)] e-mail: opris@math.uvt.ro
2006-02-01
This paper is devoted to the study of the stability of limit cycles of a nonlinear delay differential equation with a distributed delay. The equation arises from a model of population dynamics describing the evolution of a pluripotent stem cells population. We study the local asymptotic stability of the unique nontrivial equilibrium of the delay equation and we show that its stability can be lost through a Hopf bifurcation. We then investigate the stability of the limit cycles yielded by the bifurcation using the normal form theory and the center manifold theorem. We illustrate our results with some numerics.
Phillips, Gillian E; Pike, Sarah E; Jaffé, Adam; Bush, Andrew
2004-01-01
High-frequency chest compressions (HFCC) have been suggested as an alternative to conventional chest physiotherapy to aid sputum clearance in patients with cystic fibrosis (CF). We aimed to compare the active cycle of breathing techniques (ACBT) with the Hayek Oscillator Cuirass, performing HFCC on secretion clearance in children with CF during an exacerbation. Ten children (7 males; median age, 14 years; range, 9-16) received either two supervised sessions using HFCC or two self-treatment ACBT sessions in random order on successive days. Baseline pulmonary function was similar prior to treatments. Sputum weight increased significantly with ACBT compared with HFCC during treatment (5.2 g vs. 1.1 g, P HFCC. Compared with ACBT, HFCC by Hayek Cuirass is not an effective airway clearance treatment modality for children with CF during an infective exacerbation.
Kumar, Parvendra
2012-01-01
We report a study on the ultrafast coherent population oscillations (UCPO) in sodium atoms induced by the frequency modulated few-cycle optical pulse trains. The phenomenon of UCPO is investigated by numerically solving the appropriate density matrix equations beyond the rotating wave approximation. We demonstrate that the quantum state of the atoms and the frequency of UCPO may be controlled by controlling the number of pulses in the pulse trains and the pulse repetition time respectively. Moreover, the robustness of population transfer against the variation of laser pulse parameters is also investigated. The proposed scheme may be useful for the creation of atomic beam in selected quantum state for desired time duration and may have potential applications in ultrafast optical switching.
Global study of Rayleigh-Duffing oscillators
Chen, Hebai; Zou, Lan
2016-04-01
In this paper we investigate the global dynamics of Rayleigh-Duffing oscillators with global parameters, including equilibria at both finity and infinity, existences and coexistence of limit cycles and homoclinic loops. In fact, this oscillator will occur Hopf bifurcations, homoclinic bifurcations and double limit cycle bifurcations. Moreover, we find that the homoclinic bifurcation of this oscillator is special which is a gluing bifurcation. The global bifurcation diagram and all phase portrait are given, and numerical simulations are shown to verify our analysis finally.
Feillet, Céline; Horst, Gijsbertus Theodorus Johannes van der; Lévi, Francis A.; Rand, D. A.; Delaunay, Franck
2015-01-01
Uncontrolled cell proliferation is one of the key features leading to cancer. Seminal works in chronobiology have revealed that disruption of the circadian timing system in mice, either by surgical, genetic, or environmental manipulation, increased tumor development. In humans, shift work is a risk factor for cancer. Based on these observations, the link between the circadian clock and cell cycle has become intuitive. But despite identification of molecular connections between the two process...
Entrainment range of nonidentical circadian oscillators by a light-dark cycle
Gu, Changgui; Xu, Jinshan; Liu, Zonghua; Rohling, Jos H. T.
2013-08-01
The suprachiasmatic nucleus (SCN) is a principal circadian clock in mammals, which controls physiological and behavioral daily rhythms. The SCN has two main features: Maintaining a rhythmic cycle of approximately 24 h in the absence of a light-dark cycle (free-running period) and the ability to entrain to external light-dark cycles. Both free-running period and range of entrainment vary from one species to another. To understand this phenomenon, we investigated the diversity of a free-running period by the distribution of coupling strengths in our previous work [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.80.030904 80, 030904(R) (2009)]. In this paper we numerically found that the dispersion of intrinsic periods among SCN neurons influence the entrainment range of the SCN, but has little influence on the free-running periods under constant darkness. This indicates that the dispersion of coupling strengths determines the diversity in free-running periods, while the dispersion of intrinsic periods determines the diversity in the entrainment range. A theoretical analysis based on two coupled neurons is presented to explain the results of numerical simulations.
UNIQUENESS OF LIMIT CYCLE FOR A CLASS OF QUARTIC SYSTEM ACCOMPANYING WITH QUADRATIC SYSTEM
无
2008-01-01
In this paper,we consider a class of quartic system,which is more general and realistic than the quartic accompanying system. Consequently,we obtain sufficient conditions concerning the uniqueness of limit cycle as well as some other in-depth conclusions.
HOPF BIFURCATION AND UNIQUENESS OF LIMIT CYCLE FOR A CLASS OF QUARTIC SYSTEM
无
2007-01-01
This paper studies a class of quartic system which is more general and realistic than the quartic accompanying system.x' = -y + ex + lx2 + mxy + ny2, y' = x(1 - Ay)(1 + Cy2), (*)where C ＞ 0. Sufficient conditions are obtained for the uniqueness of limit cycle of system (*)and some more in-depth conclusion such as Hopf bifurcation.
On the Stable Limit Cycle of a Weight-Driven Pendulum Clock
Llibre, J; Teixeira, M. A.
2010-01-01
In a recent paper (Denny 2002 Eur. J. Phys. 23 449-58), entitled "The pendulum clock: a venerable dynamical system", Denny showed that in a first approximation the steady-state motion of a weight-driven pendulum clock is shown to be a stable limit cycle. He placed the problem in a historical context and obtained an approximate solution using the…
THE UNIQUENESS OF LIMIT CYCLE AND CRITICAL POINT FOR A CLASS OF CUBIC SYSTEM
无
2008-01-01
In this paper,we consider an accompany system concerning some class of cubic system. We then prove that the system has at most one limit cycle. Finally,we obtain the topological structure of both the critical points at infinity and the singular points lying on invariant lines.
BIFURCATIONS OF SUBHARMONIC SOLUTIONS IN PERIODIC PERTURBATION OF A HYPERBOLIC LIMIT CYCLE
韩茂安; 顾圣士
2002-01-01
Bifurcations of subharmonic solutions of order m of a planar periodic perturbed system near a hyperbolic limit cycle are discussed. By using a Poincare map and the method of rescaling a discriminating condition for the existence of subharmonic solutions of order m is obtained. An example is given in the end of the paper.
A limit-cycle self-organizing map architecture for stable arm control.
Huang, Di-Wei; Gentili, Rodolphe J; Katz, Garrett E; Reggia, James A
2017-01-01
Inspired by the oscillatory nature of cerebral cortex activity, we recently proposed and studied self-organizing maps (SOMs) based on limit cycle neural activity in an attempt to improve the information efficiency and robustness of conventional single-node, single-pattern representations. Here we explore for the first time the use of limit cycle SOMs to build a neural architecture that controls a robotic arm by solving inverse kinematics in reach-and-hold tasks. This multi-map architecture integrates open-loop and closed-loop controls that learn to self-organize oscillatory neural representations and to harness non-fixed-point neural activity even for fixed-point arm reaching tasks. We show through computer simulations that our architecture generalizes well, achieves accurate, fast, and smooth arm movements, and is robust in the face of arm perturbations, map damage, and variations of internal timing parameters controlling the flow of activity. A robotic implementation is evaluated successfully without further training, demonstrating for the first time that limit cycle maps can control a physical robot arm. We conclude that architectures based on limit cycle maps can be organized to function effectively as neural controllers. Copyright © 2016 Elsevier Ltd. All rights reserved.
Explosion of limit cycles and chaotic waves in a simple nonlinear chemical system
Brøns, Morten; Sturis, Jeppe
2001-01-01
A model of an autocatalytic chemical reaction was employed to study the explosion of limit cycles and chaotic waves in a nonlinear chemical system. The bifurcation point was determined using asymptotic analysis and perturbations. Scaling laws for amplitude and period were derived. A strong...
The Goodwin model revisited: Hopf bifurcation, limit-cycle, and periodic entrainment
Woller, Aurore; Gonze, Didier; Erneux, Thomas
2014-08-01
The three-variable Goodwin oscillator is a minimal model demonstrating the emergence of oscillations in simple biochemical feedback systems. As a prototypical oscillator, this model was extensively studied from a theoretical point of view and applied to various biological systems, including circadian clocks. Here, we reexamine this model, derive analytically the amplitude equation near the Hopf bifurcation and investigate the effect of a periodic modulation of the oscillator. In particular, we compare the entrainment performance when the free oscillator displays either self-sustained or damped oscillations. We discuss the results in the context of circadian oscillators.
Bridel-Bertomeu, Thibault; Gicquel, L. Y. M.; Staffelbach, G.
2017-06-01
Rotating cavity flows are essential components of industrial applications but their dynamics are still not fully understood when it comes to the relation between the fluid organization and monitored pressure fluctuations. From computer hard-drives to turbo-pumps of space launchers, designed devices often produce flow oscillations that can either destroy the component prematurely or produce too much noise. In such a context, large scale dynamics of high Reynolds number rotor/stator cavities need better understanding especially at the flow limit-cycle or associated statistically stationary state. In particular, the influence of curvature as well as cavity aspect ratio on the large scale organization and flow stability at a fixed rotating disc Reynolds number is fundamental. To probe such flows, wall-resolved large eddy simulation is applied to two different rotor/stator cylindrical cavities and one annular cavity. Validation of the predictions proves the method to be suited and to capture the disc boundary layer patterns reported in the literature. It is then shown that in complement to these disc boundary layer analyses, at the limit-cycle the rotating flows exhibit characteristic patterns at mid-height in the homogeneous core pointing the importance of large scale features. Indeed, dynamic modal decomposition reveals that the entire flow dynamics are driven by only a handful of atomic modes whose combination links the oscillatory patterns observed in the boundary layers as well as in the core of the cavity. These fluctuations form macro-structures, born in the unstable stator boundary layer and extending through the homogeneous inviscid core to the rotating disc boundary layer, causing its instability under some conditions. More importantly, the macro-structures significantly differ depending on the configuration pointing the need for deeper understanding of the influence of geometrical parameters as well as operating conditions.
Coupled oscillators on evolving networks
Singh, R. K.; Bagarti, Trilochan
2016-12-01
In this work we study coupled oscillators on evolving networks. We find that the steady state behavior of the system is governed by the relative values of the spread in natural frequencies and the global coupling strength. For coupling strong in comparison to the spread in frequencies, the system of oscillators synchronize and when coupling strength and spread in frequencies are large, a phenomenon similar to amplitude death is observed. The network evolution provides a mechanism to build inter-oscillator connections and once a dynamic equilibrium is achieved, oscillators evolve according to their local interactions. We also find that the steady state properties change by the presence of additional time scales. We demonstrate these results based on numerical calculations studying dynamical evolution of limit-cycle and van der Pol oscillators.
Roberts, K.; Paytan, A.; Field, C. B.; Lecher, A.; Kendall, C.; Silva, S. R.; Peek, S.
2016-12-01
Phosphorus (P) is often a limiting nutrient in terrestrial systems. It has recently been proposed to play an even greater role in ecosystems experiencing some of the many predicted effects of climate change, in particular release from nitrogen limitation. To investigate the potential for P limitation, and P cycling under various controlled conditions we participated in the ongoing Jasper Ridge Global Change Experiment (JRGCE). For 18 years the JRGCE has been manipulating four key parameters predicted to change in the future in a Californian grassland system. Elevated Nitrogen deposition, increased precipitation, increased pCO2, and increased temperature are applied and monitored in a split plot system at the Jasper Ridge Biological Preserve in the eastern foothills of the Santa Cruz Mountains, California. In this study we utilize the oxygen isotopes of phosphate to investigate P cycling in soils at JRGCE in conjunction with phosphate enzyme activity and other parameters to attempt to elucidate factors influencing P limitation and cycling. A fractional soil extraction process for phosphate enables separation of several operationally defined P pools, and provides auxiliary information regarding the relative concentrations of bio-available P, and relevant minerals in this grassland system under the various conditions.
D. Altadill
1994-06-01
Full Text Available Seasonal and solar cycle variations of the quasi-two- and five-day oscillation amplitudes off f0F2 are evaluated by moving periodogram analysis. The 23 year time series (1964-1986 of fOF2 hourly values of Kaliningrad (54.7°N, 20.62°E, covering the solar cycles 20 and 21, is used for the analysis. Long term variations of these amplitudes are modulated by the 11-year solar cycle and are simultaneously influenced by the geomagnetic activity. The annual variation of the quasi-two- and five-day oscillation amplitudes has very clear maxima near the equinoxes. The mechanism of the influence of the travelling planetary waves in the meteor wind region by vertical plasma drift to the F2-layer electron density maximum is discussed.
Flow mechanism of self-induced reversed limit-cycle wing rock for a chined forebody configuration
Shi, Wei; Deng, Xueying; Wang, Yankui; Li, Qian
2015-11-01
The wing rock phenomenon reduces the maneuverability and affects the flight safety of modern advanced fighters, such as the F-35, which have chined forebodies. Understanding the flow mechanism is critical to suppressing this phenomenon. In this study, experiments were conducted to reveal the motion and flow behavior over a chined forebody configuration. The tests were performed in a wind tunnel at an angle of attack of 50∘ with a Reynolds number of 1.87 × 105. Reversed limit-cycle oscillation was discovered in the free-to-roll tests. The unstable rolling moment around zero roll angle in the static case suggests that the model tends to be driven away from zero roll angle. Thus, the model cannot maintain its equilibrium at zero roll angle during free-to-roll motion. The unstable rolling moment is generated by the wing vortex structure above the upward wing, which is induced by the forebody asymmetric vortices. During wing rock, the wing vortex structure appears above the upward wing at a large roll angle after crossing zero roll angle owing to a time lag in the forebody vortex position, which is conducive to the motion. The forebody asymmetric vortices are thus the key to induce and maintain the motion.
Mehdizadeh, Sina; Arshi, Ahmed Reza; Davids, Keith
2015-06-01
Identification of control strategies during agility performance is significant in understanding movement behavior. This study aimed at providing a fundamental mathematical model for describing the motion of participants during an agility drill and to determine whether skill level constrained model components. Motion patterns of two groups of skilled and unskilled participants (n=8 in each) during performance of a forward/backward agility drill modeled as limit-cycles. Participant movements were recorded by motion capture of a reflective marker attached to the sacrum of each individual. Graphical and regression analyses of movement kinematics in Hooke's plane, phase plane and velocity profile were performed to determine components of the models. Results showed that the models of both skilled and unskilled groups had terms from Duffing stiffness as well as Van der Pol damping oscillators. Data also indicated that the proposed models captured on average 97% of the variance for both skilled and unskilled groups. Findings from this study revealed the movement patterning associated with skilled and unskilled performance in a typical forward/backward agility drill which might be helpful for trainers and physiotherapists in enhancing agility.
Characteristics of the Limit Cycle of a Reciprocating Quantum Heat Engine
Feldmann, T; Feldmann, Tova; Kosloff, Ronnie
2004-01-01
When a reciprocating heat engine is started it eventually settles to a stable mode of operation. The approach of a first principle quantum heat engine toward this stable limit cycle is studied. The engine is based on a working medium consisting of an ensemble of quantum systems composed of two coupled spins. A four stroke cycle of operation is studied, with two {\\em isochore} branches where heat is transferred from the hot/cold baths and two {\\em adiabats} where work is exchanged. The dynamics is generated by a completely positive map. It has been shown that the performance of this model resembles an engine with intrinsic friction. The quantum conditional entropy is employed to prove the monotonic approach to a limit cycle. Other convex measures, such as the quantum distance display the same monotonic approach. The equations of motion of the engine are solved for the different branches and are combined to a global propagator that relates the state of the engine in the beginning of the cycle to the state after...
Theoretical and Experimental Study of Hopf Bifurcation and Limit Cycles of Railway Vehicle Hunting
Zeng Jing; Zhang Weihua; Shen Zhiyun
1996-01-01
The nonlinear hunting stability of railway vehicles is studied theoretically and experimentally in this paper. The Hopf bifurcation point is determined through calculating the eigenvalues of the system linearization equations incorporating with the golden cut method. The bifurcated limit cycles are computed by use of the shooting method to solve the boundary value problem of the system differential equations. Experimental validation to the numerical results is carricd out by utilizing the full scale roller test rig.
THE CRITERION FOR THE STABILITY OF A MULTIPLE LIMIT CYCLE UNDER HIGHER DEGENERATIONS
无
2011-01-01
In this paper, we obtain the exact computation formulae to determine the stability of a multiple limit cycle with the third or fourth order degenerations. We employ the method of computing the expansion of the Poincar′e map around the closed orbit using "normal bundle" coordinates parameterized by time variable in a neighborhood of the closed orbit. An example is given to show the feasibility of our results.
Existence of limit cycles in the Solow model with delayed-logistic population growth.
Bianca, Carlo; Guerrini, Luca
2014-01-01
This paper is devoted to the existence and stability analysis of limit cycles in a delayed mathematical model for the economy growth. Specifically the Solow model is further improved by inserting the time delay into the logistic population growth rate. Moreover, by choosing the time delay as a bifurcation parameter, we prove that the system loses its stability and a Hopf bifurcation occurs when time delay passes through critical values. Finally, numerical simulations are carried out for supporting the analytical results.
Bifurcations of limit cycles in a Z6-equivariant planar vector field of degree 5
无
2002-01-01
A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H(2k + 1) ≥ (2k + 1)2 - 1 for the perturbed Hamiltonian systems.
On the limit cycle for the 1/r^2 potential in momentum space
Hammer, H. -W.; Swingle, Brian G.
2005-01-01
The renormalization of the attractive 1/r^2 potential has recently been studied using a variety of regulators. In particular, it was shown that renormalization with a square well in position space allows multiple solutions for the depth of the square well, including, but not requiring a renormalization group limit cycle. Here, we consider the renormalization of the 1/r^2 potential in momentum space. We regulate the problem with a momentum cutoff and absorb the cutoff dependence using a moment...
SU Tonghua; XUE Feng; SUN Hongchuan; ZHOU Guangqing
2015-01-01
On the basis of more than 200-year control run, the performance of the climate system model of Chinese Academy of Sciences (CAS-ESM-C) in simulating the El Niño-Southern Oscillation (ENSO) cycle is evalu-ated, including the onset, development and decay of the ENSO. It is shown that, the model can reasonably simulate the annual cycle and interannual variability of sea surface temperature (SST) in the tropical Pacif-ic, as well as the seasonal phase-locking of the ENSO. The model also captures two prerequisites for the El Niño onset, i.e., a westerly anomaly and a warm SST anomaly in the equatorial western Pacific. Owing to too strong forcing from an extratropical meridional wind, however, the westerly anomaly in this region is largely overestimated. Moreover, the simulated thermocline is much shallower with a weaker slope. As a result, the warm SST anomaly from the western Pacific propagates eastward more quickly, leading to a faster develop-ment of an El Niño. During the decay stage, owing to a stronger El Niño in the model, the secondary Gill-type response of the tropical atmosphere to the eastern Pacific warming is much stronger, thereby resulting in a persistent easterly anomaly in the western Pacific. Meanwhile, a cold anomaly in the warm pool appears as a result of a lifted thermocline via Ekman pumping. Finally, an El Niño decays into a La Niña through their interactions. In addition, the shorter period and larger amplitude of the ENSO in the model can be attribut-ed to a shallower thermocline in the equatorial Pacific, which speeds up the zonal redistribution of a heat content in the upper ocean.
The Renormalization Group Limit Cycle for the 1/r^2 Potential
Braaten, E; Braaten, Eric; Phillips, Demian
2004-01-01
Previous work has shown that if an attractive 1/r^2 potential is regularized at short distances by a spherical square-well potential, renormalization allows multiple solutions for the depth of the square well. The depth can be chosen to be a continuous function of the short-distance cutoff R, but it can also be a log-periodic function of R with finite discontinuities, corresponding to a renormalization group (RG) limit cycle. We consider the regularization with a delta-shell potential. In this case, the coupling constant is uniquely determined to be a log-periodic function of R with infinite discontinuities, and an RG limit cycle is unavoidable. In general, a regularization with an RG limit cycle is selected as the correct renormalization of the 1/r^2 potential by the conditions that the cutoff radius R can be made arbitrarily small and that physical observables are reproduced accurately at all energies much less than hbar^2/mR^2.
Koshelets, V. P.; Shitov, S. V.; Dmitriev, P. N.
2003-01-01
to 712 GHz, limited only by the gap frequency of Nb. This enabled us to phase lock the FFO in the frequency range 500-712 GHz where continuous frequency tuning is possible; resulting in an absolute FFO phase noise as low as -80 dBc at 707 GHz. Comprehensive measurements of the FFO radiation linewidth...
Capuano, P.; De Lauro, E.; De Martino, S.; Falanga, M.
2012-11-01
We investigate the physical processes that generate the ocean tides, whose understanding has important influence on the marine activities. We analyze historical sea-level oscillations, continuously recorded from six stations in the North Atlantic Ocean spanning a time period of eighty years from 1926. In this paper, an Independent-Component-Analysis-based approach is adopted to obtain a clear identification of the main tidal constituents in term of waveform in time domain from the simultaneously recorded signals. This technique separates at most six nonlinear tidal components which are weakly superimposed. The fundamental objective is to extract information on the degree of complexity of the involved dynamics and on the very long-term tidal constituents. This is particularly significant to understand the response of the ocean to the tidal forcing. We put the emphasis on the near-bidecadal time scale and its influence on the short-periods tides. In details the Moon 18.6 y nodal cycle modulation acts in the ocean in quite an analogous manner to the fortnightly modulation in many shallow seas. Our results give new insights into the evidence for an 18.6 y effect in the climate/ocean variation whose physical mechanism details remain murky.
Agafonova, N.; Aleksandrov, A.; Anokhina, A.; Aoki, S.; Ariga, A.; Ariga, T.; Bender, D.; Bertolin, A.; Bodnarchuk, I.; Bozza, C.; Brugnera, R.; Buonaura, A.; Buontempo, S.; Büttner, B.; Chernyavsky, M.; Chukanov, A.; Consiglio, L.; D'Ambrosio, N.; De Lellis, G.; De Serio, M.; Del Amo Sanchez, P.; Di Crescenzo, A.; Di Ferdinando, D.; Di Marco, N.; Dmitrievski, S.; Dracos, M.; Duchesneau, D.; Dusini, S.; Dzhatdoev, T.; Ebert, J.; Ereditato, A.; Fini, R. A.; Fukuda, T.; Galati, G.; Garfagnini, A.; Goldberg, J.; Gornushkin, Y.; Grella, G.; Guler, A. M.; Gustavino, C.; Hagner, C.; Hara, T.; Hollnagel, A.; Hosseini, B.; Ishiguro, K.; Jakovcic, K.; Jollet, C.; Kamiscioglu, C.; Kamiscioglu, M.; Kim, J. H.; Kim, S. H.; Kitagawa, N.; Klicek, B.; Kodama, K.; Komatsu, M.; Kose, U.; Kreslo, I.; Lauria, A.; Ljubicic, A.; Longhin, A.; Malgin, A.; Malenica, M.; Mandrioli, G.; Matsuo, T.; Matveev, V.; Mauri, N.; Medinaceli, E.; Meregaglia, A.; Mikado, S.; Monacelli, P.; Montesi, M. C.; Morishima, K.; Muciaccia, M. T.; Naganawa, N.; Naka, T.; Nakamura, M.; Nakano, T.; Nakatsuka, Y.; Niwa, K.; Ogawa, S.; Omura, T.; Ozaki, K.; Paoloni, A.; Paparella, L.; Park, B. D.; Park, I. G.; Pasqualini, L.; Pastore, A.; Patrizii, L.; Pessard, H.; Podgrudkov, D.; Polukhina, N.; Pozzato, M.; Pupilli, F.; Roda, M.; Roganova, T.; Rokujo, H.; Rosa, G.; Ryazhskaya, O.; Sato, O.; Schembri, A.; Shakirianova, I.; Shchedrina, T.; Sheshukov, A.; Shibuya, H.; Shiraishi, T.; Shoziyoev, G.; Simone, S.; Sioli, M.; Sirignano, C.; Sirri, G.; Spinetti, M.; Stanco, L.; Starkov, N.; Stellacci, S. M.; Stipcevic, M.; Strolin, P.; Takahashi, S.; Tenti, M.; Terranova, F.; Tioukov, V.; Tufanli, S.; Vilain, P.; Vladymyrov, M.; Votano, L.; Vuilleumier, J. L.; Wilquet, G.; Wonsak, B.; Yoon, C. S.; Zemskova, S.
2015-06-01
The OPERA experiment, exposed to the CERN to Gran Sasso ν μ beam, collected data from 2008 to 2012. Four oscillated ν τ Charged Current interaction candidates have been detected in appearance mode, which are consistent with ν μ → ν τ oscillations at the atmospheric Δ m 2 within the "standard" three-neutrino framework. In this paper, the OPERA ν τ appearance results are used to derive limits on the mixing parameters of a massive sterile neutrino.
Atakishiyev, N.M. [Instituto de Matematicas. Universidad Nacional Autonoma de Mexico. Cuernavaca, Morelos (Mexico); Jafarov, E.I.; Nagiyev, S.M. [Institute of Physics, Azerbaijan Academy of Sciences. Baku, Azerbaijan (Azerbaijan); Wolf, K.B. [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas. Universidad Nacional Autonoma de Mexico. Cuernavaca, Morelos (Mexico)
1998-10-01
Meixner oscillators have a ground state and an energy spectrum that is equally spaced; they are a two-parameter family of models that satisfy a Hamiltonian equation with a difference operator. Meixner oscillators include as limits and particular cases the Charlier, Kravchuk and Hermite (common quantum-mechanical) harmonic oscillators. By the Sommerfeld-Watson transformation they are also related with a relativistic model of the linear harmonic oscillator, built in terms of the Meixner-Pollaczek polynomials, and their continuous weight function. We construct explicitly the corresponding coherent states with the dynamical symmetry group Sp(2,R). The reproducing kernel for the wavefunctions of these models is also found. (Author)
Li, Fenfang; Nguyen, Dang Minh; Ohl, Claus-Dieter
2016-01-01
We report about an intriguing boiling regime occurring for small heaters embedded on the boundary in subcooled water. The microheater is realized by focusing a continuous wave laser beam to about $10\\,\\mu$m in diameter onto a 165\\,nm-thick layer of gold, which is submerged in water. After an initial vaporous explosion a single bubble oscillates continuously and repeatably at several $100\\,$kHz. The microbubble's oscillations are accompanied with bubble pinch-off leading to a stream of gaseous bubbles into the subcooled water. The self-driven bubble oscillation is explained with a thermally kicked oscillator caused by the non-spherical collapses and by surface pinning. Additionally, Marangoni stresses induce a recirculating streaming flow which transports cold liquid towards the microheater reducing diffusion of heat along the substrate and therefore stabilizing the phenomenon to many million cycles. We speculate that this oscillate boiling regime may allow to overcome the heat transfer thresholds observed dur...
Adamson, P.; An, F. P.; Anghel, I.; Aurisano, A.; Balantekin, A. B.; Band, H. R.; Barr, G.; Bishai, M.; Blake, A.; Blyth, S.; Bock, G. J.; Bogert, D.; Cao, D.; Cao, G. F.; Cao, J.; Cao, S. V.; Carroll, T. J.; Castromonte, C. M.; Cen, W. R.; Chan, Y. L.; Chang, J. F.; Chang, L. C.; Chang, Y.; Chen, H. S.; Chen, Q. Y.; Chen, R.; Chen, S. M.; Chen, Y.; Chen, Y. X.; Cheng, J.; Cheng, J.-H.; Cheng, Y. P.; Cheng, Z. K.; Cherwinka, J. J.; Childress, S.; Chu, M. C.; Chukanov, A.; Coelho, J. A. B.; Corwin, L.; Cronin-Hennessy, D.; Cummings, J. P.; de Arcos, J.; De Rijck, S.; Deng, Z. Y.; Devan, A. V.; Devenish, N. E.; Ding, X. F.; Ding, Y. Y.; Diwan, M. V.; Dolgareva, M.; Dove, J.; Dwyer, D. A.; Edwards, W. R.; Escobar, C. O.; Evans, J. J.; Falk, E.; Feldman, G. J.; Flanagan, W.; Frohne, M. V.; Gabrielyan, M.; Gallagher, H. R.; Germani, S.; Gill, R.; Gomes, R. A.; Gonchar, M.; Gong, G. H.; Gong, H.; Goodman, M. C.; Gouffon, P.; Graf, N.; Gran, R.; Grassi, M.; Grzelak, K.; Gu, W. Q.; Guan, M. Y.; Guo, L.; Guo, R. P.; Guo, X. H.; Guo, Z.; Habig, A.; Hackenburg, R. W.; Hahn, S. R.; Han, R.; Hans, S.; Hartnell, J.; Hatcher, R.; He, M.; Heeger, K. M.; Heng, Y. K.; Higuera, A.; Holin, A.; Hor, Y. K.; Hsiung, Y. B.; Hu, B. Z.; Hu, T.; Hu, W.; Huang, E. C.; Huang, H. X.; Huang, J.; Huang, X. T.; Huber, P.; Huo, W.; Hussain, G.; Hylen, J.; Irwin, G. M.; Isvan, Z.; Jaffe, D. E.; Jaffke, P.; James, C.; Jen, K. L.; Jensen, D.; Jetter, S.; Ji, X. L.; Ji, X. P.; Jiao, J. B.; Johnson, R. A.; de Jong, J. K.; Joshi, J.; Kafka, T.; Kang, L.; Kasahara, S. M. S.; Kettell, S. H.; Kohn, S.; Koizumi, G.; Kordosky, M.; Kramer, M.; Kreymer, A.; Kwan, K. K.; Kwok, M. W.; Kwok, T.; Lang, K.; Langford, T. J.; Lau, K.; Lebanowski, L.; Lee, J.; Lee, J. H. C.; Lei, R. T.; Leitner, R.; Leung, J. K. C.; Li, C.; Li, D. J.; Li, F.; Li, G. S.; Li, Q. J.; Li, S.; Li, S. C.; Li, W. D.; Li, X. N.; Li, Y. F.; Li, Z. B.; Liang, H.; Lin, C. J.; Lin, G. L.; Lin, S.; Lin, S. K.; Lin, Y.-C.; Ling, J. J.; Link, J. M.; Litchfield, P. J.; Littenberg, L.; Littlejohn, B. R.; Liu, D. W.; Liu, J. C.; Liu, J. L.; Loh, C. W.; Lu, C.; Lu, H. Q.; Lu, J. S.; Lucas, P.; Luk, K. B.; Lv, Z.; Ma, Q. M.; Ma, X. B.; Ma, X. Y.; Ma, Y. Q.; Malyshkin, Y.; Mann, W. A.; Marshak, M. L.; Martinez Caicedo, D. A.; Mayer, N.; McDonald, K. T.; McGivern, C.; McKeown, R. D.; Medeiros, M. M.; Mehdiyev, R.; Meier, J. R.; Messier, M. D.; Miller, W. H.; Mishra, S. R.; Mitchell, I.; Mooney, M.; Moore, C. D.; Mualem, L.; Musser, J.; Nakajima, Y.; Naples, D.; Napolitano, J.; Naumov, D.; Naumova, E.; Nelson, J. K.; Newman, H. B.; Ngai, H. Y.; Nichol, R. J.; Ning, Z.; Nowak, J. A.; O'Connor, J.; Ochoa-Ricoux, J. P.; Olshevskiy, A.; Orchanian, M.; Pahlka, R. B.; Paley, J.; Pan, H.-R.; Park, J.; Patterson, R. B.; Patton, S.; Pawloski, G.; Pec, V.; Peng, J. C.; Perch, A.; Pfützner, M. M.; Phan, D. D.; Phan-Budd, S.; Pinsky, L.; Plunkett, R. K.; Poonthottathil, N.; Pun, C. S. J.; Qi, F. Z.; Qi, M.; Qian, X.; Qiu, X.; Radovic, A.; Raper, N.; Rebel, B.; Ren, J.; Rosenfeld, C.; Rosero, R.; Roskovec, B.; Ruan, X. C.; Rubin, H. A.; Sail, P.; Sanchez, M. C.; Schneps, J.; Schreckenberger, A.; Schreiner, P.; Sharma, R.; Moed Sher, S.; Sousa, A.; Steiner, H.; Sun, G. X.; Sun, J. L.; Tagg, N.; Talaga, R. L.; Tang, W.; Taychenachev, D.; Thomas, J.; Thomson, M. A.; Tian, X.; Timmons, A.; Todd, J.; Tognini, S. C.; Toner, R.; Torretta, D.; Treskov, K.; Tsang, K. V.; Tull, C. E.; Tzanakos, G.; Urheim, J.; Vahle, P.; Viaux, N.; Viren, B.; Vorobel, V.; Wang, C. H.; Wang, M.; Wang, N. Y.; Wang, R. G.; Wang, W.; Wang, X.; Wang, Y. F.; Wang, Z.; Wang, Z. M.; Webb, R. C.; Weber, A.; Wei, H. Y.; Wen, L. J.; Whisnant, K.; White, C.; Whitehead, L.; Whitehead, L. H.; Wise, T.; Wojcicki, S. G.; Wong, H. L. H.; Wong, S. C. F.; Worcester, E.; Wu, C.-H.; Wu, Q.; Wu, W. J.; Xia, D. M.; Xia, J. K.; Xing, Z. Z.; Xu, J. L.; Xu, J. Y.; Xu, Y.; Xue, T.; Yang, C. G.; Yang, H.; Yang, L.; Yang, M. S.; Yang, M. T.; Ye, M.; Ye, Z.; Yeh, M.; Young, B. L.; Yu, Z. Y.; Zeng, S.; Zhan, L.; Zhang, C.; Zhang, H. H.; Zhang, J. W.; Zhang, Q. M.; Zhang, X. T.; Zhang, Y. M.; Zhang, Y. X.; Zhang, Z. J.; Zhang, Z. P.; Zhang, Z. Y.; Zhao, J.; Zhao, Q. W.; Zhao, Y. B.; Zhong, W. L.; Zhou, L.; Zhou, N.; Zhuang, H. L.; Zou, J. H.; Daya Bay Collaboration
2016-10-01
Searches for a light sterile neutrino have been performed independently by the MINOS and the Daya Bay experiments using the muon (anti)neutrino and electron antineutrino disappearance channels, respectively. In this Letter, results from both experiments are combined with those from the Bugey-3 reactor neutrino experiment to constrain oscillations into light sterile neutrinos. The three experiments are sensitive to complementary regions of parameter space, enabling the combined analysis to probe regions allowed by the Liquid Scintillator Neutrino Detector (LSND) and MiniBooNE experiments in a minimally extended four-neutrino flavor framework. Stringent limits on sin22 θμ e are set over 6 orders of magnitude in the sterile mass-squared splitting Δ m412. The sterile-neutrino mixing phase space allowed by the LSND and MiniBooNE experiments is excluded for Δ m412<0.8 eV2 at 95 % CLs .
Bay, The Daya; Adamson, P; An, F P; Anghel, I; Aurisano, A; Balantekin, A B; Band, H R; Barr, G; Bishai, M; Blake, A; Bock, S Blyth G J; Bogert, D; Cao, D; Cao, G F; Cao, J; Cao, S V; Carroll, T J; Castromonte, C M; Cen, W R; Chan, Y L; Chang, J F; Chang, L C; Chang, Y; Chen, H S; Chen, Q Y; Chen, R; Chen, S M; Chen, Y; Chen, Y X; Cheng, J; Cheng, J -H; Chen, Y P; Cheng, Z K; Cherwinka, J J; Childress, S; Chu, M C; Chukanov, A; Coelho, J A B; Corwin, L; Cronin-Hennessy, D; Cummings, J P; de Arcos, J; De Rijck, S; Deng, Z Y; Devan, A V; Devenish, N E; Ding, X F; Ding, Y Y; Diwan, M V; Dolgareva, M; Dove, J; Dwyer, D A; Edwards, W R; Escobar, C O; Evans, J J; Falk, E; Feldman, G J; Flanagan, W; Frohne, M V; Gabrielyan, M; Gallagher, H R; Germani, S; Gill, R; Gomes, R A; Gonchar, M; Gong, G H; Gong, H; Goodman, M C; Gouffon, P; Graf, N; Gran, R; Grassi, M; Grzelak, K; Gu, W Q; Guan, M Y; Guo, L; Guo, R P; Guo, X H; Guo, Z; Habig, A; Hackenburg, R W; Hahn, S R; Han, R; Hans, S; Hartnell, J; Hatcher, R; He, M; Heeger, K M; Heng, Y K; Higuera, A; Holin, A; Hor, Y K; Hsiung, Y B; Hu, B Z; Hu, T; Hu, W; Huang, E C; Huang, H X; Huang, J; Huang, X T; Huber, P; Huo, W; Hussain, G; Hylen, J; Irwin, G M; Isvan, Z; Jaffe, D E; Jaffke, P; James, C; Jen, K L; Jensen, D; Jetter, S; Ji, X L; Ji, X P; Jiao, J B; Johnson, R A; de Jong, J K; Joshi, J; Kafka, T; Kang, L; Kasahara, S M S; Kettell, S H; Kohn, S; Koizumi, G; Kordosky, M; Kramer, M; Kreymer, A; Kwan, 1 K K; Kwok, M W; Kwok, T; Lang, K; Langford, T J; Lau, K; Lebanowski, L; Lee, J; Lee, J H C; Lei, R T; Leitner, R; Leung, J K C; Li, C; Li, D J; Li, F; Li, G S; Li, Q J; Li, S; Li, S C; Li, W D; Li, X N; Li, Y F; Li, Z B; Liang, H; Lin, C J; Lin, G L; Lin, S; Lin, S K; Lin, Y -C; Link, J J Ling J M; Litchfield, P J; Littenberg, L; Littlejohn, B R; Liu, D W; Liu, J C; Liu, J L; Loh, C W; Lu, C; Lu, H Q; Lu, J S; Lucas, P; Luk, K B; Lv, Z; Ma, Q M; Ma, X B; Ma, X Y; Ma, Y Q; Malyshkin, Y; Mann, W A; Marshak, M L; Caicedo, D A Martinez; Mayer, N; McDonald, K T; McGivern, C; McKeown, R D; Medeiros, M M; Mehdiyev, R; Meier, J R; Messier, M D; Miller, W H; Mishra, S R; Mitchell, I; Mooney, M; Moore, C D; Mualem, L; Musser, J; Nakajima, Y; Naples, D; Napolitano, J; Naumov, D; Naumova, E; Nelson, J K; Newman, H B; Ngai, H Y; Nichol, R J; Ning, Z; Nowak, A; O'Connor, J; Ochoa-Ricoux, J P; Olshevskiy, A; Orchanian, M; R.,; Pahlka, R B; Paley, J; Pan, H -R; Park, J; Patterson, R B; Patton, S; Pawloski, G; Pec, V; Peng, J C; Perch, A; Pfutzner, M M; Phan, D D; Phan-Budd, S; Pinsky, L; Plunkett, R K; Poonthottathil, N; Pun, C S J; Qi, F Z; Qi, M; Qian, X; Qiu, X; Radovic, A; Raper, N; Rebel, B; Ren, J; Rosenfeld, C; Rosero, R; Roskovec, B; Ruan, X C; Rubin, H A; Sail, P; Sanchez, M C; Schneps, J; Schreckenberger, A; Schreiner, P; Sharma, R; Sher, S Moed; Sousa, A; Steiner, H; Sun, G X; Sun, J L; Tagg, N; Talaga, R L; Tang, W; Taychenachev, D; Thomas, J; Thomson, M A; Timmons, X Tian A; Todd, J; Tognini, S C; Toner, R; Torretta, D; Treskov, K; Tsang, K V; Tull, C E; Tzanakos, G; Urheim, J; Vahle, P; Viaux, N; Viren, B; Vorobel, V; Wang, C H; Wang, M; Wang, N Y; Wang, R G; Wang, W; Wang, X; Wang, Y F; Wang, Z; Wang, Z M; Webb, R C; Weber, A; Wei, H Y; Wen, L J; Whisnant, K; White, C; Whitehead, L Whitehead L H; Wise, T; Wojcicki, S G; Wong, H L H; Wong, S C F; Worcester, E; Wu, C -H; Wu, Q; Wu, W J; Xia, D M; Xia, J K; Xing, Z Z; Xu, J L; Xu, J Y; Xu, Y; Xue, T; Yang, C G; Yang, H; Yang, L; Yang, M S; Yang, M T; Ye., M; Ye, Z; Yeh, M; Young, B L; Yu, Z Y; Zeng, S; Zhang, L ZhanC; Zhang, H H; Zhang, J W; Zhang, Q M; Zhang, X T; Zhang, Y M; Zhang, Y X; Zhang, Z J; Zhang, Z P; Zhang, Z Y; Zhao, J; Zhao, Q W; Zhao, Y B; Zhong, W L; Zhou, L; Zhou, N; Zhuang, H L; Zou, J H
2016-01-01
Searches for a light sterile neutrino have been independently performed by the MINOS and the Daya Bay experiments using the muon (anti)neutrino and electron antineutrino disappearance channels, respectively. In this Letter, results from both experiments are combined with those from the Bugey-3 reactor neutrino experiment to constrain oscillations into light sterile neutrinos. The three experiments are sensitive to complementary regions of parameter space, enabling the combined analysis to probe regions allowed by the LSND and MiniBooNE experiments in a minimally extended four-neutrino flavor framework. Stringent limits on $\\sin^2 2\\theta_{\\mu e}$ are set over six orders of magnitude in the sterile mass-squared splitting $\\Delta m^2_{41}$. The sterile-neutrino mixing phase space allowed by the LSND and MiniBooNE experiments is excluded for $\\Delta m^2_{41} < 0.8$ eV$^2$ at 95\\% C.L.
Ye, Xujun, E-mail: yexujun@cc.hirosaki-u.ac.jp [College of Biosystems Engineering and Food Science, Zhejiang University, Hangzhou 310058 (China); Faculty of Agriculture and Life Sciences, Hirosaki University, Aomori 036-8561 (Japan); Sakai, Kenshi, E-mail: ken@cc.tuat.ac.jp [Environmental and Agricultural Engineering Department, Tokyo University of Agriculture and Technology, Tokyo 183-8509 (Japan)
2013-12-15
Alternate bearing or masting is a yield variability phenomenon in perennial crops. The complex dynamics in this phenomenon have stimulated much ecological research. Motivated by data from an eight-year experiment with forty-eight individual trees, we explored the mechanism inherent to these dynamics in Satsuma mandarin (Citrus unshiu Marc.). By integrating high-resolution imaging technology, we found that the canopy structure and reproduction output of individual citrus crops are mutually dependent on each other. Furthermore, it was revealed that the mature leaves in early season contribute their energy to the fruiting of the current growing season, whereas the younger leaves show a delayed contribution to the next growing season. We thus hypothesized that the annual yield variability might be caused by the limited and time-delayed resource allocation in individual plants. A novel lattice model based on this hypothesis demonstrates that this pattern of resource allocation will generate oscillations and chaos in citrus yield.
Wang, H.Q.; Xu, G.S.; Guo, H.Y.;
2012-01-01
-frequency oscillation, termed a limit-cycle state, appears at the edge during the quiescent phase with good energy and particle confinement. Detailed measurements by edge Langmuir probes show modulation interaction and strong three-wave coupling between the low-frequency oscillations and high-frequency-broadband (80......The first high confinement H-mode plasma has been obtained in the Experimental Advanced Superconducting Tokamak (EAST) with about 1 MW lower hybrid current drive after wall conditioning by lithium evaporation and real-time injection of Li powder. Following the L–H transition, a small-amplitude, low....... And the measurements demonstrate that the energy gain of zonal flows is of the same order as the energy loss of turbulence. This strongly suggests the interactions between zonal flows and high-frequency turbulences at the pedestal during the limit-cycle state....
J. A. Gallego
2012-01-01
Full Text Available Walking on irregular surfaces and in the presence of unexpected events is a challenging problem for bipedal machines. Up to date, their ability to cope with gait disturbances is far less successful than humans’: Neither trajectory controlled robots, nor dynamic walking machines (Limit Cycle Walkers are able to handle them satisfactorily. On the contrary, humans reject gait perturbations naturally and efficiently relying on their sensory organs that, if needed, elicit a recovery action. A similar approach may be envisioned for bipedal robots and exoskeletons: An algorithm continuously observes the state of the walker and, if an unexpected event happens, triggers an adequate reaction. This paper presents a monitoring algorithm that provides immediate detection of any type of perturbation based solely on a phase representation of the normal walking of the robot. The proposed method was evaluated in a Limit Cycle Walker prototype that suffered push and trip perturbations at different moments of the gait cycle, providing 100% successful detections for the current experimental apparatus and adequately tuned parameters, with no false positives when the robot is walking unperturbed.
Koshelets, V. P.; Shitov, S. V.; Dmitriev, P. N.;
2003-01-01
to 712 GHz, limited only by the gap frequency of Nb. This enabled us to phase lock the FFO in the frequency range 500-712 GHz where continuous frequency tuning is possible; resulting in an absolute FFO phase noise as low as -80 dBc at 707 GHz. Comprehensive measurements of the FFO radiation linewidth...... have been performed using an integrated SIS harmonic mixer. The influence of FFO parameters on radiation linewidth, particularly the effect of the differential resistances associated both with the bias current and the applied magnetic field has been studied in order to further optimize the FFO design....... A new approach with a self-shielded FFO has been developed and experimentally tested....
Bursting Ca2+ Oscillations and Synchronization in Coupled Cells
JI Quan-Bao; LU Qi-Shao; Yang Zhuo-Qin; Duan Li-Xia
2008-01-01
A mathematical model proposed by Grubelnk et al. [Biophys. Chem. 94 (2001) 59] is employed to study the physiological role of mitochondria and the cytosolic proteins in generating complex Ca2+ oscillations. Intracellular bursting calcium oscillations of point-point, point cycle and two-folded limit cycle types are observed and explanations are given based on the fast/slow dynamical analysis, especially for point-cycle and two-folded limit cycle types, which have not been reported before. Furthermore, synchronization of coupled bursters of Ca2+oscillations via gap junctions and the effect of bursting types on synchronization of coupled cells are studied. It is argued that bursting oscillations of point-point type may be superior to achieve synchronization than that of point-cycle type.
A Data-constrained Estimate of the Global Ocean Iron Cycle: Budgets, Timescales, and Iron Limitation
Frants, M.; Holzer, M. B.; DeVries, T. J.; Matear, R.
2014-12-01
The oceanic iron cycle is estimated by optimizing a simple steady-state model based on a data-assimilated global circulation, with a prescribed optimized phosphorus cycle and a prescribed aeolian source pattern. Key biogeochemical parameters are determined by minimizing a suitably weighted quadratic misfit between the model's dissolved iron concentration and a global data set of sparse measurements. The global dissolved iron inventory is estimated to be (7.1±0.1)×1011 mol Fe, of which (6.9±0.1)×1011 mol Fe is bound to organic ligands and hence bioavailable, while the remainder is "free" iron. The aeolian iron input rate is estimated at (3.3±0.5)×109 mol Fe/year, corresponding to a bulk residence time for bioavailable iron of 215±40 years, comparable to the bulk biological cycling timescale estimated at 246±24 years. Iron limitation is quantified in terms of the difference [Fe∗] between the actual iron concentration and that needed to utilize the available phosphate. The optimized model captures the observed high-nutrient, low-chlorophyll regions of the ocean as iron-limited regions with [Fe∗]iron age, ΓFe, as the mean time since iron at a given point was last injected from the atmosphere and compute ΓFe using an equivalent linear formulation of the model. In the euphotic zone, ΓFe ranges from a few decades or less in regions of high aeolian input to ˜1800 years in the Southern Ocean. The patterns of ΓFe show that iron is supplied to the Southern Ocean euphotic zone primarily from depth rather than being advected within the thermocline following deposition from continental dust plumes. Because [Fe∗] is negative in the deep southern oceans, upwelling waters maintain Southern Ocean iron limitation.
Qualitative analysis of the Rössler equations: Bifurcations of limit cycles and chaotic attractors
Barrio, Roberto; Blesa, Fernando; Serrano, Sergio
2009-06-01
In this paper we study different aspects of the paradigmatic Rössler model. We perform a detailed study of the local and global bifurcations of codimension one and two of limit cycles. This provides us a global idea of the three-parametric evolution of the system. We also study the regions of parameters where we may expect a chaotic behavior by the use of different Chaos Indicators. The combination of the different techniques gives an idea of the different routes to chaos and the different kinds of chaotic attractors we may found in this system.
Reactive Coupling Effects on Amplitude Death of Coupled Limit-Cycle Systems
WANG Jin-Hua; LI Xiao-Wen
2009-01-01
Amplitude death in coupled limit-cycle systems induced by the reactive coupling is studied. The presence of reactive coupling parameter changes the amplitude death process of the system,and increases the critical coupling strength for the emergence of amplitude death.When the systems are in the state of complete or partial amplitude death,increasing the reactive coupling will increase the number of partial synchronization groups,implying the increase of disorder of the system.Increasing the reactive coupling makes the elimination of the amplitude death of the systems harder.
Feng, Miao; Zhen, Xiao; Zheng, Chan; Huang, Juan; Zhan, Hong-Bing
2008-01-01
Optical limiting (OL) cycling performance and photostability of vanadyl phthalocyanines (VOPcs) and naphthalocyanines (VONcs) were studied. The results show that although vanadyl 2,11,20,29-tetra-tert-butyl-2,3-naphthalocyanine has the most pronounced OL effect originally, it is not a promising OL material due to its poor photostability. Meanwhile, vanadyl 2,9, 16,23-etraphenoxy-29H, 31H-phthalocyanine is considered to be a potential OL material, owing to its considerable OL effect and good photostability. A possible photochemical mechanism behind the reverse saturable absorption (RSA) and photolysis process of the studied species is proposed.
Phase reduction theory for hybrid nonlinear oscillators
Shirasaka, Sho; Kurebayashi, Wataru; Nakao, Hiroya
2017-01-01
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of limit-cycle oscillations in rhythmic systems, has mostly been restricted to smooth dynamical systems. Here we develop a general phase reduction theory for weakly perturbed limit cycles in hybrid dynamical systems that facilitates analysis, control, and optimization of nonlinear oscillators whose smooth models are unavailable or intractable. On the basis of the generalized theory, we analyze injection locking of hybrid limit-cycle oscillators by periodic forcing and reveal their characteristic synchronization properties, such as ultrafast and robust entrainment to the periodic forcing and logarithmic scaling at the synchronization transition. We also illustrate the theory by analyzing the synchronization dynamics of a simple physical model of biped locomotion.
Nonlinear dynamics of self-oscillating polymer gels
无
2010-01-01
Self-oscillating polymer gels driven by Belousov-Zhabotinsky (BZ) chemical reaction are a new class of functional gels that have a wide range of potential applications (e.g., autonomously functioning membranes, actuate artificial muscles). However, the precise control of these gels has been an issue due to limited investigations of the influences of key system parameters on the characteristics of BZ gels. To address this deficiency, we studied the self-oscillating behavior of BZ gels using the nonline-ar dynamics theory and an Oregonator-like model, with focus placed upon the influences of various system parameters. The analysis of the oscillation phase indicated that the dynamic response of BZ gels represents the classical limit cycle oscillation. We then investigated the characteristics of the limit cycle oscillation and quantified the influences of key parameters (i.e., ini-tial reactant concentration, oxidation and reduction rate of catalyst, and response coefficient) on the self-oscillating behavior of BZ gels. The results demonstrated that sustained limit cycle oscillation of BZ gels can be achieved only when these key pa-rameters meet certain requirements, and that the pattern, period and amplitude of the oscillation are significantly influenced by these parameters. The results obtained in this study could enable the controlled self-oscillation of BZ gels system. This has several potential applications such as controlled drug delivery, miniature peristaltic pumps and microactuators.
Aram, Lior; Braun, Tslil; Braverman, Carmel; Kaplan, Yosef; Ravid, Liat; Levin-Zaidman, Smadar; Arama, Eli
2016-04-04
How cells avoid excessive caspase activity and unwanted cell death during apoptotic caspase-mediated removal of large cellular structures is poorly understood. We investigate caspase-mediated extrusion of spermatid cytoplasmic contents in Drosophila during spermatid individualization. We show that a Krebs cycle component, the ATP-specific form of the succinyl-CoA synthetase β subunit (A-Sβ), binds to and activates the Cullin-3-based ubiquitin ligase (CRL3) complex required for caspase activation in spermatids. In vitro and in vivo evidence suggests that this interaction occurs on the mitochondrial surface, thereby limiting the source of CRL3 complex activation to the vicinity of this organelle and reducing the potential rate of caspase activation by at least 60%. Domain swapping between A-Sβ and the GTP-specific SCSβ (G-Sβ), which functions redundantly in the Krebs cycle, show that the metabolic and structural roles of A-Sβ in spermatids can be uncoupled, highlighting a moonlighting function of this Krebs cycle component in CRL activation.
Oscillations of a Simple Pendulum with Extremely Large Amplitudes
Butikov, Eugene I.
2012-01-01
Large oscillations of a simple rigid pendulum with amplitudes close to 180[degrees] are treated on the basis of a physically justified approach in which the cycle of oscillation is divided into several stages. The major part of the almost closed circular path of the pendulum is approximated by the limiting motion, while the motion in the vicinity…
The Kepler Light Curve of V344 Lyrae: Constraining the Thermal-viscous Limit Cycle Instability
Cannizzo, J. K.; Still, M. D.; Howell, S. B.; Wood, M. A.; Smale, A. P.
2010-12-01
We present time-dependent modeling based on the accretion disk limit cycle model for a 270 d light curve of the short-period SU UMa-type dwarf nova V344 Lyr taken by Kepler. The unprecedented precision and cadence (1 minute) far surpass that generally available for long-term light curves. The data encompass two superoutbursts and 17 normal (i.e., short) outbursts. The main decay of the superoutbursts is nearly perfectly exponential, decaying at a rate ~12 d mag-1, while the much more rapid decays of the normal outbursts exhibit a faster-than-exponential shape. Our modeling using the basic accretion disk limit cycle can produce the main features of the V344 Lyr light curve, including the peak outburst brightness. Nevertheless, there are obvious deficiencies in our model light curves. (1) The rise times we calculate, both for the normal and superoutbursts, are too fast. (2) The superoutbursts are too short. (3) The shoulders on the rise to superoutburst have more structure than the shoulders in the observed superoutbursts and are too slow, comprising about a third to half of the total viscous plateau, rather than the ~10% observed. However, one of the αcold αhot interpolation schemes we investigate (one that is physically motivated) does yield longer superoutbursts with suitably short, less structured shoulders.
The Kepler Light Curve of V344 Lyrae: Constraining the Thermal-Viscous Limit Cycle Instability
Cannizzo, J K; Howell, S B; Wood, M A; Smale, A P
2010-01-01
We present time dependent modeling based on the accretion disk limit cycle model for a 270 d light curve of the short period SU UMa-type dwarf nova V344 Lyr taken by Kepler. The unprecedented precision and cadence (1 minute) far surpass that generally available for long term light curves. The data encompass two superoutbursts and 17 normal (i.e., short) outbursts. The main decay of the superoutbursts is nearly perfectly exponential, decaying at a rate ~12 d/mag, while the much more rapid decays of the normal outbursts exhibit a faster-than-exponential shape. Our modeling using the basic accretion disk limit cycle can produce the main features of the V344 Lyr light curve, including the peak outburst brightness. Nevertheless there are obvious deficiencies in our model light curves: (1) The rise times we calculate, both for the normal and superoutbursts, are too fast. (2) The superoutbursts are too short. (3) The shoulders on the rise to superoutburst have more structure than the shoulder in the observed superou...
Unsteady surface pressure measurements on a slender delta wing undergoing limit cycle wing rock
Arena, Andrew S., Jr.; Nelson, Robert C.
1991-01-01
An experimental investigation of slender wing limit cycle motion known as wing rock was investigated using two unique experimental systems. Dynamic roll moment measurements and visualization data on the leading edge vortices were obtained using a free to roll apparatus that incorporates an airbearing spindle. In addition, both static and unsteady surface pressure data was measured on the top and bottom surfaces of the model. To obtain the unsteady surface pressure data a new computer controller drive system was developed to accurately reproduce the free to roll time history motions. The data from these experiments include, roll angle time histories, vortex trajectory data on the position of the vortices relative to the model's surface, and surface pressure measurements as a function of roll angle when the model is stationary or undergoing a wing rock motion. The roll time history data was numerically differentiated to determine the dynamic roll moment coefficient. An analysis of these data revealed that the primary mechanism for the limit cycle behavior was a time lag in the position of the vortices normal to the wing surface.
Canard-induced mixed mode oscillations in an excitable glow discharge plasmas
Nurujjaman, M
2014-01-01
We demonstrated experimentally canard induced mixed mode oscillations (MMO) in an excitable glow discharge plasma, and the results are validated through numerical solution of the FitzHugh Nagumo (FHN) model. When glow discharge plasma is perturbed by applying a magnetic field, it shows mixed mode oscillatory activity, i.e., quasiperiodic small oscillations interposed with large bounded limit cycles oscillations. The initial quasiperiodic oscillations were observed to change into large amplitude limit cycle oscillations with magnetic field, and the number of these oscillation increases with increase in the magnetic field. Fourier analysis of both numerical and experimental results show that the origin of these oscillations are canard-induced phenomena, which occurs near the threshold of the control parameter. Further, the phase space plots also confirm that the oscillations are basically canard-induced MMOs.
Gupta, S.; Potters, M.G.; Ruffo, S.
2012-01-01
We study synchronization in a system of phase-only oscillators residing on the sites of a one-dimensional periodic lattice. The oscillators interact with a strength that decays as a power law of the separation along the lattice length and is normalized by a size-dependent constant. The exponent α of
Shaw, Kendrick M; Thomas, Peter J
2011-01-01
Rhythmic behaviors in neural systems often combine features of limit cycle dynamics (stability and periodicity) with features of near heteroclinic or near homoclinic cycle dynamics (extended dwell times in localized regions of phase space). Proximity of a limit cycle to one or more saddle equilibria can have a profound effect on the timing of trajectory components and response to both fast and slow perturbations, providing a possible mechanism for adaptive control of rhythmic motions. Reyn showed that for a planar dynamical system with a stable heteroclinic cycle (or separatrix polygon), small perturbations satisfying a net inflow condition will generically give rise to a stable limit cycle (Reyn, 1980; Guckenheimer and Holmes, 1983). Here we consider the asymptotic behavior of the infinitesimal phase response curve (iPRC) for examples of two systems satisfying Reyn's inflow criterion, (i) a smooth system with a chain of four hyperbolic saddle points and (ii) a piecewise linear system corresponding to local l...
Adamson, P; An, F P; Anghel, I; Aurisano, A; Balantekin, A B; Band, H R; Barr, G; Bishai, M; Blake, A; Blyth, S; Bock, G J; Bogert, D; Cao, D; Cao, G F; Cao, J; Cao, S V; Carroll, T J; Castromonte, C M; Cen, W R; Chan, Y L; Chang, J F; Chang, L C; Chang, Y; Chen, H S; Chen, Q Y; Chen, R; Chen, S M; Chen, Y; Chen, Y X; Cheng, J; Cheng, J-H; Cheng, Y P; Cheng, Z K; Cherwinka, J J; Childress, S; Chu, M C; Chukanov, A; Coelho, J A B; Corwin, L; Cronin-Hennessy, D; Cummings, J P; de Arcos, J; De Rijck, S; Deng, Z Y; Devan, A V; Devenish, N E; Ding, X F; Ding, Y Y; Diwan, M V; Dolgareva, M; Dove, J; Dwyer, D A; Edwards, W R; Escobar, C O; Evans, J J; Falk, E; Feldman, G J; Flanagan, W; Frohne, M V; Gabrielyan, M; Gallagher, H R; Germani, S; Gill, R; Gomes, R A; Gonchar, M; Gong, G H; Gong, H; Goodman, M C; Gouffon, P; Graf, N; Gran, R; Grassi, M; Grzelak, K; Gu, W Q; Guan, M Y; Guo, L; Guo, R P; Guo, X H; Guo, Z; Habig, A; Hackenburg, R W; Hahn, S R; Han, R; Hans, S; Hartnell, J; Hatcher, R; He, M; Heeger, K M; Heng, Y K; Higuera, A; Holin, A; Hor, Y K; Hsiung, Y B; Hu, B Z; Hu, T; Hu, W; Huang, E C; Huang, H X; Huang, J; Huang, X T; Huber, P; Huo, W; Hussain, G; Hylen, J; Irwin, G M; Isvan, Z; Jaffe, D E; Jaffke, P; James, C; Jen, K L; Jensen, D; Jetter, S; Ji, X L; Ji, X P; Jiao, J B; Johnson, R A; de Jong, J K; Joshi, J; Kafka, T; Kang, L; Kasahara, S M S; Kettell, S H; Kohn, S; Koizumi, G; Kordosky, M; Kramer, M; Kreymer, A; Kwan, K K; Kwok, M W; Kwok, T; Lang, K; Langford, T J; Lau, K; Lebanowski, L; Lee, J; Lee, J H C; Lei, R T; Leitner, R; Leung, J K C; Li, C; Li, D J; Li, F; Li, G S; Li, Q J; Li, S; Li, S C; Li, W D; Li, X N; Li, Y F; Li, Z B; Liang, H; Lin, C J; Lin, G L; Lin, S; Lin, S K; Lin, Y-C; Ling, J J; Link, J M; Litchfield, P J; Littenberg, L; Littlejohn, B R; Liu, D W; Liu, J C; Liu, J L; Loh, C W; Lu, C; Lu, H Q; Lu, J S; Lucas, P; Luk, K B; Lv, Z; Ma, Q M; Ma, X B; Ma, X Y; Ma, Y Q; Malyshkin, Y; Mann, W A; Marshak, M L; Martinez Caicedo, D A; Mayer, N; McDonald, K T; McGivern, C; McKeown, R D; Medeiros, M M; Mehdiyev, R; Meier, J R; Messier, M D; Miller, W H; Mishra, S R; Mitchell, I; Mooney, M; Moore, C D; Mualem, L; Musser, J; Nakajima, Y; Naples, D; Napolitano, J; Naumov, D; Naumova, E; Nelson, J K; Newman, H B; Ngai, H Y; Nichol, R J; Ning, Z; Nowak, J A; O'Connor, J; Ochoa-Ricoux, J P; Olshevskiy, A; Orchanian, M; Pahlka, R B; Paley, J; Pan, H-R; Park, J; Patterson, R B; Patton, S; Pawloski, G; Pec, V; Peng, J C; Perch, A; Pfützner, M M; Phan, D D; Phan-Budd, S; Pinsky, L; Plunkett, R K; Poonthottathil, N; Pun, C S J; Qi, F Z; Qi, M; Qian, X; Qiu, X; Radovic, A; Raper, N; Rebel, B; Ren, J; Rosenfeld, C; Rosero, R; Roskovec, B; Ruan, X C; Rubin, H A; Sail, P; Sanchez, M C; Schneps, J; Schreckenberger, A; Schreiner, P; Sharma, R; Moed Sher, S; Sousa, A; Steiner, H; Sun, G X; Sun, J L; Tagg, N; Talaga, R L; Tang, W; Taychenachev, D; Thomas, J; Thomson, M A; Tian, X; Timmons, A; Todd, J; Tognini, S C; Toner, R; Torretta, D; Treskov, K; Tsang, K V; Tull, C E; Tzanakos, G; Urheim, J; Vahle, P; Viaux, N; Viren, B; Vorobel, V; Wang, C H; Wang, M; Wang, N Y; Wang, R G; Wang, W; Wang, X; Wang, Y F; Wang, Z; Wang, Z M; Webb, R C; Weber, A; Wei, H Y; Wen, L J; Whisnant, K; White, C; Whitehead, L; Whitehead, L H; Wise, T; Wojcicki, S G; Wong, H L H; Wong, S C F; Worcester, E; Wu, C-H; Wu, Q; Wu, W J; Xia, D M; Xia, J K; Xing, Z Z; Xu, J L; Xu, J Y; Xu, Y; Xue, T; Yang, C G; Yang, H; Yang, L; Yang, M S; Yang, M T; Ye, M; Ye, Z; Yeh, M; Young, B L; Yu, Z Y; Zeng, S; Zhan, L; Zhang, C; Zhang, H H; Zhang, J W; Zhang, Q M; Zhang, X T; Zhang, Y M; Zhang, Y X; Zhang, Z J; Zhang, Z P; Zhang, Z Y; Zhao, J; Zhao, Q W; Zhao, Y B; Zhong, W L; Zhou, L; Zhou, N; Zhuang, H L; Zou, J H
2016-10-07
Searches for a light sterile neutrino have been performed independently by the MINOS and the Daya Bay experiments using the muon (anti)neutrino and electron antineutrino disappearance channels, respectively. In this Letter, results from both experiments are combined with those from the Bugey-3 reactor neutrino experiment to constrain oscillations into light sterile neutrinos. The three experiments are sensitive to complementary regions of parameter space, enabling the combined analysis to probe regions allowed by the Liquid Scintillator Neutrino Detector (LSND) and MiniBooNE experiments in a minimally extended four-neutrino flavor framework. Stringent limits on sin^{2}2θ_{μe} are set over 6 orders of magnitude in the sterile mass-squared splitting Δm_{41}^{2}. The sterile-neutrino mixing phase space allowed by the LSND and MiniBooNE experiments is excluded for Δm_{41}^{2}<0.8 eV^{2} at 95% CL_{s}.
Barbosa, Valquiria Porfirio [Universidade Federal do Amazonas (UFAM). Inst. de Ciencias Exatas. Dept. de Geociencias (Brazil); Cunha, Armando Antonio Scarparo [Unidade de Operacoes de Exploracao e Producao da Amazonia, Exploracao, Gerencia de Sedimentologia e Estratigrafia (Brazil)], e-mail: scarparo@petrobras.com.br; Shimabukuro, Seirin [Centro de Pesquisas da Petrobras (CENPES). P e D em Geociencias, Gerencia de Bio-Estratigrafia e Paleoecologia (Brazil)], e-mail: seirin@petrobras.com.br; Gamboa, Luiz Antonio Pierantoni [Universidade Federal Fluminense (UFF), Niteroi. RJ (Brazil). Centro de Estudos Gerais. Inst. de Geociencias], e-mail: luizgamboa@gmail.com
2010-05-15
An integrated paleoecological, biostratigraphic and cyclostratigraphic study was carried out on sedimentary rhythm sequences in the Oligocene-Miocene of the Campos Basin, Brazil. The bio stratigraphic data combined with the spectral analysis performed on numerical data based on carbonate content variations of cores from well A, Campos Basin, reveal a periodicity related to the Milankovitch cycles. Benthic foraminiferal biofacies oscillations recognized in these cores have the same frequency and phase of long eccentricity cycles (400 Ka). Paleoceanographic changes (such as changes in ocean currents, water temperature and food supply) can modify the distribution and frequency patterns of foraminifera assemblages. However, the method used to interpret the biofacies, the geological context of the studied area and the proposed genetic model to explain the origin of these rhythmically patterned rocks, suggest that changes in foraminiferal biofacies are directly related to the paleobathymetry variations induced by glacio-eustatic oscillations of relative sea level . According to the proposed model, productivity-dilution cycles were instrumental in the origin of these marl-limestone couplets. During regressive phases, conditions were established to increase continental runoff to a bathyal setting. The increase of continental runoff with decrease of contribution of the main carbonate components led to the deposition of marlstone. During the transgressive phase, the relative reduction in clay input from continental sediments, favored a productivity growth of pelagic carbonate (calcareous nannofossil and planktonic foraminifera), which created conditions facilitating the deposition of limestone layers. The paleobathymetry oscillations, interpreted from the benthic foraminifera assemblage, and the formation of couplets, seems to be in phase with the transgressive-regressive cycles indicating a common cause to both processes. (author)
Precise numerical results for limit cycles in the quantum three-body problem
Mohr, R F; Hammer, H W; Perry, R J; Wilson, K G
2006-01-01
The study of the three-body problem with short-range attractive two-body forces has a rich history going back to the 1930's. Recent applications of effective field theory methods to atomic and nuclear physics have produced a much improved understanding of this problem, and we elucidate some of the issues using renormalization group ideas applied to precise nonperturbative calculations. These calculations provide 11-12 digits of precision for the binding energies in the infinite cutoff limit. The method starts with this limit as an approximation to an effective theory and allows cutoff dependence to be systematically computed as an expansion in powers of inverse cutoffs and logarithms of the cutoff. Renormalization of three-body bound states requires a short range three-body interaction, with a coupling that is governed by a precisely mapped limit cycle of the renormalization group. Additional three-body irrelevant interactions must be determined to control subleading dependence on the cutoff and this control ...
Limit cycles by FEM for a one - parameter dynamical system associated to the Luo - Rudy I model
Bichir, Cătălin Liviu; Amuzescu, Bogdan; Nistor, Gheorghe; Popescu, Marin; Flonta, Maria-Luiza; Corlan, Alexandru Dan; Svab, Istvan
2011-01-01
An one - parameter dynamical system is associated to the mathematical problem governing the membrane excitability of a ventricular cardiomyocyte, according to the Luo-Rudy I model. Limit cycles are described by the solutions of an extended system. A finite element method time approximation (FEM) is used in order to formulate the approximate problem. Starting from a Hopf bifurcation point, approximate limit cycles are obtained, step by step, using an arc-length-continuation method and Newton's method. Some numerical results are presented.
Chavarriga, Javier [Departament de Matematica, Universitat de Lleida, Avda, Jaume II 69, 25001 Lleida (Spain)]. E-mail: chava@eup.udl.es; Garcia, Isaac A. [Departament de Matematica, Universitat de Lleida, Avda, Jaume II 69, 25001 Lleida (Spain)]. E-mail: garcia@eup.udl.es; Sorolla, Jordi [Departament de Matematica, Universitat de Lleida, Avda, Jaume II 69, 25001 Lleida (Spain)]. E-mail: jsorolla@matematica.udl.es
2005-04-01
Any quadratic system with limit cycles can be written in one of the three families stated by the Chinese classification. In this paper we consider family (I), i.e., x-bar ={delta}x-y+-bar x2+mxy+ny2,y-bar =x. We show that the degree of its real irreducible invariant algebraic curves is bounded by 3. By the way, we prove that there is not any algebraic limit cycle for this family.
Floating Silicon Method single crystal ribbon - observations and proposed limit cycle theory
Kellerman, Peter; Kernan, Brian; Helenbrook, Brian T.; Sun, Dawei; Sinclair, Frank; Carlson, Frederick
2016-10-01
In the Floating Silicon Method (FSM), a single-crystal Si ribbon is grown while floating on the surface of a Si melt. In this paper, we describe the phenomenology of FSM, including the observation of approximately regularly spaced "facet lines" on the ribbon surface whose orientation aligns with (111) crystal planes. Sb demarcation experiments sectioned through the thickness of the ribbon reveal that the solid/melt interface consists of dual (111) planes and that the leading edge facet growth is saccadic in nature, rather than steady-state. To explain this behavior, we propose a heuristic solidification limit cycle theory, using a continuum level of description with anisotropic kinetics as developed by others, and generalizing the interface kinetics to include a roughening transition as well as a re-faceting mechanism that involves curvature and the Gibbs-Thomson effect.
Controlling the Limit-Cycle of the Ziegler Column via a Tuned Piezoelectric Damper
Francesco D’Annibale
2015-01-01
Full Text Available This paper is about the nonlinear analysis of a piezoelectric controlled Ziegler column. The piezoelectric controller, here referred to as Tuned Piezoelectric Damper (TPD, possesses evanescent characteristics and, moreover, it is tuned to the first natural frequency of the mechanical system, thus resembling the well-known Tuned Mass Damper. This means that the flow of energy between mechanical and electrical subsystems is driven by the resonance (Den Hartog principle and magnified by the singularity of the evanescent electrical characteristics. Numerical simulations, showing how the proposed control strategy is effective in increasing the linear stability domain and decreasing the amplitude of the limit-cycles in the postcritical range, are presented.
Normal form and limit cycle bifurcation of piecewise smooth differential systems with a center
Wei, Lijun; Zhang, Xiang
2016-07-01
In this paper we prove that any Σ-center (either nondegenerate or degenerate) of a planar piecewise Cr smooth vector field Z is topologically equivalent to that of Z0: (x ˙ , y ˙) = (- 1 , 2 x) for y ≥ 0, (x ˙ , y ˙) = (1 , 2 x) for y ≤ 0, and that the homeomorphism between Z and Z0 is Cr smoothness when restricted to each side of the switching line except at the center p. We illustrate by examples that there are degenerate Σ-centers whose flows are conjugate to that of Z0, and also there exist nondegenerate Σ-centers whose flows cannot be conjugate to that of Z0. Finally applying the normal form Z0 together with the piecewise smooth equivalence, we study the number of limit cycles which can be bifurcated from the Σ-center of Z.
D. S. Goll
2012-09-01
Full Text Available Terrestrial carbon (C cycle models applied for climate projections simulate a strong increase in net primary productivity (NPP due to elevated atmospheric CO_{2} concentration during the 21st century. These models usually neglect the limited availability of nitrogen (N and phosphorus (P, nutrients that commonly limit plant growth and soil carbon turnover. To investigate how the projected C sequestration is altered when stoichiometric constraints on C cycling are considered, we incorporated a P cycle into the land surface model JSBACH (Jena Scheme for Biosphere–Atmosphere Coupling in Hamburg, which already includes representations of coupled C and N cycles.
The model reveals a distinct geographic pattern of P and N limitation. Under the SRES (Special Report on Emissions Scenarios A1B scenario, the accumulated land C uptake between 1860 and 2100 is 13% (particularly at high latitudes and 16% (particularly at low latitudes lower in simulations with N and P cycling, respectively, than in simulations without nutrient cycles. The combined effect of both nutrients reduces land C uptake by 25% compared to simulations without N or P cycling. Nutrient limitation in general may be biased by the model simplicity, but the ranking of limitations is robust against the parameterization and the inflexibility of stoichiometry. After 2100, increased temperature and high CO_{2} concentration cause a shift from N to P limitation at high latitudes, while nutrient limitation in the tropics declines. The increase in P limitation at high-latitudes is induced by a strong increase in NPP and the low P sorption capacity of soils, while a decline in tropical NPP due to high autotrophic respiration rates alleviates N and P limitations. The quantification of P limitation remains challenging. The poorly constrained processes of soil P sorption and biochemical mineralization are identified as the main uncertainties in the strength of P limitation
Prediction of pilot induced oscillations
Valentin PANĂ
2011-03-01
Full Text Available An important problem in the design of flight-control systems for aircraft under pilotedcontrol is the determination of handling qualities and pilot-induced oscillations (PIO tendencieswhen significant nonlinearities exist in the vehicle description. The paper presents a method to detectpossible pilot-induced oscillations of Category II (with rate and position limiting, a phenomenonusually due to a misadaptation between the pilot and the aircraft response during some tasks in whichtight closed loop control of the aircraft is required from the pilot. For the analysis of Pilot in the LoopOscillations an approach, based on robust stability analysis of a system subject to uncertainparameters, is proposed. In this analysis the nonlinear elements are substituted by linear uncertainparameters. This approach assumes that PIO are characterized by a limit cycle behavior.
John Alexander Taborda
2014-04-01
Full Text Available In this paper, we propose a novel strategy for the synthesis and the classification of nonsmooth limit cycles and its bifurcations (named Non-Standard Bifurcations or Discontinuity Induced Bifurcations or DIBs in n-dimensional piecewise-smooth dynamical systems, particularly Continuous PWS and Discontinuous PWS (or Filippov-type PWS systems. The proposed qualitative approach explicitly includes two main aspects: multiple discontinuity boundaries (DBs in the phase space and multiple intersections between DBs (or corner manifolds—CMs. Previous classifications of DIBs of limit cycles have been restricted to generic cases with a single DB or a single CM. We use the definition of piecewise topological equivalence in order to synthesize all possibilities of nonsmooth limit cycles. Families, groups and subgroups of cycles are defined depending on smoothness zones and discontinuity boundaries (DB involved. The synthesized cycles are used to define bifurcation patterns when the system is perturbed with parametric changes. Four families of DIBs of limit cycles are defined depending on the properties of the cycles involved. Well-known and novel bifurcations can be classified using this approach.
Domínguez-Villar, David; Wang, Xianfeng; Krklec, Kristina; Cheng, Hai; Edwards, R. Lawrence
2016-04-01
We present a speleothem δ18O record from Kaite Cave in northern Iberian Peninsula covering the last 9.7 ka BP. The record is constructed from four different stalagmites that replicate each other. The age model is based on 63 U-Th dates and over 4500 laminae providing a robust time frame for the record. The δ18O record has characteristic millennial oscillations through the Holocene with periodicity around 2 ka during the Late Holocene and around 1 ka during the Early Holocene. Causes of the millennial δ18O variability are not dominated by the amount of rainfall or atmospheric temperature and other controls of the water cycle are more relevant. The aquifer at this site filters any seasonal bias and speleothems records the inter-annual δ18O variability in precipitation. On the other hand, moisture source analysis at this site shows that significant amount of precipitation is from recycled moisture (continental origin). A variable proportion of this parameter is capable to impact significantly past values of δ18O in precipitation. Thus, we interpret the millennial oscillations of the δ18O record as changes in the hydrological cycle resulting from variable percentages of the recycled precipitation over the Iberian Peninsula. We found that variable amount of recycled precipitation in Iberian Peninsula is related to the location of the Iceland Low pressure cell, although does not correlate with NAO index. Correlation of Kaite δ18O record during the Holocene with other representative records suggests that millennial oscillations are caused by variability of the Gulf Stream/North Atlantic Current that affects atmospheric pressure fields in the North Atlantic. Further correlation of Kaite δ18O record along the world supports that the recorded millennial oscillations of the water cycle are related to persistent variability on the tropical North Atlantic. Only during periods of major sea-ice variability in high-latitudes of the North Atlantic, the later region replaces
Genes adopt non-optimal codon usage to generate cell cycle-dependent oscillations in protein levels
Frenkel-Morgenstern, Milana; Danon, Tamar; Christian, Thomas
2012-01-01
The cell cycle is a temporal program that regulates DNA synthesis and cell division. When we compared the codon usage of cell cycle-regulated genes with that of other genes, we discovered that there is a significant preference for non-optimal codons. Moreover, genes encoding proteins that cycle a...
A Design Principle for a Posttranslational Biochemical Oscillator
Craig C. Jolley
2012-10-01
Full Text Available Multisite phosphorylation plays an important role in biological oscillators such as the circadian clock. Its general role, however, has been elusive. In this theoretical study, we show that a simple substrate with two modification sites acted upon by two opposing enzymes (e.g., a kinase and a phosphatase can show oscillations in its modification state. An unbiased computational analysis of this oscillator reveals two common characteristics: a unidirectional modification cycle and sequestering of an enzyme by a specific modification state. These two motifs cause a substrate to act as a coupled system in which a unidirectional cycle generates single-molecule oscillators, whereas sequestration synchronizes the population by limiting the available enzyme under conditions in which substrate is in excess. We also demonstrate the conditions under which the oscillation period is temperature compensated, an important feature of the circadian clock. This theoretical model will provide a framework for analyzing and synthesizing posttranslational oscillators.
Estimate of the upper limit of amplitude of Solar Cycle No. 23
Silbergleit, V. M; Larocca, P. A [Departamento de Fisica, UBA (Argentina)
2001-07-01
AA* indices of values greater than 60 10{sup -9} Tesla are considered in order to characterize geomagnetic storms since the available series of these indices comprise the years from 1868 to 1998 (The longest existing interval of geomagnetic activity). By applying the precursor technique we have performed an analysis of the storm periods and the solar activity, obtaining a good correlation between the number of storms ({alpha})(characterized by the AA* indices) and the amplitudes of each solar cycle ({zeta}) and those of the next ({mu}). Using the multiple regression method applied to {alpha}=A+B{zeta} +C{mu}, the constants are calculated and the values found are: A=-33 {+-}18, B= 0.74{+-}0.13 y C= 0.56{+-}0.13. The present statistical method indicates that the current solar cycle (number 23) would have an upper limit of 202{+-}57 monthy mean sunspots. This value indicates that the solar activity would be high causing important effects on the Earth's environment. [Spanish] Se consideran los valores de los indices AA* de valor mayor que 60 10{sup -9} Tesla para caracterizar tormentas geomagneticas ya que las series disponibles de estos indices van desde 1868 hasta 1998 (el mas largo intervalo de la actividad geomagnetica existente). Aplicando la tecnica del precursor hemos realizado un analisis de los periodos de tormentas y la actividad solar obteniendo una buena correlacion entre el numero de tormentas ({alpha}) (caracterizado por los indices AA*) y las amplitudes de los ciclos solares corriente ({zeta}) y el proximo ({mu}). Usando el metodo de regresion multiple aplicado a {alpha}=A+B{zeta} +C{mu}, las consonantes resultaron: A=-33 {+-}18, B= 0.74{+-}0.13 y C= 0.56{+-}0.13. El metodo estadistico presentado indica que el ciclo actual (numero 23) tendria un pico de 202{+-} 57 manchas mensuales promedio. Este valor indica que la actividad solar seria alta produciendo importantes efectos en el medio ambiente terrestre.
von Kann, S.; Snoeijer, Jacobus Hendrikus; van der Meer, Roger M.
2013-01-01
We present results for objects settling in a cornstarch suspension. Two surprising phenomena can be found in concentrated suspensions. First, the settling object does not attain a terminal velocity but exhibits oscillations around a terminal velocity when traveling through the bulk of the liquid. Se
Estimating the phase of synchronized oscillators
Revzen, Shai; Guckenheimer, John M.
2008-11-01
The state of a collection of phase-locked oscillators is determined by a single phase variable or cyclic coordinate. This paper presents a computational method, Phaser, for estimating the phase of phase-locked oscillators from limited amounts of multivariate data in the presence of noise and measurement errors. Measurements are assumed to be a collection of multidimensional time series. Each series consists of several cycles of the same or similar systems. The oscillators within each system are not assumed to be identical. Using measurements of the noise covariance for the multivariate input, data from the individual oscillators in the system are combined to reduce the variance of phase estimates for the whole system. The efficacy of the algorithm is demonstrated on experimental and model data from biomechanics of cockroach running and on simulated oscillators with varying levels of noise.
Phase reduction approach to synchronisation of nonlinear oscillators
Nakao, Hiroya
2016-04-01
Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are often modelled as nonlinear limit-cycle oscillators. In this article, we briefly review phase reduction theory, which is a simple and powerful method for analysing the synchronisation properties of limit-cycle oscillators exhibiting rhythmic dynamics. Through phase reduction theory, we can systematically simplify the nonlinear multi-dimensional differential equations describing a limit-cycle oscillator to a one-dimensional phase equation, which is much easier to analyse. Classical applications of this theory, i.e. the phase locking of an oscillator to a periodic external forcing and the mutual synchronisation of interacting oscillators, are explained. Further, more recent applications of this theory to the synchronisation of non-interacting oscillators induced by common noise and the dynamics of coupled oscillators on complex networks are discussed. We also comment on some recent advances in phase reduction theory for noise-driven oscillators and rhythmic spatiotemporal patterns.
Yasuda, Ichiro
2009-03-01
Time-series of Pacific Decadal Oscillation (PDO) reconstructed from tree-rings in Western North America is found to have a statistically significant periodicity of 18.6-year period lunar nodal tidal cycle; negative (positive) PDO tends to occur in the period of strong (weak) diurnal tide. In the 3rd and 5th (10th, 11th and 13rd) year after the maximum diurnal tide, mean-PDO takes significant negative (positive) value, suggesting that the Aleutian Low is weak (strong), western-central North Pacific in 30-50°N is warm (cool) and equator-eastern rim of the Pacific is cool (warm). This contributes to climate predictability with a time-table from the astronomical tidal cycle.
Smirnov, D A; Velazquez, J L P; Wennberg, R A; Bezruchko, B P
2005-01-01
We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D.A. Smirnov and B.P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely applicable. Namely, although the expressions for the estimators and their confidence bands are derived for linear uncoupled oscillators under the influence of independent sources of Gaussian white noise, they turn out to allow reliable characterization of coupling from relatively short time series for different properties of noise, significant phase nonlinearity of the oscillators, and non-vanishing coupling between them. We apply the estimators to analyze a two-channel human intracranial epileptic electroencephalogram (EEG) recording with the purpose of epileptic focus localization.
Mathematical Models of Biochemical Oscillations
Conrad, Emery David
1999-01-01
The goal of this paper is to explain the mathematics involved in modeling biochemical oscillations. We first discuss several important biochemical concepts fundamental to the construction of descriptive mathematical models. We review the basic theory of differential equations and stability analysis as it relates to two-variable models exhibiting oscillatory behavior. The importance of the Hopf Bifurcation will be discussed in detail for the central role it plays in limit cycle behavior and...
Chuderski, Adam; Andrelczyk, Krzysztof
2015-02-01
Several existing computational models of working memory (WM) have predicted a positive relationship (later confirmed empirically) between WM capacity and the individual ratio of theta to gamma oscillatory band lengths. These models assume that each gamma cycle represents one WM object (e.g., a binding of its features), whereas the theta cycle integrates such objects into the maintained list. As WM capacity strongly predicts reasoning, it might be expected that this ratio also predicts performance in reasoning tasks. However, no computational model has yet explained how the differences in the theta-to-gamma ratio found among adult individuals might contribute to their scores on a reasoning test. Here, we propose a novel model of how WM capacity constraints figural analogical reasoning, aimed at explaining inter-individual differences in reasoning scores in terms of the characteristics of oscillatory patterns in the brain. In the model, the gamma cycle encodes the bindings between objects/features and the roles they play in the relations processed. Asynchrony between consecutive gamma cycles results from lateral inhibition between oscillating bindings. Computer simulations showed that achieving the highest WM capacity required reaching the optimal level of inhibition. When too strong, this inhibition eliminated some bindings from WM, whereas, when inhibition was too weak, the bindings became unstable and fell apart or became improperly grouped. The model aptly replicated several empirical effects and the distribution of individual scores, as well as the patterns of correlations found in the 100-people sample attempting the same reasoning task. Most importantly, the model's reasoning performance strongly depended on its theta-to-gamma ratio in same way as the performance of human participants depended on their WM capacity. The data suggest that proper regulation of oscillations in the theta and gamma bands may be crucial for both high WM capacity and effective complex
Global dynamics of a stochastic neuronal oscillator
Yamanobe, Takanobu
2013-11-01
Nonlinear oscillators have been used to model neurons that fire periodically in the absence of input. These oscillators, which are called neuronal oscillators, share some common response structures with other biological oscillations such as cardiac cells. In this study, we analyze the dependence of the global dynamics of an impulse-driven stochastic neuronal oscillator on the relaxation rate to the limit cycle, the strength of the intrinsic noise, and the impulsive input parameters. To do this, we use a Markov operator that both reflects the density evolution of the oscillator and is an extension of the phase transition curve, which describes the phase shift due to a single isolated impulse. Previously, we derived the Markov operator for the finite relaxation rate that describes the dynamics of the entire phase plane. Here, we construct a Markov operator for the infinite relaxation rate that describes the stochastic dynamics restricted to the limit cycle. In both cases, the response of the stochastic neuronal oscillator to time-varying impulses is described by a product of Markov operators. Furthermore, we calculate the number of spikes between two consecutive impulses to relate the dynamics of the oscillator to the number of spikes per unit time and the interspike interval density. Specifically, we analyze the dynamics of the number of spikes per unit time based on the properties of the Markov operators. Each Markov operator can be decomposed into stationary and transient components based on the properties of the eigenvalues and eigenfunctions. This allows us to evaluate the difference in the number of spikes per unit time between the stationary and transient responses of the oscillator, which we show to be based on the dependence of the oscillator on past activity. Our analysis shows how the duration of the past neuronal activity depends on the relaxation rate, the noise strength, and the impulsive input parameters.
Hydrodynamic synchronization of nonlinear oscillators at low Reynolds number.
Leoni, M; Liverpool, T B
2012-04-01
We introduce a generic model of a weakly nonlinear self-sustained oscillator as a simplified tool to study synchronization in a fluid at low Reynolds number. By averaging over the fast degrees of freedom, we examine the effect of hydrodynamic interactions on the slow dynamics of two oscillators and show that they can lead to synchronization. Furthermore, we find that synchronization is strongly enhanced when the oscillators are nonisochronous, which on the limit cycle means the oscillations have an amplitude-dependent frequency. Nonisochronity is determined by a nonlinear coupling α being nonzero. We find that its (α) sign determines if they synchronize in phase or antiphase. We then study an infinite array of oscillators in the long-wavelength limit, in the presence of noise. For α>0, hydrodynamic interactions can lead to a homogeneous synchronized state. Numerical simulations for a finite number of oscillators confirm this and, when α<0, show the propagation of waves, reminiscent of metachronal coordination.
Scafetta, Nicola
2013-01-01
Power spectra of global surface temperature (GST) records reveal major periodicities at about 9.1, 10-11, 19-22 and 59-62 years. The Coupled Model Intercomparison Project 5 (CMIP5) general circulation models (GCMs), to be used in the IPCC (2013), are analyzed and found not able to reconstruct this variability. From 2000 to 2013.5 a GST plateau is observed while the GCMs predicted a warming rate of about 2 K/century. In contrast, the hypothesis that the climate is regulated by specific natural oscillations more accurately fits the GST records at multiple time scales. The climate sensitivity to CO2 doubling should be reduced by half, e.g. from the IPCC-2007 2.0-4.5 K range to 1.0-2.3 K with 1.5 C median. Also modern paleoclimatic temperature reconstructions yield the same conclusion. The observed natural oscillations could be driven by astronomical forcings. Herein I propose a semi empirical climate model made of six specific astronomical oscillations as constructors of the natural climate variability spanning ...
Suppression of oscillations in mean-field diffusion
Neeraj Kumar Kamal; Pooja Rani Sharma; Manish Dev Shrimali
2015-02-01
We study the role of mean-field diffusive coupling on suppression of oscillations for systems of limit cycle oscillators. We show that this coupling scheme not only induces amplitude death (AD) but also oscillation death (OD) in coupled identical systems. The suppression of oscillations in the parameter space crucially depends on the value of mean-field diffusion parameter. It is also found that the transition from oscillatory solutions to OD in conjugate coupling case is different from the case when the coupling is through similar variable. We rationalize our study using linear stability analysis.
Gust, Kurt A; Collier, Zachary A; Mayo, Michael L; Stanley, Jacob K; Gong, Ping; Chappell, Mark A
2016-07-01
Life cycle assessment (LCA) has considerable merit for holistic evaluation of product planning, development, production, and disposal, with the inherent benefit of providing a forecast of potential health and environmental impacts. However, a technical review of current life cycle impact assessment (LCIA) methods revealed limitations within the biological effects assessment protocols, including: simplistic assessment approaches and models; an inability to integrate emerging types of toxicity data; a reliance on linear impact assessment models; a lack of methods to mitigate uncertainty; and no explicit consideration of effects in species of concern. The purpose of the current study is to demonstrate that a new concept in toxicological and regulatory assessment, the adverse outcome pathway (AOP), has many useful attributes of potential use to ameliorate many of these problems, to expand data utility and model robustness, and to enable more accurate and defensible biological effects assessments within LCIA. Background, context, and examples have been provided to demonstrate these potential benefits. We additionally propose that these benefits can be most effectively realized through development of quantitative AOPs (qAOPs) crafted to meet the needs of the LCIA framework. As a means to stimulate qAOP research and development in support of LCIA, we propose 3 conceptual classes of qAOP, each with unique inherent attributes for supporting LCIA: 1) mechanistic, including computational toxicology models; 2) probabilistic, including Bayesian networks and supervised machine learning models; and 3) weight of evidence, including models built using decision-analytic methods. Overall, we have highlighted a number of potential applications of qAOPs that can refine and add value to LCIA. As the AOP concept and support framework matures, we see the potential for qAOPs to serve a foundational role for next-generation effects characterization within LCIA. Integr Environ Assess Manag
Core-oscillator model of Caulobacter crescentus
Vandecan, Yves; Biondi, Emanuele; Blossey, Ralf
2016-06-01
The gram-negative bacterium Caulobacter crescentus is a powerful model organism for studies of bacterial cell cycle regulation. Although the major regulators and their connections in Caulobacter have been identified, it still is a challenge to properly understand the dynamics of its circuitry which accounts for both cell cycle progression and arrest. We show that the key decision module in Caulobacter is built from a limit cycle oscillator which controls the DNA replication program. The effect of an induced cell cycle arrest is demonstrated to be a key feature to classify the underlying dynamics.
Nonlinear self-excited oscillations of a ducted flame
Dowling, A. P.
1997-09-01
Self-excited oscillations of a confined flame, burning in the wake of a bluff-body flame-holder, are considered. These oscillations occur due to interaction between unsteady combustion and acoustic waves. According to linear theory, flow disturbances grow exponentially with time. A theory for nonlinear oscillations is developed, exploiting the fact that the main nonlinearity is in the heat release rate, which essentially ‘saturates’. The amplitudes of the pressure fluctuations are sufficiently small that the acoustic waves remain linear. The time evolution of the oscillations is determined by numerical integration and inclusion of nonlinear effects is found to lead to limit cycles of finite amplitude. The predicted limit cycles are compared with results from experiments and from linear theory. The amplitudes and spectra of the limit-cycle oscillations are in reasonable agreement with experiment. Linear theory is found to predict the frequency and mode shape of the nonlinear oscillations remarkably well. Moreover, we find that, for this type of nonlinearity, describing function analysis enables a good estimate of the limit-cycle amplitude to be obtained from linear theory.
Wright, A Harrison; DeLong, John M; Gunawardena, Arunika H L A N; Prange, Robert K
2011-03-01
The lower oxygen limit (LOL) in plants may be identified through the measure of respiratory gases [i.e. the anaerobic compensation point (ACP) or the respiratory quotient breakpoint (RQB)], but recent work shows it may also be identified by a sudden rise in dark minimum fluorescence (F(o)). The interrelationship between aerobic respiration and fermentative metabolism, which occur in the mitochondria and cytosol, respectively, and fluorescence, which emanates from the chloroplasts, is not well documented in the literature. Using spinach (Spinacia oleracea), this study showed that F(o) and photochemical quenching (q(P)) remained relatively unchanged until O(2) levels dropped below the LOL. An over-reduction of the plastoquinone (PQ) pool is believed to increase F(o) under dark + anoxic conditions. It is proposed that excess cytosolic reductant due to inhibition of the mitochondria's cytochrome oxidase under low-O(2), may be the primary reductant source. The maximum fluorescence (F(m)) is largely unaffected by low-O(2) in the dark, but was severely quenched, mirroring changes to the xanthophyll de-epoxidation state (DEPS), under even low-intensity light (≈4 μmol m(-2) s(-1)). In low light, the low-O(2)-induced increase in F(o) was also quenched, likely by non-photochemical and photochemical means. The degree of quenching in the light was negatively correlated with the level of ethanol fermentation in the dark. A discussion detailing the possible roles of cyclic electron flow, the xanthophyll cycle, chlororespiration and a pathway we termed 'chlorofermentation' were used to interpret fluorescence phenomena of both spinach and apple (Malus domestica) over a range of atmospheric conditions under both dark and low-light.
Real-time wavelet detection of crashes in limit cycles of non-stationary fusion plasmas
Berkel, M. van, E-mail: m.v.berkel@tue.nl [Eindhoven University of Technology, Department of Mechanical Engineering, Control Systems Technology Group, PO Box 513, 5600 MB Eindhoven (Netherlands); FOM-Institute for Plasma Physics Rijnhuizen, Association EURATOM-FOM, Trilateral Euregio Cluster, PO Box 1207, 3430 BE Nieuwegein (Netherlands); Witvoet, G.; Baar, M.R. de [Eindhoven University of Technology, Department of Mechanical Engineering, Control Systems Technology Group, PO Box 513, 5600 MB Eindhoven (Netherlands); FOM-Institute for Plasma Physics Rijnhuizen, Association EURATOM-FOM, Trilateral Euregio Cluster, PO Box 1207, 3430 BE Nieuwegein (Netherlands); Nuij, P.W.J.M. [Eindhoven University of Technology, Department of Mechanical Engineering, Control Systems Technology Group, PO Box 513, 5600 MB Eindhoven (Netherlands); Morsche, H.G. ter [Eindhoven University of Technology, Department of Mathematics and Computer Science, PO Box 513, 5600 MB Eindhoven (Netherlands); Steinbuch, M. [Eindhoven University of Technology, Department of Mechanical Engineering, Control Systems Technology Group, PO Box 513, 5600 MB Eindhoven (Netherlands)
2011-12-15
Highlights: Black-Right-Pointing-Pointer We propose a new wavelet-based method for accurate and robust detection of limit cycle crashes in fusion plasmas. Black-Right-Pointing-Pointer The method is optimized for real-time applications such that it has small delay. Black-Right-Pointing-Pointer The method is implemented in a real-time algorithm and is tested on experimental data. Black-Right-Pointing-Pointer Almost all crashes are detected flawlessly including off-waveforms with high SNR. - Abstract: The high performance mode (H-mode) is one of the baseline plasma scenarios for the experimental fusion reactor ITER. This scenario features a periodic crash-like reorganization of the plasma pressure and the magnetic flux in the plasma core and plasma periphery. The core instability is often referred to as the sawtooth instability while the instability at the edge of the plasma is referred to as ELM. In this paper we present an algorithm for optimized (low latency, robust and high fidelity) real-time sensing of the crashes. The algorithm is based on time-scale wavelet theory and edge-detection. It is argued that detection of crashes has considerably less delay than the other methods. The realized accuracy of the detection algorithm is well below the uncertainty of the crash period for most crashes. Multiresolution analysis enables distinction between different sizes of sawtooth crashes due to the different sizes of wavelets (scales), resulting in an algorithm, which is robust and accurate. Although strictly speaking, the crash detection method is demonstrated for sawteeth measured with ECE only, it can be applied to any periodic crash, measured with any temporally resolved data. Note that the possibility of differentiating between crash like events of different nature depends on their individual time-scales and used measurement setup.
The hype cycle in 3D displays: inherent limits of autostereoscopy
Grasnick, Armin
2013-06-01
Since a couple of years, a renaissance of 3dimensional cinema can be observed. Even though the stereoscopy was quite popular within the last 150 years, the 3d cinema has disappeared and re-established itself several times. The first boom in the late 19th century stagnated and vanished after a few years of success, the same happened again in 50's and 80's of the 20th century. With the commercial success of the 3d blockbuster "Avatar" in 2009, at the latest, it is obvious that the 3d cinema is having a comeback. How long will it last this time? There are already some signs of a declining interest in 3d movies, as the discrepancy between expectations and the results delivered becomes more evident. From the former hypes it is known: After an initial phase of curiosity (high expectations and excessive fault tolerance), a phase of frustration and saturation (critical analysis and subsequent disappointment) will follow. This phenomenon is known as "Hype Cycle" The everyday experienced evolution of technology has conditioned the consumers. The expectation "any technical improvement will preserve all previous properties" cannot be fulfilled with present 3d technologies. This is an inherent problem of stereoscopy and autostereoscopy: The presentation of an additional dimension caused concessions in relevant characteristics (i.e. resolution, brightness, frequency, viewing area) or leads to undesirable physical side effects (i.e. subjective discomfort, eye strain, spatial disorientation, feeling of nausea). It will be verified that the 3d apparatus (3d glasses or 3d display) is also the source for these restrictions and a reason for decreasing fascination. The limitations of present autostereoscopic technologies will be explained.
Evidence That the Pi Release Event Is the Rate-Limiting Step in the Nitrogenase Catalytic Cycle.
Yang, Zhi-Yong; Ledbetter, Rhesa; Shaw, Sudipta; Pence, Natasha; Tokmina-Lukaszewska, Monika; Eilers, Brian; Guo, Qingjuan; Pokhrel, Nilisha; Cash, Valerie L; Dean, Dennis R; Antony, Edwin; Bothner, Brian; Peters, John W; Seefeldt, Lance C
2016-07-05
Nitrogenase reduction of dinitrogen (N2) to ammonia (NH3) involves a sequence of events that occur upon the transient association of the reduced Fe protein containing two ATP molecules with the MoFe protein that includes electron transfer, ATP hydrolysis, Pi release, and dissociation of the oxidized, ADP-containing Fe protein from the reduced MoFe protein. Numerous kinetic studies using the nonphysiological electron donor dithionite have suggested that the rate-limiting step in this reaction cycle is the dissociation of the Fe protein from the MoFe protein. Here, we have established the rate constants for each of the key steps in the catalytic cycle using the physiological reductant flavodoxin protein in its hydroquinone state. The findings indicate that with this reductant, the rate-limiting step in the reaction cycle is not protein-protein dissociation or reduction of the oxidized Fe protein, but rather events associated with the Pi release step. Further, it is demonstrated that (i) Fe protein transfers only one electron to MoFe protein in each Fe protein cycle coupled with hydrolysis of two ATP molecules, (ii) the oxidized Fe protein is not reduced when bound to MoFe protein, and (iii) the Fe protein interacts with flavodoxin using the same binding interface that is used with the MoFe protein. These findings allow a revision of the rate-limiting step in the nitrogenase Fe protein cycle.
Life cycle assessment as a method of limitation of a negative environment impact of castings
M. Holtzer
2011-07-01
Full Text Available Casting production constitutes environmental problems going far beyond the foundry plant area. Applying a notion of the life cycle the input (suppliers side and output factors (clients side can be identified. The foundry plant activities for the environment hazard mitigation can be situated on various stages of the casting life cycle. The environment impact of motorisation castings made of different materials – during the whole life cycle of castings – are discussed in the paper. It starts from the charge material production, then follows via the casting process, car assembly, car exploitation and ends at the car breaking up for scrap.
Cell cycle phase expansion in nitrogen-limited cultures of Saccharomyces cerevisiae
1980-01-01
The time and coordination of cell cycle events were examined in the budding yeast Saccharomyces cerevisiae. Whole-cell autoradiographic techniques and time-lapse photography were used to measure the duration of the S, G1, and G2 phases, and the cell cycle positions of "start" and bud emergence, in cells whose growth rates were determined by the source of nitrogen. It was observed that the G1, S, and G2 phases underwent a proportional expansion with increasing cell cycle length, with the S pha...
Formation of multiple subpulses in a free-electron laser operating in the limit-cycle mode
Knippels, G.M.H.; van der Meer, A. F. G.; Mols, Rfxam; Oepts, D.; van Amersfoort, P. W.
1996-01-01
The evolution of the longitudinal pulse shape and the spectrum of the short-pulse, far-infrared free-electron laser FELIX are investigated. Depending on the amount of cavity desynchronization applied, the laser is found to operate in the stable-focus mode or in the limit-cycle mode. In the latter ca
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing
2010-12-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
National Aeronautics and Space Administration — The proposed research program will develop a physics-based identification, modeling and risk management infrastructure for aeroelastic transonic flutter and...
Paramonov, Guennaddi K; Bandrauk, Andre D
2016-01-01
Non Born-Oppenheimer quantum dynamics of H$_{2}^{+}$ excited by shaped one-cycle laser pulses linearly polarized along the molecular axis have been studied by the numerical solution of the time-dependent Schr\\"odinger equation within a %three-body three-dimensional model, including the internuclear separation, $R$, and the electron coordinates $z$ and $\\rho$. Laser carrier frequencies corresponding to the wavelengths $\\lambda_{l}=25$~nm through $\\lambda_{l}=400$~nm were used and the amplitudes of the pulses were chosen such that the energy of H$_{2}^{+}$ was close to its dissociation threshold at the end of any laser pulse applied. It is shown that there exists a characteristic oscillation frequency $\\omega_{\\rm osc} \\simeq 0.2265$~au (corresponding to the period of $\\tau_{\\rm osc} \\simeq 0.671$~fs and the wavelength of $\\lambda_{\\rm osc} \\simeq 200$~nm) that manifests itself as a "carrier" frequency of temporally shaped oscillations of the time-dependent expectation values $\\langle z \\rangle$ and $\\langle \\p...
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2007-01-01
The North Atlantic Oscillation (NAO) is one of the leading modes of climate variability in the Northern Hemisphere. It has been shown that it clearly relates to changes in meteorological variables, such as surface temperature, at hemispherical scales. However, recent studies have revealed that the NAO spatial pattern also depends upon solar forcing. The refore, its effects on meteorological variables must vary depending upon this factor. Moreover, it could be that the Sun affects climate through variability patterns, a hypothesis that is the focus of this study. We find that the relationship between the NAO/AO and hemispheric temperature varies depending upon solar activity. The results show a positive significant correlation only when solar activity is high. Also, the results support the idea that solar activity influences tropospheric climate fluctuations in the Northern Hemisphere via the fluctuations of the stratospheric polar vortex.
Human TRIB2 Oscillates during the Cell Cycle and Promotes Ubiquitination and Degradation of CDC25C
Liang, Kai Ling; Paredes, Roberto; Carmody, Ruaidhri; Eyers, Patrick A.; Meyer, Stefan; McCarthy, Tommie V.; Keeshan, Karen
2016-01-01
Tribbles homolog 2 (TRIB2) is a member of the mammalian Tribbles family of serine/threonine pseudokinases (TRIB1-3). Studies of TRIB2 indicate that many of the molecular interactions between the single Drosophila Tribbles (Trbl) protein and interacting partners are evolutionary conserved. In this study, we examined the relationship between TRIB2 and cell division cycle 25 (CDC25) family of dual-specificity protein phosphatases (mammalian homologues of Drosophila String), which are key physiological cell cycle regulators. Using co-immunoprecipitation we demonstrate that TRIB2 interacts with CDC25B and CDC25C selectively. Forced overexpression of TRIB2 caused a marked decrease in total CDC25C protein levels. Following inhibition of the proteasome, CDC25C was stabilized in the nuclear compartment. This implicates TRIB2 as a regulator of nuclear CDC25C turnover. In complementary ubiquitination assays, we show that TRIB2-mediated degradation of CDC25C is associated with lysine-48-linked CDC25C polyubiquitination driven by the TRIB2 kinase-like domain. A cell cycle associated role for TRIB2 is further supported by the cell cycle regulated expression of TRIB2 protein levels. Our findings reveal mitotic CDC25C as a new target of TRIB2 that is degraded via the ubiquitin proteasome system. Inappropriate CDC25C regulation could mechanistically underlie TRIB2 mediated regulation of cellular proliferation in neoplastic cells. PMID:27563873
Köhn, Jörg
2010-01-01
We propose a scheme for ultrafast real-time imaging of laser-induced collective electron oscillations (Mie plasmons) in gas phase metal clusters by interferometrically stable scanning of two intense few-cycle optical laser pulses. The feasibility of our nonlinear spectral interferometry method with experimentally accessible observables is tested in a theoretical case study on simple-metal clusters (Na$_{147}$). The results show that the plasmon period and lifetime as well as the phase and relative amplitude of the collective electron motion can be extracted with sub-fs resolution. The access to nonlinear response effects, as the demonstrated increase of the plasmon lifetime with laser intensity due to ionization-induced contraction of the electron cloud, opens up vast opportunities for interrogating ultrafast many-particle dynamics in nanosystems under strong laser fields with unprecedented resolution.
Zhang, Hengli; Liu, Xiaomeng; Li, Daijun; Shi, Peng; Schell, Alex; Haas, Claus Rüdige; Du, Keming
2007-09-10
A near-diffraction-limited, stable, 18 mJ green source with a pulse width of 16.7 ns was generated at a 1 kHz repetition rate by frequency doubling of diode stacks end-pumped electro-optically Q-switched slab Nd:YAG oscillator-amplifier system. The pump to green optical conversion efficiency was 10.7%. At the output energy of 15 mJ at 532 nm, the M2 factors were 1.3 and 1.7 in the unstable and stable directions, respectively. The energy pulse stability was approximately 0.8%.
The limits of the possible: models of power supply and demand in cycling.
Olds, T; Norton, K; Craig, N; Olive, S; Lowe, E
1995-06-01
This paper outlines a general strategy for mathematical modeling of cycling performance. This strategy involves formulating one expression describing the power available for external work from physiological sources. The variables used in this expression include maximal aerobic power (VO2max), fractional utilisation of VO2max, mechanical efficiency, maximal accumulated oxygen deficit, and the time constants relating to the expression of aerobic and anaerobic capacities. A second expression describing the power demand of cycling is then constructed. The variables used in this expression include the mass, projected frontal area and drag characteristics of the system, the coefficient of rolling resistance, environmental variables such as temperature, barometric pressure, relative humidity, wind speed and direction and the slope of the course. The two expressions are equated and solved using an iterative procedure. Two series of trials were used to assess the predictive accuracy of the model, one using track endurance performances and the other a 26 km road time-trial. The correlations between actual and predicted times have been excellent (0.92-0.95, p cycling performance. A range of options designed to improve cycling performance is described.
Annual cycle of Antarctic baseline aerosol: controlled by photooxidation-limited aerosol formation
M. Fiebig
2013-09-01
Full Text Available This article investigates the annual cycle observed in the Antarctic baseline aerosol scattering coefficient, total particle number concentration, and particle number size distribution (PNSD as measured at Troll Atmospheric Observatory. Mie-theory shows that the annual cycles in microphysical and optical aerosol properties have a common cause. By comparison with observations at other Antarctic stations, it is shown that the annual cycle is not a local phenomenon, but common to Central Antarctic baseline air masses. Observations of ground-level ozone at Troll as well as backward plume calculations for the air masses arriving at Troll demonstrate that the baseline air masses originate from the free troposphere and lower stratosphere region, and descend over the Central Antarctic continent. The Antarctic summer PNSD is dominated by particles with diameters 3/(MJ m. Further research is proposed to investigate the applicability of this number to other atmospheric reservoirs, and to use the observed annual cycle in Antarctic baseline aerosol properties as a benchmark for the representation of natural atmospheric aerosol processes in climate models.
Cohen, S.A.; Hosea, J.C.; Timberlake, J.R.
1984-10-19
A limiter with a specially contoured front face is provided. The front face of the limiter (the plasma-side face) is flat with a central indentation. In addition, the limiter shape is cylindrically symmetric so that the limiter can be rotated for greater heat distribution. This limiter shape accommodates the various power scrape-off distances lambda p, which depend on the parallel velocity, V/sub parallel/, of the impacting particles.
Efimov-like phase of a three-stranded DNA and the renormalization-group limit cycle
Pal, Tanmoy; Sadhukhan, Poulomi; Bhattacharjee, Somendra M.
2015-04-01
A three-stranded DNA with short range base pairings only is known to exhibit a classical analog of the quantum Efimov effect, viz., a three-chain bound state at the two-chain melting point where no two are bound. By using a nonperturbative renormalization-group method for a rigid duplex DNA and a flexible third strand, with base pairings and strand exchange, we show that the Efimov-DNA is associated with a limit cycle type behavior of the flow of an effective three-chain interaction. The analysis also shows that thermally generated bubbles play an essential role in producing the effect. A toy model for the flow equations shows the limit cycle in an extended three-dimensional parameter space of the two-chain coupling and a complex three-chain interaction.
Yusen Wu
2015-01-01
Full Text Available With the aid of computer algebra system Mathematica 8.0 and by the integral factor method, for a family of generalized nilpotent systems, we first compute the first several quasi-Lyapunov constants, by vanishing them and rigorous proof, and then we get sufficient and necessary conditions under which the systems admit analytic centers at the origin. In addition, we present that seven amplitude limit cycles can be created from the origin. As an example, we give a concrete system with seven limit cycles via parameter perturbations to illustrate our conclusion. An interesting phenomenon is that the exponent parameter n controls the singular point type of the studied system. The main results generalize and improve the previously known results in Pan.
Bulcsú eSándor
2015-12-01
Full Text Available We investigate the sensorimotor loop of simple robots simulated within the LPZRobots environment from the point of view of dynamical systems theory. For a robot with a cylindrical shaped body and an actuator controlled by a single proprioceptual neuron we find various types of periodic motions in terms of stable limit cycles. These are self-organized in the sense, that the dynamics of the actuator kicks in only, for a certain range of parameters, when the barrel is already rolling, stopping otherwise. The stability of the resulting rolling motions terminates generally, as a function of the control parameters, at points where fold bifurcations of limit cycles occur. We find that several branches of motion types exist for the same parameters, in terms of the relative frequencies of the barrel and of the actuator, having each their respective basins of attractions in terms of initial conditions. For low drivings stable limit cycles describing periodic and drifting back-and-forth motions are found additionally. These modes allow to generate symmetry breaking explorative behavior purely by the timing an otherwise neutral signal with respect to the cyclic back-and-forth motion of the robot.
Sándor, Bulcsú; Martin, Laura; Gros, Claudius
2016-01-01
We investigate the sensorimotor loop of simple robots simulated within the LPZRobots environment from the point of view of dynamical systems theory. For a robot with a cylindrical shaped body and an actuator controlled by a single proprioceptual neuron we find various types of periodic motions in terms of stable limit cycles. These are self-organized in the sense, that the dynamics of the actuator kicks in only, for a certain range of parameters, when the barrel is already rolling, stopping otherwise. The stability of the resulting rolling motions terminates generally, as a function of the control parameters, at points where fold bifurcations of limit cycles occur. We find that several branches of motion types exist for the same parameters, in terms of the relative frequencies of the barrel and of the actuator, having each their respective basins of attractions in terms of initial conditions. For low drivings stable limit cycles describing periodic and drifting back-and-forth motions are found additionally. T...
Life cycle-based water assessment of a hand dishwashing product: opportunities and limitations.
Van Hoof, Gert; Buyle, Bea; Kounina, Anna; Humbert, Sebastien
2013-10-01
It is only recently that life cycle-based indicators have been used to evaluate products from a water use impact perspective. The applicability of some of these methods has been primarily demonstrated on agricultural materials or products, because irrigation requirements in food production can be water-intensive. In view of an increasing interest on life cycle-based water indicators from different products, we ran a study on a hand dishwashing product. A number of water assessment methods were applied with the purpose of identifying both product improvement opportunities, as well as understanding the potential for underlying database and methodological improvements. The study covered the entire life cycle of the product and focused on environmental issues related to water use, looking in-depth at inventory, midpoint, and endpoint methods. "Traditional" water emission driven methods, such as freshwater eutrophication, were excluded from the analysis. The use of a single formula with the same global supply chain, manufactured in 1 location was evaluated in 2 countries with different water scarcity conditions. The study shows differences ranging up to 4 orders in magnitude for indicators with similar units associated with different water use types (inventory methods) and different cause-effect chain models (midpoint and endpoint impact categories). No uncertainty information was available on the impact assessment methods, whereas uncertainty from stochastic variability was not available at the time of study. For the majority of the indicators studied, the contribution from the consumer use stage is the most important (>90%), driven by both direct water use (dishwashing process) as well as indirect water use (electricity generation to heat the water). Creating consumer awareness on how the product is used, particularly in water-scarce areas, is the largest improvement opportunity for a hand dishwashing product. However, spatial differentiation in the inventory and
Rannama, Indrek; Port, Kristjan; Bazanov, Boriss
2012-01-01
Maximum gears for youth category riders are limited. As a result, youth category riders are regularly compelled to ride in a high cadence regime. The aim of this study was to investigate if regular work at high cadence regime due to limited transmission in youth category riders reflects in effectual cadence at the point of maximal power generation during the 10 second sprint effort. 24 junior and youth national team cyclist’s average maximal peak power at various cadence regimes was registere...
Turconi, Roberto; Boldrin, Alessio; Astrup, Thomas Fruergaard
2013-01-01
identified as follows: the energy recovery efficiency and the flue gas cleaning system for fossil fuel technologies; the electricity mix used during both the manufacturing and the construction phases for nuclear and renewable technologies; and the type, quality and origin of feedstock, as well as the amount......Electricity generation is a key contributor to global emissions of greenhouse gases (GHG), NOx and SO2 and their related environmental impact. A critical review of 167 case studies involving the life cycle assessment (LCA) of electricity generation based on hard coal, lignite, natural gas, oil...
Sarah R Smith
2016-12-01
Full Text Available Environmental fluctuations affect distribution, growth and abundance of diatoms in nature, with iron (Fe availability playing a central role. Studies on the response of diatoms to low Fe have either utilized continuous (24 hr illumination or sampled a single time of day, missing any temporal dynamics. We profiled the physiology, metabolite composition, and global transcripts of the pennate diatom Phaeodactylum tricornutum during steady-state growth at low, intermediate, and high levels of dissolved Fe over light:dark cycles, to better understand fundamental aspects of genetic control of physiological acclimation to growth under Fe-limitation. We greatly expand the catalog of genes involved in the low Fe response, highlighting the importance of intracellular trafficking in Fe-limited diatoms. P. tricornutum exhibited transcriptomic hallmarks of slowed growth leading to prolonged periods of cell division/silica deposition, which could impact biogeochemical carbon sequestration in Fe-limited regions. Light harvesting and ribosome biogenesis transcripts were generally reduced under low Fe while transcript levels for genes putatively involved in the acquisition and recycling of Fe were increased. We also noted shifts in expression towards increased synthesis and catabolism of branched chain amino acids in P. tricornutum grown at low Fe whereas expression of genes involved in central core metabolism were relatively unaffected, indicating that essential cellular function is protected. Beyond the response of P. tricornutum to low Fe, we observed major coordinated shifts in transcript control of primary and intermediate metabolism over light:dark cycles which contribute to a new view of the significance of distinctive diatom pathways, such as mitochondrial glycolysis and the ornithine-urea cycle. This study provides new insight into transcriptional modulation of diatom physiology and metabolism across light:dark cycles in response to Fe availability
The limits of bioenergy for mitigating global life-cycle greenhouse gas emissions from fossil fuels
Staples, Mark D.; Malina, Robert; Barrett, Steven R. H.
2017-01-01
The size of the global bioenergy resource has been studied extensively; however, the corresponding life-cycle greenhouse gas benefit of bioenergy remains largely unexplored at the global scale. Here we quantify the optimal use of global bioenergy resources to offset fossil fuels in 2050. We find that bioenergy could reduce life-cycle emissions from fossil fuel-derived electricity and heat, and liquid fuels, by a maximum of 4.9-38.7 Gt CO2e, or 9-68%, and that offsetting electricity and heat with bioenergy is on average 1.6-3.9 times more effective for emissions mitigation than offsetting liquid fuels. At the same time, liquid fuels make up 18-49% of the optimal allocation of bioenergy in our results for 2050, indicating that a mix of bioenergy end-uses maximizes life-cycle emissions reductions. Finally, emissions reductions are maximized by limiting deployment of total available primary bioenergy to 29-91% in our analysis, demonstrating that life-cycle emissions are a constraint on the usefulness of bioenergy for mitigating global climate change.
Nicholas Stacey
2012-11-01
Full Text Available A WHO and UNICEF joint report states that in 2008, 884 million people lacked access to potable drinking water. A life-cycle approach to develop potable water systems may improve the sustainability for such systems, however, a review of the literature shows that such an approach has primarily been used for urban systems located in resourced countries. Although urbanization is increasing globally, over 40 percent of the world’s population is currently rural with many considered poor. In this paper, we present a first step towards using life-cycle assessment to develop sustainable rural water systems in resource-limited countries while pointing out the needs. For example, while there are few differences in costs and environmental impacts for many improved rural water system options, a system that uses groundwater with community standpipes is substantially lower in cost that other alternatives with a somewhat lower environmental inventory. However, a LCA approach shows that from institutional as well as community and managerial perspectives, sustainability includes many other factors besides cost and environment that are a function of the interdependent decision process used across the life cycle of a water system by aid organizations, water user committees, and household users. These factors often present the biggest challenge to designing sustainable rural water systems for resource-limited countries.
Surjo R Soekadar
2014-03-01
Full Text Available Objective: Transcranial direct current stimulation (tDCS improves motor learning and can influence emotional processing or attention. However, it remained unclear whether learned electroencephalography (EEG-based brain-machine interface (BMI control during tDCS is feasible and how application of transcranial electric currents during BMI control would interfere with feature-extraction of physiological brain signals. Here we tested this combination and evaluated stimulation-dependent artifacts across different EEG frequencies and stability of motor imagery-based BMI control. Approach: Ten healthy volunteers were invited to two BMI-sessions, each comprising two 60-trial blocks. During the trials, modulation of mu-rhythms (8-15Hz associated with motor imagery recorded over C4 was translated into online cursor movements on a computer screen. During block 2, either sham (session A or anodal tDCS (session B was applied at 1mA with the stimulation electrode placed 1cm anterior of C4. Main results: tDCS was associated with a significant signal power increase in the lower frequencies most evident in the signal spectrum of the EEG channel closest to the stimulation electrode. Stimulation-dependent signal power increase exhibited a decay of 12dB per decade, leaving frequencies above 9Hz unaffected. Analysis of BMI control performance did not indicate a difference between blocks and tDCS conditions. Conclusion: Application of tDCS during learned EEG-based self-regulation of brain oscillations above 9Hz is feasible and safe, and might improve applicability of BMI systems in patient populations.
A criterion for high-cycle fatigue life and fatigue limit prediction in biaxial loading conditions
ukasz Pejkowski; Dariusz Skibicki
2016-01-01
This paper presents a criterion for high-cycle fatigue life and fatigue strength estimation under periodic proportional and non-proportional cyclic loading. The cri-terion is based on the mean and maximum values of the second invariant of the stress deviator. Important elements of the criterion are: function of the non-proportionality of fatigue loading and the materials parameter that expresses the materials sensitivity to non-proportional loading. The methods for the materials parameters determination uses three S–N curves: tension–compression, torsion, and any non-proportional loading proposed. The criterion has been verified using experimental data, and the results are included in the paper. These results should be considered as promis-ing. The paper also includes a proposal for multiaxial fatigue models classification due to the approach for the non-proportionality of loading.
Nutrient limitation and physiology mediate the fine-scale (de)coupling of biogeochemical cycles.
Appling, Alison P; Heffernan, James B
2014-09-01
Nutrients in the environment are coupled over broad timescales (days to seasons) when organisms add or withdraw multiple nutrients simultaneously and in ratios that are roughly constant. But at finer timescales (seconds to days), nutrients become decoupled if physiological traits such as nutrient storage limits, circadian rhythms, or enzyme kinetics cause one nutrient to be processed faster than another. To explore the interactions among these coupling and decoupling mechanisms, we introduce a model in which organisms process resources via uptake, excretion, growth, respiration, and mortality according to adjustable trait parameters. The model predicts that uptake can couple the input of one nutrient to the export of another in a ratio reflecting biological demand stoichiometry, but coupling occurs only when the input nutrient is limiting. Temporal nutrient coupling may, therefore, be a useful indicator of ecosystem limitation status. Fine-scale patterns of nutrient coupling are further modulated by, and potentially diagnostic of, physiological traits governing growth, uptake, and internal nutrient storage. Together, limitation status and physiological traits create a complex and informative relationship between nutrient inputs and exports. Understanding the mechanisms behind that relationship could enrich interpretations of fine-scale time-series data such as those now emerging from in situ solute sensors.
C.H. Hommes; M.I. Ochea
2010-01-01
This paper investigates, by means of simple, three and four strategy games, the occurrence of periodic and chaotic behaviour in a smooth version of the Best Response Dynamics, the Logit Dynamics. The main finding is that, unlike Replicator Dynamics, generic Hopf bifurcation and thus, stable limit cy
Feng, Likui; Shou, Qingyao; Butcher, Rebecca A.
2016-01-01
L-Rhamnose is a common component of cell-wall polysaccharides, glycoproteins and some natural products in bacteria and plants, but is rare in fungi and animals. In the present study, we identify and characterize a biosynthetic pathway for dTDP-rhamnose in Caenorhabditis elegans that is highly conserved across nematode species. We show that RML-1 activates glucose 1-phosphate (Glc-1-P) in the presence of either dTTP or UTP to yield dTDP-glucose or UDP-glucose, respectively. RML-2 is a dTDP-glucose 4,6-dehydratase, converting dTDP-glucose into dTDP-4-keto-6-deoxyglucose. Using mass spectrometry and NMR spectroscopy, we demonstrate that coincubation of dTDP-4-keto-6-deoxyglucose with RML-3 (3,5-epimerase) and RML-4 (4-keto-reductase) produces dTDP-rhamnose. RML-4 could only be expressed and purified in an active form through co-expression with a co-regulated protein, RML-5, which forms a complex with RML-4. Analysis of the sugar nucleotide pool in C. elegans established the presence of dTDP-rhamnose in vivo. Targeting the expression of the rhamnose biosynthetic genes by RNAi resulted in significant reductions in dTDP-rhamnose, but had no effect on the biosynthesis of a closely related sugar, ascarylose, found in the ascaroside pheromones. Therefore, the rhamnose and ascarylose biosynthetic pathways are distinct. We also show that transcriptional reporters for the rhamnose biosynthetic genes are expressed highly in the embryo, in the hypodermis during molting cycles and in the hypodermal seam cells specifically before the molt to the stress-resistant dauer larval stage. These expression patterns suggest that rhamnose biosynthesis may play an important role in hypodermal development or the production of the cuticle or surface coat during molting. PMID:27009306
Feng, Likui; Shou, Qingyao; Butcher, Rebecca A
2016-06-01
L-Rhamnose is a common component of cell-wall polysaccharides, glycoproteins and some natural products in bacteria and plants, but is rare in fungi and animals. In the present study, we identify and characterize a biosynthetic pathway for dTDP-rhamnose in Caenorhabditis elegans that is highly conserved across nematode species. We show that RML-1 activates glucose 1-phosphate (Glc-1-P) in the presence of either dTTP or UTP to yield dTDP-glucose or UDP-glucose, respectively. RML-2 is a dTDP-glucose 4,6-dehydratase, converting dTDP-glucose into dTDP-4-keto-6-deoxyglucose. Using mass spectrometry and NMR spectroscopy, we demonstrate that coincubation of dTDP-4-keto-6-deoxyglucose with RML-3 (3,5-epimerase) and RML-4 (4-keto-reductase) produces dTDP-rhamnose. RML-4 could only be expressed and purified in an active form through co-expression with a co-regulated protein, RML-5, which forms a complex with RML-4. Analysis of the sugar nucleotide pool in C. elegans established the presence of dTDP-rhamnose in vivo Targeting the expression of the rhamnose biosynthetic genes by RNAi resulted in significant reductions in dTDP-rhamnose, but had no effect on the biosynthesis of a closely related sugar, ascarylose, found in the ascaroside pheromones. Therefore, the rhamnose and ascarylose biosynthetic pathways are distinct. We also show that transcriptional reporters for the rhamnose biosynthetic genes are expressed highly in the embryo, in the hypodermis during molting cycles and in the hypodermal seam cells specifically before the molt to the stress-resistant dauer larval stage. These expression patterns suggest that rhamnose biosynthesis may play an important role in hypodermal development or the production of the cuticle or surface coat during molting.
Diagnosing phosphorus limitations in natural terrestrial ecosystems in carbon cycle models
Sun, Yan; Peng, Shushi; Goll, Daniel S.; Ciais, Philippe; Guenet, Bertrand; Guimberteau, Matthieu; Hinsinger, Philippe; Janssens, Ivan A.; Peñuelas, Josep; Piao, Shilong; Poulter, Benjamin; Violette, Aurélie; Yang, Xiaojuan; Yin, Yi; Zeng, Hui
2017-07-01
Most of the Earth System Models (ESMs) project increases in net primary productivity (NPP) and terrestrial carbon (C) storage during the 21st century. Despite empirical evidence that limited availability of phosphorus (P) may limit the response of NPP to increasing atmospheric CO2, none of the ESMs used in the previous Intergovernmental Panel on Climate Change assessment accounted for P limitation. We diagnosed from ESM simulations the amount of P need to support increases in carbon uptake by natural ecosystems using two approaches: the demand derived from (1) changes in C stocks and (2) changes in NPP. The C stock-based additional P demand was estimated to range between -31 and 193 Tg P and between -89 and 262 Tg P for Representative Concentration Pathway (RCP) 2.6 and RCP8.5, respectively, with negative values indicating a P surplus. The NPP-based demand, which takes ecosystem P recycling into account, results in a significantly higher P demand of 648-1606 Tg P for RCP2.6 and 924-2110 Tg P for RCP8.5. We found that the P demand is sensitive to the turnover of P in decomposing plant material, explaining the large differences between the NPP-based demand and C stock-based demand. The discrepancy between diagnosed P demand and actual P availability (potential P deficit) depends mainly on the assumptions about availability of the different soil P forms. Overall, future P limitation strongly depends on both soil P availability and P recycling on ecosystem scale.
Heebner, John E; Sridharan, Arun K; Dawson, Jay W; Messerly, Michael J; Pax, Paul H; Shverdin, Miro Y; Beach, Raymond J; Barty, Chris P J
2010-07-05
We present a detailed theoretical investigation of cladding-pumped Raman fiber amplification in an unexplored parameter space of high conversion efficiency (> 60%) and high brightness enhancement (> 1000). Fibers with large clad-to-core diameter ratios can provide a promising means for Raman-based brightness enhancement of diode pump sources. Unfortunately, the diameter ratio cannot be extended indefinitely since the intensity generated in the core can greatly exceed that in the cladding long before the pump is fully depleted. If left uncontrolled, this leads to the generation of parasitic second-order Stokes wavelengths in the core, limiting the conversion efficiency and as we will show, clamping the achievable brightness enhancement. Using a coupled-wave formalism, we present the upper limit on brightness enhancement as a function of diameter ratio for conventionally guided fibers. We further present strategies for overcoming this limit based upon depressed well core designs. We consider two configurations: 1) pulsed cladding-pumped Raman fiber amplifier (CPRFA) and 2) cw cladding-pumped Raman fiber laser (CPRFL).
Mixed-Mode Oscillations in a piecewise linear system with multiple time scale coupling
Fernández-García, S.; Krupa, M.; Clément, F.
2016-10-01
In this work, we analyze a four dimensional slow-fast piecewise linear system with three time scales presenting Mixed-Mode Oscillations. The system possesses an attractive limit cycle along which oscillations of three different amplitudes and frequencies can appear, namely, small oscillations, pulses (medium amplitude) and one surge (largest amplitude). In addition to proving the existence and attractiveness of the limit cycle, we focus our attention on the canard phenomena underlying the changes in the number of small oscillations and pulses. We analyze locally the existence of secondary canards leading to the addition or subtraction of one small oscillation and describe how this change is globally compensated for or not with the addition or subtraction of one pulse.
Robustness of synthetic oscillators in growing and dividing cells
Paijmans, Joris; Lubensky, David K.; Rein ten Wolde, Pieter
2017-05-01
Synthetic biology sets out to implement new functions in cells, and to develop a deeper understanding of biological design principles. Elowitz and Leibler [Nature (London) 403, 335 (2000), 10.1038/35002125] showed that by rational design of the reaction network, and using existing biological components, they could create a network that exhibits periodic gene expression, dubbed the repressilator. More recently, Stricker et al. [Nature (London) 456, 516 (2008), 10.1038/nature07389] presented another synthetic oscillator, called the dual-feedback oscillator, which is more stable. Detailed studies have been carried out to determine how the stability of these oscillators is affected by the intrinsic noise of the interactions between the components and the stochastic expression of their genes. However, as all biological oscillators reside in growing and dividing cells, an important question is how these oscillators are perturbed by the cell cycle. In previous work we showed that the periodic doubling of the gene copy numbers due to DNA replication can couple not only natural, circadian oscillators to the cell cycle [Paijmans et al., Proc. Natl. Acad. Sci. (USA) 113, 4063 (2016), 10.1073/pnas.1507291113], but also these synthetic oscillators. Here we expand this study. We find that the strength of the locking between oscillators depends not only on the positions of the genes on the chromosome, but also on the noise in the timing of gene replication: noise tends to weaken the coupling. Yet, even in the limit of high levels of noise in the replication times of the genes, both synthetic oscillators show clear signatures of locking to the cell cycle. This work enhances our understanding of the design of robust biological oscillators inside growing and diving cells.
An efficient method for simulation of noisy coupled multi-dimensional oscillators
Stinchcombe, Adam R.; Forger, Daniel B.
2016-09-01
We present an efficient computational method for the study of populations of noisy coupled oscillators. By taking a population density approach in which the probability density of observing an oscillator at a point of state space is the primary variable instead of the states of all of the oscillators, we are able to seamlessly account for intrinsic noise within the oscillators and global coupling within the population. The population is assumed to consist of a large number of oscillators so that the noise process is well sampled over the population. Our numerical method is able to solve the governing equation even in the challenging case of limit cycle oscillators with a large number of state variables. Instead of simulating a prohibitive number of oscillators, our particle method simulates relatively few particles allowing for the efficient solution of the governing equation.
Synchronization of Two Remote Nanomechanical Oscillators
2013-08-17
oscillators integrated inside an optical racetrack cavity. We show that this leads to a limit cycle in the reduced three- dimensional mechanical phase...linked in an optical racetrack (Fig. 1(a)); The resonators are mechanically isolated, due to their large separation (~ 80 m), ensuring that any...resonators ~ 2 kHz [13]. Figure 1. (a) Micrograph of a racetrack cavity with two 110nm x 500nm x 10um suspended portions as nanomechanical
PERFORMANCE IMPROVEMENT OF A CHEMICAL REACTOR BY NONLINEAR NATURAL OSCILLATIONS
RAY, AK
1995-01-01
The dynamic behaviour of two coupled continuous stirred tank reactors in sequence is studied when the first reactor is being operated under limit cycle regimes producing self-sustained natural oscillations. The periodic output from the first reactor is then used as a forced input into the second rea
Non-algebraic oscillations for predator-prey models
Ferragut, Antoni
2014-01-01
The authors are partially supported by grants MTM2008-03437 and 2009SGR-410. The first author is additionally partially supported by grants Juan de la Cierva and MTM2009-14163-C02-02. We prove that the limit cycle oscillations of the celebrated Rosenzweig-MacArthur differential system and other predator-prey models are non-algebraic.
Limits to biodiversity cycles from a unified model of mass-extinction events
Feulner, Georg
2011-04-01
Episodes of species mass extinction dramatically affected the evolution of life on Earth, but their causes remain a source of debate. Even more controversy surrounds the hypothesis of periodicity in the fossil record, with conflicting views still being published in the scientific literature, often even based on the same state-of-the-art datasets. From an empirical point of view, limitations of the currently available data on extinctions and possible causes remain an important issue. From a theoretical point of view, it is likely that a focus on single extinction causes and strong periodic forcings has strongly contributed to this controversy. Here I show that if there is a periodic extinction signal at all, it is much more likely to result from a combination of a comparatively weak periodic cause and various random factors. Tests of this unified model of mass extinctions on the available data show that the model is formally better than a model with random extinction causes only. However, the contribution of the periodic component is small compared to factors such as impacts or volcanic eruptions.
Amplitude death and resurgence of oscillation in networks of mobile oscillators
Majhi, Soumen; Ghosh, Dibakar
2017-05-01
The phenomenon of amplitude death has been explored using a variety of different coupling strategies in the last two decades. In most of the works, the basic coupling arrangement is considered to be static over time, although many realistic systems exhibit significant changes in the interaction pattern as time varies. In this article, we study the emergence of amplitude death in a dynamical network composed of time-varying interaction amidst a collection of random walkers in a finite region of three-dimensional space. We consider an oscillator for each walker and demonstrate that depending upon the network parameters and hence the interaction between them, the global oscillation in the network gets suppressed. In this framework, the vision range of each oscillator decides the number of oscillators with which it interacts. In addition, with the use of an appropriate feedback parameter in the coupling strategy, we articulate how the suppressed oscillation can be resurrected in the systems' parameter space. The phenomenon of amplitude death and the resurgence of oscillation is investigated taking limit cycle and chaotic oscillators for broad ranges of the parameters, like the interaction strength k between the entities, the vision range r and the speed of movement v.
Jadin, Evgeny; Wei, Ke; Chen, Wen; Wang, Lin
Questions of the interannual variations of the extra-tropical stratospheric dynamics, its rela-tionship with the sea surface temperature (SST) anomalies in the North Pacific (Pacific Decadal Oscillation -PDO) in early winter (November-December), Quasi-Biennial Oscillation (QBO) (Holton-Tan relations), a decadal modulation by the 11-year Solar Cycle (SC) (Labitzke, van Loon -LvL correlations) in late winter (January-February) are discussed. In early winter, the interannual changes of the planetary wave activity define partly the variations of the strato-spheric circulation in subsequent January [Zyulyaeva and Jadin, 2009]. The interannual and decadal variations of the stratospheric wave activity appear to be associated with those of the PDO [Jadin et al. 2009]. A decadal period from the mid-1970s to mid-1990s of the violation of the Holton-Tan (HT) relationship corresponds well to that of the positive PDO phase (anoma-lously cold SSTs in the central North Pacific). Using the NCEP and ERA-40 monthly mean reanalysis datasets, the three-dimensional Eliassen-Palm fluxes are calculated. The results of the analysis of relations between the upward/downward propagation of planetary waves in the lower stratosphere ("stratospheric bridge"), their interaction with the zonal wind and the HT and LvL correlations for January-February are presented. In contrast with early winter, the large role in the wave-zonal flow interaction plays the downward propagation of planetary waves from the stratosphere to the troposphere over Canada and North Atlantic ("stratospheric wave hole") responsible for the sink of the eddy energy from the stratosphere. One can suggest that there are two dominant regimes in the stratosphere-troposphere coupling in late winter: 1) the "ventilation regime" with the strong penetration of planetary waves from the troposphere over north Eurasia and their strong downward propagation over Canada and North Atlantic, and 2) the "blocking regime" with the weak those
Rodrigues, R. de Lima [Universidade Federal de Campina Grande (UFCG), Cuite, PB (Brazil). Centro de Tecnologia. Unidade Academica de Educacao]. E-mail: rafael@df.ufcg.edu.br; rafaelr@cbpf.br
2007-07-01
In the present work we obtain a new representation for the Dirac oscillator based on the Clifford algebra C 7. The symmetry breaking and the energy eigenvalues for our model of the Dirac oscillator are studied in the non-relativistic limit. (author)
Sano, Kazuhiro; Ōno, Yoshiaki
2016-12-01
We investigate anomalous oscillations due to the Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects of the one-dimensional Hubbard ring with flux in the strong coupling limit. By using the exact diagonalization method and the Shiba transformation, we examine the energies of the ground-state and a few excited states in the presence of the flux producing the AB or AC effect, where the transformation not only reverses the sign of the interaction U but also exchanges the role between the AB and AC effects in the model Hamiltonian. We systematically classify the AB and AC oscillations by using the number of minima Nmin of the ground-state energy as a function of a normalized phase shift ϕ for 0 ≤ ϕ effects. For example, it is shown that Nmin is given by NL - Ne (NL - N↑ + N↓) for the AB (AC) effect in the very strong attraction, where NL, Ne, N↑, and N↓ are the system size, the total number of electrons, the number of electrons with up-spin, and the number of electrons with down-spin, respectively, under the condition of NL > Ne > N↓ > N↑. In more special cases, such as for a half-filled band and the spin-balanced case (NL = Ne and N↓ = N↑), we find Nmin to be 0 (2) for the AB (AC) effect in the case of very strong repulsion. These results show us the nature of interesting phenomena originating from the interplay between the strong correlation and the quantum interference effect in a mesoscopic ring.
UNIQUENESS AND DISTRIBUTION OF LIMIT CYCLES FOR BOUNDED QUADRATIC SYSTEM%有界二次系统极限环的唯一性及分布
宋矞
2001-01-01
In this paper, we first give a necessary and sufficient condition of a quadratic system with three finite critical points being bounded, and then, we use the methods and conclusions of [11] to provide some uniqueness theorems of limit cycles for bounded quadratic systems. As well, we prove that any bounded quadratic system can not have (2, 2)-distribution of limit cycles according to these uniqueness theorems.
无
2010-01-01
In this paper, a class of simplified Type-IV predator-prey system with linear state feedback is investigated. We prove the boundedness of the positive solutions to this system, and analyze the quality of the equilibria and the existence of limit cycles of the system surrounding the positive equilibra. By Hopf bifurcation theory, the result of having two limit cycles to the system is obtained.
Formation of multiple subpulses in a free-electron laser operating in the limit-cycle mode
Knippels, G. M. H.; van der Meer, A. F. G.; Mols, R. F. X. A. M.; Oepts, D.; van Amersfoort, P. W.
1996-03-01
The evolution of the longitudinal pulse shape and the spectrum of the short-pulse, far-infrared free-electron laser FELIX are investigated. Depending on the amount of cavity desynchronization applied, the laser is found to operate in the stable-focus mode or in the limit-cycle mode. In the latter case, autocorrelation measurements that are made with a setup that is based on second-harmonic generation in CdTe show the formation of a train of up to four subpulses. These are separated by the synchrotron length, and the corresponding sidebands in the spectrum are separated by the synchrotron frequency, in excellent agreement with theory. The measurements are made at a wavelength of 24.5 μm.
Martin, Laura; Sándor, Bulcsú; Gros, Claudius
2016-01-01
We examine the hypothesis, that short-term synaptic plasticity (STSP) may generate self-organized motor patterns. We simulated sphere-shaped autonomous robots, within the LPZRobots simulation package, containing three weights moving along orthogonal internal rods. The position of a weight is controlled by a single neuron receiving excitatory input from the sensor, measuring its actual position, and inhibitory inputs from the other two neurons. The inhibitory connections are transiently plastic, following physiologically inspired STSP-rules. We find that a wide palette of motion patterns are generated through the interaction of STSP, robot, and environment (closed-loop configuration), including various forward meandering and circular motions, together with chaotic trajectories. The observed locomotion is robust with respect to additional interactions with obstacles. In the chaotic phase the robot is seemingly engaged in actively exploring its environment. We believe that our results constitute a concept of proof that transient synaptic plasticity, as described by STSP, may potentially be important for the generation of motor commands and for the emergence of complex locomotion patterns, adapting seamlessly also to unexpected environmental feedback. We observe spontaneous and collision induced mode switchings, finding in addition, that locomotion may follow transiently limit cycles which are otherwise unstable. Regular locomotion corresponds to stable limit cycles in the sensorimotor loop, which may be characterized in turn by arbitrary angles of propagation. This degeneracy is, in our analysis, one of the drivings for the chaotic wandering observed for selected parameter settings, which is induced by the smooth diffusion of the angle of propagation. PMID:27803661
Entrainment and stimulated emission of ultrasonic piezoelectric auto-oscillators.
Weaver, Richard L; Lobkis, Oleg I; Yamilov, Alexey
2007-12-01
Theoretical modeling and laboratory tests are conducted for nonlinear auto-oscillating piezoelectric ultrasonic devices coupled to reverberant elastic bodies. The devices are shown to exhibit behavior familiar from the theory of coupled auto-oscillators. In particular, these spontaneously emitting devices adjust their limit-cycle frequency to the spectrum of the body. It is further shown that the auto-oscillations can be entrained by an applied field; an incident wave at a frequency close to the frequency of the natural limit cycle entrains the oscillator. Special attention is paid to the phase of entrainment. Depending on details, the phase is such that the oscillator can be in a state of stimulated emission: the incident field amplifies the ultrasonic power emitted by the oscillator. These behaviors are essential to eventual design of an ultrasonic system that would consist of a number of such devices all synchronized to their mutual field, a system that would be an analog to a laser. A prototype uaser is constructed.
Ghanbari, K.; Ghoranneviss, M.; Elahi, A. Salar
2015-01-01
Runaway electrons in tokamaks can cause serious damage to the first wall of the reactor and decrease its life time. Also, hard x-ray emission generated from high energy runaway electrons lead to the plasma energy loss. Therefore, suggesting methods to minimize runaway electron in tokamaks are very important. Applying external resonant field is one of the methods for controlling the Magneto Hydrodynamic (MHD) activity. Relation between the MHD activity and runaway electrons has already been studied (Jaspers et al. 1994; Ghanbari et al. 2012) Jaspers, R., et al. 1994 Phys. Rev. Lett. 72, 4093; Ghanbari, M. R., et al. 2012a Phys. Scr. 83, 055501. Present study attempts to investigate the effects of limiter biasing and Resonant Helical magnetic Field (RHF) on the generation of runaway electrons. For this purpose, plasma parameters such as plasma current, MHD oscillation, loop voltage, emitted hard x-ray intensity, Halpha impurity, safety factor in the presence and absence of external fields, were measured. Frequency activity was investigated with FFT analysis. The results show that applying resonant fields can control the MHD activity, and then hard x-ray emitted from the runaway electrons.
P. Meena
2008-01-01
Full Text Available This research was to study the effect of inner diameter and inclination angles on operation limit of a closed loop oscillating heat pipes with check valves (CLOHP/CV. A set of CLOHP/CV was made of copper tubes in combination of following dimension: 1.77 and 2.03 mm inside diameter: 10 turn, with R123 was used as the working fluid. The working fluid was filled in the tube at the filling ratio of 50%. The inclination angles were 0, 20, 40, 60, 80 and 90° with 5 equal lengths for evaporator, adiabatic and condenser sections. The evaporator section was given heat by heater while the condenser section was cooled by volume water in a cold bath. The adiabatic section was properly insulated. In the test operation, it could be concluded as follows. It indicated that when the inner diameter changed from 1.77-2.03 mm the critical temperature increased. And when increase the inclination angles from 0 until to 90° the critical temperature increased.
Aubert, Bernard; Abrams, G S; Adye, T; Ahmed, S; Alam, M S; Albert, J; Aleksan, Roy; Allison, J; Allmendinger, T; Altenburg, D; Andreotti, M; Angelini, C; Aston, D; Azzolini, V; Baak, M; Back, J J; Bailey, S; Baldini-Ferroli, R; Band, H R; Banerjee, Sw; Barate, R; Bard, D J; Barlow, N R; Barlow, R J; Bartoldus, R; Batignani, G; Bauer, J M; Beck, T W; Behera, P K; Bellini, F; Benayoun, M; Berger, N; Bernard, D; Berryhill, J W; Best, D; Bettarini, S; Bettoni, D; Bevan, A J; Bhimji, W; Bianchi, F; Blanc, F; Blaylock, G; Blinov, V E; Bloom, P; Bóna, M; Bondioli, M; Bonneaud, G R; Borean, C; Borgland, A W; Bosisio, L; Boutigny, D; Bowerman, D A; Boyarski, A M; Boyd, J T; Bozzi, C; Brandenburg, G; Brandt, T; Brau, B; Brau, J E; Breon, A B; Briand, H; Brochard, F; Brose, J; Brown, C L; Brown, C M; Brown, D N; Bruinsma, M; Brunet, S; Bucci, F; Buchmüller, O L; Bugg, W; Bukin, A D; Bulten, H J; Burchat, Patricia R; Button-Shafer, J; Buzzo, A; Côté, D; Cahn, R N; Calabrese, R; Calcaterra, A; Calderini, G; Campagnari, C; Capra, R; Carpinelli, M; Cartaro, C; Cavallo, N; Cavoto, G; Chao, M; Charles, E; Chauveau, J; Chen, A; Chen, E; Chen, J C; Chen, S; Cheng, C H; Chevalier, N; Christ, S; Cibinetto, G; Clark, P J; Cochran, J; Colberg, T; Colecchia, F; Coleman, J P; Contri, R; Convery, M R; Cormack, C M; Cossutti, F; Cottingham, W N; Couderc, F; Cowan, G; Cowan, R; Crawley, H B; Cremaldi, L M; Cristinziani, M; Crosetti, G; Çuhadar-Dönszelmann, T; Dahmes, B; Dallapiccola, C; Danielson, N; Dasu, S; Datta, M; Dauncey, P D; David, P; Davier, M; Davis, D; Day, C T; De Groot, N; De Nardo, Gallieno; Del Buono, L; Del Gamba, V; Della Ricca, G; Di Lodovico, F; Dickopp, M; Dittongo, S; Dong, D; Dorfan, J; Dorigo, A; Druzhinin, V P; Dubois-Felsmann, G P; Dujmic, D; Dunwoodie, W M; Dvoretskii, A; Eckmann, R; Edwards, A J; Egede, U; Eichenbaum, A M; Eigen, G; Eisner, A M; Elmer, P; Elsen, E E; Emery, S; Ernst, J A; Eschenburg, V; Eschrich, I; Fabozzi, F; Faccini, R; Fan, S; Farbin, A; Feltresi, E; Ferrarotto, F; Ferroni, F; Field, R C; Finocchiaro, G; Flack, R L; Flächer, H U; Flood, K T; Ford, K; Ford, W T; Forti, F; Fortin, D; Franek, B J; Frey, R; Fritsch, M; Fry, J R; Gabathuler, Erwin; Gabriel, T A; Gaidot, A; Gaillard, J M; Gaillard, J R; Galeazzi, F; Gallo, F; Gamba, D; Gamet, R; Gan, K K; Ganzhur, S F; Gary, J W; Gaspero, M; Gatto, C; Geddes, N I; Gill, M S; Giorgi, M A; Giraud, P F; Gladney, L; Glanzman, T; Godang, R; Goetzen, K; Golubev, V B; Gopal, G P; Gowdy, S J; Grancagnolo, S; Green, M G; Grenier, P; Gritsan, A V; Grosdidier, G; Groysman, Y; Guo, Q H; Hadavand, H K; Hadig, T; Haire, M; Halyo, V; Hamel de Monchenault, G; Hamon, O; Harrison, P F; Harrison, T J; Hart, P A; Hartfiel, C; Buchanan, B L; Harton, J L; Hast, C; Hauke, A; Hawkes, C M; Hearty, C; Held, T; Hertzbach, S S; Heusch, C A; Hicheur, A; Hill, E J; Hitlin, D G; Höcker, A; Hodgkinson, M C; Hollar, J J; Honscheid, K; Hrynóva, T; Hufnagel, D; Hulsbergen, W D; Igonkina, O; Innes, W R; Ivanchenko, V N; Izen, J M; Jackson, P D; Jacobsen, R G; Jawahery, A; Jayatilleke, S M; John, M J J; Johnson, J R; Judd, D; Kadel, R W; Kadyk, J; Kagan, H; Karyotakis, Yu; Kass, R; Kelly, M P; Kelsey, M H; Kerth, L T; Khan, A; Kim, H; Kim, P; Kirkby, D; Kitayama, I; Koch, H; Kocian, M L; Kofler, R; Kolomensky, Yu G; Koptchev, V B; Kovalskyi, D; Kowalewski, R V; Kozanecki, Witold; Kravchenko, E A; Krishnamurthy, M; Kroeger, R; Kukartsev, G; Kutter, P E; Lacker, H M; Lae, C K; Lafferty, G D; Lamsa, J; Lanceri, L; Lange, D J; Langenegger, R S; Dubitzky, U; Langer, M; Lankford, A J; Laplace, S; Latham, T E; Lavin, D; Le Clerc, C; Le Diberder, F R; Lees, J P; Legendre, M; Leith, D W G S; Lepeltier, V; Leruste, P; Levesque, J A; Levy, S L; Lewandowski, B; Li Gioi, L; Li, H; Libby, J; Lillard, V; Lista, L; Liu, R; Lo Secco, C P; Jessop, J M; Lo Vetere, M; Lockman, W S; London, G W; Long, O; Lou, X C; Lu, A; Lü, C; Luitz, S; Luppi, E; Lusiani, A; Lüth, V; Lutz, A M; Lynch, G; Lynch, H L; Lyon, A J; MacFarlane, D B; Macri, M; Mallik, G J; Grenier, U; Maly, E; Mancinelli, G; Mandelkern, M A; Mangeol, D J J; Marchiori, G; Margoni, M; Marker, C E; Marsiske, H; Martínez-Vidal, F; Mattison, T S; Mayer, B; Mazur, M A; Mazzoni, M A; McKenna, J A; McMahon, T R; Meadows, B T; Merchant, A M; Messner, R; Meyer, T I; Meyer, W T; Miftakov, V; Mihályi, A; Mir, L M; Mohanty, G B; Mohapatra, A K; Mommsen, R K; Monge, M R; Monorchio, D; Moore, T B; Morandin, M; Morgan, S E; Morganti, M; Morganti, S; Morii, M; Morton, G W; Muheim, F; Müller, D R; Müller-Pfefferkorn, R; Narsky, I; Nash, J A; Nauenberg, U; Neal, H; Negrini, M; Neri, N; Nicholson, H; Nogowski, R; O'Grady, C P; Ocariz, J; Oddone, P J; Ofte, I; Olaiya, E O; Olivas, A; Olsen, J; Onuchin, A P; Orimoto, T J; Otto, S; Ozcan, V E; Paar, H P; Paick, K; Palombo, A; Lazzaro, F; Pan, Y; Panetta, J; Panvini, R S; Paoloni, E; Paolucci, P; Parry, R J; Passaggio, S; Patel, P M; Patrignani, C; Patteri, P; Payne, D J; Pelizaeus, M; Perazzo, A; Perl, M; Peruzzi, F; Anulli, I M; Petersen, B A; Petersen, T C; Petrak, S; Petzold, A; Piatenko, T; Piccolo, D; Piccolo, M; Piemontese, L; Pierini, M; Pioppi, M; Biasini, M; Piredda, G; Pivk, M; Plaszczynski, S; Playfer, S; Pompili, A; Palano, A; Poropat, P; Porter, F C; Posocco, M; Potter, C T; Prell, S; Prepost, R; Pripstein, M; Pulliam, T; Purohit, M V; Qi, N D; Rahatlou, S; Rahimi, A M; Rama, M; Rankin, P; Ratcliff, B N; Raven, G; Re, P F; Manfredi, V R; Reidy, J; Ricciardi, S; Richman, J D; Ritchie, J L; Rizzo, G; Roat, C; Roberts, D A; Robertson, S H; Robutti, E; Roe, N A; Röthel, W; Ronan, Michael T; Roney, J M; Rong, G; Roodman, A; Roos, L; Rosenberg, E I; Rotondo, M; Ryd, A; Saeed, M A; Tehrani, F S; Saleem, M; Salnikov, A A; Salvatore, F; Samuel, A; Sanders, D A; Sandrelli, F; Santroni, A; Saremi, S; Sarti, A; Satpathy, A; Schalk, T; Schindler, R H; Schmitz, R E; Schott, G; Schrenk, S; Schubert, J; Schubert, Klaus R; Schumm, B A; Schune, M H; Schwiening, J; Schwierz, R; Schwitters, R F; Sciacca, C; Sciolla, G; Seiden, A; Sekula, S J; Serednyakov, S I; Sharma, V; Shelkov, V G; Shen, B C; Simani, M C; Simi, G; Simonetto, F; Sinev, N B; Skovpen, Yu I; Sloane, R J; Smith, A J S; Smith, J G; Snyder, A; Soffer, A; Soha, A; Sokoloff, M D; Solodov, E P; Spaan, B; Spanier, S M; Spradlin, P; Stängle, H; Steinke, M; Stelzer, J; Stoker, D P; Stroili, R; Strom, D; Stugu, B; Su, D; Sullivan, M K; Summers, D J; Sundermann, J E; T'Jampens, S; Tan, P; Tantot, L; Taras, P; Taylor, F; Taylor, G P; Telnov, A V; Teodorescu, P; Kyberd, L; Ter-Antonian, R; Therin, G; Thiebaux, C; Thiessen, D; Tiozzo, G; Tisserand, V; Toki, W H; Torrence, E; Tosi, S; Touramanis, C; Treadwell, E; Vaitsas, G; Vasileiadis, G; Vasseur, G; Vavra, J; Verderi, M; Verkerke, W; Vitale, L; Voci, C; Voena, C; Vuagnin, G; Wagner, G; Wagner, S R; Wagoner, D E; Waldi, R; Walsh, J; Wang, K; Wang, P; Wappler, F R; Watson, A T; Weaver, M; Weidemann, A W; Weinstein, A J R; Wenzel, W A; Wilden, L; Williams, D C; Williams, J C; Willocq, S; Wilson, F F; Wilson, M G; Wilson, R J; Winter, M A; Wisniewski, W J; Wittgen, M; Won, E; Wong, Q K; Wormser, G; Wright, D H; Wright, D M; Wu, J; Wu Sau Lan; Yamamoto, R K; Yang, S; Yarritu, A K; Ye, S; Yéche, C; Yi, J; Young, C C; Yu, Z; Yumiceva, F X; Yushkov, A N; Zallo, A; Zeng, Q L; Zghiche, A; Zhang, L; Zhao, H W; Zhu, Y S; Zito, M; De Sangro, R; Del Re, D; La Vaissière, C de; Von Wimmersperg-Töller, J H
2004-01-01
Using events in which one of two neutral-B mesons from the decay of an Y(4S) resonance is fully reconstructed, we set limits on the difference between the decay rates of the two neutral-B mass eigenstates and on CP, T, and CPT violation in B0-antiB0 mixing. The reconstructed decays, comprising both CP and flavor eigenstates, are obtained from 88 million Y(4S) --> Banti-B decays collected with the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. We determine six independent parameters governing oscillations (Deltam, DeltaGamma/Gamma), CPT and CP violation (Re Z, Im Z), and CP and T violation (Im lambdaCP, |q/p|), where lambdaCP characterizes B0 and anti-B0 decays to states of charmonium plus K0S or K0L. The results are sgn(Re lambdaCP)xDeltaGamma/Gamma = -0.008 +/- 0.037(stat) +/- 0.018(syst) [-0.084,0.068], |q/p| = 1.029 +/- 0.013(stat) +/- 0.011(syst) [ 1.001,1.057], (Re lambdaCP)/|lambdaCP|xRe z = 0.014 +/- 0.035(stat) +/- 0.034(syst) [-0.072,0.101], Im z = 0.038 +/- 0.029(stat) +/- 0.025(s...
P. Meena
2009-01-01
Full Text Available This research aims to the effect of evaporator section lengths and working fluids on operational limit of closed loop oscillating heat pipes with check valves (CLOHP/CV with R123 Ethanol and Water were used as the working fluids. A set of CLOHP/CV was made of copper tubes in combination of following dimension: 1.77 mm inside diameter: 10 turns: 5, 10 and 15 cm equal lengths for evaporator, adiabatic and condenser sections. The working fluid was filled in the tube at the filling ratio of 50%. The evaporator section was given heat by heater while the condenser section was cooled by volume water in a cold bath. The adiabatic section was properly insulated. In the test operation. Which the temperature at the adiabatic section was controlled at 60°C in steady-state condition. From The obtained results obtained, it could be concluded as follows. When the evaporator lengths increased from 5 cm to 10 and 15 cm the critical heat transfer flux decreased. There was working fluids change from R123 to Ethanol and water the critical heat flux decreased.
Synthesizing Virtual Oscillators to Control Islanded Inverters
Johnson, Brian B.; Sinha, Mohit; Ainsworth, Nathan G.; Dorfler, Florian; Dhople, Sairaj V.
2016-08-01
Virtual oscillator control (VOC) is a decentralized control strategy for islanded microgrids where inverters are regulated to emulate the dynamics of weakly nonlinear oscillators. Compared to droop control, which is only well defined in sinusoidal steady state, VOC is a time-domain controller that enables interconnected inverters to stabilize arbitrary initial conditions to a synchronized sinusoidal limit cycle. However, the nonlinear oscillators that are elemental to VOC cannot be designed with conventional linear-control design methods. We address this challenge by applying averaging- and perturbation-based nonlinear analysis methods to extract the sinusoidal steady-state and harmonic behavior of such oscillators. The averaged models reveal conclusive links between real- and reactive-power outputs and the terminal-voltage dynamics. Similarly, the perturbation methods aid in quantifying higher order harmonics. The resultant models are then leveraged to formulate a design procedure for VOC such that the inverter satisfies standard ac performance specifications related to voltage regulation, frequency regulation, dynamic response, and harmonic content. Experimental results for a single-phase 750 VA, 120 V laboratory prototype demonstrate the validity of the design approach. They also demonstrate that droop laws are, in fact, embedded within the equilibria of the nonlinear-oscillator dynamics. This establishes the backward compatibility of VOC in that, while acting on time-domain waveforms, it subsumes droop control in sinusoidal steady state.
Coherence versus reliability of stochastic oscillators with delayed feedback.
Goldobin, Denis S
2008-12-01
For noisy self-sustained oscillators, both reliability, the stability of a response to a noisy driving, and coherence, understood in the sense of constancy of oscillation frequency, are important characteristics. Although both characteristics and techniques for controlling them have received great attention from researchers, owing to their importance for neurons, lasers, clocks, electric generators, etc., these characteristics were previously considered separately. In this paper, a strong quantitative relation between coherence and reliability is revealed for a limit cycle oscillator subject to a weak noisy driving and a linear delayed feedback, a convection control tool. The analytical findings are verified and enriched with a numerical simulation for the Van der Pol-Duffing oscillator.
Sustained glycolytic oscillations in individual isolated yeast cells.
Gustavsson, Anna-Karin; van Niekerk, David D; Adiels, Caroline B; du Preez, Franco B; Goksör, Mattias; Snoep, Jacky L
2012-08-01
Yeast glycolytic oscillations have been studied since the 1950s in cell-free extracts and intact cells. For intact cells, sustained oscillations have so far only been observed at the population level, i.e. for synchronized cultures at high biomass concentrations. Using optical tweezers to position yeast cells in a microfluidic chamber, we were able to observe sustained oscillations in individual isolated cells. Using a detailed kinetic model for the cellular reactions, we simulated the heterogeneity in the response of the individual cells, assuming small differences in a single internal parameter. This is the first time that sustained limit-cycle oscillations have been demonstrated in isolated yeast cells. The mathematical model described here has been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/gustavsson/index.html free of charge. © 2012 The Authors Journal compilation © 2012 FEBS.
Simoes-Moreira, Jose Roberto [SISEA - Alternative Energy Systems Laboratory in the Mechl. Eng. Department at Escola Politecnica, Post-Graduation Program on Energy at Institute of Electrotechnical and Energy, University of Sao Paulo, Av. Prof. Mello Moraes, 2231, 05508-900, Sao Paulo, SP (Brazil)
2010-06-15
A Thermodynamic air-standard cycle was envisaged for Ranque-Hilsh (R-H) or Vortex Tubes to provide relevant Thermodynamic analysis and tools for setting operating limits according to the conservation laws of mass and energy, as well as the constraint of the Second Law of Thermodynamics. The study used an integral or control volume approach and resulted in establishing working equations for evaluating the performance of an R-H tube. The work proved that the coefficient of performance does not depend on the R-H tube operating mode, i.e., the same value is obtained independently if the R-H tube operates either as a heat pump or as a refrigeration device. It was also shown that the isentropic coefficient of performance displays optima values of cold and hot mass fractions for a given operating pressure ratio. Finally, the study was concluded by comparing the present analysis with some experimental data available in the literature for operating pressures ranging 2-11 atm. (author)
Lopez de Bertodano, Martín, E-mail: bertodan@purdue.edu [School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907 (United States); Fullmer, William D. [Department of Chemical and Biological Engineering, U. of Colorado, Boulder, CO 80309 (United States); Clausse, Alejandro [CNEA-CONICET and Universidad Nacional del Centro, 7000 Tandil (Argentina)
2016-12-15
A 1D TFM numerical simulation of near horizontal stratified two-phase flow is performed where the TFM, including surface tension and viscous stresses, is simplified to a two-equation model using the fixed-flux approximation. As the angle of inclination of the channel increases so does the driving body force, so the flow becomes KH unstable, and waves grow and develop nonlinearities. It is shown that these waves grow until they reach a limit cycle due to viscous dissipation at wave fronts. Upon further inclination of the channel, chaos is observed. The appearance of chaos in a 1D TFM implies a nonlinear process that transfers energy intermittently from long wavelengths where energy is produced to short wavelengths where energy is dissipated by viscosity, so that an averaged energy equilibrium in frequency space is attained. This is comparable to the well-known turbulent stability mechanism of the multi-dimensional Navier–Stokes equations, i.e., chaos implies Lyapunov stability, but in this case it is strictly a two-phase phenomenon.
Modelling of density limit phenomena in toroidal helical plasmas
Itoh, K. [National Inst. for Fusion Science, Toki, Gifu (Japan); Itoh, S.-I. [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics; Giannone, L. [Max Planck Institut fuer Plasmaphysik, EURATOM-IPP Association, Garching (Germany)
2000-03-01
The physics of density limit phenomena in toroidal helical plasmas based on an analytic point model of toroidal plasmas is discussed. The combined mechanism of the transport and radiation loss of energy is analyzed, and the achievable density is derived. A scaling law of the density limit is discussed. The dependence of the critical density on the heating power, magnetic field, plasma size and safety factor in the case of L-mode energy confinement is explained. The dynamic evolution of the plasma energy and radiation loss is discussed. Assuming a simple model of density evolution, of a sudden loss of density if the temperature becomes lower than critical value, then a limit cycle oscillation is shown to occur. A condition that divides the limit cycle oscillation and the complete radiation collapse is discussed. This model seems to explain the density limit oscillation that has been observed on the W7-AS stellarator. (author)
Modelling of density limit phenomena in toroidal helical plasmas
Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan); Itoh, Sanae-I. [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics; Giannone, Louis [EURATOM-IPP Association, Max Planck Institut fuer Plasmaphysik, Garching (Germany)
2001-11-01
The physics of density limit phenomena in toroidal helical plasmas based on an analytic point model of toroidal plasmas is discussed. The combined mechanism of the transport and radiation loss of energy is analyzed, and the achievable density is derived. A scaling law of the density limit is discussed. The dependence of the critical density on the heating power, magnetic field, plasma size and safety factor in the case of L-mode energy confinement is explained. The dynamic evolution of the plasma energy and radiation loss is discussed. Assuming a simple model of density evolution, of a sudden loss of density if the temperature becomes lower than critical value, then a limit cycle oscillation is shown to occur. A condition that divides the limit cycle oscillation and the complete radiation collapse is discussed. This model seems to explain the density limit oscillation that has been observed on the Wendelstein 7-AS (W7-AS) stellarator. (author)
Control analysis for autonomously oscillating biochemical networks.
Reijenga, Karin A; Westerhoff, Hans V; Kholodenko, Boris N; Snoep, Jacky L
2002-01-01
It has hitherto not been possible to analyze the control of oscillatory dynamic cellular processes in other than qualitative ways. The control coefficients, used in metabolic control analyses of steady states, cannot be applied directly to dynamic systems. We here illustrate a way out of this limitation that uses Fourier transforms to convert the time domain into the stationary frequency domain, and then analyses the control of limit cycle oscillations. In addition to the already known summation theorems for frequency and amplitude, we reveal summation theorems that apply to the control of average value, waveform, and phase differences of the oscillations. The approach is made fully operational in an analysis of yeast glycolytic oscillations. It follows an experimental approach, sampling from the model output and using discrete Fourier transforms of this data set. It quantifies the control of various aspects of the oscillations by the external glucose concentration and by various internal molecular processes. We show that the control of various oscillatory properties is distributed over the system enzymes in ways that differ among those properties. The models that are described in this paper can be accessed on http://jjj.biochem.sun.ac.za.
Espinosa, Ismael; Gonzalez, Hortensia; Quiza, Jorge; Gonazalez, J. Jesus; Arroyo, Ruben; Lara, Ritaluz
1995-01-01
Oscillation of electrical activity has been found in many nervous systems, from invertebrates to vertebrates including man. There exists experimental evidence of very simple circuits with the capability of oscillation. Neurons with intrinsic oscillation have been found and also neural circuits where oscillation is a property of the network. These two types of oscillations coexist in many instances. It is nowadays hypothesized that behind synchronization and oscillation there is a system of coupled oscillators responsible for activities that range from locomotion and feature binding in vision to control of sleep and circadian rhythms. The huge knowledge that has been acquired on oscillators from the times of Lord Rayleigh has made the simulation of neural oscillators a very active endeavor. This has been enhanced with more recent physiological findings about small neural circuits by means of intracellular and extracellular recordings as well as imaging methods. The future of this interdisciplinary field looks very promising; some researchers are going into quantum mechanics with the idea of trying to provide a quantum description of the brain. In this work we describe some simulations using neuron models by means of which we form simple neural networks that have the capability of oscillation. We analyze the oscillatory activity with root locus method, cross-correlation histograms, and phase planes. In the more complicated neural network models there is the possibility of chaotic oscillatory activity and we study that by means of Lyapunov exponents. The companion paper shows an example of that kind.
Z3等变近Hamiltonian系统的极限环分支%Limit Cycles Bifurcated from a Z3- equivariant Near-Hamiltonian System
杨素敏
2012-01-01
The number of limit cycles of a Z3-equivariant cubic Hamiltonian system under Z3-equivariant quartic perturbations was studied using the methods of Hopf bifurcation theory. The results show that the perturbed system can have 6 small limit cycles.%在Z3等变四次扰动下,利用Hopf分支理论的方法,证明Z3等变Hamiltonian系统可以扰动出6个小振幅极限环.
(Ⅲ)m=0类二次系统的极限环问题(Ⅲ)%LIMIT CYCLE PROBLEM OF QUADRATIC SYSTEM OF TYPE (Ⅲ)m=0,(Ⅲ)
M Ali; 罗定军
2005-01-01
To continue the discussion in (Ⅰ) and (Ⅱ),and finish the study of the limit cycle problem for quadratic system (Ⅲ)m=0 in this paper.Since there is at most one limit cycle that may be created from critical point O by Hopf bifurcation,the number of limit cycles depends on the different situations of separatrix cycle to be formed around O.If it is a homoclinic cycle passing through saddle S1 on 1+ax-y=0,which has the same stability with the limit cycle created by Hopf bifurcation,then the uniqueness of limit cycles in such cases can be proved.If it is a homoclinic cycle passing through saddle N on x=0,which has the different stability from the limit cycle created by Hopf bifurcation,then it will be a case of two limit cycles.For the case when the separatrix cycle is a heteroclinic cycle passing through two saddles at infinity,the discussion of the paper shows that the number of limit cycles will change from one to two depending on the different values of parameters of system.
Modeling microtubule oscillations
Jobs, E.; Wolf, D.E.; Flyvbjerg, H.
1997-01-01
Synchronization of molecular reactions in a macroscopic volume may cause the volume's physical properties to change dynamically and thus reveal much about the reactions. As an example, experimental time series for so-called microtubule oscillations are analyzed in terms of a minimal model...... for this complex polymerization-depolymerization cycle. The model reproduces well the qualitatively different time series that result from different experimental conditions, and illuminates the role and importance of individual processes in the cycle. Simple experiments are suggested that can further test...... and define the model and the polymer's reaction cycle....
Oscillations following periodic reinforcement.
Monteiro, Tiago; Machado, Armando
2009-06-01
Three experiments examined behavior in extinction following periodic reinforcement. During the first phase of Experiment 1, four groups of pigeons were exposed to fixed interval (FI 16s or FI 48s) or variable interval (VI 16s or VI 48s) reinforcement schedules. Next, during the second phase, each session started with reinforcement trials and ended with an extinction segment. Experiment 2 was similar except that the extinction segment was considerably longer. Experiment 3 replaced the FI schedules with a peak procedure, with FI trials interspersed with non-food peak interval (PI) trials that were four times longer. One group of pigeons was exposed to FI 20s PI 80s trials, and another to FI 40s PI 160s trials. Results showed that, during the extinction segment, most pigeons trained with FI schedules, but not with VI schedules, displayed pause-peck oscillations with a period close to, but slightly greater than the FI parameter. These oscillations did not start immediately after the onset of extinction. Comparing the oscillations from Experiments 1 and 2 suggested that the alternation of reconditioning and re-extinction increases the reliability and earlier onset of the oscillations. In Experiment 3 the pigeons exhibited well-defined pause-peck cycles since the onset of extinction. These cycles had periods close to twice the value of the FI and lasted for long intervals of time. We discuss some hypotheses concerning the processes underlying behavioral oscillations following periodic reinforcement.
Meirellesfilho, C.; Liang, Edison P.
1994-01-01
There has been, recently, a revival of the stability problem of accretion disks. Much of this renewed interest is due to recent observational data on transient soft X-ray novae, which are low-mass X-ray binaries. It is widely believed that nonsteady mass transfer from the secondary onto the compact primary, through an accretion disk, is the reason for the observed spectacular events in the form of often repetitive outbursts, with recurrence times ranging from 1 to 60 yr and duration time on the scale of months. Though not having reached yet a consensus about the nature of the mechanism that regulates the mass transfer, the disk thermal instability model seems to be favored by the fact that the rise in the hard X-ray luminosity is prior to the rise in the soft X-ray luminosity, while the mass transfer instability model seems to be hindered by the fact that the luminosity during quiescence is unable to trigger the thermal instability. However, it should be stressed that, remarkably, the X-ray light curves of these X-ray novae all show overall exponential decays, a feature quite difficult to reproduce in the framework of the viscous disk model, which yields powerlike luminosity decay. Taking into account this observational constraint, we have studied the temporal evolution of perturbations in the accretion rate, under the assumption that alpha is radial and parameter dependent. The chosen dependence is such that the model can reproduce limit cycle behavior (the system is locally unstable but globally stable). However, the kind of dependence we are looking for in alpha does not allow us to use the usual Shakura and Sunyaev procedure in the sense that we no longer can obtain a linearized continuity equation without explicit dependence on the accretion rate. This is so because now we cannot eliminate the accretion rate by using the angular momentum conservation equation.
RESPONSE OF NONLINEAR OSCILLATOR UNDER NARROW-BAND RANDOM EXCITATION
戎海武; 王向东; 孟光; 徐伟; 方同
2003-01-01
The principal resonance of Duffing oscillator to narrow-band random parametricexcitation was investigated. The method of multiple scales was used to determine theequations of modulation of amplitude and phase. The behavior, stability and bifurcation ofsteady state response were studied by means of qualitative analyses. The effects of damping,detuning, bandwidth and magnitudes of deterministic and random excitations wereanalyzed. The theoretical analyses were verified by numerical results. Theoretical analysesand numerical simulations show that when the intensity of the random excitation increases,the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle.Under some conditions the system may have two ,steady state solutions.
Dispersal and noise: Various modes of synchrony in ecological oscillators
Bressloff, Paul C.
2012-10-21
We use the theory of noise-induced phase synchronization to analyze the effects of dispersal on the synchronization of a pair of predator-prey systems within a fluctuating environment (Moran effect). Assuming that each isolated local population acts as a limit cycle oscillator in the deterministic limit, we use phase reduction and averaging methods to derive a Fokker-Planck equation describing the evolution of the probability density for pairwise phase differences between the oscillators. In the case of common environmental noise, the oscillators ultimately synchronize. However the approach to synchrony depends on whether or not dispersal in the absence of noise supports any stable asynchronous states. We also show how the combination of partially correlated noise with dispersal can lead to a multistable steady-state probability density. © 2012 Springer-Verlag Berlin Heidelberg.
Niu, Hong-quan [Brandeis Univ., Waltham, MA (United States)
2003-01-01
This thesis presents a limit on the B$0\\atop{s}$$\\bar{B}$$0\\atop{s}$ oscillation frequency from p$\\bar{p}$ collision data at √s = 1.8 TeV at CDF. The data sample used is the inclusive electron and muon trigger data of approximately 90 pb^{-1} collected during the 1993-95 run.
Oscillators and relaxation phenomena in Pleistocene climate theory
Crucifix, Michel
2011-01-01
Ice sheets appeared in the northern hemisphere around 3 million years ago and glacial-interglacial cycles have paced Earth's climate since then. Superimposed on these long glacial cycles comes an intricate pattern of millennial and sub-millennial variability, including Dansgaard-Oeschger and Heinrich events. There are numerous theories about theses oscillations. Here, we review a number of them in order draw a parallel between climatic concepts and dynamical system concepts, including, in particular, the relaxation oscillator, excitability, slow-fast dynamics and homoclinic orbits. Namely, almost all theories of ice ages reviewed here feature a phenomenon of synchronisation between internal climate dynamics and the astronomical forcing. However, these theories differ in their bifurcation structure and this has an effect on the way the ice age phenomenon could grow 3 million years ago. All theories on rapid events reviewed here rely on the concept of a limit cycle in the ocean circulation, which may be excited...
YOOER Chi-Feng; XU Jian-Xue; ZHANG Xin-Hua
2009-01-01
Mechanism of period-adding cascades with chaos in a reduced leech neuron model is suggested as the bifurcation of a saddle-node limit cycle with homoclinic orbits satisfying the "small lobe condition",instead of the blue-sky catastrophe.In every spiking adding,the new spike emerges at the end of the spiking phase of the bursters.
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…
Synchronization and desynchronization of self-sustained oscillators by common noise.
Goldobin, Denis S; Pikovsky, Arkady
2005-04-01
We consider the effect of external noise on the dynamics of limit cycle oscillators. The Lyapunov exponent becomes negative under influence of small white noise, what means synchronization of two or more identical systems subject to common noise. We analytically study the effect of small non-identities in the oscillators and in the noise, and derive statistical characteristics of deviations from the perfect synchrony. Large white noise can lead to desynchronization of oscillators, provided they are non-isochronous. This is demonstrated for the Van der Pol-Duffing system.
Clustering in Globally Coupled Oscillators Near a Hopf Bifurcation: Theory and Experiments
Kori, Hiroshi; Jain, Swati; Kiss, István Z; Hudson, John
2014-01-01
A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate analytically the phase coupling function from given limit-cycle oscillator models. Moreover, using the phase coupling function, the stability of phase clusters can be analyzed. We demonstrate our theory with the Brusselator model. Experiments are carried out to confirm the presence of phase clusters close to Hopf bifurcations with electrochemical oscillators.
Optomechanical self-oscillations in an anharmonic potential: engineering a nonclassical steady state
Grimm, Manuel; Bruder, Christoph; Lörch, Niels
2016-09-01
We study self-oscillations of an optomechanical system, where coherent mechanical oscillations are induced by a driven optical or microwave cavity, for the case of an anharmonic mechanical oscillator potential. A semiclassical analytical model is developed to characterize the limit cycle for large mechanical amplitudes corresponding to a weak nonlinearity. As a result, we predict conditions to achieve subpoissonian phonon statistics in the steady state, indicating classically forbidden behavior. We compare with numerical simulations and find very good agreement. Our model is quite general and can be applied to other physical systems such as trapped ions or superconducting circuits.
Oscillation death in a coupled van der Pol–Mathieu system
Madhurjya P Bora; Dipak Sarmah
2013-10-01
We report an investigation of the oscillation death (OD) of a parametrically excited coupled van der Pol–Mathieu (vdPM) system. The system can be considered as a pair of harmonically forced van der Pol oscillators under a double-well potential. The two oscillators are coupled with a cubic nonlinearity. We have shown that the system arrives at an OD regime when coupling strength crosses a threshold value at which the system undergoes saddle-node bifurcation and two limit cycles coalesce onto a fixed point of the system. We have further shown that this nonautonomous system possesses a centre manifold corresponding to the OD regime.
Fu, Chunjiang; Suzuki, Yasuyuki; Kiyono, Ken; Morasso, Pietro; Nomura, Taishin
2014-12-06
Stability of human gait is the ability to maintain upright posture during walking against external perturbations. It is a complex process determined by a number of cross-related factors, including gait trajectory, joint impedance and neural control strategies. Here, we consider a control strategy that can achieve stable steady-state periodic gait while maintaining joint flexibility with the lowest possible joint impedance. To this end, we carried out a simulation study of a heel-toe footed biped model with hip, knee and ankle joints and a heavy head-arms-trunk element, working in the sagittal plane. For simplicity, the model assumes a periodic desired joint angle trajectory and joint torques generated by a set of feed-forward and proportional-derivative feedback controllers, whereby the joint impedance is parametrized by the feedback gains. We could show that a desired steady-state gait accompanied by the desired joint angle trajectory can be established as a stable limit cycle (LC) for the feedback controller with an appropriate set of large feedback gains. Moreover, as the feedback gains are decreased for lowering the joint stiffness, stability of the LC is lost only in a few dimensions, while leaving the remaining large number of dimensions quite stable: this means that the LC becomes saddle-type, with a low-dimensional unstable manifold and a high-dimensional stable manifold. Remarkably, the unstable manifold remains of low dimensionality even when the feedback gains are decreased far below the instability point. We then developed an intermittent neural feedback controller that is activated only for short periods of time at an optimal phase of each gait stride. We characterized the robustness of this design by showing that it can better stabilize the unstable LC with small feedback gains, leading to a flexible gait, and in particular we demonstrated that such an intermittent controller performs better if it drives the state point to the stable manifold, rather
Complex oscillations in the combustion of acetaldehyde
Harding, Robert H.; Sevčikova, Hana; Ross, John
1988-10-01
Aperiodic dynamics are observed experimentally in the cool flame combustion region of acetaldehyde (ACH) in a continuous stirred tank reactor (CSTR). A gradual transition is seen, with variation of exit orifice size, from limit cycle oscillation to aperiodic variations in light emission, and then back to near periodic oscillations. We analyze this transition by calculating power spectra, autocorrelation functions, phase portraits, period distributions, and Poincaré sections. The variation in peak amplitude and peak-to-peak period of the temporal variations of light emission increases during the transition. There are many initial indications of a transition to chaos. However, after an in-depth analysis, given in the following article, we ascribe the transition to the presence of a Hopf bifurcation and noise: the path traced out in the constraint space by the change in exit orifice size is nearly tangent to a Hopf bifurcation set but does not cross this set.
Heteroclinic Bifurcation of Strongly Nonlinear Oscillator
ZHANG Qi-Chang; WANG Wei; LI Wei-Yi
2008-01-01
Analytical prediction of heteroclinic bifurcation of the strongly nonlinear oscillator is presented by using the extended normal form method.We consider the approximate periodic solution of the system subject to the quintic nonlinearity by introducing the undetermined fundamental frequency.For the occurrence of heteroclinicity,the bifurcation criterion is accomplished.It depends on the contact of the limit cycle with the saddle equilibrium.As is illustrated,the explicit application shows that the new results coincide very well with the results of numerical simulation when disturbing parameter is of arbitrary magnitude.PACS: 82.40.Bj,47.20.Ky,02.30.Hq
Barik, Debashis; Ball, David A; Peccoud, Jean; Tyson, John J
2016-12-01
The cell division cycle of eukaryotes is governed by a complex network of cyclin-dependent protein kinases (CDKs) and auxiliary proteins that govern CDK activities. The control system must function reliably in the context of molecular noise that is inevitable in tiny yeast cells, because mistakes in sequencing cell cycle events are detrimental or fatal to the cell or its progeny. To assess the effects of noise on cell cycle progression requires not only extensive, quantitative, experimental measurements of cellular heterogeneity but also comprehensive, accurate, mathematical models of stochastic fluctuations in the CDK control system. In this paper we provide a stochastic model of the budding yeast cell cycle that accurately accounts for the variable phenotypes of wild-type cells and more than 20 mutant yeast strains simulated in different growth conditions. We specifically tested the role of feedback regulations mediated by G1- and SG2M-phase cyclins to minimize the noise in cell cycle progression. Details of the model are informed and tested by quantitative measurements (by fluorescence in situ hybridization) of the joint distributions of mRNA populations in yeast cells. We use the model to predict the phenotypes of ~30 mutant yeast strains that have not yet been characterized experimentally.
Atakishiyev, Natig M [Centro de Ciencias FIsicas, UNAM, Apartado Postal 48-3, 62251 Cuernavaca, Morelos (Mexico); Klimyk, Anatoliy U [Centro de Ciencias FIsicas, UNAM, Apartado Postal 48-3, 62251 Cuernavaca, Morelos (Mexico); Wolf, Kurt Bernardo [Centro de Ciencias FIsicas, UNAM, Apartado Postal 48-3, 62251 Cuernavaca, Morelos (Mexico)
2004-05-28
The finite q-oscillator is a model that obeys the dynamics of the harmonic oscillator, with the operators of position, momentum and Hamiltonian being functions of elements of the q-algebra su{sub q}(2). The spectrum of position in this discrete system, in a fixed representation j, consists of 2j + 1 'sensor'-points x{sub s} = 1/2 [2s]{sub q}, s element of {l_brace}-j, -j+1, ..., j{r_brace}, and similarly for the momentum observable. The spectrum of energies is finite and equally spaced, so the system supports coherent states. The wavefunctions involve dual q-Kravchuk polynomials, which are solutions to a finite-difference Schroedinger equation. Time evolution (times a phase) defines the fractional Fourier-q-Kravchuk transform. In the classical limit as q {yields} 1 we recover the finite oscillator Lie algebra, the N = 2j {yields} {infinity} limit returns the Macfarlane-Biedenharn q-oscillator and both limits contract the generators to the standard quantum-mechanical harmonic oscillator.
Atakishiyev, Natig M.; Klimyk, Anatoliy U.; Wolf, Kurt Bernardo
2004-05-01
The finite q-oscillator is a model that obeys the dynamics of the harmonic oscillator, with the operators of position, momentum and Hamiltonian being functions of elements of the q-algebra suq(2). The spectrum of position in this discrete system, in a fixed representation j, consists of 2j + 1 'sensor'-points x_s={\\case12}[2s]_q, s\\in\\{-j,-j+1,\\ldots,j\\} , and similarly for the momentum observable. The spectrum of energies is finite and equally spaced, so the system supports coherent states. The wavefunctions involve dual q-Kravchuk polynomials, which are solutions to a finite-difference Schrödinger equation. Time evolution (times a phase) defines the fractional Fourier-q-Kravchuk transform. In the classical limit as q rarr 1 we recover the finite oscillator Lie algebra, the N = 2j rarr infin limit returns the Macfarlane-Biedenharn q-oscillator and both limits contract the generators to the standard quantum-mechanical harmonic oscillator.
Oscillate boiling from microheaters
Li, Fenfang; Gonzalez-Avila, S. Roberto; Nguyen, Dang Minh; Ohl, Claus-Dieter
2017-01-01
We report about an intriguing boiling regime occurring for small heaters embedded on the boundary in subcooled water. The microheater is realized by focusing a continuous wave laser beam to about 10 μ m in diameter onto a 165-nm-thick layer of gold, which is submerged in water. After an initial vaporous explosion a single bubble oscillates continuously and repeatedly at several 100 kHz albeit with constant laser power input. The microbubble's oscillations are accompanied with bubble pinch-off, leading to a stream of gaseous bubbles in the subcooled water. The self-driven bubble oscillation is explained with a thermally kicked oscillator caused by surface attachment and by the nonspherical collapses. Additionally, Marangoni stresses induce a recirculating streaming flow which transports cold liquid towards the microheater, reducing diffusion of heat along the substrate and therefore stabilizing the phenomenon to many million cycles. We speculate that this oscillate boiling regime may overcome the heat transfer thresholds observed during the nucleate boiling crisis and offers a new pathway for heat transfer under microgravity conditions.
Oscillations in stellar superflares
Balona, L A; Kosovichev, A; Nakariakov, V M; Pugh, C E; Van Doorsselaere, T
2015-01-01
Two different mechanisms may act to induce quasi-periodic pulsations (QPP) in whole-disk observations of stellar flares. One mechanism may be magneto-hydromagnetic (MHD) forces and other processes acting on flare loops as seen in the Sun. The other mechanism may be forced local acoustic oscillations due to the high-energy particle impulse generated by the flare (known as `sunquakes' in the Sun). We analyze short-cadence Kepler data of 257 flares in 75 stars to search for QPP in the flare decay branch or post-flare oscillations which may be attributed to either of these two mechanisms. About 18 percent of stellar flares show a distinct bump in the flare decay branch of unknown origin. The bump does not seem to be a highly-damped global oscillation because the periods of the bumps derived from wavelet analysis do not correlate with any stellar parameter. We detected damped oscillations covering several cycles (QPP), in seven flares on five stars. The periods of these oscillations also do not correlate with any ...
González-Olivares, Eduardo; González-Yañez, Betsabé; Mena-Lorca, Jaime; Flores, Jose D
2013-04-01
The main purpose of this work is to analyze a Gause type predator-prey model in which two ecological phenomena are considered: the Allee effect affecting the prey growth function and the formation of group defence by prey in order to avoid the predation. We prove the existence of a separatrix curves in the phase plane, determined by the stable manifold of the equilibrium point associated to the Allee effect, implying that the solutions are highly sensitive to the initial conditions. Trajectories starting at one side of this separatrix curve have the equilibrium point (0,0) as their ω-limit, while trajectories starting at the other side will approach to one of the following three attractors: a stable limit cycle, a stable coexistence point or the stable equilibrium point (K,0) in which the predators disappear and prey attains their carrying capacity. We obtain conditions on the parameter values for the existence of one or two positive hyperbolic equilibrium points and the existence of a limit cycle surrounding one of them. Both ecological processes under study, namely the nonmonotonic functional response and the Allee effect on prey, exert a strong influence on the system dynamics, resulting in multiple domains of attraction. Using Liapunov quantities we demonstrate the uniqueness of limit cycle, which constitutes one of the main differences with the model where the Allee effect is not considered. Computer simulations are also given in support of the conclusions.
Oscillations of a chemical garden
Pantaleone, J.; Toth, A.; Horvath, D.; Rother McMahan, J.; Smith, R.; Butki, D.; Braden, J.; Mathews, E.; Geri, H.; Maselko, J.
2008-04-01
When soluble metal salts are placed in a silicate solution, chemical gardens grow. These gardens are treelike structures formed of long, thin, hollow tubes. Here we study one particular case: a calcium nitrate pellet in a solution of sodium trisilicate. We observe that tube growth results from a relaxation oscillation. The average period and the average growth rate are approximately constant for most of the structures growth. The period does fluctuate from cycle to cycle, with the oscillation amplitude proportional to the period. Based on our observations, we develop a model of the relaxation oscillations which calculates the average oscillation period and the average tube radius in terms of fundamental membrane parameters. We also propose a model for the average tube growth rate. Predictions are made for future experiments.
A new model for realistic random perturbations of stochastic oscillators
Dieci, Luca; Li, Wuchen; Zhou, Haomin
2016-08-01
Classical theories predict that solutions of differential equations will leave any neighborhood of a stable limit cycle, if white noise is added to the system. In reality, many engineering systems modeled by second order differential equations, like the van der Pol oscillator, show incredible robustness against noise perturbations, and the perturbed trajectories remain in the neighborhood of a stable limit cycle for all times of practical interest. In this paper, we propose a new model of noise to bridge this apparent discrepancy between theory and practice. Restricting to perturbations from within this new class of noise, we consider stochastic perturbations of second order differential systems that -in the unperturbed case- admit asymptotically stable limit cycles. We show that the perturbed solutions are globally bounded and remain in a tubular neighborhood of the underlying deterministic periodic orbit. We also define stochastic Poincaré map(s), and further derive partial differential equations for the transition density function.
Complex dynamics of a particle in an oscillating potential field
BARNALI PAL; DEBJIT DUTTA; SWARUP PORIA
2017-08-01
In this paper, the classical problem of the motion of a particle in one dimension with an external time dependent field is studied from the point of view of the dynamical system. The dynamical equations of motion of the particle are formulated. Equilibrium points of the non-oscillating systems are found and their local stability natures are analysed. Effect of oscillating potential barrier is analysed through numerical simulations. Phase diagrams,bifurcation diagrams and variations of largest Lyapunov exponents are presented to show the existence of a wide range of nonlinear phenomena such as limit cycle, quasiperiodic and chaotic oscillations in the system. Effects ofnonlinear damping in the model are also reported. Analysis of the physically interesting cases where damping is proportional to higher powers of velocity are presented for the sake of generalizing our findings and establishingfirm conclusion.
Yu, Pei; Han, Maoan
2013-04-01
In this paper, we show that a Z2-equivariant 3rd-order Hamiltonian planar vector fields with 3rd-order symmetric perturbations can have at least 10 limit cycles. The method combines the general perturbation to the vector field and the perturbation to the Hamiltonian function. The Melnikov function is evaluated near the center of vector field, as well as near homoclinic and heteroclinic orbits.
Oscillation death in coupled oscillators
Wei ZOU; Xin-gang WANG; Qi ZHAO; Meng ZHAN
2009-01-01
We study dynamical behaviors in coupled nonlinear oscillators and find that under certain condi- tions, a whole coupled oscillator system can cease oscil- lation and transfer to a globally nonuniform stationary state [I.e., the so-called oscillation death (OD) state], and this phenomenon can be generally observed. This OD state depends on coupling strengths and is clearly differ- ent from previously studied amplitude death (AD) state, which refers to the phenomenon where the whole system is trapped into homogeneously steady state of a fixed point, which already exists but is unstable in the ab- sence of coupling. For larger systems, very rich pattern structures of global death states are observed. These Turing-like patterns may share some essential features with the classical Turing pattern.
Tamaru, Shingo; Kubota, Hitoshi; Yakushiji, Kay; Fukushima, Akio; Yuasa, Shinji
2017-06-01
We present a theory for analyzing the phase stability of a spin-torque oscillator (STO) stabilized by a phase-locked-loop (PLL) circuit using the STO's free-running performance and circuit parameters. We show that the linewidth measured on a spectrum analyzer, which is the most commonly used performance indicator for the phase stability of a free-running STO, is not useful for estimating the phase stability of a phase-locked STO. A more important value is the STO's frequency-error spectral density (FESD) around the PLL bandwidth. We calculate the residual phase-error spectral density (PESD) of the phase-locked STO output signal using the actual FESD of the free-running STO and circuit parameters under three different conditions, and obtain excellent agreement with experimental results. This theoretical model allows one to predict the phase error of a STO stabilized by a PLL circuit, thus giving useful guidance for designing a PLL circuit and developing a STO. The theory indicates that a reduction of the STO's FESD around the PLL bandwidth, which is governed by the thermal stability of the STO, is of prime importance for further improvement of the STO's signal quality under phase-locked oscillation.
Gorensek, M.; Edwards, T.
2009-06-11
A recuperative bayonet reactor design for the high-temperature sulfuric acid decomposition step in sulfur-based thermochemical hydrogen cycles was evaluated using pinch analysis in conjunction with statistical methods. The objective was to establish the minimum energy requirement. Taking hydrogen production via alkaline electrolysis with nuclear power as the benchmark, the acid decomposition step can consume no more than 450 kJ/mol SO{sub 2} for sulfur cycles to be competitive. The lowest value of the minimum heating target, 320.9 kJ/mol SO{sub 2}, was found at the highest pressure (90 bar) and peak process temperature (900 C) considered, and at a feed concentration of 42.5 mol% H{sub 2}SO{sub 4}. This should be low enough for a practical water-splitting process, even including the additional energy required to concentrate the acid feed. Lower temperatures consistently gave higher minimum heating targets. The lowest peak process temperature that could meet the 450-kJ/mol SO{sub 2} benchmark was 750 C. If the decomposition reactor were to be heated indirectly by an advanced gas-cooled reactor heat source (50 C temperature difference between primary and secondary coolants, 25 C minimum temperature difference between the secondary coolant and the process), then sulfur cycles using this concept could be competitive with alkaline electrolysis provided the primary heat source temperature is at least 825 C. The bayonet design will not be practical if the (primary heat source) reactor outlet temperature is below 825 C.
Mongin, Mathieu; Nelson, David M.; Pondaven, Philippe; Tréguer, Paul
2006-03-01
We previously reported the application of an upper-ocean biogeochemical model in which the elemental composition of the phytoplankton is flexible and responds to changes in light and nutrient availability [Mongin, M., Nelson, D., Pondaven, P., Brzezinski, M., Tréguer, P., 2003. Simulation of upper-ocean biogeochemistry with a flexible-composition phytoplankton model: C, N and Si cycling in the western Sargasso Sea. Deep-Sea Research I 50, 1445-1480]. That model, applied in the western Sargasso Sea, considered the cycles of C, N and Si in the upper 400 m and limitation of phytoplankton growth by N, Si and light. We now report a new version of this model that includes Fe cycling and Fe limitation and its application in the Southern Ocean. The model includes two phytoplankton groups, diatoms and non-siliceous forms. Uptake of NO 3- by phytoplankton is light dependent, but NH 4+, Si(OH) 4 and Fe uptake are not and can therefore continue through the night. The model tracks the resulting C/N and Fe/C ratios of both groups and Si/N ratio of diatoms, and permits uptake of C, N, Fe and Si to proceed independently when those ratios are close to those of nutrient-replete phytoplankton. When they indicate a deficiency cellular C, N, Fe or Si, uptake of the non-limiting elements is controlled by the content of the limiting element in accordance with the cell-quota formulation of [Droop, M., 1974. The nutrient status of algal cell in continuous culture. Journal of the Marine Biological Association of the United Kingdom 54, 825-855]. The model thus identifies the growth-limiting element and quantifies the degree of limitation from the elemental composition of the phytoplankton. We applied this model at the French KERFIX site in the Indian Ocean sector of the Southern Ocean, using meteorological forcing for that site from 1991 to 1995. As in the Sargasso Sea application, the flexible-composition structure provides simulations that are consistent with field data with only minimal
Berner, L. T.; Law, B. E.
2015-11-01
Severe droughts occurred in the western United States during recent decades, and continued human greenhouse gas emissions are expected to exacerbate warming and drying in this region. We investigated the role of water availability in shaping forest carbon cycling and morphological traits in the eastern Cascade Mountains, Oregon, focusing on the transition from low-elevation, dry western juniper (Juniperus occidentalis) woodlands to higher-elevation, wetter ponderosa pine (Pinus ponderosa) and grand fir (Abies grandis) forests. We examined 12 sites in mature forests that spanned a 1300 mm yr-1 gradient in mean growing-year climate moisture index (CMIgy ), computed annually (1964 to 2013) as monthly precipitation minus reference evapotranspiration and summed October to September. Maximum leaf area, annual aboveground productivity, and aboveground live tree biomass increased with CMIgy (r2 = 0.67-0.88, P gy (r2 = 0.53, P gy and extensive insect outbreak. Traits of stress-tolerant juniper included short stature, high wood density for cavitation resistance, and high investment in water transport relative to leaf area. Species occupying wetter areas invested more resources in height growth in response to competition for light relative to investment in hydraulic architecture. Consequently, maximum tree height, leaf area : sapwood area ratio, and stem wood density were all correlated with CMIgy . The tight coupling of forest carbon cycling and species traits with water availability suggests that warmer and drier conditions projected for the 21st century could have significant biogeochemical, ecological, and social consequences in the Pacific Northwest.
Ng Fanny
2008-12-01
Full Text Available Abstract Background The Drosophila circadian oscillator is composed of transcriptional feedback loops in which CLOCK-CYCLE (CLK-CYC heterodimers activate their feedback regulators period (per and timeless (tim via E-box mediated transcription. These feedback loop oscillators are present in distinct clusters of dorsal and lateral neurons in the adult brain, but how this pattern of expression is established during development is not known. Since CLK is required to initiate feedback loop function, defining the pattern of CLK expression in embryos and larvae will shed light on oscillator neuron development. Results A novel CLK antiserum is used to show that CLK expression in the larval CNS and adult brain is limited to circadian oscillator cells. CLK is initially expressed in presumptive small ventral lateral neurons (s-LNvs, dorsal neurons 2 s (DN2s, and dorsal neuron 1 s (DN1s at embryonic stage (ES 16, and this CLK expression pattern persists through larval development. PER then accumulates in all CLK-expressing cells except presumptive DN2s during late ES 16 and ES 17, consistent with the delayed accumulation of PER in adult oscillator neurons and antiphase cycling of PER in larval DN2s. PER is also expressed in non-CLK-expressing cells in the embryonic CNS starting at ES 12. Although PER expression in CLK-negative cells continues in ClkJrk embryos, PER expression in cells that co-express PER and CLK is eliminated. Conclusion These data demonstrate that brain oscillator neurons begin development during embryogenesis, that PER expression in non-oscillator cells is CLK-independent, and that oscillator phase is an intrinsic characteristic of brain oscillator neurons. These results define the temporal and spatial coordinates of factors that initiate Clk expression, imply that circadian photoreceptors are not activated until the end of embryogenesis, and suggest that PER functions in a different capacity before oscillator cell development is
G. Bellini
2014-01-01
Full Text Available In the last decades, a very important breakthrough has been brought about in the elementary particle physics by the discovery of the phenomenon of the neutrino oscillations, which has shown neutrino properties beyond the Standard Model. But a full understanding of the various aspects of the neutrino oscillations is far to be achieved. In this paper the theoretical background of the neutrino oscillation phenomenon is described, referring in particular to the paradigmatic models. Then the various techniques and detectors which studied neutrinos from different sources are discussed, starting from the pioneering ones up to the detectors still in operation and to those in preparation. The physics results are finally presented adopting the same research path which has been crossed by this long saga. The problems not yet fixed in this field are discussed, together with the perspectives of their solutions in the near future.
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Freire, Joana G.; Cabeza, Cecilia; Marti, Arturo; Pöschel, Thorsten; Gallas, Jason A. C.
2013-06-01
The investigation of regular and irregular patterns in nonlinear oscillators is an outstanding problem in physics and in all natural sciences. In general, regularity is understood as tantamount to periodicity. However, there is now a flurry of works proving the existence of ``antiperiodicity'', an unfamiliar type of regularity. Here we report the experimental observation and numerical corroboration of antiperiodic oscillations. In contrast to the isolated solutions presently known, we report infinite hierarchies of antiperiodic waveforms that can be tuned continuously and that form wide spiral-shaped stability phases in the control parameter plane. The waveform complexity increases towards the focal point common to all spirals, a key hub interconnecting them all.
Luo, Ercang
2012-06-01
This paper analyzes the thermodynamic cycle of oscillating-flow regenerative machines. Unlike the classical analysis of thermodynamic textbooks, the assumptions for pistons' movement limitations are not needed and only ideal flowing and heat transfer should be maintained in our present analysis. Under such simple assumptions, the meso-scale thermodynamic cycles of each gas parcel in typical locations of a regenerator are analyzed. It is observed that the gas parcels in the regenerator undergo Lorentz cycle in different temperature levels, whereas the locus of all gas parcels inside the regenerator is the Ericson-like thermodynamic cycle. Based on this new finding, the author argued that ideal oscillating-flow machines without heat transfer and flowing losses is not the Stirling cycle. However, this new thermodynamic cycle can still achieve the same efficiency of the Carnot heat engine and can be considered a new reversible thermodynamic cycle under two constant-temperature heat sinks.
L. T. Berner
2015-09-01
Full Text Available Severe droughts occurred in the western United States during recent decades and continued human greenhouse gas emissions are expected to exacerbate warming and drying in this region. We investigated the role of water availability in shaping forest carbon cycling and morphological traits in the eastern Cascade Mountains, Oregon, focusing on the transition from low-elevation, dry western juniper (Juniperus occidentalis woodlands to higher-elevation, wetter ponderosa pine (Pinus ponderosa and grand fir (Abies grandis forests. We examined 12 sites in mature forests that spanned a 1300 mm yr−1 gradient in mean growing-year climate moisture index (CMIgy , computed annually (1964 to 2013 as monthly precipitation minus reference evapotranspiration and summed October to September. Maximum leaf area, annual aboveground productivity, and aboveground live tree biomass increased with CMIgy (r2 = 0.58–0.85, P gy (r2 = 0.65, P gy and extensive insect outbreak. Traits of stress-tolerant juniper included short stature, high wood density for cavitation resistance, and high investment in water transport relative to leaf area. Species occupying wetter areas invested more resources in height growth in response to competition for light relative to investment in hydraulic architecture. Correspondingly, maximum tree height, leaf area:sapwood area ratio, and stem wood density were all correlated with CMIgy . The tight coupling of forest carbon cycling and species traits with water availability suggests that warmer and drier conditions projected for the 21st century could have significant biogeochemical, ecological, and social consequences in the Pacific Northwest.
黄文韬; 刘一戌
2004-01-01
The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin.
Can Interest-Free Finance Limit the Frequency of Crises and the Volatility of the Business Cycle?
2011-05-14
effectively pays interest. Thus, the sale of debt is prohibited. Insurance , or takaful , poses another problem. In the middle ages, when the church in...Last year, the Congress of the United States passed a bill limiting leverage on banks that pose a systemic risk to the economy. Previously, banks were...the legal theory recommends profit-and-loss-sharing (PLS) schemes, where a manager and investor each take a proportional share of profits based
Niu, H
2003-01-01
This thesis presents a limit on the B0sB&d1;0 s oscillation frequency from pp¯ collision data at s = 1.8 TeV at CDF. The data sample used is the inclusive electron and muon trigger data of approximately 90 pb−1 collected during the 1993–1995 run. The B0s meson is reconstructed as B0s → νℓDs, where D s → &phis;π or K*0 K. The initial flavor of the B0s meson is determined from the decay products of the other b- hadron in the event, using opposite-side jet charge and soft lepton tagging methods. When combined with CDF previous measurements, a lower limit of Δms > 6.3 ps−1 is determined.
Niu, Hongquan
This thesis presents a limit on the B0sB¯0 s oscillation frequency from pp¯ collision data at s = 1.8 TeV at CDF. The data sample used is the inclusive electron and muon trigger data of approximately 90 pb-1 collected during the 1993--1995 run. The B0s meson is reconstructed as B0s → nuℓDs, where D s → φpi or K*0 K. The initial flavor of the B0s meson is determined from the decay products of the other b-hadron in the event, using opposite-side jet charge and soft lepton tagging methods. When combined with CDF previous measurements, a lower limit of Deltams > 6.3 ps-1 is determined.
三次Kolmogorov捕食系统的多个稳定极限环%Multiple Stable Limit Cycles for a Cubic Kolmogorov Prey-Predator System
陆征一; 何碧
2001-01-01
构造具有三个极限环(其中两个稳定)的三次Kolmogorov系统.这个例子肯定地回答了Coleman(1982)提出的一个问题.在多项式处理中,利用了计算机代数系统Maple.%A cubic Kolmogorov prey-predator system is constructed and is shown to have three small amplitude limit cycles, among which two are stable. This can serve as an affirmative answer to a question proposed by Coleman(1982). The computer algebraic system, Maple, is applied to manipulate polynomials in dealing with the system.
Coherence stability and effect of random natural frequencies in populations of coupled oscillators
Giacomin, Giambattista; Poquet, Christophe
2011-01-01
We consider the (noisy) Kuramoto model, that is a population of N oscillators, or rotators, with mean-field interaction. Each oscillator has its own randomly chosen natural frequency (quenched disorder) and it is stirred by Brownian motion. In the limit N goes to infty this model is accurately described by a (deterministic) Fokker-Planck equation. We study this equation and obtain quantitatively sharp results in the limit of weak disorder. We show that, in general, even when the natural frequencies have zero mean the oscillators synchronize (for sufficiently strong interaction) around a common rotating phase, whose frequency is sharply estimated. We also establish the stability properties of these solutions (in fact, limit cycles). These results are obtained by identifying the stable hyperbolic manifold of stationary solutions of an associated non disordered model and by exploiting the robustness of hyperbolic structures under suitable perturbations. When the disorder distribution is symmetric the speed vanis...
Brennan, M. J.; Tang, B.; Carranza, J. C.
2016-09-01
The van der Pol oscillator is an archetypal nonlinear oscillator that has been studied for many years. It is a self-sustaining oscillator that vibrates in a limit cycle, and has the characteristic that it generates energy in the part of the cycle when the displacement is small and dissipates energy in the part of the cycle when the displacement is large. Almost all analyses for this type of oscillator have been conducted in a strict mathematical framework using the displacement and velocity of the mass to describe the motion in the phase plane. Physical insight into the behaviour is then generally only possible for very small or for very large damping nonlinearity. In this paper a fresh approach is taken. The internal forces of the Rayleigh oscillator are studied rather than van der Pol's equation as the key damping force is a function of only velocity. Simulations are presented which show how the stiffness and damping forces vary when the system is vibrating in a steady-state limit cycle.
Dorozhkin, S. I.
2015-07-01
Self-oscillations of a microwave photovoltage with irregular interruptions have been discovered in the states with vanishing dc dissipation emerging in two-dimensional electron systems under microwave irradiation. The observed picture can be caused by transitions between a stable pole and a limiting cycle in the phase space of the systems (Andronov-Hopf bifurcation) that occur owing to fluctuations.
Nonlinear effects on Turing patterns: Time oscillations and chaos
Aragón, J. L.
2012-08-08
We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems. © 2012 American Physical Society.
Generalized Predator-Prey Oscillations in Ecological and Economic Equilibrium
Samuelson, Paul A.
1971-01-01
The standard predator-prey model is generalized beyond the Volterra linear-log form. Conservative oscillations are deduced and also conversion to a variational Hamiltonian form. Generalization to more than two species is also castable into Hamiltonian form, with small vibrations around equilibrium being of undamped sinusoidal type by virtue of associated characteristic exponents all being pure imaginaries. However, introduction into ecological equilibrium of a recognition of limited space and inorganic matter destroys the autonomous periodicity of the motions and makes inapplicable the elegant formalisms of classical statistical mechanics. Introduction of simple diminishing returns leads to damped motions that are kept cyclically alive by shocks of the weather and other exogenous stochastic elements. Introduction of increasing returns solely in an interval near equilibrium leads to autonomous self-exciting oscillations near a stable limit cycle; under stochastic forcing functions, a long-run ergodic state becomes predictable. PMID:5280532
Bours, Ralph; van Zanten, Martijn; Pierik, Ronald; Bouwmeester, Harro; van der Krol, Alexander
2013-10-01
In the natural environment, days are generally warmer than the night, resulting in a positive day/night temperature difference (+DIF). Plants have adapted to these conditions, and when exposed to antiphase light and temperature cycles (cold photoperiod/warm night [-DIF]), most species exhibit reduced elongation growth. To study the physiological mechanism of how light and temperature cycles affect plant growth, we used infrared imaging to dissect growth dynamics under +DIF and -DIF in the model plant Arabidopsis (Arabidopsis thaliana). We found that -DIF altered leaf growth patterns, decreasing the amplitude and delaying the phase of leaf movement. Ethylene application restored leaf growth in -DIF conditions, and constitutive ethylene signaling mutants maintain robust leaf movement amplitudes under -DIF, indicating that ethylene signaling becomes limiting under these conditions. In response to -DIF, the phase of ethylene emission advanced 2 h, but total ethylene emission was not reduced. However, expression analysis on members of the 1-aminocyclopropane-1-carboxylic acid (ACC) synthase ethylene biosynthesis gene family showed that ACS2 activity is specifically suppressed in the petiole region under -DIF conditions. Indeed, petioles of plants under -DIF had reduced ACC content, and application of ACC to the petiole restored leaf growth patterns. Moreover, acs2 mutants displayed reduced leaf movement under +DIF, similar to wild-type plants under -DIF. In addition, we demonstrate that the photoreceptor PHYTOCHROME B restricts ethylene biosynthesis and constrains the -DIF-induced phase shift in rhythmic growth. Our findings provide a mechanistic insight into how fluctuating temperature cycles regulate plant growth.
Dynamic Behavior and Unstable State Evolution of Ocean-Atmosphere Oscillator
DONG Wenjie; FENG Guolin
2005-01-01
It is mathematically and thoroughly proved in this paper that the nonlinear stochastic ocean-atmosphere oscillator model possesses a stable limit cycle; then the model equations are transformed into the FokkerPlanck equation (FPE), and the evolution of El Nino-Southern Oscillation (ENSO) from unstable state to stable state is studied from the point of view of nonequilibrium system dynamics. The study results reveal that although the complex nonlinear ocean-atmosphere oscillator model possesses multiequilibrium states,the real climatic system possesses only a quasi-normal state and a strong ENSO cycle stable state. The first passage time between states is also given in this paper, and the theoretical computational results agree with observational data.
Application of the green function formalism to nonlinear evolution of the low gain FEL oscillator
Shvets, G. [Princeton Plasma Physics Lab., NJ (United States); Wurtele, J.S.; Gardent, D. [Massachusetts Institute of Technology, Cambridge, MA (United States)] [and others
1995-12-31
A matrix formalism for the optical pulse evolution in the frequency domain, is applied to the nonlinear regime of operation. The formalism was previously developed for studies of the linear evolution of the low-gain FEL oscillator with an arbitrary shape of the electron beam. By varying experimentally controllable parameters, such as cavity detunning and cavity losses, different regimes of operation of the FEL oscillator, such as a steady state saturation and limit cycle saturation, are studied numerically. It is demonstrated that the linear supermodes, numerically obtained from the matrix formalism, provide an appropriate framework for analyzing the periodic change in the output power in the limit cycle regime. The frequency of this oscillation is related to the frequencies of the lowest-order linear supermodes. The response of the output radiation to periodic variation of the electron energy is studied. It is found that the response is enhanced when the frequency of the energy variation corresponds to the difference of per-pass phase advances of the lowest linear supermodes. Finally, various nonlinear models are tested to capture the steady state saturation and limit cycle variation of the EM field in the oscillator cavity.
Oscillations via Spike-Timing Dependent Plasticity in a Feed-Forward Model.
Yotam Luz
2016-04-01
Full Text Available Neuronal oscillatory activity has been reported in relation to a wide range of cognitive processes including the encoding of external stimuli, attention, and learning. Although the specific role of these oscillations has yet to be determined, it is clear that neuronal oscillations are abundant in the central nervous system. This raises the question of the origin of these oscillations: are the mechanisms for generating these oscillations genetically hard-wired or can they be acquired via a learning process? Here, we study the conditions under which oscillatory activity emerges through a process of spike timing dependent plasticity (STDP in a feed-forward architecture. First, we analyze the effect of oscillations on STDP-driven synaptic dynamics of a single synapse, and study how the parameters that characterize the STDP rule and the oscillations affect the resultant synaptic weight. Next, we analyze STDP-driven synaptic dynamics of a pre-synaptic population of neurons onto a single post-synaptic cell. The pre-synaptic neural population is assumed to be oscillating at the same frequency, albeit with different phases, such that the net activity of the pre-synaptic population is constant in time. Thus, in the homogeneous case in which all synapses are equal, the post-synaptic neuron receives constant input and hence does not oscillate. To investigate the transition to oscillatory activity, we develop a mean-field Fokker-Planck approximation of the synaptic dynamics. We analyze the conditions causing the homogeneous solution to lose its stability. The findings show that oscillatory activity appears through a mechanism of spontaneous symmetry breaking. However, in the general case the homogeneous solution is unstable, and the synaptic dynamics does not converge to a different fixed point, but rather to a limit cycle. We show how the temporal structure of the STDP rule determines the stability of the homogeneous solution and the drift velocity of the
Oscillations via Spike-Timing Dependent Plasticity in a Feed-Forward Model.
Luz, Yotam; Shamir, Maoz
2016-04-01
Neuronal oscillatory activity has been reported in relation to a wide range of cognitive processes including the encoding of external stimuli, attention, and learning. Although the specific role of these oscillations has yet to be determined, it is clear that neuronal oscillations are abundant in the central nervous system. This raises the question of the origin of these oscillations: are the mechanisms for generating these oscillations genetically hard-wired or can they be acquired via a learning process? Here, we study the conditions under which oscillatory activity emerges through a process of spike timing dependent plasticity (STDP) in a feed-forward architecture. First, we analyze the effect of oscillations on STDP-driven synaptic dynamics of a single synapse, and study how the parameters that characterize the STDP rule and the oscillations affect the resultant synaptic weight. Next, we analyze STDP-driven synaptic dynamics of a pre-synaptic population of neurons onto a single post-synaptic cell. The pre-synaptic neural population is assumed to be oscillating at the same frequency, albeit with different phases, such that the net activity of the pre-synaptic population is constant in time. Thus, in the homogeneous case in which all synapses are equal, the post-synaptic neuron receives constant input and hence does not oscillate. To investigate the transition to oscillatory activity, we develop a mean-field Fokker-Planck approximation of the synaptic dynamics. We analyze the conditions causing the homogeneous solution to lose its stability. The findings show that oscillatory activity appears through a mechanism of spontaneous symmetry breaking. However, in the general case the homogeneous solution is unstable, and the synaptic dynamics does not converge to a different fixed point, but rather to a limit cycle. We show how the temporal structure of the STDP rule determines the stability of the homogeneous solution and the drift velocity of the limit cycle.
Equatorial Oscillations in Jupiter's and Saturn's Atmospheres
Flasar, F. Michael; Guerlet, S.; Fouchet, T.; Schinder, P. J.
2011-01-01
Equatorial oscillations in the zonal-mean temperatures and zonal winds have been well documented in Earth's middle atmosphere. A growing body of evidence from ground-based and Cassini spacecraft observations indicates that such phenomena also occur in the stratospheres of Jupiter and Saturn. Earth-based midinfrared measurements spanning several decades have established that the equatorial stratospheric temperatures on Jupiter vary with a cycle of 4-5 years and on Saturn with a cycle of approximately 15 years. Spectra obtained by the Composite Infrared Spectrometer (CIRS) during the Cassini swingby at the end of 2000, with much better vertical resolution than the ground-based data, indicated a series of vertically stacked warm and cold anomalics at Jupiter's equator; a similar structurc was seen at Saturn's equator in CIRS limb measurements made in 2005, in the early phase of Cassini's orbital tour. The thermal wind equation implied similar patterns of mean zonal winds increasing and decreasing with altitude. On Saturn the peak-to-pcak amplitude of this variation was nearly 200 meters per second. The alternating vertical pattern of wanner and colder cquatorial tcmperatures and easterly and westerly tendencies of the zonal winds is seen in Earth's equatorial oscillations, where the pattern descends with time, The Cassini Jupiter and early Saturn observations were snapshots within a limited time interval, and they did not show the temporal evolution of the spatial patterns. However, more recent Saturn observations by CIRS (2010) and Cassini radio-occultation soundings (2009-2010) have provided an opportunity to follow the change of the temperature-zonal wind pattern, and they suggest there is descent, at a rate of roughly one scale height over four years. On Earth, the observed descent in the zonal-mean structure is associated with the absorption of a combination of vertically propagating waves with easlerly and westerly phase velocities. The peak-to-peak zonal wind
Oscillations of thick accretion discs
Jaroszynski, M.
1986-06-15
The non-axisymmetric oscillations of polytropic, ideal fluid tori rotating in the external gravitational field of a point mass are investigated both numerically and analytically. Normal modes of oscillations are found; their classification into 'radial', 'p', 'g' and 'f' modes is done in analogy to the stellar case. The non-discrete spectrum of modes which are neutral in the limit of axisymmetric perturbations is also present.
BUZALAF, Marília Afonso Rabelo; HANNAS, Angélica Reis; MAGALHÃES, Ana Carolina; RIOS, Daniela; HONÓRIO, Heitor Marques; DELBEM, Alberto Carlos Botazzo
2010-01-01
Despite a plethora of in situ studies and clinical trials evaluating the efficacy of fluoridated dentifrices on caries control, in vitro pH cycling models are still broadly used because they mimic the dynamics of mineral loss and gain involved in caries formation. This paper critically reviews the current literature on existing pH-cycling models for the in vitro evaluation of the efficacy of fluoridated dentifrices for caries control, focusing on their strengths and limitations. A search was undertaken in the MEDLINE electronic journal database using the keywords "pH-cycling", "demineralization", "remineralization", "in vitro", "fluoride", "dentifrice". The primary outcome was the decrease of demineralization or the increase of remineralization as measured by different methods (e.g.: transverse microradiography) or tooth fluoride uptake. Inclusion of studies, data extraction and quality assessment were undertaken independently and in duplicate by two members of the review team. Disagreements were solved by discussion and consensus or by a third party. One hundred and sixteen studies were included, of which 42 addressed specifically the comparison of dentifrices using different pH-cycling models. The other studies included meta-analysis or reviews, data about the effect of different fluoride sources on de-remineralization, different methods for analysis de-remineralization and chemical variables and characteristics of dental hard tissues that might have influence on de-remineralization processes. Generally, the studies presented ability to detect known results established by clinical trials, to demonstrate dose-related responses in the fluoride content of the dentifrices, and to provide repeatability and reproducibility between tests. In order to accomplish these features satisfactorily, it is mandatory to take into account the type of substrate and baseline artificial lesion, as well as the adequate response variables and statistical approaches to be used. This
Marília Afonso Rabelo Buzalaf
2010-08-01
Full Text Available Despite a plethora of in situ studies and clinical trials evaluating the efficacy of fluoridated dentifrices on caries control, in vitro pH cycling models are still broadly used because they mimic the dynamics of mineral loss and gain involved in caries formation. This paper critically reviews the current literature on existing pH-cycling models for the in vitro evaluation of the efficacy of fluoridated dentifrices for caries control, focusing on their strengths and limitations. A search was undertaken in the MEDLINE electronic journal database using the keywords "pH-cycling", "demineralization", "remineralization", "in vitro", "fluoride", "dentifrice". The primary outcome was the decrease of demineralization or the increase of remineralization as measured by different methods (e.g.: transverse microradiography or tooth fluoride uptake. Inclusion of studies, data extraction and quality assessment were undertaken independently and in duplicate by two members of the review team. Disagreements were solved by discussion and consensus or by a third party. One hundred and sixteen studies were included, of which 42 addressed specifically the comparison of dentifrices using different pH-cycling models. The other studies included meta-analysis or reviews, data about the effect of different fluoride sources on de-remineralization, different methods for analysis de-remineralization and chemical variables and characteristics of dental hard tissues that might have influence on de-remineralization processes. Generally, the studies presented ability to detect known results established by clinical trials, to demonstrate dose-related responses in the fluoride content of the dentifrices, and to provide repeatability and reproducibility between tests. In order to accomplish these features satisfactorily, it is mandatory to take into account the type of substrate and baseline artificial lesion, as well as the adequate response variables and statistical approaches
Synchronization and Phase Dynamics of Oscillating Foils
Finkel, Cyndee L.
In this work, a two-dimensional model representing the vortices that animals produce, when they are ying/swimming, was constructed. A D{shaped cylinder and an oscillating airfoil were used to mimic these body{shed and wing{generated vortices, respectively. The parameters chosen are based on the Reynolds numbers similar to that which is observed in nature (˜10 4). In order to imitate the motion of ying/swimming, the entire system was suspended into a water channel from frictionless air{bearings. The position of the apparatus in the channel was regulated with a linear, closed loop PI controller. Thrust/drag forces were measured with strain gauges and particle image velocimetry (PIV) was used to examine the wake structure that develops. The Strouhal number of the oscillating airfoil was compared to the values observed in nature as the system transitions between the accelerated and steady states. The results suggest that self-regulation restricts the values of the Strouhal number to a certain range where no other external sensory input is necessary. As suggested by previous work, this self-regulation is a result of a limit cycle process that stems from nonlinear periodic oscillations. The limit cycles were used to examine the synchronous conditions due to the coupling of the foil and wake vortices. Noise is a factor that can mask details of the synchronization. In order to control its effect, we study the locking conditions using an analytic technique that only considers the phases. Our results show that the phase locking indices are dependent on the Strouhal value as it converges to a frequency locking ratio of ≃0:5. This indicates that synchronization occurs during cruising between the motion of the foil and the measured thrust/drag response of the uid forces. The results suggest that Strouhal number selection in steady forward natural swimming and ying is the result of a limit cycle process and not actively controlled by an organism. An implication of this is
From steady-state to synchronized yeast glycolytic oscillations II: model validation.
du Preez, Franco B; van Niekerk, David D; Snoep, Jacky L
2012-08-01
In an accompanying paper [du Preez et al., (2012) FEBS J279, 2810-2822], we adapt an existing kinetic model for steady-state yeast glycolysis to simulate limit-cycle oscillations. Here we validate the model by testing its capacity to simulate a wide range of experiments on dynamics of yeast glycolysis. In addition to its description of the oscillations of glycolytic intermediates in intact cells and the rapid synchronization observed when mixing out-of-phase oscillatory cell populations (see accompanying paper), the model was able to predict the Hopf bifurcation diagram with glucose as the bifurcation parameter (and one of the bifurcation points with cyanide as the bifurcation parameter), the glucose- and acetaldehyde-driven forced oscillations, glucose and acetaldehyde quenching, and cell-free extract oscillations (including complex oscillations and mixed-mode oscillations). Thus, the model was compliant, at least qualitatively, with the majority of available experimental data for glycolytic oscillations in yeast. To our knowledge, this is the first time that a model for yeast glycolysis has been tested against such a wide variety of independent data sets. The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/dupreez/index.html. © 2012 The Authors Journal compilation © 2012 FEBS.
Autonomous oscillation in supramolecular assemblies: Role of free energy landscape and fluctuations
Sereda, Yuriy V.; Ortoleva, Peter J.
2015-11-01
Molecular dynamics studies demonstrated that a supramolecular assembly can express autonomous structural oscillations about equilibrium. It is demonstrated here that for nanosystems such oscillations can result from the interplay of free energy landscape and structural fluctuations. Furthermore, these oscillations have intermittent character, reflecting the conflict between a tendency to oscillate due to features in the free energy landscape, and the Second Law's repression of perpetual oscillation in an isothermal, equilibrium system. The demonstration system is a T = 1 icosahedral structure constituted of 12 protein pentamers in contact with a bath at fixed temperature. The oscillations are explained in terms of a Langevin model accounting for interactions among neighboring pentamers. The model is based on a postulated free energy landscape in the 24-dimensional space of variables describing the centrifugal and rotational motion of each pentamer. The model includes features such as basins of attraction and low free energy corridors. When the system is driven slightly out of equilibrium, the oscillations are transformed into a limit cycle, as expressed in terms of power spectrum narrowing.
沈伯骞; 刘德明
2000-01-01
This paper is concerned with a cubic Kolmogorov system with a solution of central quadratic curve which neither contacts with the coordinate axes, nor passes through the origin. The conclusion is that such a system may possess limit cycles.
Coexisting Oscillation and Extreme Multistability for a Memcapacitor-Based Circuit
Guangyi Wang
2017-01-01
Full Text Available The coexisting oscillations are observed with a memcapacitor-based circuit that consists of two linear inductors, two linear resistors, and an active nonlinear charge-controlled memcapacitor. We analyze the dynamics of this circuit and find that it owns an infinite number of equilibrium points and coexisting attractors, which means extreme multistability arises. Furthermore, we also show the stability of the infinite many equilibria and analyze the coexistence of fix point, limit cycle, and chaotic attractor in detail. Finally, an experimental result of the proposed oscillator via an analog electronic circuit is given.
Newham, D J; Donaldson, N de N
2007-01-01
Spinal cord injury (SCI) leads to a partial or complete disruption of motor, sensory, and autonomic nerve pathways below the level of the lesion. In paraplegic patients, functional electrical stimulation (FES) was originally widely considered as a means to restore walking function but this was proved technically very difficult because of the numerous degrees of freedom involved in walking. FES cycling was developed for people with SCI and has the advantages that cycling can be maintained for reasonably long periods in trained muscles and the risk of falls is low. In the article, we review research findings relevant to the successful application of FES cycling including the effects on muscle size, strength and function, and the cardiovascular and bone changes. We also describe important practical considerations in FES cycling regarding the application of surface electrodes, training and setting up the stimulator limitations, implanted stimulators and FES cycling including FES cycling in groups and other FES exercises such as FES rowing.
van der Most, Robbert G; Currie, Andrew J; Mahendran, Sathish; Prosser, Amy; Darabi, Anna; Robinson, Bruce W S; Nowak, Anna K; Lake, Richard A
2009-08-01
Tumor cell death potentially engages with the immune system. However, the efficacy of anti-tumor chemotherapy may be limited by tumor-driven immunosuppression, e.g., through CD25+ regulatory T cells. We addressed this question in a mouse model of mesothelioma by depleting or reconstituting CD25+ regulatory T cells in combination with two different chemotherapeutic drugs. We found that the efficacy of cyclophosphamide to eradicate established tumors, which has been linked to regulatory T cell depletion, was negated by adoptive transfer of CD25+ regulatory T cells. Analysis of post-chemotherapy regulatory T cell populations revealed that cyclophosphamide depleted cycling (Ki-67(hi)) T cells, including foxp3+ regulatory CD4+ T cells. Ki-67(hi) CD4+ T cells expressed increased levels of two markers, TNFR2 and ICOS, that have been associated with a maximally suppressive phenotype according to recently published studies. This suggest that cyclophosphamide depletes a population of maximally suppressive regulatory T cells, which may explain its superior anti-tumor efficacy in our model. Our data suggest that regulatory T cell depletion could be used to improve the efficacy of anti-cancer chemotherapy regimens. Indeed, we observed that the drug gemcitabine, which does not deplete cycling regulatory T cells, eradicates established tumors in mice only when CD25+ CD4+ T cells are concurrently depleted. Cyclophosphamide could be used to achieve regulatory T cell depletion in combination with chemotherapy.
Aoi, Yuki; Kawashima, Shigehiro A; Simanis, Viesturs; Yamamoto, Masayuki; Sato, Masamitsu
2014-07-01
Analogue-sensitive (as) mutants of kinases are widely used to selectively inhibit a single kinase with few off-target effects. The analogue-sensitive mutant cdc2-as of fission yeast (Schizosaccharomyces pombe) is a powerful tool to study the cell cycle, but the strain displays meiotic defects, and is sensitive to high and low temperature even in the absence of ATP-analogue inhibitors. This has limited the use of the strain for use in these settings. Here, we used in vivo selection for intragenic suppressor mutations of cdc2-as that restore full function in the absence of ATP-analogues. The cdc2-asM17 underwent meiosis and produced viable spores to a similar degree to the wild-type strain. The suppressor mutation also rescued the sensitivity of the cdc2-as strain to high and low temperature, genotoxins and an anti-microtubule drug. We have used cdc2-asM17 to show that Cdc2 activity is required to maintain the activity of the spindle assembly checkpoint. Furthermore, we also demonstrate that maintenance of the Shugoshin Sgo1 at meiotic centromeres does not require Cdc2 activity, whereas localization of the kinase aurora does. The modified cdc2-asM17 allele can be thus used to analyse many aspects of cell-cycle-related events in fission yeast.
Torsional oscillations and observed rotational period variations in early-type stars
Krticka, J; Henry, G W; Kurfurst, P; Karlicky, M
2016-01-01
Some chemically peculiar stars in the upper main sequence show rotational period variations of unknown origin. We propose these variations are a consequence of the propagation of internal waves in magnetic rotating stars that lead to the torsional oscillations of the star. We simulate the magnetohydrodynamic waves and calculate resonant frequencies for two stars that show rotational variations: CU Vir and HD 37776. We provide updated analyses of rotational period variations in these stars and compare our results with numerical models. For CU Vir, the length of the observed rotational-period cycle, $\\mathit\\Pi=67.6(5)$ yr, can be well reproduced by the models, which predict a cycle length of 51 yr. However, for HD 37776, the observed lower limit of the cycle length, $\\mathit\\Pi\\geq100$ yr, is significantly longer than the numerical models predict. We conclude that torsional oscillations provide a reasonable explanation at least for the observed period variations in CU Vir.
Circadian clock feedback cycle through NAMPT-mediated NAD+ biosynthesis.
Ramsey, Kathryn Moynihan; Yoshino, Jun; Brace, Cynthia S; Abrassart, Dana; Kobayashi, Yumiko; Marcheva, Biliana; Hong, Hee-Kyung; Chong, Jason L; Buhr, Ethan D; Lee, Choogon; Takahashi, Joseph S; Imai, Shin-Ichiro; Bass, Joseph
2009-05-01
The circadian clock is encoded by a transcription-translation feedback loop that synchronizes behavior and metabolism with the light-dark cycle. Here we report that both the rate-limiting enzyme in mammalian nicotinamide adenine dinucleotide (NAD+) biosynthesis, nicotinamide phosphoribosyltransferase (NAMPT), and levels of NAD+ display circadian oscillations that are regulated by the core clock machinery in mice. Inhibition of NAMPT promotes oscillation of the clock gene Per2 by releasing CLOCK:BMAL1 from suppression by SIRT1. In turn, the circadian transcription factor CLOCK binds to and up-regulates Nampt, thus completing a feedback loop involving NAMPT/NAD+ and SIRT1/CLOCK:BMAL1.
Power oscillation damping controller
2012-01-01
A power oscillation damping controller is provided for a power generation device such as a wind turbine device. The power oscillation damping controller receives an oscillation indicating signal indicative of a power oscillation in an electricity network and provides an oscillation damping control...
On periodic solutions of Goodwin's business cycle model with only floor in induced investment
Antonova, A. O.; Reznik, S. N.; Todorov, M. D.
2013-10-01
We present here an analytical solution of Goodwin's business cycle model in the form of delay differential equation with fixed delay θ and piecewise linear accelerator with only the floor (or the ceiling). We conclude that in this model the time behavior of the solution similar to Goodwin's limit cycle is not possible. These solution looks similar to the oscillation with a period θ, the amplitude of the oscillation growing exponentially to infinity as t →∞. The conditions for existence of the periodic solution in Goodwin's model with fixed delay for the nonlinear accelerator are also discussed.
Popovic, Zorana B.; Kim, Moonil; Rutledge, David B.
1988-01-01
Loading a two-dimensional grid with active devices offers a means of combining the power of solid-state oscillators in the microwave and millimeter-wave range. The grid structure allows a large number of negative resistance devices to be combined. This approach is attractive because the active devices do not require an external locking signal, and the combining is done in free space. In addition, the loaded grid is a planar structure amenable to monolithic integration. Measurements on a 25-MESFET grid at 9.7 GHz show power-combining and frequency-locking without an external locking signal, with an ERP of 37 W. Experimental far-field patterns agree with theoretical results obtained using reciprocity.
Analysis of a free oscillation atom interferometer
Kafle, Rudra P; Zozulya, Alex A
2011-01-01
We analyze a Bose-Einstein condensate (BEC) - based free oscillation atom Michelson interferometer in a weakly confining harmonic magnetic trap. A BEC at the center of the trap is split into two harmonics by a laser standing wave. The harmonics move in opposite directions with equal speeds and turn back under the influence of the trapping potential at their classical turning points. The harmonics are allowed to pass through each other and a recombination pulse is applied when they overlap at the end of a cycle after they return for the second time. We derive an expression for the contrast of the interferometric fringes and obtain the fundamental limit of performance of the interferometer in the parameter space.
Inhomogeneous stationary and oscillatory regimes in coupled chaotic oscillators.
Liu, Weiqing; Volkov, Evgeny; Xiao, Jinghua; Zou, Wei; Zhan, Meng; Yang, Junzhong
2012-09-01
The dynamics of linearly coupled identical Lorenz and Pikovsky-Rabinovich oscillators are explored numerically and theoretically. We concentrate on the study of inhomogeneous stable steady states ("oscillation death (OD)" phenomenon) and accompanying periodic and chaotic regimes that emerge at an appropriate choice of the coupling matrix. The parameters, for which OD occurs, are determined by stability analysis of the chosen steady state. Three model-specific types of transitions to and from OD are observed: (1) a sharp transition to OD from a nonsymmetric chaotic attractor containing random intervals of synchronous chaos; (2) transition to OD from the symmetry-breaking chaotic regime created by negative coupling; (3) supercritical bifurcation of OD into inhomogeneous limit cycles and further evolution of the system to inhomogeneous chaotic regimes that coexist with complete synchronous chaos. These results may fill a gap in the understanding of the mechanism of OD in coupled chaotic systems.
Nonlinear dynamics of the wake of an oscillating cylinder
Olinger, D. J.; Sreenivasan, K. R.
1988-02-01
The wake of an oscillating cylinder at low Reynolds numbers is a nonlinear system in which a limit cycle due to natural vortex shedding is modulated, generating in phase space a flow on a torus. It is experimentally shown that the system displays Arnol'd tongues for rational frequency ratios, and approximates the devil's staircase along the critical line. The 'singularity spectrum' as well as spectral peaks at various Fibonacci sequences accompanying quasi-periodic transition to chaos shows that the system belongs to the same universality class as the sine circle map.
Oscillations in the bistable regime of neuronal networks.
Roxin, Alex; Compte, Albert
2016-07-01
Bistability between attracting fixed points in neuronal networks has been hypothesized to underlie persistent activity observed in several cortical areas during working memory tasks. In network models this kind of bistability arises due to strong recurrent excitation, sufficient to generate a state of high activity created in a saddle-node (SN) bifurcation. On the other hand, canonical network models of excitatory and inhibitory neurons (E-I networks) robustly produce oscillatory states via a Hopf (H) bifurcation due to the E-I loop. This mechanism for generating oscillations has been invoked to explain the emergence of brain rhythms in the β to γ bands. Although both bistability and oscillatory activity have been intensively studied in network models, there has not been much focus on the coincidence of the two. Here we show that when oscillations emerge in E-I networks in the bistable regime, their phenomenology can be explained to a large extent by considering coincident SN and H bifurcations, known as a codimension two Takens-Bogdanov bifurcation. In particular, we find that such oscillations are not composed of a stable limit cycle, but rather are due to noise-driven oscillatory fluctuations. Furthermore, oscillations in the bistable regime can, in principle, have arbitrarily low frequency.
Lindberg, Erik
1997-01-01
In order to obtain insight in the nature of nonlinear oscillators the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator are found and displayed as functions of time. A number of oscillators are studied including Dewey's oscillator (piecewise linear...... with negative resistance), Kennedy's Colpitts-oscillator (with and without chaos) and a new 4'th order oscillator with hyper-chaos....
Optical realization of the dissipative quantum oscillator
Longhi, Stefano
2016-01-01
An optical realization of the damped quantum oscillator, based on transverse light dynamics in an optical resonator with slowly-moving mirrors, is theoretically suggested. The optical resonator setting provides a simple implementation of the time-dependent Caldirola-Kanai Hamiltonian of the dissipative quantum oscillator, and enables to visualize the effects of damped oscillations in the classical (ray optics) limit and wave packet collapse in the quantum (wave optics) regime.
Oscillating Permanent Magnets.
Michaelis, M. M.; Haines, C. M.
1989-01-01
Describes several ways to partially levitate permanent magnets. Computes field line geometries and oscillation frequencies. Provides several diagrams illustrating the mechanism of the oscillation. (YP)
Coexisting Oscillation and Extreme Multistability for a Memcapacitor-Based Circuit
Guangyi Wang; Chuanbao Shi; Xiaowei Wang; Fang Yuan
2017-01-01
The coexisting oscillations are observed with a memcapacitor-based circuit that consists of two linear inductors, two linear resistors, and an active nonlinear charge-controlled memcapacitor. We analyze the dynamics of this circuit and find that it owns an infinite number of equilibrium points and coexisting attractors, which means extreme multistability arises. Furthermore, we also show the stability of the infinite many equilibria and analyze the coexistence of fix point, limit cycle, and c...
Solar neutrinos: Oscillations or No-oscillations?
Smirnov, A Yu
2016-01-01
The Nobel prize in physics 2015 has been awarded "... for the discovery of neutrino oscillations which show that neutrinos have mass". While SuperKamiokande (SK), indeed, has discovered oscillations, SNO observed effect of the adiabatic (almost non-oscillatory) flavor conversion of neutrinos in the matter of the Sun. Oscillations are irrelevant for solar neutrinos apart from small $\
Pallud, C.; Meile, C.; Fendorf, S.
2007-12-01
Structured soils are typically heterogeneous composites of chemical and biological constituents within an intricate physical framework, which has variable geometry, composition and stability expressed over spatial scales of several orders of magnitude. In such settings, solutes move preferentially (by advection) through macropores and slowly (by diffusion) into intra-aggregate micropores, which promotes the establishment of redox gradients at the aggregate scale. Consequently, in such structured environments characterized by mass transfer limitation and redox gradients within soil aggregates, metals distribution can be strongly localized and the interrelated transport and biogeochemical processes control the fate of redox-sensitive contaminants and metals. Iron (hydr)oxides are particularly ubiquitous in soils and sediments and hence exert a pronounced effect on the fate and transport of nutrients and contaminants. As they are subject to both biotic and abiotic redox transformations, iron cycling depends on a tight interplay between hydrodynamic transport, and (bio)geochemical reactions depending on substrate distribution and microbial activity patterns. In this study, we present an experimental/modelling approach aimed at a qualitative and quantitative understanding of bioreductive processes at the microscale, and between advective and diffusive domains. Artificial soil aggregates, representing systems of intermediate complexity, were used to study the coupling of physical, chemical, and biological processes affecting iron oxides transformations, under environmentally relevant geometries. We used novel aggregate-based reaction flow cell experiments and reactive transport modeling to determine mass transfer and biogeochemical redox controls on the cycling of iron ranging from micropore- to aggregate-scales. Aggregates were made of ferrihydrite coated-sand and inoculated with Shewanella putrefaciens. Lactate was added in the input solution. Chemical gradients
Bellopede, Rossana; Castelletto, Eleonora; Marini, Paola; Zichella, Lorena
2015-04-01
The recent European standard EN 16306:2013 specifies laboratory methodology on the determination of the resistance to thermal and moisture cycling of marble for cladding of building façades. In particular measurements of bowing and flexural strength should be performed before and at the end of the ageing cycles. Bowing is measured on specimens of dimension 30*100*400mm exposed to moisture from beneath and heating (gradually till 80°C) on the upper face. The flexural strength should be measured both on reference and on exposed specimens in order to assess the variation of mechanical properties. Additional non-destructive tests are foreseen but are not compulsory for the standard. Moreover, the Annex A of the EN 16306, contains a guidance of the limit values that could be useful for the building planner for façade panels dimensioning. Different varieties of marble (two from Italy, one from Greece and three from Portugal) have been tested by means of this laboratory ageing test. Non-destructive tests such as the measurements of Ultrasonic Pulse Velocity (UPV), porosity, and water absorption have been executed together with the conventional flexural strength test. Image analysis on thin sections soaked with methylene blue have been analysed to further investigate the correlation between porosity and tendency to bowing. Base on the results obtained, some consideration on the decrease of mechanical resistance and the bowing in relation to the variety of marble tested and the limit values indicated the Annex A of EN 16306 can be drawn. Besides, from the data analysed a deepened discussion has been made. It is known that bowing and rapid strength loss occur in some varieties of marble when used as exterior cladding but further considerations can be made: bowing and flexural strength are correlate and in which way? Often the bowing is related to the decrease of flexural strength but it happens that there is a decrease in the mechanical resistance of the stone also
Lee, Chin Yik; Li, Larry Kin Bong; Juniper, Matthew P.; Cant, Robert Stewart
2016-01-01
Turbulent premixed flames often experience thermoacoustic instabilities when the combustion heat release rate is in phase with acoustic pressure fluctuations. Linear methods often assume a priori that oscillations are periodic and occur at a dominant frequency with a fixed amplitude. Such assumptions are not made when using nonlinear analysis. When an oscillation is fully saturated, nonlinear analysis can serve as a useful avenue to reveal flame behaviour far more elaborate than period-one limit cycles, including quasi-periodicity and chaos in hydrodynamically or thermoacoustically self-excited system. In this paper, the behaviour of a bluff-body stabilised turbulent premixed propane/air flame in a model jet-engine afterburner configuration is investigated using computational fluid dynamics. For the frequencies of interest in this investigation, an unsteady Reynolds-averaged Navier-Stokes approach is found to be appropriate. Combustion is represented using a modified laminar flamelet approach with an algebraic closure for the flame surface density. The results are validated by comparison with existing experimental data and with large eddy simulation, and the observed self-excited oscillations in pressure and heat release are studied using methods derived from dynamical systems theory. A systematic analysis is carried out by increasing the equivalence ratio of the reactant stream supplied to the premixed flame. A strong variation in the global flame structure is observed. The flame exhibits a self-excited hydrodynamic oscillation at low equivalence ratios, becomes steady as the equivalence ratio is increased to intermediate values, and again exhibits a self-excited thermoacoustic oscillation at higher equivalence ratios. Rich nonlinear behaviour is observed and the investigation demonstrates that turbulent premixed flames can exhibit complex dynamical behaviour including quasiperiodicity, limit cycles and period-two limit cycles due to the interactions of various
Self-regulation of turbulence in low rotation DIII-D QH-mode with an oscillating transport barrier
Barada, Kshitish; Rhodes, T. L.; Burrell, K. H.; Zeng, L.; Chen, Xi
2016-10-01
We present observations of turbulence and flow shear limit cycle oscillations (LCOs) in wide pedestal QH-mode DIII-D tokamak plasmas that are consistent with turbulence self-regulation. In this low input torque regime, both edge harmonic oscillations (EHOs) and ELMs are absent. LCOs of ExB velocity shear and ñ present predator-prey like behavior in these fully developed QH-mode plasmas. During these limit cycle oscillations, the ExB poloidal flows possess a long-range toroidal correlation consistent with turbulence generated zonal flow activity. Further, these limit cycle oscillations are observed in a broad range of edge parameters including ne, Te, floor Langmuir probe ion saturation current, and radial electric field Er. TRANSP calculations of transport indicate little change between the EHO and LCO wide pedestal phases. These observations are consistent with LCO driven transport that may play a role in maintaining the profiles below ELM threshold in the EHO-free steady state wide pedestal QH-mode regime. Work supported by the US DOE under DE-FG02-08ER54984 and DE-FC02-04ER54698.
Ewing, S. A.; Wankel, S. D.; Michalski, G.; Kendall, C.; Thiemens, M. H.; Amundson, R.
2006-12-01
Triple oxygen isotope analysis (Δ17O) provides a powerful tracer of nitrate formed by photochemical oxidation in the atmosphere. The resulting high, positive values of Δ17O are extremely sensitive to biological N cycling in the biosphere, which rapidly eliminates the photochemical signal through in-situ nitrate production (Δ17O = 0‰), coupled with uptake or other transformation of atmospheric nitrate. In surface waters, pulses of nitrate with high Δ17O values signal flushing by stormflow. In soil nitrate, high Δ17O values have provided an indicator of long-term hyperaridity in the Atacama Desert and Antarctica, where the photochemical signal is preserved as a function of extremely limited soil moisture, and thus extremely limited biology. Yet a relationship between nitrate Δ17O and nitrate δ15N values has proved elusive, despite control of both parameters by biology. We applied coupled analysis of Δ17O and δ15N in soil nitrate to a series of arid to hyperarid soils (21-2 mm rain y-1) in the Atacama Desert. These soils represent the transition from biotic soils, in which N is rapidly cycled and mostly present in organic forms (ON), to largely abiotic, hyperarid soils in which both atmospheric nitrate and ON accumulate. Detailed depth trends indicate that controls on soil non- atmospheric nitrate isotope values become increasingly abiotic as rainfall decreases and nitrate Δ17O values increase. In the most hyperarid soil, Δ17O values indicate that 80% of soil nitrate is unaltered atmospheric deposition, and vary by only ~3 ‰ with depth. Yet nitrate δ15N values increase from -2 to +8 ‰ with depth - the greatest variation among the three soils. The depth integrated nitrate δ15N value for this soil is 5.3 ‰, more enriched than surface values, likely deposition values, and values in the less arid soils. This suggests that even under conditions of accumulating atmospheric N in soils, with minimal biological activity and dissolved loss, in-situ nitrate
Florio, Alessandro; Pommier, Thomas; Gervaix, Jonathan; Bréfort, Caroline; Bérard, Annette; Le Roux, Xavier
2017-04-01
Introduction Maize inoculation with the plant-growth promoting rhizobacterium Azospirillum stimulates root growth and carbon, C, exudation, thereby enabling a better exploitation of soil and enhancing plant uptake of nitrogen, N. This can modulate the availability of N in the rhizosphere, by enhancing plant-microbe competition for N and modifying rhizosphere environmental variables important for N-cycling microbial communities, i.e. the amount of soil mineral N and oxygen availability. We tested the hypothesis that inoculation-induced stimulation of root N uptake and C exudation would enhance plant competition over microorganisms for N while increasing C availability for heterotrophs, thus leading to (i) a decrease of nitrifier abundance and activity, and (ii) a decrease or increase of denitrifier abundance and activity depending on the level of denitrifier limitation by N and C. Methods The extent of inoculation-induced changes in microbial activities (potential nitrification and denitrification), abundances and diversity of (de)nitrifiers as well as in root functional traits was assessed at 4 dates over two consecutive years in a multi-site field trial. Measurements were performed for the 6- and 12-leaves maize stages. In a second experiment, we artificially altered the level of denitrifier limitation by N and C in a greenhouse pot experiment by applying synthetic root exudates to inoculated and non-inoculated maize plants. Inoculation-induced response to nutrient limitation on microbial N-related activities and abundances was assessed for the 6-leaves stage maizeplants. Results Inoculation resulted in an idiosyncratic response of nitrification and nitrifier (AOA, AOB) abundance, which varied from one sampling date to another at a given site, and between sites and treatments at a given date. Modifications of water balance and soil moisture rather than increased plant-nitrifiers competition for soil NH4+ were the main drivers of nitrification. Conversely
Quantum noise-induced chaotic oscillations
Bag, Bidhan Chandra; Ray, Deb Shankar
1999-01-01
We examine the weak quantum noise limit of Wigner equation for phase space distribution functions. It has been shown that the leading order quantum noise described in terms of an auxiliary Hamiltonian manifests itself as an additional fluctuational degree of freedom which may induce chaotic and regular oscillations in a nonlinear oscillator.
Quantum noise-induced chaotic oscillations
Bag, B C; Bag, Bidhan Chandra; Ray, Deb Shankar
1999-01-01
We examine the weak quantum noise limit of Wigner equation for phase space distribution functions. It has been shown that the leading order quantum noise described in terms of an auxilliary Hamiltonian manifests itself as an additional fluctuational degree of freedom which may induce chaotic and regular oscillations in a nonlinear oscillator.
Shanbhag D
2012-07-01
Full Text Available Introduction: Hygiene-related practices of adolescents during menstruation are of importance, as it has a health impact in terms of increased vulnerability to reproductive tract infections (RTI. Therefore, increased knowledge about menstruation right from childhood may escalate safe practices and may help in mitigating the suffering of women.Objectives: To assess the perceptions and practices regarding menstrual hygiene among selected high school girls in a resource limited settings in area around Bangalore city. Methodology: This was a cross sectional study done in four selected Government High Schools in rural areas around Bangalore City. A pre-designed, pre-tested and structured questionnaire was administered. Results: A total of 506 girls were interviewed. The average age was 14.08 with Standard deviation of 1.06 and range between 12-16yrs. 99.6% of the students had heard of menstruation and 57.9% had acquired this even knowledge before attaining menarche. 73.7% knew that menstruation was a normal phenomenon but only 28.7% had knowledge regarding menstruation. 48.1% did not know that menstruation was related to pregnancy. Only 44.1% used sanitary pad during the menstrual cycles. Among those who used cloth, only 31.3% used soap and water to clean them. 56.8% used soap and water to clean their genital organs and 88.8% of the girls took bath daily during menstruation
J. W. Fourqurean
2015-07-01
Full Text Available Striking spatial patterns in stable isotope ratios (isoscapes and elemental ratios (stoichioscapes of seagrass leaves and the water column nutrients indicate general P-limitation of both water column and benthic primary productivity on the Bermuda Platform, and they highlight the role of the Bermuda Islands as a source of N and P. We found consistent differences among the four seagrass species (Syringodium filiforme, Thalassia testudinum, Halodule sp. and Halophila decipiens in the N, P, δ13C and δ15N of leaf tissues. The δ15N of seagrass leaves was especially variable, with values from −10.1 to 8.8‰, greatly expanding the reported range of values for all seagrass species globally. Spatial patterns from both the water column and the seagrass leaves indicated that P availability was higher near shore, and δ15N values suggest this was likely a result of human waste disposal. Spatially-contiguous areas of extremely depleted seagrass δ15N suggest unique N sources and cycling compared to other seagrass-dominated environments. Seagrass N : P values were not as far from the stoichiometric balance between N and P availability as in the water column, and there were no strong relationships between the water column N : P and the seagrass N : P. Such isoscapes and stoichioscapes provide valuable ecogeochemical tools to infer ecosystem processes as well as provide information that can inform food web and animal movement studies.
CPT-Odd resonances in neutrino oscillations
Barger; Pakvasa; Weiler; Whisnant
2000-12-11
We consider the consequences for future neutrino factory experiments of small CPT-odd interactions in neutrino oscillations. The nu(&mgr;)-->nu(&mgr;) and nu;(&mgr;)-->nu;(&mgr;) survival probabilities at a baseline L = 732 km can test for CPT-odd contributions at orders of magnitude better sensitivity than present neutrino sector limits. Interference between the CPT-violating interaction and CPT-even mass terms in the Lagrangian can lead to a resonant enhancement of the oscillation amplitude. For oscillations in matter, a simultaneous enhancement of both neutrino and antineutrino oscillation amplitudes is possible.
Oscillations of Eccentric Pulsons
Christiansen, Peter Leth; Groenbech-Jensen, Niels; Lomdahl, Peter;
1997-01-01
Perturbation theory for elliptic pulsons is developed and predicts pulson and eccentricity oscillations. The pulson oscillation period is predicted qualitatively correct.......Perturbation theory for elliptic pulsons is developed and predicts pulson and eccentricity oscillations. The pulson oscillation period is predicted qualitatively correct....
Local and global bifurcations at infinity in models of glycolytic oscillations
Sturis, Jeppe; Brøns, Morten
1997-01-01
We investigate two models of glycolytic oscillations. Each model consists of two coupled nonlinear ordinary differential equations. Both models are found to have a saddle point at infinity and to exhibit a saddle-node bifurcation at infinity, giving rise to a second saddle and a stable node...... at infinity. Depending on model parameters, a stable limit cycle may blow up to infinite period and amplitude and disappear in the bifurcation, and after the bifurcation, the stable node at infinity then attracts all trajectories. Alternatively, the stable node at infinity may coexist with either a stable...... sink (not at infinity) or a stable limit cycle. This limit cycle may then disappear in a heteroclinic bifurcation at infinity in which the unstable manifold from one saddle at infinity joins the stable manifold of the other saddle at infinity. These results explain prior reports for one of the models...
``Quorum sensing'' generated multistability and chaos in a synthetic genetic oscillator
Potapov, I.; Zhurov, B.; Volkov, E.
2012-06-01
We model the dynamics of the synthetic genetic oscillator Repressilator equipped with quorum sensing. In addition to a circuit of 3 genes repressing each other in a unidirectional manner, the model includes a phase-repulsive type of the coupling module implemented as the production of a small diffusive molecule—autoinducer (AI). We show that the autoinducer (which stimulates the transcription of a target gene) is responsible for the disappearance of the limit cycle (LC) through the infinite period bifurcation and the formation of a stable steady state (SSS) for sufficiently large values of the transcription rate. We found conditions for hysteresis between the limit cycle and the stable steady state. The parameters' region of the hysteresis is determined by the mRNA to protein lifetime ratio and by the level of transcription-stimulating activity of the AI. In addition to hysteresis, increasing AI-dependent stimulation of transcription may lead to the complex dynamic behavior which is characterized by the appearance of several branches on the bifurcation continuation, containing different regular limit cycles, as well as a chaotic regime. The multistability which is manifested as the coexistence between the stable steady state, limit cycles, and chaos seems to be a novel type of the dynamics for the ring oscillator with the added quorum sensing positive feedback.
Dynamical quorum-sensing in oscillators coupled through an external medium
Schwab, David J.; Baetica, Ania; Mehta, Pankaj
2012-11-01
Many biological and physical systems exhibit population-density-dependent transitions to synchronized oscillations in a process often termed “dynamical quorum sensing”. Synchronization frequently arises through chemical communication via signaling molecules distributed through an external medium. We study a simple theoretical model for dynamical quorum sensing: a heterogenous population of limit-cycle oscillators diffusively coupled through a common medium. We show that this model exhibits a rich phase diagram with four qualitatively distinct physical mechanisms that can lead to a loss of coherent population-level oscillations, including a novel mechanism arising from effective time-delays introduced by the external medium. We derive a single pair of analytic equations that allow us to calculate phase boundaries as a function of population density and show that the model reproduces many of the qualitative features of recent experiments on Belousov-Zhabotinsky catalytic particles as well as synthetically engineered bacteria.
Bashkirtseva, Irina; Ryazanova, Tatyana; Ryashko, Lev
2015-10-01
We study a stochastic dynamics of systems with hard excitement of auto-oscillations possessing a bistability mode with coexistence of the stable equilibrium and limit cycle. A principal difference in the results of the impact of additive and parametric random disturbances is shown. For the stochastic van der Pol oscillator with increasing parametric noise, qualitative transformations of the probability density function form "crater"-"peak+crater"-"peak" are demonstrated by numerical simulation. An analytical investigation of such P bifurcations is carried out for the stochastic Hopf-like model with hard excitement of self-oscillations. A detailed parametric description of the response of this model on the additive and multiplicative noise and corresponding stochastic bifurcations are presented and discussed.
Modeling the Aerodynamic Lift Produced by Oscillating Airfoils at Low Reynolds Number
Khalid, Muhammad Saif Ullah
2015-01-01
For present study, setting Strouhal Number (St) as control parameter, numerical simulations for flow past oscillating NACA-0012 airfoil at 1,000 Reynolds Numbers (Re) are performed. Temporal profiles of unsteady forces; lift and thrust, and their spectral analysis clearly indicate the solution to be a period-1 attractor for low Strouhal numbers. This study reveals that aerodynamic forces produced by plunging airfoil are independent of initial kinematic conditions of airfoil that proves the existence of limit cycle. Frequencies present in the oscillating lift force are composed of fundamental (fs), even and odd harmonics (3fs) at higher Strouhal numbers. Using numerical simulations, shedding frequencies (f_s) were observed to be nearly equal to the excitation frequencies in all the cases. Unsteady lift force generated due to the plunging airfoil is modeled by modified van der Pol oscillator. Using method of multiple scales and spectral analysis of steady-state CFD solutions, frequencies and damping terms in th...
Willocq, S
2002-01-01
We review new studies of the time dependence of B0s - B0s-bar mixing by the ALEPH, DELPHI and SLD Collaborations, with an emphasis on the different analysis methods used. Combining all available results yields a preliminary lower limit on the oscillation frequency of dms > 14.4 ps-1 at the 95% C.L.
Ikuhiro Yamaguchi
Full Text Available Time delay is known to induce sustained oscillations in many biological systems such as electroencephalogram (EEG activities and gene regulations. Furthermore, interactions among delay-induced oscillations can generate complex collective rhythms, which play important functional roles. However, due to their intrinsic infinite dimensionality, theoretical analysis of interacting delay-induced oscillations has been limited. Here, we show that the two primary methods for finite-dimensional limit cycles, namely, the center manifold reduction in the vicinity of the Hopf bifurcation and the phase reduction for weak interactions, can successfully be applied to interacting infinite-dimensional delay-induced oscillations. We systematically derive the complex Ginzburg-Landau equation and the phase equation without delay for general interaction networks. Based on the reduced low-dimensional equations, we demonstrate that diffusive (linearly attractive coupling between a pair of delay-induced oscillations can exhibit nontrivial amplitude death and multimodal phase locking. Our analysis provides unique insights into experimentally observed EEG activities such as sudden transitions among different phase-locked states and occurrence of epileptic seizures.
Mass transfer cycles in cataclysmic variables
King, A. R.; Frank, J.; Kolb, U.; Ritter, H.
1995-01-01
It is well known that in cataclysmic variables the mass transfer rate must fluctuate about the evolutionary mean on timescales too long to be directly observable. We show that limit-cycle behavior can occur if the radius change of the secondary star is sensitive to the instantaneous mass transfer rate. The only reasonable way in which such a dependence can arise is through irradiation of this star by the accreting component. The system oscillates between high states, in which irradiation causes slow expansion of the secondary and drives an elevated transfer rate, and low states, in which this star contracts.
The free energy cost of accurate biochemical oscillations
Cao, Yuansheng; Ouyang, Qi; Tu, Yuhai
2015-01-01
Oscillation is an important cellular process that regulates timing of different vital life cycles. However, in the noisy cellular environment, oscillations can be highly inaccurate due to phase fluctuations. It remains poorly understood how biochemical circuits suppress phase fluctuations and what is the incurred thermodynamic cost. Here, we study four different types of biochemical oscillations representing three basic oscillation motifs shared by all known oscillatory systems. We find that the phase diffusion constant follows the same inverse dependence on the free energy dissipation per period for all systems studied. This relationship between the phase diffusion and energy dissipation is shown analytically in a model of noisy oscillation. Microscopically, we find that the oscillation is driven by multiple irreversible cycles that hydrolyze the fuel molecules such as ATP; the number of phase coherent periods is proportional to the free energy consumed per period. Experimental evidence in support of this un...
Ma, Hongbin
2015-01-01
This book presents the fundamental fluid flow and heat transfer principles occurring in oscillating heat pipes and also provides updated developments and recent innovations in research and applications of heat pipes. Starting with fundamental presentation of heat pipes, the focus is on oscillating motions and its heat transfer enhancement in a two-phase heat transfer system. The book covers thermodynamic analysis, interfacial phenomenon, thin film evaporation, theoretical models of oscillating motion and heat transfer of single phase and two-phase flows, primary factors affecting oscillating motions and heat transfer, neutron imaging study of oscillating motions in an oscillating heat pipes, and nanofluid’s effect on the heat transfer performance in oscillating heat pipes. The importance of thermally-excited oscillating motion combined with phase change heat transfer to a wide variety of applications is emphasized. This book is an essential resource and learning tool for senior undergraduate, gradua...
Phenomenology of neutrino oscillations
G Rajasekaran
2000-07-01
The phenomenology of solar, atmospheric, supernova and laboratory neutrino oscillations is described. Analytical formulae for matter effects are reviewed. The results from oscillations are confronted with neutrinoless double beta decay.
Sanin, A.; Semyonov, E.
2012-01-01
Numerical integration of the non-stationary Schrödinger equation with Duffing potential depending on two coordinates has been carried out. Oscillation types and the influence of coupling between two oscillators on frequency spectra are analyzed in detail.
Recurrence analysis and synchronization of oscillators with coexisting attractors
Kwuimy, C.A. Kitio, E-mail: kwuimy@yahoo.fr [Center for Nonlinear Dynamics and Control, Department of Mechanical Engineering, Villanova University, 800 Lancaster Avenue, Villanova, PA 19085 (United States); Kadji, H.G. Enjieu, E-mail: hkadji@monell.org [Monell Chemical Senses Center, 3500 Market Street, Philadelphia, PA 19104 (United States)
2014-06-13
Highlights: • We establish existence conditions for limit cycles in an enzyme–substrate reaction. • The recurrence quantification analysis is utilized to explore the system behavior. • Birhythmicity, various bifurcations and chaos are analyzed. • The cross recurrence analysis is utilized to investigate synchronization states. • Chaos synchronization mostly occurs for negative values of the coupling strength. - Abstract: The method of recurrence plots (RPs) has been traditionally used for experimental time series analysis with no comparison with the mathematical model. This is in part because of lack of nonlinear analysis of mathematical model based on the recurrence quantification analysis (RQA) parameters. The paper provides substantial information about the mathematical and numerical analysis and synchronization of a multi-limit cycle oscillator from the RQA perspective. The recurrence quantification analysis parameters are used to discuss the birhythmic behavior of the system, as well as various bifurcations (quasi-periodicity, periodicity and chaos) in the system response. Finally, the results of the method of RPs are compared to those of phase diagrams and the problem of synchronization of limit cycle and chaotic response is discussed by the mean of cross recurrence.
Experiments on oscillator ensembles with global nonlinear coupling
Temirbayev, Amirkhan A.; Zhanabaev, Zeinulla Zh.; Tarasov, Stanislav B.; Ponomarenko, Vladimir I.; Rosenblum, Michael
2012-01-01
We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a nonlinear phase-shifting unit in the global feedback loop. With an increase in the coupling strength we first observe formation and then destruction of a synchronous cluster, so that the dependence of the order parameter on the coupling strength is not monotonic. After destruction of the cluster the ensemble remains nevertheless coherent, i.e., it exhibits an oscillatory collective mode (mean field). We show that the system is now in a self-organized quasiperiodic state, predicted in Rosenblum and Pikovsky [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.98.064101 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. Without a nonlinear phase-shifting unit, the system exhibits a standard Kuramoto-like transition to a fully synchronous state. We demonstrate a good correspondence between the experiment and previously developed theory. We also propose a simple measure which characterizes the macroscopic incoherence-coherence transition in a finite-size ensemble.
Experiments on oscillator ensemble with global nonlinear coupling
Rosenblum, Michael; Temirbayev, Amirkhan; Zhanabaev, Zeinulla; Tarasov, Stanislav; Ponomarenko, Vladimir
2012-02-01
We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a linear or nonlinear phase-shifting unit in the global feedback loop. With linear unit we observe, with increase of the coupling strength, a standard Kuramoto-like transition to a fully synchronous state; the threshold of the transition depends on the phase shift. In case of nonlinear global coupling we first observe a transition to a state when approximately half of the population forms a synchronous cluster. With further increase of the coupling strength we observe destruction of this cluster and formation of a self-organized quasiperiodic state, predicted in [M. Rosenblum and A. Pikovsky, PRL, 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. The transition is characterized by a non-monotonic dependence of the order parameter on the coupling strength. We demonstrate a good correspondence between theory and experiment.
Effects of noise on the phase dynamics of nonlinear oscillators
Daffertshofer, A.
1998-07-01
Various properties of human rhythmic movements have been successfully modeled using nonlinear oscillators. However, despite some extensions towards stochastical differential equations, these models do not comprise different statistical features that can be explained by nondynamical statistics. For instance, one observes certain lag one serial correlation functions for consecutive periods during periodic motion. This work aims at an extension of dynamical descriptions in terms of stochastically forced nonlinear oscillators such as ξ¨+ω20ξ=n(ξ,ξ˙)+q(ξ,ξ˙)Ψ(t), where the nonlinear function n(ξ,ξ˙) generates a limit cycle and Ψ(t) denotes colored noise that is multiplied via q(ξ,ξ˙). Nonlinear self-excited systems have been frequently investigated, particularly emphasizing stability properties and amplitude evolution. Thus, one can focus on the effects of noise on the frequency or phase dynamics that can be analyzed by use of time-dependent Fokker-Planck equations. It can be shown that noise multiplied via polynoms of arbitrary finite order cannot generate the desired period correlation but predominantly results in phase diffusion. The system is extended in terms of forced oscillators in order to find a minimal model producing the required error correction.
Neutrino Masses and Oscillations
Valle, J W F
2005-01-01
I summarize the status of three--neutrino oscillations that follow from combining the relevant world's data. The discussion includes the small parameters Delta_m-sol/Delta_m-atm and \\sin^2\\theta_{13}, which characterize the strength of CP violation in neutrino oscillations, the impact of oscillation data on the prospects for probing the absolute scale of neutrino mass in \
The colpitts oscillator family
Lindberg, Erik; Murali, K.; Tamasevicius, A.
A tutorial study of the Colpitts oscillator family defined as all oscillators based on a nonlinear amplifier and a three- terminal linear resonance circuit with one coil and two capacitors. The original patents are investigated. The eigenvalues of the linearized Jacobian for oscillators based...
Paul G. Higgs
2016-06-01
Full Text Available A long-standing problem for the origins of life is that polymerization of many biopolymers, including nucleic acids and peptides, is thermodynamically unfavourable in aqueous solution. If bond making and breaking is reversible, monomers and very short oligomers predominate. Recent experiments have shown that wetting and drying cycles can overcome this problem and drive the formation of longer polymers. In the dry phase, bond formation is favourable, but diffusion is restricted, and bonds only form between monomers that are initially close together. In the wet phase, some of the bonds are hydrolyzed. However, repositioning of the molecules allows new bonds to form in the next dry phase, leading to an increase in mean polymer length. Here, we consider a simple theoretical model that explains the effect of cycling. There is an equilibrium length distribution with a high mean length that could be achieved if diffusion occurred freely in the dry phase. This equilibrium is inaccessible without diffusion. A single dry cycle without diffusion leads to mean lengths much shorter than this. Repeated cycling leads to a significant increase in polymerization relative to a single cycle. In the most favourable case, cycling leads to the same equilibrium length distribution as would be achieved if free diffusion were possible in the dry phase. These results support the RNA World scenario by explaining a potential route to synthesis of long RNAs; however, they also imply that cycling would be beneficial to the synthesis of other kinds of polymers, including peptides, where bond formation involves a condensation reaction.
Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator.
Zakharova, A; Vadivasova, T; Anishchenko, V; Koseska, A; Kurths, J
2010-01-01
We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs.
Scaling Laws in the Transient Dynamics of Firefly-like Oscillators
Rubido, N; Cabeza, C; Marti, A [Igua 4225, Instituto de Fisica, Facultad de Ciencias, Montevideo (Uruguay); Ramirez Avila, G M, E-mail: nrubido@fisica.edu.uy [Institut fuer Physik, Humboldt Universitaet zu Berlin (Germany)
2011-03-01
Fireflies constitute a paradigm of pulse-coupled oscillators. In order to tackle the problems related to synchronisation transients of pulse-coupled oscillators, a Light-Controlled Oscillator (LCO) model is presented. A single LCO constitutes a one-dimensional relaxation oscillator described by two distinct time-scales meant to mimic fireflies in the sense that: it is capable of emitting light in a pulse-like fashion and detect the emitted by others in order to adjust its oscillation. We present dynamical results for two interacting LCOs in the torus for all possible coupling configurations. Transient times to the synchronous limit cycle are obtained experimentally and numerically as a function of initial conditions and coupling strengths. Scaling laws are found based on dimensional analysis and critical exponents calculated, thus, global dynamic is restricted. Furthermore, an analytical orthogonal transformation that allows to calculate Floquet multipliers directly from the time series is presented. As a consequence, local dynamics is also fully characterized. This transformation can be easily extended to a system with an arbitrary number of interacting LCOs.
Neutrino oscillations: theory and phenomenology
Akhmedov, E.K., E-mail: akhmedov@ictp.trieste.it [Department of Theoretical Physics, Royal Institute of Technology, AlbaNova University Center, SE-106 91 Stockholm (Sweden)
2011-12-15
A brief overview of selected topics in the theory and phenomenology of neutrino oscillations is given. These include: oscillations in vacuum and in matter; phenomenology of 3-flavour neutrino oscillations; CP and T violation in neutrino oscillations in vacuum and in matter; matter effects on {nu}{sub {mu}}{r_reversible}{nu}{sub {tau}} oscillations; parametric resonance in neutrino oscillations inside the earth; oscillations below and above the MSW resonance; unsettled issues in the theory of neutrino oscillations.
Synchronization in interacting populations of heterogeneous oscillators with time-varying coupling.
So, Paul; Cotton, Bernard C; Barreto, Ernest
2008-09-01
In many networks of interest (including technological, biological, and social networks), the connectivity between the interacting elements is not static, but changes in time. Furthermore, the elements themselves are often not identical, but rather display a variety of behaviors, and may come in different classes. Here, we investigate the dynamics of such systems. Specifically, we study a network of two large interacting heterogeneous populations of limit-cycle oscillators whose connectivity switches between two fixed arrangements at a particular frequency. We show that for sufficiently high switching frequency, this system behaves as if the connectivity were static and equal to the time average of the switching connectivity. We also examine the mechanisms by which this fast-switching limit is approached in several nonintuitive cases. The results illuminate novel mechanisms by which synchronization can arise or be thwarted in large populations of coupled oscillators with nonstatic coupling.
Covariant harmonic oscillators and coupled harmonic oscillators
Han, Daesoo; Kim, Young S.; Noz, Marilyn E.
1995-01-01
It is shown that the system of two coupled harmonic oscillators shares the basic symmetry properties with the covariant harmonic oscillator formalism which provides a concise description of the basic features of relativistic hadronic features observed in high-energy laboratories. It is shown also that the coupled oscillator system has the SL(4,r) symmetry in classical mechanics, while the present formulation of quantum mechanics can accommodate only the Sp(4,r) portion of the SL(4,r) symmetry. The possible role of the SL(4,r) symmetry in quantum mechanics is discussed.
Osemwenkha, Abieyuwa; Osaikhuwuomwan, James
2016-03-01
Controlled ovarian hyperstimulation is one of the major steps of in vitro fertilization. The inaccessibility or non-visualization of developing follicles on transvaginal sonography (the preferred imaging method) may be misjudged as a poor response, resulting in cycle cancellation. It is necessary to scrupulously appraise proxy indicators for ovarian response, such as estradiol levels, endometrial thickness, and other individual clinical characteristics. This can prompt meticulous transabdominal ultrasound follicular monitoring and oocyte retrieval with the goal of averting cycle cancellation and improving treatment outcomes.
Nature's Autonomous Oscillators
Mayr, H. G.; Yee, J.-H.; Mayr, M.; Schnetzler, R.
2012-01-01
Nonlinearity is required to produce autonomous oscillations without external time dependent source, and an example is the pendulum clock. The escapement mechanism of the clock imparts an impulse for each swing direction, which keeps the pendulum oscillating at the resonance frequency. Among nature's observed autonomous oscillators, examples are the quasi-biennial oscillation and bimonthly oscillation of the Earth atmosphere, and the 22-year solar oscillation. The oscillations have been simulated in numerical models without external time dependent source, and in Section 2 we summarize the results. Specifically, we shall discuss the nonlinearities that are involved in generating the oscillations, and the processes that produce the periodicities. In biology, insects have flight muscles, which function autonomously with wing frequencies that far exceed the animals' neural capacity; Stretch-activation of muscle contraction is the mechanism that produces the high frequency oscillation of insect flight, discussed in Section 3. The same mechanism is also invoked to explain the functioning of the cardiac muscle. In Section 4, we present a tutorial review of the cardio-vascular system, heart anatomy, and muscle cell physiology, leading up to Starling's Law of the Heart, which supports our notion that the human heart is also a nonlinear oscillator. In Section 5, we offer a broad perspective of the tenuous links between the fluid dynamical oscillators and the human heart physiology.
Long-lasting oscillations in the electro-oxidation of formic acid on PtSn intermetallic surfaces.
Perini, Nickson; Batista, Bruno C; Angelo, Antonio C D; Epstein, Irving R; Varela, Hamilton
2014-06-23
Even when in contact with virtually infinite reservoirs, natural and manmade oscillators typically drift in phase space on a time-scale considerably slower than that of the intrinsic oscillator. A ubiquitous example is the inexorable aging process experienced by all living systems. Typical electrocatalytic reactions under oscillatory conditions oscillate for only a few dozen stable cycles due to slow surface poisoning that ultimately results in destruction of the limit cycle. We report the observation of unprecedented long-lasting temporal oscillations in the electro-oxidation of formic acid on an ordered intermetallic PtSn phase. The introduction of Sn substantially increases the catalytic activity and retards the irreversible surface oxidation, which results in the stabilization of more than 2200 oscillatory cycles in about 40 h; a 30-40-fold stabilization with respect to the behavior of pure Pt surfaces. The dynamics were modeled and numerical simulations point to the surface processes underlying the high stability. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Chen, Zheng; McKnight, Steven L
2007-12-01
The circadian clock drives endogenous oscillations of cellular and physiological processes with a periodicity of approximately 24 h. Progression of the cell division cycle (CDC) has been found to be coupled to the circadian clock, and it has been postulated that gating of the CDC by the circadian cycle may have evolved to protect DNA from the mutagenic effects of ultraviolet light. When grown under nutrient-limiting conditions in a chemostat, prototrophic strains of budding yeast, Saccharomyces cerevisiae, adopt a robust metabolic cycle of ultradian dimensions that temporally compartmentalizes essential cellular events. The CDC is gated by this yeast metabolic cycle (YMC), with DNA replication strictly segregated away from the oxidative phase when cells are actively respiring. Mutants impaired in such gating allow DNA replication to take place during the respiratory phase of the YMC and have been found to suffer significantly elevated rates of spontaneous mutation. Analogous to the circadian cycle, the YMC also employs the conserved DNA checkpoint kinase Rad53/Chk2 to facilitate coupling with the CDC. These studies highlight an evolutionarily conserved mechanism that seems to confine cell division to particular temporal windows to prevent DNA damage. We hypothesize that DNA damage itself might constitute a "zeitgeber", or time giver, for both the circadian cycle and the metabolic cycle. We discuss these findings in the context of a unifying theme underlying the circadian and metabolic cycles, and explore the relevance of cell cycle gating to human diseases including cancer.
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
2016-07-01
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.
Axion Induced Oscillating Electric Dipole Moments
Hill, Christopher T
2015-01-01
The axion electromagnetic anomaly induces an oscillating electric dipole for any static magnetic dipole. Static electric dipoles do not produce oscillating magnetic moments. This is a low energy theorem which is a consequence of the space-time dependent cosmic background field of the axion. The electron will acquire an oscillating electric dipole of frequency $m_a$ and strength $\\sim 10^{-32}$ e-cm, two orders of magnitude above the nucleon, and within four orders of magnitude of the present standard model DC limit. This may suggest sensitive new experimental venues for the axion dark matter search.
Optoelectronic Oscillators for Communication Systems
Romeira, Bruno; Figueiredo, José
We introduce and report recent developments on a novel five port optoelectronic voltage controlled oscillator consisting of a resonant tunneling diode (RTD) optical-waveguide integrated with a laser diode. The RTD-based optoelectronic oscillator (OEO) has both optical and electrical input and output ports, with the fifth port allowing voltage control. The RTD-OEO locks to reference radio-frequency (RF) sources by either optical or electrical injection locking techniques allowing remote synchronization, eliminating the need of impedance matching between traditional RF oscillators. RTD-OEO functions include generation, amplification and distribution of RF carriers, clock recovery, carrier recovery, modulation and demodulation and frequency synthesis. Self-injection locking operation modes, where small portions of the output electrical/optical signals are fed back into the electrical/optical input ports, are also proposed. The self-phase locked loop configuration can give rise to low-noise high-stable oscillations, not limited by the RF source performance and with no need of external optoelectronic conversion.
A memristor-based third-order oscillator: beyond oscillation
Talukdar, Abdul Hafiz Ibne
2012-10-06
This paper demonstrates the first third-order autonomous linear time variant circuit realization that enhances parametric oscillation through the usage of memristor in conventional oscillators. Although the output has sustained oscillation, the linear features of the conventional oscillators become time dependent. The poles oscillate in nonlinear behavior due to the oscillation of memristor resistance. The mathematical formulas as well as SPICE simulations are introduced for the memristor-based phase shift oscillator showing a great matching.
Nuclear propelled vessels and neutrino oscillation experiments.
Detwiler, J; Gratta, G; Tolich, N; Uchida, Y
2002-11-04
We study the effect of naval nuclear reactors on the study of neutrino oscillations. We find that the presence of naval reactors at unknown locations and times may limit the accuracy of future very long baseline reactor-based neutrino oscillation experiments. At the same time, we argue that a nuclear powered surface ship such as a large Russian icebreaker may provide an ideal source for precision experiments.
Building better oscillators using nonlinear dynamics and pattern formation
M C Cross; Eyal Kenig; John-Mark A Allen
2015-03-01
Frequency and time references play an essential role in modern technology and in living systems. The precision of self-sustained oscillations is limited by the effects of noise, which becomes evermore important as the sizes of the devices become smaller. In this paper, we review our recent theoretical results on using nonlinear dynamics and pattern formation to reduce the effects of noise and improve the frequency precision of oscillators, with particular reference to ongoing experiments on oscillators based on nanomechanical resonators. We discuss using resonator nonlinearity, novel oscillator architectures and the synchronization of arrays of oscillators, to improve the frequency precision.
Automatic oscillator frequency control system
Smith, S. F. (Inventor)
1985-01-01
A frequency control system makes an initial correction of the frequency of its own timing circuit after comparison against a frequency of known accuracy and then sequentially checks and corrects the frequencies of several voltage controlled local oscillator circuits. The timing circuit initiates the machine cycles of a central processing unit which applies a frequency index to an input register in a modulo-sum frequency divider stage and enables a multiplexer to clock an accumulator register in the divider stage with a cyclical signal derived from the oscillator circuit being checked. Upon expiration of the interval, the processing unit compares the remainder held as the contents of the accumulator against a stored zero error constant and applies an appropriate correction word to a correction stage to shift the frequency of the oscillator being checked. A signal from the accumulator register may be used to drive a phase plane ROM and, with periodic shifts in the applied frequency index, to provide frequency shift keying of the resultant output signal. Interposition of a phase adder between the accumulator register and phase plane ROM permits phase shift keying of the output signal by periodic variation in the value of a phase index applied to one input of the phase adder.
Kato, Shoji
2016-01-01
This book presents the current state of research on disk oscillation theory, focusing on relativistic disks and tidally deformed disks. Since the launch of the Rossi X-ray Timing Explorer (RXTE) in 1996, many high-frequency quasiperiodic oscillations (HFQPOs) have been observed in X-ray binaries. Subsequently, similar quasi-periodic oscillations have been found in such relativistic objects as microquasars, ultra-luminous X-ray sources, and galactic nuclei. One of the most promising explanations of their origin is based on oscillations in relativistic disks, and a new field called discoseismology is currently developing. After reviewing observational aspects, the book presents the basic characteristics of disk oscillations, especially focusing on those in relativistic disks. Relativistic disks are essentially different from Newtonian disks in terms of several basic characteristics of their disk oscillations, including the radial distributions of epicyclic frequencies. In order to understand the basic processes...
Interglacials, Milankovitch Cycles, and Carbon Dioxide
Marsh, Gerald E
2010-01-01
The existing understanding of interglacial periods is that they are initiated by Milankovitch cycles enhanced by rising atmospheric carbon dioxide concentrations. During interglacials, global temperature is also believed to be primarily controlled by carbon dioxide concentrations, modulated by internal processes such as the Pacific Decadal Oscillation and the North Atlantic Oscillation. Recent work challenges the fundamental basis of these conceptions.
Directional Transverse Oscillation Vector Flow Estimation
Jensen, Jørgen Arendt
2017-01-01
A method for estimating vector velocities using transverse oscillation (TO) combined with directional beamforming is presented. In Directional Transverse Oscillation (DTO) a normal focused field is emitted and the received signals are beamformed in the lateral direction transverse to the ultrasou...... increase in SD to 15.7%, but a maintained bias of -3.5% from 126 to 156 mm. Data for a pulsating flow has also been acquired for 15 cardiac cycles using a CompuFlow 1000 pump. The relative SD was here 7.4% for a femoral artery waveform....
The GONG Site Survey. [solar oscillations
Hill, Frank; Ambastha, Ashok; Ball, Warren; Duhalde, Oscar; Farris, Don; Fischer, George; Hieda, Les; Zhen, Huang; Ingram, Bob; Jackson, Patty
1988-01-01
The Global Oscillation Network Group (GONG) project is planning to place six observing stations around the world to observe the solar oscillations as continuously as possible. The procedures that are being used to select the six sites are described. Results of measurements of cloud cover obtained by networks of 6 (out of 10) radiometers show a duty cycle of over 93 percent, with the first diurnal sidelobe in the window power spectrum suppressed by a factor of 400. The results are in good agreement with the predictions of a computer model of the expected cloud cover at individual sites.
Synchronization of oscillators in complex networks
Louis M Pecora
2008-06-01
Theory of identical or complete synchronization of identical oscillators in arbitrary networks is introduced. In addition, several graph theory concepts and results that augment the synchronization theory and a tie in closely to random, semirandom, and regular networks are introduced. Combined theories are used to explore and compare three types of semirandom networks for their efficacy in synchronizing oscillators. It is shown that the simplest -cycle augmented by a few random edges or links are the most efficient network that will guarantee good synchronization.
Effect of boundary on controlled memristor-based oscillator
Fouda, Mohamed E.
2012-10-01
Recently, the applications of memristors have spread into many fields and especially in the circuit theory. Many models have been proposed for the HP-memristor based on the window functions. In this paper, we introduce a complete mathematical analysis of the controlled reactance-less oscillator for two different window functions of Joglekar\\'s model (linear and nonlinear dopant drift) to discuss the effect of changing the window function on the oscillator\\'s behavior. The generalized necessary and sufficient conditions based on the circuit elements and control voltages for both the linear and nonlinear models are introduced. Moreover, closed form expressions for the oscillation frequency and duty cycle are derived for these models and verified using PSPICE simulations showing an excellent matching. Finally a comparison between the linear and nonlinear models which shows their effect on the oscillation frequency and conditions of oscillation is introduced. © 2012 IEEE.
Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators
Senthilkumar, D. V.; Muruganandam, P.; Lakshmanan, M.; Kurths, J.
2010-01-01
Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at $(mN_c+1)$-th oscillators in the ring, where $m$ is an integer and $N_c$ is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by siz...