Analytical approximations for the amplitude and period of a relaxation oscillator
Golkhou Vahid
2009-01-01
Full Text Available Abstract Background Analysis and design of complex systems benefit from mathematically tractable models, which are often derived by approximating a nonlinear system with an effective equivalent linear system. Biological oscillators with coupled positive and negative feedback loops, termed hysteresis or relaxation oscillators, are an important class of nonlinear systems and have been the subject of comprehensive computational studies. Analytical approximations have identified criteria for sustained oscillations, but have not linked the observed period and phase to compact formulas involving underlying molecular parameters. Results We present, to our knowledge, the first analytical expressions for the period and amplitude of a classic model for the animal circadian clock oscillator. These compact expressions are in good agreement with numerical solutions of corresponding continuous ODEs and for stochastic simulations executed at literature parameter values. The formulas are shown to be useful by permitting quick comparisons relative to a negative-feedback represillator oscillator for noise (10× less sensitive to protein decay rates, efficiency (2× more efficient, and dynamic range (30 to 60 decibel increase. The dynamic range is enhanced at its lower end by a new concentration scale defined by the crossing point of the activator and repressor, rather than from a steady-state expression level. Conclusion Analytical expressions for oscillator dynamics provide a physical understanding for the observations from numerical simulations and suggest additional properties not readily apparent or as yet unexplored. The methods described here may be applied to other nonlinear oscillator designs and biological circuits.
Active optomechanics through relaxation oscillations
Princepe, Debora; Frateschi, Newton
2014-01-01
We propose an optomechanical laser based on III-V compounds which exhibits self-pulsation in the presence of a dissipative optomechanical coupling. In such a laser cavity, radiation pressure drives the mechanical degree of freedom and its back-action is caused by the mechanical modulation of the cavity loss rate. Our numerical analysis shows that even in a wideband gain material, such dissipative coupling couples the mechanical oscillation with the laser relaxation oscillations process. Laser self-pulsation is observed for mechanical frequencies below the laser relaxation oscillation frequency under sufficiently high optomechanical coupling factor.
Asymptotic representation of relaxation oscillations in lasers
Grigorieva, Elena V
2017-01-01
In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.
Nanoscale relaxation oscillator
Zettl, Alexander K.; Regan, Brian C.; Aloni, Shaul
2009-04-07
A nanoscale oscillation device is disclosed, wherein two nanoscale droplets are altered in size by mass transport, then contact each other and merge through surface tension. The device may also comprise a channel having an actuator responsive to mechanical oscillation caused by expansion and contraction of the droplets. It further has a structure for delivering atoms between droplets, wherein the droplets are nanoparticles. Provided are a first particle and a second particle on the channel member, both being made of a chargeable material, the second particle contacting the actuator portion; and electrodes connected to the channel member for delivering a potential gradient across the channel and traversing the first and second particles. The particles are spaced apart a specified distance so that atoms from one particle are delivered to the other particle by mass transport in response to the potential (e.g. voltage potential) and the first and second particles are liquid and touch at a predetermined point of growth, thereby causing merging of the second particle into the first particle by surface tension forces and reverse movement of the actuator. In a preferred embodiment, the channel comprises a carbon nanotube and the droplets comprise metal nanoparticles, e.g. indium, which is readily made liquid.
Control linearity and jitter of relaxation oscillators
Gierkink, Sander Laurentius Johannes
1999-01-01
The body of this thesis (chapters 3,4 and 5) deals with the analysis and improvement of a specific class of voltage- or current controlled oscillators (VCO’s respectively CCO’s) called relaxation oscillators. Before going into detail on this particular class of oscillators, first the function and ap
Improved memristor-based relaxation oscillator
Mosad, Ahmed G.
2013-09-01
This paper presents an improved memristor-based relaxation oscillator which offers higher frequency and wider tunning range than the existing reactance-less oscillators. It also has the capability of operating on two positive supplies or alternatively a positive and negative supply. Furthermore, it has the advantage that it can be fully integrated on-chip providing an area-efficient solution. On the other hand, The oscillation concept is discussed then a complete mathematical analysis of the proposed oscillator is introduced. Furthermore, the power consumption of the new relaxation circuit is discussed and validated by the PSPICE circuit simulations showing an excellent agreement. MATLAB results are also introduced to demonstrate the resistance range and the corresponding frequency range which can be obtained from the proposed relaxation oscillator. © 2013 Elsevier Ltd.
Amplitude envelope synchronization in coupled chaotic oscillators.
Gonzalez-Miranda, J M
2002-03-01
A peculiar type of synchronization has been found when two Van der Pol-Duffing oscillators, evolving in different chaotic attractors, are coupled. As the coupling increases, the frequencies of the two oscillators remain different, while a synchronized modulation of the amplitudes of a signal of each system develops, and a null Lyapunov exponent of the uncoupled systems becomes negative and gradually larger in absolute value. This phenomenon is characterized by an appropriate correlation function between the returns of the signals, and interpreted in terms of the mutual excitation of new frequencies in the oscillators power spectra. This form of synchronization also occurs in other systems, but it shows up mixed with or screened by other forms of synchronization, as illustrated in this paper by means of the examples of the dynamic behavior observed for three other different models of chaotic oscillators.
The use of (double) relaxation oscillation SQUIDs as a sensor
Duuren, van M.J.; Brons, G.C.S.; Kattouw, H.; Flokstra, J.; Rogalla, H.
1997-01-01
Relaxation Oscillation SQUIDs (ROSs) and Double Relaxation Oscillation SQUIDs (DROSs) are based on relaxation oscillations that are induced in hysteretic dc SQUIDs by an external L-R shunt. The relaxation frequency of a ROS varies with the applied flux Φ, whereas the output of a DROS is a dc voltage
The use of (double) relaxation oscillation SQUIDs as a sensor
van Duuren, M.J.; Brons, G.C.S.; Kattouw, H.; Flokstra, Jakob; Rogalla, Horst
1997-01-01
Relaxation Oscillation SQUIDs (ROSs) and Double Relaxation Oscillation SQUIDs (DROSs) are based on relaxation oscillations that are induced in hysteretic dc SQUIDs by an external L-R shunt. The relaxation frequency of a ROS varies with the applied flux Φ, whereas the output of a DROS is a dc
Noise in (double) relaxation oscillation SQUIDs
Adelerhof, Derk Jan; Adelerhof, Derk Jan; Flokstra, Jakob; Rogalla, Horst
1994-01-01
We have modelled the effect of two intrinsic noise sources on the flux noise spectral density of (Double) Relaxation Oscillation SQUIDs ((D)ROSs) based on hysteretic Josephson tunnel junctions. An important noise source is the spread in the critical current of the SQUID due to thermal fluctuations.
Leiser, Randolph J.; Rotstein, Horacio G.
2017-08-01
Oscillations in far-from-equilibrium systems (e.g., chemical, biochemical, biological) are generated by the nonlinear interplay of positive and negative feedback effects operating at different time scales. Relaxation oscillations emerge when the time scales between the activators and the inhibitors are well separated. In addition to the large-amplitude oscillations (LAOs) or relaxation type, these systems exhibit small-amplitude oscillations (SAOs) as well as abrupt transitions between them (canard phenomenon). Localized cluster patterns in networks of relaxation oscillators consist of one cluster oscillating in the LAO regime or exhibiting mixed-mode oscillations (LAOs interspersed with SAOs), while the other oscillates in the SAO regime. Because the individual oscillators are monostable, localized patterns are a network phenomenon that involves the interplay of the connectivity and the intrinsic dynamic properties of the individual nodes. Motivated by experimental and theoretical results on the Belousov-Zhabotinsky reaction, we investigate the mechanisms underlying the generation of localized patterns in globally coupled networks of piecewise-linear relaxation oscillators where the global feedback term affects the rate of change of the activator (fast variable) and depends on the weighted sum of the inhibitor (slow variable) at any given time. We also investigate whether these patterns are affected by the presence of a diffusive type of coupling whose synchronizing effects compete with the symmetry-breaking global feedback effects.
Han, Wenchen; Cheng, Hongyan; Dai, Qionglin; Li, Haihong; Ju, Ping; Yang, Junzhong
2016-10-01
In this work, we investigate the dynamics in a ring of identical Stuart-Landau oscillators with conjugate coupling systematically. We analyze the stability of the amplitude death and find the stability independent of the number of oscillators. When the amplitude death state is unstable, a large number of states such as homogeneous oscillation death, heterogeneous oscillation death, homogeneous oscillation, and wave propagations are found and they may coexist. We also find that all of these states are related to the unstable spatial modes to the amplitude death state.
Amplitudes of stellar oscillations the implications for asteroseismology
Kjeldsen, H
1994-01-01
There are no good predictions for the amplitudes expected from solar-like oscillations in other stars. In the absence of a definitive model for convection, which is thought to be the mechanism that excites these oscillations, the amplitudes for both velocity and luminosity measurements must be estimated by scaling from the Sun. In the case of luminosity measurements, even this is difficult because of disagreement over the solar amplitude. This last point has lead us to investigate whether the luminosity amplitude of oscillations (dL/L) can be derived from the velocity amplitude v_osc. Using linear theory and observational data, we show that p-mode oscillations in a large sample of pulsating stars satisfy (dL/L)_bol proportional to v_osc/T_eff. Using this relationship, together with the best estimate of v_osc(Sun) = (23.4 +/- 1.4) cm/s, we estimate the luminosity amplitude of solar oscillations at 550 nm to be dL/L = (4.7 +/- 0.3) ppm. Next we discuss how to scale the amplitude of solar-like (i.e., convectivel...
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…
A digital Double Relaxation Oscillation SQUID for particle detector readout
Podt, M.; Keizer, D.; Flokstra, Jakob; Rogalla, Horst
2000-01-01
Double Relaxation Oscillation SQUIDs (DROSs) are based on relaxation oscillations that are generated in hysteretic dc SQUIDs by an external L–R shunt. We realized a DROS with the complete flux-locked loop circuitry on one single chip, the Smart DROS. The pulsed output of the Smart DROS enables a
Phase Synchronization of Coupled Rossler Oscillators: Amplitude Effect
LI Xiao-Wen; ZHENG Zhi-Gang
2007-01-01
Phase synchronization of two linearly coupled Rossler oscillators with parameter misfits is explored.It is found that depending on parameter mismatches,the synchronization of phases exhibits different manners.The synchronization regime can be divided into three regimes.For small mismatches,the amplitude-insensitive regime gives the phase-dominant synchronization; When the parameter misfit increases,the amplitudes and phases of oscillators are correlated,and the amplitudes will dominate the synchronous dynamics for very large mismatches.The lag time among phases exhibits a power law when phase synchronization is achieved.
Thermodynamic constraints on the amplitude of quantum oscillations
Shekhter, Arkady; Modic, K. A.; McDonald, R. D.; Ramshaw, B. J.
2017-03-01
Magneto-quantum oscillation experiments in high-temperature superconductors show a strong thermally induced suppression of the oscillation amplitude approaching the critical dopings [B. J. Ramshaw et al., Science 348, 317 (2014), 10.1126/science.aaa4990; H. Shishido et al., Phys. Rev. Lett. 104, 057008 (2010), 10.1103/PhysRevLett.104.057008; P. Walmsley et al., Phys. Rev. Lett. 110, 257002 (2013), 10.1103/PhysRevLett.110.257002]—in support of a quantum-critical origin of their phase diagrams. We suggest that, in addition to a thermodynamic mass enhancement, these experiments may directly indicate the increasing role of quantum fluctuations that suppress the quantum oscillation amplitude through inelastic scattering. We show that the traditional theoretical approaches beyond Lifshitz-Kosevich to calculate the oscillation amplitude in correlated metals result in a contradiction with the third law of thermodynamics and suggest a way to rectify this problem.
The accretion rate dependence of burst oscillation amplitude
Ootes, Laura S; Galloway, Duncan K; Wijnands, Rudy
2016-01-01
Neutron stars in low mass X-ray binaries exhibit oscillations during thermonuclear bursts, attributed to asymmetric brightness patterns on the burning surfaces. All models that have been proposed to explain the origin of these asymmetries (spreading hotspots, surface waves, and cooling wakes) depend on the accretion rate. By analysis of archival RXTE data of six oscillation sources, we investigate the accretion rate dependence of the amplitude of burst oscillations. This more than doubles the size of the sample analysed previously by Muno et al. (2004), who found indications for a relationship between accretion rate and oscillation amplitudes. We find that burst oscillation signals can be detected at all observed accretion rates. Moreover, oscillations at low accretion rates are found to have relatively small amplitudes ($A_\\text{rms}\\leq0.10$) while oscillations detected in bursts observed at high accretion rates cover a broad spread in amplitudes ($0.05\\leq A_\\text{rms}\\leq0.20$). In this paper we present t...
Memristor-based relaxation oscillators using digital gates
Khatib, Moustafa A.
2012-11-01
This paper presents two memristor-based relaxation oscillators. The proposed oscillators are designed without the need of any reactive elements, i.e., capacitor or inductor. As the \\'resistance storage\\' property of the memristor can be exploited to generate the oscillation. The proposed oscillators have the advantage that they can be fully integrated on-chip giving an area-efficient solution. Furthermore, these oscillators give higher frequency other than the existing reactance-less oscillator and provide a wider range of the resistance. The concept of operation and the mathematical analysis for the proposed oscillators are explained and verified with circuit simulations showing an excellent agreement. © 2012 IEEE.
Relaxation oscillations in a laser with a Gaussian mirror.
Mossakowska-Wyszyńska, Agnieszka; Witoński, Piotr; Szczepański, Paweł
2002-03-20
We present an analysis of the relaxation oscillations in a laser with a Gaussian mirror by taking into account the three-dimensional spatial field distribution of the laser modes and the spatial hole burning effect. In particular, we discuss the influence of the Gaussian mirror peak reflectivity and a Gaussian parameter on the damping rate and frequency of the relaxation oscillation for two different laser structures, i.e., with a classically unstable resonator and a classically stable resonator.
Oscillator death induced by amplitude-dependent coupling in repulsively coupled oscillators
Liu, Weiqing; Xiao, Guibao; Zhu, Yun; Zhan, Meng; Xiao, Jinghua; Kurths, Jürgen
2015-05-01
The effects of amplitude-dependent coupling on oscillator death (OD) are investigated for two repulsively coupled Lorenz oscillators. Based on numerical simulations, it is shown that as constraint strengths on the amplitude-dependent coupling change, an oscillatory state may undergo a transition to an OD state. The parameter regimes of the OD domain are theoretically determined, which coincide well with the numerical results. An electronic circuit is set up to exhibit the transition process to the OD state with an amplitude-dependent coupling. These findings may have practical importance on chaos control and oscillation depression.
Frequency and amplitude stabilization in MEMS and NEMS oscillators
Chen, Changyao; Lopez, Omar Daniel; Czaplewski, David A.
2017-06-14
This invention comprises a nonlinear micro- and nano-mechanical resonator that can maintain frequency of operation and amplitude of operation for a period of time after all external power has been removed from the device. Utilizing specific nonlinear dynamics of the micromechanical resonator, mechanical energy at low frequencies can be input and stored in higher frequencies modes, thus using the multiple degrees of freedom of the resonator to extend its energy storage capacity. Furthermore, the energy stored in multiple vibrational modes can be used to maintain the resonator oscillating for a fixed period of time, even without an external power supply. This is the first demonstration of an "autonomous" frequency source that can maintain a constant frequency and vibrating amplitude when no external power is provided, making it ideal for applications requiring an oscillator in low power, or limited and intermittent power supplies.
Relaxation of a qubit measured by a driven Duffing oscillator
Serban, I; Wilhelm, F K
2009-01-01
We investigate the relaxation of a superconducting qubit for the case when its detector, the Josephson bifurcation amplifier, remains latched in one of its two (meta)stable states of forced vibrations. The qubit relaxation rates are different in different states. They can display strong dependence on the qubit frequency and resonant enhancement, which is due to {\\em quasienergy resonances}. Coupling to the driven oscillator changes the effective temperature of the qubit.
Relaxation oscillations, stability, and cavity feedback in a superradiant Raman laser
Bohnet, Justin G; Weiner, Joshua M; Cox, Kevin C; Thompson, James K
2012-01-01
We experimentally study the relaxation oscillations and amplitude stability properties of an optical laser operating deep into the bad-cavity regime using a laser-cooled $^{87}$Rb Raman laser. By combining measurements of the laser light field with non-demolition measurements of the atomic populations, we infer the response of the the gain medium represented by a collective atomic Bloch vector. The results are qualitatively explained with a simple model. Measurements and theory are extended to include the effect of intermediate repumping states on the closed-loop stability of the oscillator and the role of cavity-feedback on stabilizing or enhancing relaxation oscillations. This experimental study of the stability of an optical laser operating deep into the bad-cavity regime will guide future development of superradiant lasers with ultranarrow linewidths.
Relaxation oscillations, stability, and cavity feedback in a superradiant Raman laser.
Bohnet, Justin G; Chen, Zilong; Weiner, Joshua M; Cox, Kevin C; Thompson, James K
2012-12-21
We experimentally study the relaxation oscillations and amplitude stability properties of an optical laser operating deep into the bad-cavity regime using a laser-cooled ^{87}Rb Raman laser. By combining measurements of the laser light field with nondemolition measurements of the atomic populations, we infer the response of the gain medium represented by a collective atomic Bloch vector. The results are qualitatively explained with a simple model. Measurements and theory are extended to include the effect of intermediate repumping states on the closed-loop stability of the oscillator and the role of cavity feedback on stabilizing or enhancing relaxation oscillations. This experimental study of the stability of an optical laser operating deep into the bad-cavity regime will guide future development of superradiant lasers with ultranarrow linewidths.
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.
Relaxing Oscillation of the Machine-Unit
Bohumil Skala
2008-01-01
Full Text Available To understand the behavior of the Earth´s geomagnetic field, many theories have been created. One of the possible approaches is the Rikitake dynamo and chaotic theory. This paper describes the first step, i.e. how to verify the chaotic theory simulated result by a practical test. This first step is the oscillating machine unit. The asynchronous motor working point is moving from the stable part of its torque characteristic to the labile part due to the enormous loading. In the labile part the speed slows down and loading has to be decreased. Then the motor moves back to the stable part of characteristic.
Relaxation oscillation SQUIDs with high dV/dfi
Adelerhof, Derk Jan; Adelerhof, D.J.; Nijstad, H.; Nijstad, H.; Flokstra, Jakob; Rogalla, Horst
1993-01-01
Relaxation oscillation SQUIDs (ROSs) based on Nb/Al, AlOx /Al/Nb Josephson tunnel junctions have been designed and fabricated. The hysteretic SQUIDs (superconducting quantum interference devices) have a maximum critical current of about 130 μA and an inductance of 20 pH. A voltage modulation of 40
Relaxation Oscillations in New IS-LM Model
Volná, Barbora
2012-01-01
In this paper, we create new version of IS-LM model. The original IS-LM model has two main deficiencies: assumptions of constant price level and of strictly exogenous money supply. New IS-LM model eliminates these deficiencies. In the second section, we prove the existence of relaxation oscillations in this new IS-LM model.
Revoking amplitude and oscillation deaths by low-pass filter in coupled oscillators
Zou, Wei; Zhan, Meng; Kurths, Jürgen
2017-06-01
When in an ensemble of oscillatory units the interaction occurs through a diffusion-like manner, the intrinsic oscillations can be quenched through two structurally different scenarios: amplitude death (AD) and oscillation death (OD). Unveiling the underlying principles of stable rhythmic activity against AD and OD is a challenging issue of substantial practical significance. Here, by developing a low-pass filter (LPF) to track the output signals of the local system in the coupling, we show that it can revoke both AD and OD, and even the AD to OD transition, thereby giving rise to oscillations in coupled nonlinear oscillators under diverse death scenarios. The effectiveness of the local LPF is proven to be valid in an arbitrary network of coupled oscillators with distributed propagation delays. The constructive role of the local LPF in revoking deaths provides a potential dynamic mechanism of sustaining a reliable rhythmicity in real-world systems.
Frequencies and amplitudes of high-degree solar oscillations
Kaufman, James Morris
Measurements of some of the properties of high-degree solar p- and f-mode oscillations are presented. Using high-resolution velocity images from Big Bear Solar Observatory, we have measured mode frequencies, which provide information about the composition and internal structure of the Sun, and mode velocity amplitudes (corrected for the effects of atmospheric seeing), which tell us about the oscillation excitation and damping mechanisms. We present a new and more accurate table of the Sun's acoustic vibration frequencies, nunl, as a function of radial order n and spherical harmonic degree l. These frequencies are averages over azimuthal order m and approximate the normal mode frequencies of a nonrotating spherically symmetric Sun near solar minimum. The frequencies presented here are for solar p- and f-modes with 180 less than or = l less than or = 1920, 0 less than or = n less than or = 8, and 1.7 mHz less than or = nunl less than or = 5.3 mHz. The uncertainties, sigmanl, in the frequencies areas are as low as 3.1 micro-Hz. The theoretically expected f-mode frequencies are given by omega squared = gkh approx. = gl/R, where g is the gravitational acceleration at the surface, kh is the horizontal component of the wave vector, and R is the radius of the Sun. We find that the observed frequencies are significantly less than expected for l greater than 1000, for which we have no explanation. Observations of high-degree oscillations, which have very small spatial features, suffer from the effects of atmospheric image blurring and image motion (or 'seeing'), thereby reducing the amplitudes of their spatial-frequency components. In an attempt to correct the velocity amplitudes for these effects, we simultaneously measured the atmospheric modulation transfer function (MTF) by looking at the effects of seeing on the solar limb. We are able to correct the velocity amplitudes using the MTF out to l approx. = 1200. We find that the frequency of the peak velocity power (as a
Fast relaxation transients in a kicked damped oscillator
Urquizu, Merce [Laboratori d' Estudis Geofisics ' Eduard Fontsere' , IEC, Barcelona (Spain); Correig, Antoni M. [Departament d' Astronomical i Meteorologia, Laboratori d' Estudis Geofisics Eduard Fontsere, UB Marti Franques 1, E-08028 Barcelona (Spain) and Laboratori d' Estudis Geofisics ' Eduard Fontsere' , IEC, Barcelona (Spain)]. E-mail: ton.correig@am.ub.es
2007-08-15
Although nonlinear relaxation transients are very common in nature, very few studies are devoted to its characterization, mainly due to its short time duration. In this paper, we present a study about the nature of relaxation transients in a kicked damped oscillator, in which transients are generated in terms of continuous fast changes in the parameters of the system. We have found that transient dynamics can be described, rather than in terms of bifurcation dynamics, in terms of instantaneous stretching factors, which are related to the stability of fixed points of the corresponding stroboscopic maps.
Review of relaxation oscillations in plasma processing discharges
Zhou Zhu-Wen; M.A.Lieberman; Sungjin Kim
2007-01-01
Relaxation oscillations due to plasma instabilities at frequencies ranging from a few Hz to tens of kHz have been observed in various types of plasma processing discharges.Relaxation oscillations have been observed in electropositive capacitive discharges between a powered anode and a metallic chamber whose periphery iS grounded through a slot with dielectric spacers.The oscillations of time-varying optical emission from the main discharge chamber show,for example,a high-frequency (～40 kHz) relaxation oscillation at 13.33Pa,with an absorbed power being nearly the peripheral breakdown power,and a low-frequency (～3 Hz) oscillation,with an even higher absorbed power.The high-frequency oscillation is found to ignite plasma in the slot,but usually not in the peripheral chamber.The kilohertz oscillations are modelled using an electromagnetic model of the slot impedance,coupled to a circuit analysis of the system including the matching network.The model results are in general agreement with the experimental observations,and indicate a variety of behaviours dependent on the matching conditions.In low-pressure inductive discharges,oscillations appear in the transition between low-density capacitively driven and high-density inductively driven discharges when attaching gases such as SF6 and Ar/SF6 mixtures are used.Oscillations of charged particles,plasma potential,and light,at frequencies ranging from a few Hz to tens of kHz,are seen for gas pressures between 0.133 Pa and 13.33 Pa and discharge powers in a range of 75-1200 W.The region of instability increases as the plasma becomes more electronegative,and the frequency of plasma oscillation increases as the power,pressure,and gas flow rate increase.A volume-averaged (global) model of the kilohertz instability has been developed;the results obtained from the model agree well with the experimental observations.
Low-Frequency Relaxation Oscillations in Capacitive Discharge Processes
ZHOU Zhu-Wen; M.A.LIEBERMAN; Sungjin KIM; JI Shi-Yin; DENG Ming-Sen; SUN Guang-Yu
2008-01-01
Low-frequency (2.72-3.70 Hz) relaxation oscillations at 100m Tort at higher absorbed power were observed from time-varying optical emission of the main discharge chamber and the periphery.We interpret the low frequency oscillations using an electromagnetic model of the slot impedance with parallel connection variational peripheral capacitance,coupled to a circuit analysis of the system including the matching network.The model results are in general agreement with the experimental observations,and indicate a variety of bchaviours dependent on the matching conditions.
RS trigger based relaxation oscillator for temperature measurement circuit
ZOU Zhi-ge; ZOU Xue-cheng; JIAN Wen-xiang; LEI Jian-ming
2008-01-01
Resistance-to-time converter is always used for digital temperature measurement. An reset-set (RS) trigger based, relaxation oscillator based temperature measurement circuit, which is used to convert the change of thermistor sensor into a frequency signal for later processing, has been presented in this article. The RS trigger, which is composed of two inverters designed with distinct logical transition threshold voltages by changing the metal-oxide-semiconductor (MOS) transistor gains, has the same function as the Schmitt trigger in the relaxation oscillator. The advantage of the RS trigger based Schmitt trigger is that it reduces the dependence to supply voltage, chip temperature, and process variation. This temperature measurement circuit has been applied in a clinical thermometer chip that can measure temperature to an accuracy of better than 0.05℃ down to 1.1 V battery voltage. It is fabricated in 0.5double metal single poly complementary MOS (CMOS) process.
Streaming vorticity flux from oscillating walls with finite amplitude
Wu, J. Z.; Wu, X. H.; Wu, J. M.
1993-01-01
How to describe vorticity creation from a moving wall is a long standing problem. This paper discusses relevant issues at the fundamental level. First, it is shown that the concept of 'vorticity flux due to wall acceleration' can be best understood by following fluid particles on the wall rather than observing the flow at fixed spatial points. This is of crucial importance when the time-averaged flux is to be considered. The averaged flux has to be estimated in a wall-fixed frame of reference (in which there is no flux due to wall acceleration at all); or, if an inertial frame of reference is used, the generalized Lagrangian mean (GLM) also gives the same result. Then, for some simple but typical configurations, the time-averaged vorticity flux from a harmonically oscillating wall with finite amplitude is analyzed, without appealing to small perturbation. The main conclusion is that the wall oscillation will produce an additional mean vorticity flux (a fully nonlinear streaming effect), which is partially responsible for the mechanism of vortex flow control by waves. The results provide qualitative explanation for some experimentally and/or computationally observed phenomena.
Streaming vorticity flux from oscillating walls with finite amplitude
Wu, J. Z.; Wu, X. H.; Wu, J. M.
1993-01-01
How to describe vorticity creation from a moving wall is a long standing problem. This paper discusses relevant issues at the fundamental level. First, it is shown that the concept of 'vorticity flux due to wall acceleration' can be best understood by following fluid particles on the wall rather than observing the flow at fixed spatial points. This is of crucial importance when the time-averaged flux is to be considered. The averaged flux has to be estimated in a wall-fixed frame of reference (in which there is no flux due to wall acceleration at all); or, if an inertial frame of reference is used, the generalized Lagrangian mean (GLM) also gives the same result. Then, for some simple but typical configurations, the time-averaged vorticity flux from a harmonically oscillating wall with finite amplitude is analyzed, without appealing to small perturbation. The main conclusion is that the wall oscillation will produce an additional mean vorticity flux (a fully nonlinear streaming effect), which is partially responsible for the mechanism of vortex flow control by waves. The results provide qualitative explanation for some experimentally and/or computationally observed phenomena.
Transition to Amplitude Death in Coupled System with Small Number of Nonlinear Oscillators
CHEN Hai-Ling; YANG Jun-Zhong
2009-01-01
In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either.
Quantifying phase-amplitude coupling in neuronal network oscillations.
Onslow, Angela C E; Bogacz, Rafal; Jones, Matthew W
2011-03-01
Neuroscience time series data from a range of techniques and species reveal complex, non-linear interactions between different frequencies of neuronal network oscillations within and across brain regions. Here, we briefly review the evidence that these nested, cross-frequency interactions act in concert with linearly covariant (within-frequency) activity to dynamically coordinate functionally related neuronal ensembles during behaviour. Such studies depend upon reliable quantification of cross-frequency coordination, and we compare the properties of three techniques used to measure phase-amplitude coupling (PAC)--Envelope-to-Signal Correlation (ESC), the Modulation Index (MI) and Cross-Frequency Coherence (CFC)--by standardizing their filtering algorithms and systematically assessing their robustness to noise and signal amplitude using artificial signals. Importantly, we also introduce a freely-downloadable method for estimating statistical significance of PAC, a step overlooked in the majority of published studies. We find that varying data length and noise levels leads to the three measures differentially detecting false positives or correctly identifying frequency bands of interaction; these conditions should therefore be taken into careful consideration when selecting PAC analyses. Finally, we demonstrate the utility of the three measures in quantifying PAC in local field potential data simultaneously recorded from rat hippocampus and prefrontal cortex, revealing a novel finding of prefrontal cortical theta phase modulating hippocampal gamma power. Future adaptations that allow detection of time-variant PAC should prove essential in deciphering the roles of cross-frequency coupling in mediating or reflecting nervous system function.
Relaxation oscillation model of hemodynamic parameters in the cerebral vessels
Cherevko, A. A.; Mikhaylova, A. V.; Chupakhin, A. P.; Ufimtseva, I. V.; Krivoshapkin, A. L.; Orlov, K. Yu
2016-06-01
Simulation of a blood flow under normality as well as under pathology is extremely complex problem of great current interest both from the point of view of fundamental hydrodynamics, and for medical applications. This paper proposes a model of Van der Pol - Duffing nonlinear oscillator equation describing relaxation oscillations of a blood flow in the cerebral vessels. The model is based on the patient-specific clinical experimental data flow obtained during the neurosurgical operations in Meshalkin Novosibirsk Research Institute of Circulation Pathology. The stability of the model is demonstrated through the variations of initial data and coefficients. It is universal and describes pressure and velocity fluctuations in different cerebral vessels (arteries, veins, sinuses), as well as in a laboratory model of carotid bifurcation. Derived equation describes the rheology of the ”blood stream - elastic vessel wall gelatinous brain environment” composite system and represents the state equation of this complex environment.
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...
Time-varying interaction leads to amplitude death in coupled nonlinear oscillators
Awadhesh Prasad
2013-09-01
A new form of time-varying interaction in coupled oscillators is introduced. In this interaction, each individual oscillator has always time-independent self-feedback while its interaction with other oscillators are modulated with time-varying function. This interaction gives rise to a phenomenon called amplitude death even in diffusively coupled identical oscillators. The nonlinear variation of the locus of bifurcation point is shown. Results are illustrated with Landau–Stuart (LS) and Rössler oscillators.
Gonzalez, Oscar J. Avella; van Aerde, Karlijn I.; van Elburg, Ronald A. J.; Poil, Simon-Shlomo; Mansvelder, Huibert D.; Linkenkaer-Hansen, Klaus; van Pelt, Jaap; van Ooyen, Arjen
2012-01-01
Electrical oscillations in neuronal network activity are ubiquitous in the brain and have been associated with cognition and behavior. Intriguingly, the amplitude of ongoing oscillations, such as measured in EEG recordings, fluctuates irregularly, with episodes of high amplitude alternating with epi
Relaxation Oscillation with Picosecond Spikes in a Conjugated Polymer Laser
Wafa Musa Mujamammi
2016-10-01
Full Text Available Optically pumped conjugated polymer lasers are good competitors for dye lasers, often complementing and occasionally replacing them. This new type of laser material has broad bandwidths and high optical gains comparable to conventional laser dyes. Since the Stokes’ shift is unusually large, the conjugated polymer has a potential for high power laser action, facilitated by high concentration. This paper reports the results of a new conjugated polymer, the poly[(9,9-dioctyl-2,7-divinylenefluorenylene-alt-co-{2-methoxy-5-(2-ethylhexyloxy-1,4-phenylene}](PFO-co-MEH-PPV material, working in the green region. Also discussed are the spectral and temporal features of the amplified spontaneous emissions (ASE from the conjugated polymer PFO-co-MEH-PPV in a few solvents. When pumped by the third harmonic of the Nd:YAG laser of 10 ns pulse width, the time-resolved spectra of the ASE show relaxation oscillations and spikes of 600 ps pulses. To the best of our knowledge, this is the first report on relaxation oscillations in conjugated-polymer lasers.
The effect of airway pressure and oscillation amplitude on ventilation in pre-term infants
Miedema, M.; de Jongh, Franciscus H.C.; Frerichs, I.; van Veenendaal, M.B.; van Kaam, A.H.
2012-01-01
We determined the effect of lung recruitment and oscillation amplitude on regional oscillation volume and functional residual capacity (FRC) in high-frequency oscillatory ventilation (HFOV) used in pre-term infants with respiratory distress syndrome (RDS). Changes in lung volume, oscillation volume
A photonic ultra-wideband pulse generator based on relaxation oscillations of a semiconductor laser
Yu, Xianbin; Gibbon, Timothy Braidwood; Pawlik, Michal;
2009-01-01
A photonic ultra-wideband (UWB) pulse generator based on relaxation oscillations of a semiconductor laser is proposed and experimentally demonstrated. We numerically simulate the modulation response of a direct modulation laser (DML) and show that due to the relaxation oscillations of the laser...
Impact of luminescence quenching on relaxation-oscillation frequency in solid-state lasers
Agazzi, L.; Bernhardi, Edward; Worhoff, Kerstin; Pollnau, Markus
Measurement of the laser relaxation-oscillation frequency as a function of pump rate allows one to determine parameters of the laser medium or cavity. We show that luminescence quenching of a fraction of the rare-earth ions in a solid-state laser affects the relaxation oscillations, resulting in
Experimental observation of partial amplitude death in coupled chaotic oscillators
Liu Wei-Qing; Yang Jun-Zhong; Xiao Jing-Hua
2006-01-01
The dynamics of coupled Lorenz circuits is investigated experimentally. The partial amplitude death reported in Phys. Rev. E 72, 057201 (2005) is verified by physical experiments with electronic circuits. With the increase of coupling constant, the coupled circuits undergo the transition from the breakdown of both the reflection symmetry and the translational symmetry to the partial amplitude death. Its stability is also confirmed by analysing the effects of noise.
Relaxation oscillations and hierarchy of feedbacks in MAPK signaling
Kochańczyk, Marek; Kocieniewski, Paweł; Kozłowska, Emilia; Jaruszewicz-Błońska, Joanna; Sparta, Breanne; Pargett, Michael; Albeck, John G.; Hlavacek, William S.; Lipniacki, Tomasz
2017-01-01
We formulated a computational model for a MAPK signaling cascade downstream of the EGF receptor to investigate how interlinked positive and negative feedback loops process EGF signals into ERK pulses of constant amplitude but dose-dependent duration and frequency. A positive feedback loop involving RAS and SOS, which leads to bistability and allows for switch-like responses to inputs, is nested within a negative feedback loop that encompasses RAS and RAF, MEK, and ERK that inhibits SOS via phosphorylation. This negative feedback, operating on a longer time scale, changes switch-like behavior into oscillations having a period of 1 hour or longer. Two auxiliary negative feedback loops, from ERK to MEK and RAF, placed downstream of the positive feedback, shape the temporal ERK activity profile but are dispensable for oscillations. Thus, the positive feedback introduces a hierarchy among negative feedback loops, such that the effect of a negative feedback depends on its position with respect to the positive feedback loop. Furthermore, a combination of the fast positive feedback involving slow-diffusing membrane components with slower negative feedbacks involving faster diffusing cytoplasmic components leads to local excitation/global inhibition dynamics, which allows the MAPK cascade to transmit paracrine EGF signals into spatially non-uniform ERK activity pulses.
Decayless low-amplitude kink oscillations: a common phenomenon in the solar corona?
Anfinogentov, S A; Nisticò, G
2015-01-01
We investigate the decayless regime of coronal kink oscillations recently discovered in the Solar Dynamics Observatory (SDO)/AIA data. In contrast to decaying kink oscillations that are excited by impulsive dynamical processes, this type of transverse oscillations is not connected to any external impulsive impact, such as a flare or CME, and does not show any significant decay. Moreover the amplitude of these decayless oscillations is typically lower than that of decaying oscillations. The aim of this research is to estimate the prevalence of this phenomenon and its characteristic signatures. We analysed 21 active regions (NOAA 11637--11657) observed in January 2013 in the 171 A channel of SDO/AIA. For each active region we inspected six hours of observations, constructing time-distance plots for the slits positioned across pronounced bright loops. The oscillatory patterns in time-distance plots were visually identified and the oscillation periods and amplitudes were measured. We also estimated the length of ...
Observational Study of Large Amplitude Longitudinal Oscillations in a Solar Filament
Knizhnik, K; Muglach, K; Gilbert, H; Kucera, T; Karpen, J
2013-01-01
On 20 August 2010 an energetic disturbance triggered damped large-amplitude longitudinal (LAL) oscillations in almost an entire filament. In the present work we analyze this periodic motion in the filament to characterize the damping and restoring mechanism of the oscillation. Our method involves placing slits along the axis of the filament at different angles with respect to the spine of the filament, finding the angle at which the oscillation is clearest, and fitting the resulting oscillation pattern to decaying sinusoidal and Bessel functions. These functions represent the equations of motion of a pendulum damped by mass accretion. With this method we determine the period and the decaying time of the oscillation. Our preliminary results support the theory presented by Luna and Karpen (2012) that the restoring force of LAL oscillations is solar gravity in the tubes where the threads oscillate, and the damping mechanism is the ongoing accumulation of mass onto the oscillating threads. Following an earlier pa...
Van der Pol and the history of relaxation oscillations: toward the emergence of a concept
Ginoux, Jean-Marc
2014-01-01
Relaxation oscillations are commonly associated with the name of Balthazar van der Pol via his eponymous paper (Philosophical Magazine, 1926) in which he apparently introduced this terminology to describe the nonlinear oscillations produced by self-sustained oscillating systems such as a triode circuit. Our aim is to investigate how relaxation oscillations were actually discovered. Browsing the literature from the late 19th century, we identified four self-oscillating systems in which relaxation oscillations have been observed: i) the series dynamo machine conducted by G\\'erard-Lescuyer (1880), ii) the musical arc discovered by Duddell (1901) and investigated by Blondel (1905), iii) the triode invented by de Forest (1907) and, iv) the multivibrator elaborated by Abraham and Bloch (1917). The differential equation describing such a self-oscillating system was proposed by Poincar\\'e for the musical arc (1908), by Janet for the series dynamo machine (1919), and by Blondel for the triode (1919). Once Janet (1919)...
Braun, David J.; Sutas, Andrius; Vijayakumar, Sethu
2017-01-01
Theory predicts that parametrically excited oscillators, tuned to operate under resonant condition, are capable of large-amplitude oscillation useful in diverse applications, such as signal amplification, communication, and analog computation. However, due to amplitude saturation caused by nonlinearity, lack of robustness to model uncertainty, and limited sensitivity to parameter modulation, these oscillators require fine-tuning and strong modulation to generate robust large-amplitude oscillation. Here we present a principle of self-tuning parametric feedback excitation that alleviates the above-mentioned limitations. This is achieved using a minimalistic control implementation that performs (i) self-tuning (slow parameter adaptation) and (ii) feedback pumping (fast parameter modulation), without sophisticated signal processing past observations. The proposed approach provides near-optimal amplitude maximization without requiring model-based control computation, previously perceived inevitable to implement optimal control principles in practical application. Experimental implementation of the theory shows that the oscillator self-tunes itself near to the onset of dynamic bifurcation to achieve extreme sensitivity to small resonant parametric perturbations. As a result, it achieves large-amplitude oscillations by capitalizing on the effect of nonlinearity, despite substantial model uncertainties and strong unforeseen external perturbations. We envision the present finding to provide an effective and robust approach to parametric excitation when it comes to real-world application.
Orozco-Santillán, Arturo; Ruiz-Boullosa, Ricardo; Cutanda Henríquez, Vicente
2007-01-01
published on the topic predicts that these instabilities appear when the levitator is driven with a frequency above the resonant frequency of the empty device. The theory also shows that the instabilities can either saturate to a state with constant amplitude, or they can grow without limit until the object...... pressure amplitude in the cavity because of the presence of the sample. The theory predicts that the phase difference depends on the speed of the oscillating object. In this paper, we give for the first time experimental evidence that shows the existence of the phase difference, and that it is negatively...... proportional to the oscillation frequency of the levitated sample. We also present experimental results that show that the oscillational instabilities can be reduced if the amplitude of the acoustic wave is increased; as a result, stable conditions can be obtained where the oscillations of the sphere...
The analysis of high amplitude of potential oscillations near the hollow cathode of ion thruster
Qin, Yu; Xie, Kan; Guo, Ning; Zhang, Zun; Zhang, Cen; Gu, Zengjie; Zhang, Yu; Jiang, Zhaorui; Ouyang, Jiting
2017-05-01
The influence of gas flow, current level, and different shapes of anode on the oscillation amplitude and the characteristics of the hollow cathode discharge were investigated. The average plasma potential, temporal measurements of plasma potential, ion density, the electron temperature, as well as waveforms of plasma potential for test conditions were measured. At the same time, the time-resolved images of the plasma plume were also recorded. The results show that the potential oscillations appear at high discharge current or low flow rate. The potential oscillation boundaries, the position of maximum amplitude of plasma potential, and the position where the highest ion density was observed, were found. Both of the positions are affected by different shapes of anode configurations. This high amplitude of potential oscillations is ionization-like instabilities. The xenon ions ionized in space was analyzed for the fast potential rise and spatial dissipation of the space xenon ions was the reason for the gradual potential delay.
Nonlinear Vibration of Oscillation Systems using Frequency-Amplitude Formulation
A. Fereidoon
2012-01-01
Full Text Available In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifth-order nonlinearity for two examples using He's Frequency-Amplitude Formulation (HFAF.The effectiveness and convenience of the method is illustrated in these examples. It will be shown that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems.
Van der Pol and the history of relaxation oscillations: toward the emergence of a concept.
Ginoux, Jean-Marc; Letellier, Christophe
2012-06-01
Relaxation oscillations are commonly associated with the name of Balthazar van der Pol via his paper (Philosophical Magazine, 1926) in which he apparently introduced this terminology to describe the nonlinear oscillations produced by self-sustained oscillating systems such as a triode circuit. Our aim is to investigate how relaxation oscillations were actually discovered. Browsing the literature from the late 19th century, we identified four self-oscillating systems in which relaxation oscillations have been observed: (i) the series dynamo machine conducted by Gérard-Lescuyer (1880), (ii) the musical arc discovered by Duddell (1901) and investigated by Blondel (1905), (iii) the triode invented by de Forest (1907), and (iv) the multivibrator elaborated by Abraham and Bloch (1917). The differential equation describing such a self-oscillating system was proposed by Poincaré for the musical arc (1908), by Janet for the series dynamo machine (1919), and by Blondel for the triode (1919). Once Janet (1919) established that these three self-oscillating systems can be described by the same equation, van der Pol proposed (1926) a generic dimensionless equation which captures the relevant dynamical properties shared by these systems. Van der Pol's contributions during the period of 1926-1930 were investigated to show how, with Le Corbeiller's help, he popularized the "relaxation oscillations" using the previous experiments as examples and, turned them into a concept.
The energetics of flow through a rapidly oscillating tube with slowly varying amplitude.
Whittaker, Robert J; Heil, Matthias; Waters, Sarah L
2011-07-28
Motivated by the problem of self-excited oscillations in fluid-filled collapsible tubes, we examine the flow structure and energy budget of flow through an elastic-walled tube. Specifically, we consider the case in which a background axial flow is perturbed by prescribed small-amplitude high-frequency long-wavelength oscillations of the tube wall, with a slowly growing or decaying amplitude. We use a multiple-scale analysis to show that, at leading order, we recover the constant-amplitude equations derived by Whittaker et al. (Whittaker et al. 2010 J. Fluid Mech. 648, 83-121. (doi:10.1017/S0022112009992904)) with the effects of growth or decay entering only at first order. We also quantify the effects on the flow structure and energy budget. Finally, we discuss how our results are needed to understand and predict an instability that can lead to self-excited oscillations in collapsible-tube systems.
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.
Adelerhof, D.J.; Duuren, van M.J.; Flokstra, J.; Rogalla, H.; Kawai, J.; Kado, H.
1995-01-01
The experimental sensitivity of double relaxation oscillation SQUIDs (DROSs) has been compared with theory and with the results obtained by numerical simulations. The experimental sensitivity ranges from 60 to 13h, where h is Planck's constant, for relaxation frequencies from 0.4 up to 10 GHz. For l
Adelerhof, D.J.; Adelerhof, Derk Jan; van Duuren, M.J.; Flokstra, Jakob; Rogalla, Horst; Kawai, J.; Kado, H.
1995-01-01
The experimental sensitivity of double relaxation oscillation SQUIDs (DROSs) has been compared with theory and with the results obtained by numerical simulations. The experimental sensitivity ranges from 60 to 13h, where h is Planck's constant, for relaxation frequencies from 0.4 up to 10 GHz. For
The role of amplitude-to-phase conversion in the generation of oscillator flicker phase noise
Hearn, C. P.
1985-01-01
The role of amplitude-to-phase conversion as a factor in feedback oscillator flicker phase noise is examined. A limiting stage consisting of parallel-connected opposite polarity diodes operating in a circuit environment contining reactance is shown to exhibit amplitude-to-phase conversion. This mechanism coupled with resistive upconversion provides an indirect route for very low frequency flicker noise to be transferred into the phase of an oscillator signal. It is concluded that this effect is more significant in the lower frequency regimes where the onlinear reactances associated with active devices are overwhelmed by linear reactive elements.
Manimala, James M; Sun, C T
2016-06-01
The amplitude-dependent dynamic response in acoustic metamaterials having nonlinear local oscillator microstructures is studied using numerical simulations on representative discrete mass-spring models. Both cubically nonlinear hardening and softening local oscillator cases are considered. Single frequency, bi-frequency, and wave packet excitations at low and high amplitude levels were used to interrogate the models. The propagation and attenuation characteristics of harmonic waves in a tunable frequency range is found to correspond to the amplitude and nonlinearity-dependent shifts in the local resonance bandgap for such nonlinear acoustic metamaterials. A predominant shift in the propagated wave spectrum towards lower frequencies is observed. Moreover, the feasibility of amplitude and frequency-dependent selective filtering of composite signals consisting of individual frequency components which fall within propagating or attenuating regimes is demonstrated. Further enrichment of these wave manipulation mechanisms in acoustic metamaterials using different combinations of nonlinear microstructures presents device implications for acoustic filters and waveguides.
High sensitivity double relaxation oscillation superconducting quantum interference devices
Adelerhof, Derk Jan; Adelerhof, Derk Jan; Kawai, Jun; Uehara, Gen; Kado, Hisashi
1994-01-01
Double relaxation oscillationsuperconducting quantum interference devices(SQUIDs) (DROSs) have been fabricated with estimated relaxation frequencies up to 14 GHz. Both the intrinsic flux noise and the performance in a flux locked loop with direct voltage readout have been studied. In flux locked
The effects of dual-channel coupling on the transition from amplitude death to oscillation death
Chen, Jiangnan; Liu, Weiqing; Zhu, Yun; Xiao, Jinghua
2016-07-01
Oscillation quenching including amplitude death (AD) and oscillation death (OD) in addition to the transition processes between them have been hot topics in aspect of chaos control, physical and biological applications. The effects of dual-channel coupling on the AD and OD dynamics regimes, and their transition processes in coupled nonidentical oscillators are explored numerically and theoretically. Our results indicate that an additional repulsive coupling tends to shrink the AD domain while it enlarges the OD domain, however, an additional attractive coupling acts inversely. As a result, the transitions from AD to OD are replaced by transitions from oscillation state (OS) to AD or from OS to OD in the dual-channel coupled oscillators with different frequency mismatches. Our results are helpful to better understand the control of AD and OD and their transition processes.
Zhu, Weiping; Xu, Peng; Xu, Dong; Zhang, Meimei; Liu, Huiming; Gong, Linghui; Lu, Junfeng
2014-05-01
To study the effects of the thermal relaxation, the blood perfusion and the oscillating of ambient heat flux on the living tissue temperature in detail, we analytically investigated the one-dimensional CV model, a thermal wave model presented by Cattaneo and Vernott, for Pennes' bio-heat transfer equation under oscillating second-kind boundary condition. The results showed that the blood perfusion has the effect of maintaining the tissue's temperature. The heat propagation velocity decreases with the thermal relaxation time, while the absolute value of tissue's mean excess temperature at steady state increases with the thermal relaxation time. When the ambient heat flux oscillates, the tissue's temperature oscillates in the same period with a lag time. The results obtained in this paper are valuable for the research reference on the topic of tumor hyperthermia, heat injury, etc.
On the amplitude and phase errors of quadrature LC-tank CMOS oscillators
Mazzanti, Andrea; Svelto, Francesco; Andreani, Pietro
2006-01-01
An analytic approach for the estimation of the phase and amplitude imbalances caused by component mismatches and parasitic magnetic fields in two popular quadrature LC oscillators is presented. Very simple and closed-form equations are derived, proving that, although the two topologies share...
Damped large amplitude oscillations in a solar prominence and a bundle of coronal loops
Zhang, Quanhao; Liu, Rui; Shen, Chenglong; Zhang, Min; Gou, Tingyu; Liu, Jiajia; Liu, Kai; Zhou, Zhenjun; Wang, Shui
2016-01-01
We investigate the evolutions of two prominences (P1,P2) and two bundles of coronal loops (L1,L2), observed with SDO/AIA near the east solar limb on 2012 September 22. It is found that there were large-amplitude oscillations in P1 and L1, but no detectable motions in P2 and L2. These transverse oscillations were triggered by a large-scale coronal wave, originating from a large flare in a remote active region behind the solar limb. By carefully comparing the locations and heights of these oscillating and non-oscillating structures, we conclude that the propagating height of the wave is between 50 Mm and 130 Mm. The wave energy deposited in the oscillating prominence and coronal loops is at least of the order of $10^{28}$ erg. Furthermore, local magnetic field strength and Alfv\\'{e}n speeds are derived from the oscillating periods and damping time scales, which are extracted from the time series of the oscillations. It is demonstrated that oscillations can be used in not only coronal seismology, but also reveal...
Observational Study of Large Amplitude Longitudinal Oscillations in a Solar Filament
Knizhnik, Kalman; Luna, Manuel; Muglach, Karin; Gilbert, Holly; Kucera, Therese; Karpen, Judith
2014-01-01
On 20 August 2010 an energetic disturbance triggered damped large-amplitude longitudinal (LAL) oscillations in almost an entire filament. In the present work we analyze this periodic motion in the filament to characterize the damping and restoring mechanism of the oscillation. Our method involves placing slits along the axis of the filament at different angles with respect to the spine of the filament, finding the angle at which the oscillation is clearest, and fitting the resulting oscillation pattern to decaying sinusoidal and Bessel functions. These functions represent the equations of motion of a pendulum damped by mass accretion. With this method we determine the period and the decaying time of the oscillation. Our preliminary results support the theory presented by Luna and Karpen (2012) that the restoring force of LAL oscillations is solar gravity in the tubes where the threads oscillate, and the damping mechanism is the ongoing accumulation of mass onto the oscillating threads. Following an earlier paper, we have determined the magnitude and radius of curvature of the dipped magnetic flux tubes hosting a thread along the filament, as well as the mass accretion rate of the filament threads, via the fitted parameters.
Taniguchi, Tomohiro, E-mail: tomohiro-taniguchi@aist.go.jp; Kubota, Hitoshi; Imamura, Hiroshi [National Institute of Advanced Industrial Science and Technology (AIST), Spintronics Research Center, Tsukuba 305-8568 (Japan); Tsunegi, Sumito [Unité Mixte de Physique CNRS/Thales and Université Paris Sud 11, 1 Ave. A. Fresnel, Palaiseau (France)
2015-05-07
Oscillation frequency of spin torque oscillator with a perpendicularly magnetized free layer and an in-plane magnetized pinned layer is theoretically investigated by taking into account the field-like torque. It is shown that the field-like torque plays an important role in finding the balance between the energy supplied by the spin torque and the dissipation due to the damping, which results in a steady precession. The validity of the developed theory is confirmed by performing numerical simulations based on the Landau-Lifshitz-Gilbert equation.
A Closed Form Solution for Nonlinear Oscillators Frequencies Using Amplitude-Frequency Formulation
A. Barari
2012-01-01
Full Text Available Many nonlinear systems in industry including oscillators can be simulated as a mass-spring system. In reality, all kinds of oscillators are nonlinear due to the nonlinear nature of springs. Due to this nonlinearity, most of the studies on oscillation systems are numerically carried out while an analytical approach with a closed form expression for system response would be very useful in different applications. Some analytical techniques have been presented in the literature for the solution of strong nonlinear oscillators as well as approximate and numerical solutions. In this paper, Amplitude-Frequency Formulation (AFF approach is applied to analyze some periodic problems arising in classical dynamics. Results are compared with another approximate analytical technique called Energy Balance Method developed by the authors (EBM and also numerical solutions. Close agreement of the obtained results reveal the accuracy of the employed method for several practical problems in engineering.
Amplitude and phase noises of a spin-transfer nano-oscillator synchronized by a phase-lock loop
Mitrofanov, A. A.; Safin, A. R.; Udalov, N. N.
2015-08-01
We have studied the amplitude and phase noises of a spin-transfer nano-oscillator (STNO) with a phase synchronization system (phase-lock loop, PLL). Spectral characteristics of the amplitude and phase noises of the isochronous and nonisochronous STNO are obtained and compared to the analogous characteristics of an autonomous (nonsynchronized) oscillator. The PLL bandwidth is determined.
Large-Amplitude, Pair-Creating Oscillations in Pulsar and Black Hole Magnetospheres
Levinson, A; Judge, A; Luo, Q; Levinson, Amir; Melrose, Don; Judge, Alex; Luo, Qinghuan
2005-01-01
A time-dependent model for pair creation in a pulsar magnetosphere is developed. It is argued that the parallel electric field that develops in a charge-starved region (a gap) of a pulsar magnetosphere oscillates with large amplitude. Electrons and positrons are accelerated periodically and the amplitude of the oscillations is assumed large enough to cause creation of upgoing and downgoing pairs at different phases of the oscillation. With a charge-starved initial condition, we find that the oscillations result in bursts of pair creation in which the pair density rises exponentially with time. The pair density saturates at $N_\\pm\\simeq E_{0}^2/(8\\pi m_ec^2\\Gamma_{\\rm thr})$, where $E_0$ is the parallel electric field in the charge-starved initial state, and $\\Gamma_{\\rm thr}$ is the Lorentz factor for effec tive pair creation. The frequency of oscillations following the pair creation burst is given roughly by $\\omega_{\\rm osc}=eE_0/(8m_ec\\Gamma_{\\rm thr})$. A positive feedback keeps the system stable, such th...
Zimmerman, William B
2005-10-05
The hypothesis that frequency and amplitude response can be used in a complicated metabolic pathway kinetics model for optimal parameter estimation, as speculated by its successful prior usage for a mechanical oscillator and a heterogeneous chemical system, is tested here. Given the complexity of the glycolysis model of yeast chosen, this question is limited to three kinetics parameters of the 87 in the in vitro model developed in the literature. The direct application of the approach, used with the uninformed selection of operating conditions for the oscillation of external glucose concentration, led to miring the data assimilation process in local minima. Application of linear systems theory, however, identified two natural resonant frequencies that, when excited by external forced oscillations of the same frequency, result in the expression of many harmonics in the Fourier spectra, that is, information-rich experiments. A single such information-rich experiment at one of the resonant frequencies was sufficient to break away from the local minima to find the optimum kinetics parameter estimates. The resonant frequencies themselves represent oscillation modes in glycolysis akin to those previously observed. Furthermore, operation of the bioreactor with large amplitude oscillations of glucose feed (25%) leads to enhanced ethanol average yield by 1.6% at the resonant frequency.
Roncin, Vincent; Hayau, Jean-François; Besnard, Pascal; Simon, Jean-Claude; Van Dijk, F; Shen, Alexandre; Duan, Guang-Hua
2014-01-01
We propose in this communication an experimental study of the relaxation oscillations behavior in mode-locked lasers. The semiconductor self-pulsating laser diode is composed by two gain sections, without saturable absorber. It is made of bulk structure and designed for optical telecommunication applications. This specific device allows two different regimes of optical modulation: the first one corresponds to the resonance of the relaxation oscillations and the second one, to the mode-locking regime at FSR value. This singular behavior leads us to characterize the self-pulsations which are coexisting in the laser and to describe two regimes of output modulation: the first one appears thanks to the resonance of the oscillation relaxation and the other one corresponds to the FSR of the Fabry-Perot laser at 40 GHz.
Relaxation oscillations in long-pulsed random lasers
Molen, van der Karen L.; Mosk, Allard P.; Lagendijk, Ad
2009-01-01
We have measured the evolution of the intensity emitted by a random laser during a pump pulse that is comparable in duration to the spontaneous emission decay time. The time traces of our random laser, consisting of titanium dioxide particles and sulforhodamine B dye, show clear relaxation oscillati
Derivation of amplitude equations for nonlinear oscillators subject to arbitrary forcing.
Mayol, Catalina; Toral, Raúl; Mirasso, Claudio R
2004-06-01
By using a generalization of the multiple scales technique we develop a method to derive amplitude equations for zero-dimensional forced systems. The method allows to consider either additive or multiplicative forcing terms and can be straightforwardly applied to the case that the forcing is white noise. We give examples of the use of this method to the case of the van der Pol-Duffing oscillator. The writing of the amplitude equations in terms of a Lyapunov potential allow us to obtain an analytical expression for the probability distribution function which reproduces reasonably well the numerical simulation results.
Blue Sky Catastrophe in Systems with Non-classical Relaxation Oscillations
S. D. Glyzin
2015-01-01
Full Text Available The feasibility of a known blue-sky bifurcation in a class of three-dimensional singularly perturbed systems of ordinary differential equations with one fast and two slow variables is studied. A characteristic property of the considered systems is that they permit so-called nonclassic relaxation oscillations, that is, oscillations with slow components asymptotically close to time-discontinuous functions and a δ-like fast component. Cases when blue-sky bifurcation leads to a relaxation cycle or stable two-dimensional torus are analyzed. Also the question of homoclinic structure emergence is considered.
Stello, D; Kallinger, T; Basu, S; Mosser, B; Hekker, S; Mathur, S; Garcia, R A; Bedding, T R; Kjeldsen, H; Gilliland, R L; Verner, G A; Chaplin, W J; Benomar, O; Meibom, S; Grundahl, F; Elsworth, Y P; Molenda-Zakowicz, J; Szabó, R; Christensen-Dalsgaard, J; Tenenbaum, P; Twicken, J D; Uddin, K
2011-01-01
Scaling relations that link asteroseismic quantities to global stellar properties are important for gaining understanding of the intricate physics that underpins stellar pulsation. The common notion that all stars in an open cluster have essentially the same distance, age, and initial composition, implies that the stellar parameters can be measured to much higher precision than what is usually achievable for single stars. This makes clusters ideal for exploring the relation between the mode amplitude of solar-like oscillations and the global stellar properties. We have analyzed data obtained with NASA's Kepler space telescope to study solar-like oscillations in 100 red giant stars located in either of the three open clusters, NGC 6791, NGC 6819, and NGC 6811. By fitting the measured amplitudes to predictions from simple scaling relations that depend on luminosity, mass, and effective temperature, we find that the data cannot be described by any power of the luminosity-to-mass ratio as previously assumed. As a...
Den Satipar
2017-01-01
Full Text Available A new configuration of voltage-mode quadrature sinusoidal oscillator is proposed. The proposed oscillator employs two voltage differencing current conveyors (VDCCs, two resistors, and two grounded capacitors. In this design, the use of multiple/dual output terminal active building block is not required. The tuning of frequency of oscillation (FO can be done electronically by adjusting the bias current of active device without affecting condition of oscillation (CO. The electronic tuning can be done by controlling the bias current using a digital circuit. The amplitude of two sinusoidal outputs is equal when the frequency of oscillation is tuned. This makes the sinusoidal output voltages meet good total harmonic distortions (THD. Moreover, the proposed circuit can provide the sinusoidal output current with high impedance which is connected to external load or to another circuit without the use of buffer device. To confirm that the oscillator can generate the quadrature sinusoidal output signal, the experimental results using VDCC constructed from commercially available ICs are also included. The experimental results agree well with theoretical anticipation.
Measurements of wall heat transfer in the presence of large-amplitude combustion-driven oscillations
Perry, E. H.; Culick, F. E. C.
1974-01-01
In the studies reported use was made of the T-burner to obtain a correlation between the average heat transfer coefficient along the burner and the amplitude of the flow oscillations. The T-burner used consists of a centrally-vented cylindrical chamber with disks of solid propellant bonded in each end. The obtained data provide a basis for predicting heat transfer rates in other combustion chambers containing oscillatory flows.
Nitta, Junsaku; Bergsten, Tobias
2008-03-01
Time reversal symmetric Al’tshuler-Aronov-Spivak (AAS) oscillations are measured in an array of InGaAs mesoscopic loops. We confirm that gate voltage dependence of h/2 e period oscillations is due to spin interference from the effect of ensemble average on the AAS and Aharonov-Bohm (AB) amplitudes. This spin interference is based on the time reversal Aharonov-Casher (AC) effect. The AC interference oscillations are controlled over several periods. This result shows evidence for electrical manipulation of the spin precession angle in an InGaAs two-dimensional electron gas channel. We control the precession rate in a precise and predictable way with an electrostatic gate.
Tu, Yiheng; Zhang, Zhiguo; Tan, Ao; Peng, Weiwei; Hung, Yeung Sam; Moayedi, Massieh; Iannetti, Gian Domenico; Hu, Li
2016-02-01
Ongoing fluctuations of intrinsic cortical networks determine the dynamic state of the brain, and influence the perception of forthcoming sensory inputs. The functional state of these networks is defined by the amplitude and phase of ongoing oscillations of neuronal populations at different frequencies. The contribution of functionally different cortical networks has yet to be elucidated, and only a clear dependence of sensory perception on prestimulus alpha oscillations has been clearly identified. Here, we combined electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) in a large sample of healthy participants to investigate how ongoing fluctuations in the activity of different cortical networks affect the perception of subsequent nociceptive stimuli. We observed that prestimulus EEG oscillations in the alpha (at bilateral central regions) and gamma (at parietal regions) bands negatively modulated the perception of subsequent stimuli. Combining information about alpha and gamma oscillations predicted subsequent perception significantly more accurately than either measure alone. In a parallel experiment, we found that prestimulus fMRI activity also modulated the perception of subsequent stimuli: perceptual ratings were higher when the BOLD signal was higher in nodes of the sensorimotor network and lower in nodes of the default mode network. Similar to what observed in the EEG data, prediction accuracy was improved when the amplitude of prestimulus BOLD signals in both networks was combined. These findings provide a comprehensive physiological basis to the idea that dynamic changes in brain state determine forthcoming behavioral outcomes. Hum Brain Mapp 37:501-514, 2016. © 2015 Wiley Periodicals, Inc.
High and low frequency relaxation oscillations in a capacitive discharge plasma
Zhou Zhu-Wen; Sungjin Kim; Ji Shi-Yin; Sun Guang-Yu; Deng Ming-Sen
2008-01-01
Both high and low frequency relaxation oscillations have been observed in an argon capacitive discharge connected to a peripheral grounded chamber through a slot with dielectric spacers.The oscillations,observed from time-varying optical emission of the main discharge chamber,show,for example,a high frequency(46 kHz)relaxation oscillation at 100 mTorr,with an absorbed power near the peripheral breakdown,and a low frequency(2.7-3.7 Hz)oscillation,at a higher absorbed power.The high frequency oscillation is found to ignite a plasma in the slot,but usually not in the periphery.The high frequency oscillation is interpreted by using an electromagnetic model of the slot impedance,combined with the circuit analysis of the system including a matching network.The model is further developed by using a parallel connection of variable peripheral capacitance to analyse the low frequency oscillation.The results obtained from the model are in agreement with the experimental observations and indicate that a variety of behaviours are dependent on the matching conditions.
3-channel double relaxation oscillation SQUID magnetometer system with simple readout electronics
Lee, Y.H.; Kim, J.M.; Kwon, H.C.; Park, Y.K.; Park, J.C.; Duuren, van M.J.; Adelerhof, D.J.; Flokstra, J.; Rogalla, H.
1995-01-01
Recently several approaches have been made to simplify the readout scheme of the standard dc SQUID. A double relaxation oscillation SQUID(DROS) consisting of a hysteretic dc SQUID and a reference junction in series shunted by an inductor and a resistor can provide a very large flux-to-voltage transf
A 1-MHz low noise preamlifier based on Double Relaxation Oscillation SQUIDs
Hamster, A.W.; van Duuren, M.J.; Brons, G.C.S.; Flokstra, Jakob; Rogalla, Horst
1999-01-01
A low noise and wideband preamplifier based on Double Relaxation Oscillation Superconducting Quantum Interference Devices (DROSs) has been realized. A major advantage of a DROS is that it can be operated in a simple flux modulation. So far, biomagnetic measurements performed in our group required
A 90μW 12MHz Relaxation Oscillator with a -162dB FOM
Geraedts, P.F.J.; van Tuijl, Adrianus Johannes Maria; Klumperink, Eric A.M.; Wienk, Gerhardus J.M.; Nauta, Bram
2008-01-01
A relaxation oscillator exploits a noise filtering technique implemented with a switched-capacitor circuit to minimize phase noise. A 65nm CMOS design produces a sawtooth waveform, has a frequency tuning range of 1 to 12MHz and a constant frequency-tuning gain. By minimizing and balancing noise
Mikicin, Mirosław; Kowalczyk, Marek
2015-09-01
The aim of the present study was to investigate the effect of regular audio-visual relaxation combined with Schultz's autogenic training on: (1) the results of behavioral tests that evaluate work performance during burdensome cognitive tasks (Kraepelin test), (2) changes in classical EEG alpha frequency band, neocortex (frontal, temporal, occipital, parietal), hemisphere (left, right) versus condition (only relaxation 7-12 Hz). Both experimental (EG) and age-and skill-matched control group (CG) consisted of eighteen athletes (ten males and eight females). After 7-month training EG demonstrated changes in the amplitude of mean electrical activity of the EEG alpha bend at rest and an improvement was significantly changing and an improvement in almost all components of Kraepelin test. The same examined variables in CG were unchanged following the period without the intervention. Summing up, combining audio-visual relaxation with autogenic training significantly improves athlete's ability to perform a prolonged mental effort. These changes are accompanied by greater amplitude of waves in alpha band in the state of relax. The results suggest usefulness of relaxation techniques during performance of mentally difficult sports tasks (sports based on speed and stamina, sports games, combat sports) and during relax of athletes.
Output-Feedback Control of a Chaotic MEMS Resonator for Oscillation Amplitude Enhancement
Alexander Jimenez-Triana
2014-01-01
Full Text Available The present work addresses the problem of chaos control in an electrostatic MEMS resonator by using an output-feedback control scheme. One of the unstable orbits immersed in the chaotic attractor is stabilized in order to produce a sustained oscillation of the movable plate composing the microstructure. The orbit is carefully chosen so as to produce a high amplitude oscillation. This approach allows the enhancement of oscillation amplitude of the resonator at a reduced control effort, since the unstable orbit already exists in the system and it is not necessary to spend energy to create it. Realistic operational conditions of the MEMS are considered including parametric uncertainties in the model and constraints due to the difficulty in measuring the speed of the plates of the microstructure. A control law is constructed recursively by using the technique of backstepping. Finally, numerical simulations are carried out to confirm the validity of the developed control scheme and to demonstrate the effect of controlling orbits immersed in the chaotic attractor.
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.
Hedin, Eva M K; Hult, Karl; Mouritsen, Ole G; Høyrup, Pernille
2004-08-31
Electron spin resonance (ESR) spectroscopy in combination with site-directed spin labeling (SDSL) is a powerful tool for determining protein structure, dynamics and interactions. We report here a method for determining interactions between spin labels and paramagnetic relaxation agents, which is performed under subsaturating conditions. The low microwave-field amplitude employed (h(1)spin-spin-relaxation time, T(2e), is measured by this method, and compared to classical progressive power saturation performed on a free spin label, (1-oxyl-2,2,5,5-tetramethyl-Delta(3)-pyrroline-3-methyl)methanethiosulfonate (MTSL), and a spin-labeled protein (Thermomyces lanuginosa lipase, TLL-I252C), employing the water-soluble relaxation agent chromium(III) oxalate (Crox) in concentrations between 0-10 mM. The low-amplitude theory showed excellent agreement with that of classical power saturation in quantifying Crox-induced relaxation enhancement. Low-amplitude measurements were then performed using a standard resonator, with Crox, on 11 spin-labeled TLL mutants displaying rotational correlation times in the motional narrowing regime. All spin-labeled proteins exhibited significant changes in T(2e). We postulate that this novel method is especially suitable for studying moderately immobilized spin labels, such as those positioned at exposed sites in a protein. This method should prove useful for research groups with access to any ESR instrumentation.
Barban C.
2013-03-01
Full Text Available CoRoT and Kepler measurements reveal us that the amplitudes of solar-like oscillations detected in red giant stars scale from stars to stars in a characteristic way. This observed scaling relation is not yet fully understood but constitutes potentially a powerful diagnostic about mode physics. Quasi-adiabatic theoretical scaling relations in terms of mode amplitudes result in systematic and large differences with the measurements performed for red giant stars. The use of a non-adiabatic intensity-velocity relation derived from a non-adiabatic pulsation code significantly reduces the discrepancy with the CoRoT measurements. The origin of the remaining difference is still unknown. Departure from adiabatic eigenfunction is a very likely explanation that is investigated in the present work using a 3D hydrodynamical model of the surface layers of a representative red giant star.
Amplitude Expansions for Instabilities in Populations of Globally-Coupled Oscillators
Crawford, J D
1994-01-01
We analyze the nonlinear dynamics near the incoherent state in a mean-field model of coupled oscillators. The population is described by a Fokker-Planck equation for the distribution of phases, and we apply center-manifold reduction to obtain the amplitude equations for steady-state and Hopf bifurcation from the equilibrium state with a uniform phase distribution. When the population is described by a native frequency distribution that is reflection-symmetric about zero, the problem has circular symmetry. In the limit of zero extrinsic noise, although the critical eigenvalues are embedded in the continuous spectrum, the nonlinear coefficients in the amplitude equation remain finite in contrast to the singular behavior found in similar instabilities described by the Vlasov-Poisson equation. For a bimodal reflection-symmetric distribution, both types of bifurcation are possible and they coincide at a codimension-two Takens Bogdanov point. The steady-state bifurcation may be supercritical or subcritical and prod...
Non-Linear High Amplitude Oscillations in Wave-shaped Resonators
Antao, Dion; Farouk, Bakhtier
2011-11-01
A numerical and experimental study of non-linear, high amplitude standing waves in ``wave-shaped'' resonators is reported here. These waves are shock-less and can generate peak acoustic overpressures that can exceed the ambient pressure by three/four times its nominal value. A high fidelity compressible axisymmetric computational fluid dynamic model is used to simulate the phenomena in cylindrical and arbitrarily shaped axisymmetric resonators. Working fluids (Helium, Nitrogen and R-134a) at various operating pressures are studied. The experiments are performed in a constant cross-section cylindrical resonator in atmospheric pressure nitrogen and helium to provide model validation. The high amplitude non-linear oscillations demonstrated can be used as a prime mover in a variety of applications including thermoacoustic cryocooling. The work reported is supported by the US National Science Foundation under grant CBET-0853959.
Lozano-Soldevilla, Diego; ter Huurne, Niels; Oostenveld, Robert
2016-01-01
Neuronal oscillations support cognitive processing. Modern views suggest that neuronal oscillations do not only reflect coordinated activity in spatially distributed networks, but also that there is interaction between the oscillations at different frequencies. For example, invasive recordings in animals and humans have found that the amplitude of fast oscillations (>40 Hz) occur non-uniformly within the phase of slower oscillations, forming the so-called cross-frequency coupling (CFC). However, the CFC patterns might be influenced by features in the signal that do not relate to underlying physiological interactions. For example, CFC estimates may be sensitive to spectral correlations due to non-sinusoidal properties of the alpha band wave morphology. To investigate this issue, we performed CFC analysis using experimental and synthetic data. The former consisted in a double-blind magnetoencephalography pharmacological study in which participants received either placebo, 0.5 or 1.5 mg of lorazepam (LZP; GABAergic enhancer) in different experimental sessions. By recording oscillatory brain activity with during rest and working memory (WM), we were able to demonstrate that posterior alpha (8–12 Hz) phase was coupled to beta-low gamma band (20–45 Hz) amplitude envelope during all sessions. Importantly, bicoherence values around the harmonics of the alpha frequency were similar both in magnitude and topographic distribution to the cross-frequency coherence (CFCoh) values observed in the alpha-phase to beta-low gamma coupling. In addition, despite the large CFCoh we found no significant cross-frequency directionality (CFD). Critically, simulations demonstrated that a sizable part of our empirical CFCoh between alpha and beta-low gamma coupling and the lack of CFD could be explained by two-three harmonics aligned in zero phase-lag produced by the physiologically characteristic alpha asymmetry in the amplitude of the peaks relative to the troughs. Furthermore, we
Diego Lozano-Soldevilla
2016-08-01
Full Text Available Neuronal oscillations support cognitive processing. Modern views suggest that neuronal oscillations do not only reflect coordinated activity in spatially distributed networks, but also that there is interaction between the oscillations at different frequencies. For example, invasive recordings in animals and humans have found that the amplitude of fast oscillations (> 40 Hz occur non-uniformly within the phase of slower oscillations, forming the so-called cross-frequency coupling (CFC. However, the CFC patterns be influenced by features in the signal that do not relate to underlying physiological interactions. For example, CFC estimates may be sensitive to spectral correlations due to non-sinusoidal properties of the alpha band wave morphology. To investigate this issue, we performed CFC analysis using experimental and synthetic data. The former consisted in a double-blind magnetoencephalography pharmacological study in which participants received either placebo, 0.5 mg or 1.5 mg of lorazepam (LZP; GABAergic enhancer in different experimental sessions. By recording oscillatory brain activity with during rest and working memory (WM, we were able to demonstrate that posterior alpha (8 – 12 Hz phase was coupled to beta-low gamma band (20 – 45 Hz amplitude envelope during all sessions. Importantly, bicoherence values around the harmonics of the alpha frequency were similar both in magnitude and topographic distribution to the cross-frequency coherence (CFCoh values observed in the alpha-phase to beta-low gamma coupling. In addition, despite the large CFCoh we found no significant cross-frequency directionality (CFD. Critically, simulations demonstrated that a sizable part of our empirical CFCoh between alpha and beta-low gamma coupling and the lack of CFD could be explained by two-three harmonics aligned in zero phase-lag produced by the physiologically characteristic alpha asymmetry in the amplitude of the peaks relative to the troughs
Cheng, Min-Chi; Chi, Yu-Chieh; Li, Yi-Cheng; Tsai, Cheng-Ting; Lin, Gong-Ru
2014-06-30
By up-shifting the relaxation oscillation peak and suppressing its relative intensity noise in a weak-resonant-cavity Fabry-Perot laser diode (WRC-FPLD) under intense injection-locking, the directly modulated transmission of optical 16 quadrature amplitude modulation (QAM) orthogonal frequency division multiplexing (OFDM) data-stream is demonstrated. The total bit rate of up to 20 Gbit/s within 5-GHz bandwidth is achieved by using the OFDM subcarrier pre-leveling technique. With increasing the injection-locking power from -12 to -3 dBm, the effective reduction on threshold current of the WRC-FPLD significantly shifts its relaxation oscillation frequency from 5 to 7.5 GHz. This concurrently induces an up-shift of the peak relative intensity noise (RIN) of the WRC-FPLD, and effectively suppresses the background RIN level to -104 dBc/Hz within the OFDM band between 3 and 6 GHz. The enhanced signal-to-noise ratio from 16 to 20 dB leads to a significant reduction of bit-error-rate (BER) of the back-to-back transmitted 16-QAM-OFDM data from 1.3 × 10(-3) to 5 × 10(-5), which slightly degrades to 1.1 × 10(-4) after 25-km single-mode fiber (SMF) transmission. However, the enlarged injection-locking power from -12 to -3 dBm inevitably declines the modulation throughput and increases its negative throughput slope from -0.8 to -1.9 dBm/GHz. After pre-leveling the peak amplitude of the OFDM subcarriers to compensate the throughput degradation of the directly modulated WRC-FPLD, the BER under 25-km SMF transmission can be further improved to 3 × 10(-5) under a receiving power of -3 dBm.
Coupling dynamics of Nb/Nb2O5 relaxation oscillators.
Li, Shuai; Liu, Xinjun; Nandi, Sanjoy Kumar; Venkatachalam, Dinesh Kumar; Elliman, Robert Glen
2017-03-24
The coupling dynamics of capacitively coupled Nb/Nb2O5 relaxation oscillators are shown to exhibit rich collective behaviour depending on the negative differential resistance response of the individual devices, the operating voltage and the coupling capacitance. These coupled oscillators are shown to exhibit stable frequency and phase locking states at source voltages as low as 2.2 V, with frequency control in the range from 0.85 to 16.2 MHz and frequency tunability of ∼8 MHz V(-1). The experimental realisation of such compact, scalable and low power coupled-oscillator systems is of particular significance for the development and implementation of large oscillator networks in non-Boolean computing architectures.
Fantazzini, Paola; Galassi, Francesca; Bortolotti, Villiam; Brown, Robert J. S.; Vittur, Franco
2011-06-01
When inverting nuclear magnetic resonance relaxation data in order to obtain quasi-continuous distributions of relaxation times for fluids in porous media, it is common practice to impose a non-negative (NN) constraint on the distributions. While this approach can be useful in reducing the effects of data distortion and/or preventing wild oscillations in the distributions, it may give misleading results in the presence of real negative amplitude components. Here, some examples of valid negative components for articular cartilage and hydrated collagen are given. Articular cartilage is a connective tissue, consisting mainly of collagen, proteoglycans and water, which can be considered, in many aspects, as a porous medium. Separate T1 relaxation data are obtained for low-mobility ('solid') macromolecular 1H and for higher-mobility ('liquid') 1H by the separation of these components in free induction decays, with α denoting the solid/liquid 1H ratio. When quasi-continuous distributions of relaxation times (T1) of the solid and liquid signal components of cartilage or collagen are computed from experimental relaxation data without imposing the usual NN constraint, valid negative peaks may appear. The features of the distributions, in particular negative peaks, and the fact that peaks at longer times for macromolecular and water protons are at essentially the same T1, are interpreted as the result of a magnetization exchange between these two spin pools. For the only-slightly-hydrated collagen samples, with α>1, the exchange leads to small negative peaks at short T1 times for the macromolecular component. However, for the cartilage, with substantial hydration or for a strongly hydrated collagen sample, both with αLt1, the behavior is reversed, with a negative peak for water at short times. The validity of a negative peak may be accepted (dismissed) by a high (low) cost of NN in error of fit. Computed distributions for simulated data using observed signal
Villanueva, Walter; Li, Hua [Division of Nuclear Power Safety, Royal Institute of Technology (KTH), Roslagstullsbacken 21, SE-10691 Stockholm (Sweden); Puustinen, Markku [Nuclear Engineering, LUT School of Energy Systems, Lappeenranta University of Technology (LUT), FIN-53851 Lappeenranta (Finland); Kudinov, Pavel, E-mail: pavel@safety.sci.kth.se [Division of Nuclear Power Safety, Royal Institute of Technology (KTH), Roslagstullsbacken 21, SE-10691 Stockholm (Sweden)
2015-12-15
Highlights: • Available data on steam injection into subcooled pool is generalized. • Scaling approach is proposed on amplitude and frequency of chugging oscillations. • The scaled amplitude has a maximum at Froude number Fr ≈ 2.8. • The scaled frequency has a minimum at Fr ≈ 6. • Both amplitude and frequency has a strong dependence on pool bulk temperature. - Abstract: Steam venting and condensation into a subcooled pool of water through a blowdown pipe can undergo a phenomenon called chugging, which is an oscillation of the steam–water interface inside the blowdown pipe. The momentum that is generated by the oscillations is directly proportional to the oscillations’ amplitude and frequency, according to the synthetic jet theory. Higher momentum can enhance pool mixing and positively affect the pool's pressure suppression capacity by reducing thermal stratification. In this paper, we present a generalization of available experimental data on the amplitude and frequency of oscillations during chugging. We use experimental data obtained in different facilities at different scales to suggest a scaling approach for non-dimensional amplitude and frequency of the oscillations. We demonstrate that the Froude number Fr (which relates the inertial forces to gravitational forces) can be used as a scaling criterion in this case. The amplitude has maximum at Fr ≈ 2.8. There is also a strong dependence of the amplitude on temperature; the lower the bulk temperature is the higher the scaled amplitude. A known analytical theory can only capture the decreasing trend in amplitude for Fr > 2.8 and fails to capture the increasing trend and the temperature dependence. Similarly, there is a minimum of the non-dimensional frequency at Fr ≈ 6. A strong dependence on temperature is also observed for Fr > 6; the lower the bulk temperature is the higher the scaled frequency. The known analytical theory is able to capture qualitatively the general trend in
Li, Qun; Zheng, Chen-Guang; Cheng, Ning; Wang, Yi-Yi; Yin, Tao; Zhang, Tao
2016-06-01
An increasing number of studies pays attention to cross-frequency coupling in neuronal oscillations network, as it is considered to play an important role in exchanging and integrating of information. In this study, two generalized algorithms, phase-amplitude coupling-evolution map approach and phase-amplitude coupling-conditional mutual information which have been developed and applied originally in an identical rhythm, are generalized to measure cross-frequency coupling. The effectiveness of quantitatively distinguishing the changes of coupling strength from the measurement of phase-amplitude coupling (PAC) is demonstrated based on simulation data. The data suggest that the generalized algorithms are able to effectively evaluate the strength of PAC, which are consistent with those traditional approaches, such as PAC-PLV and PAC-MI. Experimental data, which are local field potentials obtained from anaesthetized SD rats, have also been analyzed by these two generalized approaches. The data show that the theta-low gamma PAC in the hippocampal CA3-CA1 network is significantly decreased in the glioma group compared to that in the control group. The results, obtained from either simulation data or real experimental signals, are consistent with that of those traditional approaches PAC-MI and PAC-PLV. It may be considered as a proper indicator for the cross frequency coupling in sub-network, such as the hippocampal CA3 and CA1.
Large amplitude oscillation of a boiling bubble growing at a wall in stagnation flow
Geld, C.W.M. van der; Berg, R. van de; Peukert, P. [Eindhoven University of Technology, Eindhoven (Netherlands). Faculty of Mechanical Engineering], e-mail: C.W.M._v.d.Geld@tue.nl
2009-07-01
A boiling bubble is created on an artificial site that is part of a bubble generator that is mounted at the center of a pipe. Downflow of water impinges on the bubble generator and creates a stagnation flow above the artificial cavity. Stable axisymmetric elongation in the direction away from the wall and multiple shape oscillation cycles are observed. The time of growth and attachment is typically of the order of 250 ms. Amongst the length scales that characterize the bubble shape is the radius of curvature of the upper part of the bubble, R. The period of oscillation, T, is strongly dependent on time, as is R. The parameters C and m in the defining equation T = C R{sup m} {radical}({rho}L/{sigma}) have been determined by fitting to data of more than 100 bubbles. For each operating condition, the same values of C and m have been found. The value of m is 1.49 {+-} 0.02, which is explained from the continuous growth of the bubble and from the relation to the period of oscillation of a free bubble deforming in the fundamental mode corresponding to the third Legendre Polynomial. For the latter, R is the radius of the volume-equivalent sphere, R{sub 0}, and C is {radical}12, while for attached boiling bubbles C is found to amount 1.9{radical}12. The difference is easily explained from the continuous growth, difference in definition, finite amplitude oscillation and proximity of the wall. (author)
Relaxation of two coupled quantum oscillators to quasi-equilibrium states based on path integrals
Dorofeyev, Illarion
2013-01-01
The paper addresses the problem of relaxation of open quantum systems. Using the path integral methods we found an analytical expression for time-dependent density matrix of two coupled quantum oscillators interacting with different baths of oscillators. The expression for density matrix was found in the linear regime with respect to the coupling constant between selected oscillators. Time-dependent spatial variances and covariance were investigated analytically and numerically. It was shown that asymptotic variances in the long-time limit are always in accordance with the fluctuation dissipation theorem despite on their initial values. In the weak coupling approach there is good reason to believe that subsystems asymptotically in equilibrium at their own temperatures even despite of the arbitrary difference in temperatures within the whole system.
Agazzi, L.; Bernhardi, E.H.; Wörhoff, K.; Pollnau, M.
2012-01-01
The impact of luminescence quenching on rare-earth-ion doped lasers is investigated, and we show that the expression for the relaxation oscillation frequency needs to be modified to take the quenching properly into account.
Agazzi, L.; Bernhardi, Edward; Worhoff, Kerstin; Pollnau, Markus
The impact of luminescence quenching on rare-earth-ion doped lasers is investigated, and we show that the expression for the relaxation oscillation frequency needs to be modified to take the quenching properly into account.
Ma, Wei; Lin, Yiyu; Liu, Siqi; Zheng, Xudong; Jin, Zhonghe
2017-02-01
This paper reports a novel oscillation control algorithm for MEMS vibratory gyroscopes using a modified electromechanical amplitude modulation (MEAM) technique, which enhances the robustness against the frequency variation of the driving mode, compared to the conventional EAM (CEAM) scheme. In this approach, the carrier voltage exerted on the proof mass is frequency-modulated by the drive resonant frequency. Accordingly, the pick-up signal from the interface circuit involves a constant-frequency component that contains the amplitude and phase information of the vibration displacement. In other words, this informational detection signal is independent of the mechanical resonant frequency, which varies due to different batches, imprecise micro-fabrication and changing environmental temperature. In this paper, the automatic gain control loop together with the phase-locked loop are simultaneously analyzed using the averaging method and Routh-Hurwitz criterion, deriving the stability condition and the parameter optimization rules of the transient response. Then, a simulation model based on the real system is set up to evaluate the control algorithm. Further, the proposed MEAM method is tested using a field-programmable-gate-array based digital platform on a capacitive vibratory gyroscope. By optimizing the control parameters, the transient response of the drive amplitude reveals a settling time of 45.2 ms without overshoot, according well with the theoretical prediction and simulation results. The first measurement results show that the amplitude variance of the drive displacement is 12 ppm in an hour while the phase standard deviation is as low as 0.0004°. The mode-split gyroscope operating under atmospheric pressure demonstrates an outstanding performance. By virtue of the proposed MEAM method, the bias instability and angle random walk are measured to be 0.9° h-1 (improved by 2.4 times compared to the CEAM method) and 0.068° (√h)-1 (improved by 1.4 times
On the robustness of the pendulum model for large-amplitude longitudinal oscillations in prominences
Luna, M; Khomenko, E; Collados, M; de Vicente, A
2015-01-01
Large-amplitude longitudinal oscillations (LALOs) in prominences are spectacular manifestations of the solar activity. In such events nearby energetic disturbances induce periodic motions on filaments with displacements comparable to the size of the filaments themselves and with velocities larger than 20 km/s. The pendulum model, in which the gravity projected along a rigid magnetic field is the restoring force, was proposed to explain these events. However, it can be objected that in a realistic situation where the magnetic field reacts to the mass motion of the heavy prominence, the simplified pendulum model could be no longer valid. We have performed non-linear time-dependent numerical simulations of LALOs considering a dipped magnetic field line structure. In this work we demonstrate that for even relatively weak magnetic fields the pendulum model works very well. We therefore validate the pendulum model and show its robustness, with important implications for prominence seismology purposes. With this mod...
Stello, Dennis; Huber, Daniel; Kallinger, Thomas;
2011-01-01
with NASA's Kepler space telescope to study solar-like oscillations in 100 red giant stars located in either of the three open clusters, NGC 6791, NGC 6819, and NGC 6811. By fitting the measured amplitudes to predictions from simple scaling relations that depend on luminosity, mass, and effective...... temperature, we find that the data cannot be described by any power of the luminosity-to-mass ratio as previously assumed. As a result we provide a new improved empirical relation which treats luminosity and mass separately. This relation turns out to also work remarkably well for main-sequence and subgiant......Scaling relations that link asteroseismic quantities to global stellar properties are important for gaining understanding of the intricate physics that underpins stellar pulsations. The common notion that all stars in an open cluster have essentially the same distance, age, and initial composition...
Remote synchronization of amplitudes across an experimental ring of non-linear oscillators
Minati, Ludovico
2015-12-01
In this paper, the emergence of remote synchronization in a ring of 32 unidirectionally coupled non-linear oscillators is reported. Each oscillator consists of 3 negative voltage gain stages connected in a loop to which two integrators are superimposed and receives input from its preceding neighbour via a "mixing" stage whose gains form the main system control parameters. Collective behaviour of the network is investigated numerically and experimentally, based on a custom-designed circuit board featuring 32 field-programmable analog arrays. A diverse set of synchronization patterns is observed depending on the control parameters. While phase synchronization ensues globally, albeit imperfectly, for certain control parameter values, amplitudes delineate subsets of non-adjacent but preferentially synchronized nodes; this cannot be trivially explained by synchronization paths along sequences of structurally connected nodes and is therefore interpreted as representing a form of remote synchronization. Complex topology of functional synchronization thus emerges from underlying elementary structural connectivity. In addition to the Kuramoto order parameter and cross-correlation coefficient, other synchronization measures are considered, and preliminary findings suggest that generalized synchronization may identify functional relationships across nodes otherwise not visible. Further work elucidating the mechanism underlying this observation of remote synchronization is necessary, to support which experimental data and board design materials have been made freely downloadable.
Rotationally relaxed, grating tuned laser oscillations in optically pumped C/sub 2/D/sub 2/
Fischer, T.A.; Wittig, C.
1982-07-15
Rotationally relaxed, grating tuned laser oscillations are obtained in the frequency range 500--562 cm/sup -1/ via the optical pumping of C/sub 2/D/sub 2//He mixtures with a transverse, electric, atmospheric (TEA) CO/sub 2/ laser. Strong Q-branch oscillations at 530.8 cm/sup -1/ are also reported.
Multi-frequency excitation of stiffened triangular plates for large amplitude oscillations
Askari, H.; Saadatnia, Z.; Esmailzadeh, E.; Younesian, D.
2014-10-01
Free and forced vibrations of triangular plate are investigated. Diverse types of stiffeners were attached onto the plate to suppress the undesirable large-amplitude oscillations. The governing equation of motion for a triangular plate, based on the von Kármán theory, is developed and the nonlinear ordinary differential equation of the system using Galerkin approach is obtained. Closed-form expressions for the free undamped and large-amplitude vibration of an orthotropic triangular elastic plate are presented using the two well-known analytical methods, namely, the energy balance method and the variational approach. The frequency responses in the closed-form are presented and their sensitivities with respect to the initial amplitudes are studied. An error analysis is performed and the vibration behavior, as well as the accuracy of the solution methods, is evaluated. Different types of the stiffened triangular plates are considered in order to cover a wide range of practical applications. Numerical simulations are carried out and the validity of the solution procedure is explored. It is demonstrated that the two methods of energy balance and variational approach have been quite straightforward and reliable techniques to solve those nonlinear differential equations. Subsequently, due to the importance of multiple resonant responses in engineering design, multi-frequency excitations are considered. It is assumed that three periodic forces are applied to the plate in three specific positions. The multiple time scaling method is utilized to obtain approximate solutions for the frequency resonance cases. Influences of different parameters, namely, the position of applied forces, geometry and the number of stiffeners on the frequency response of the triangular plates are examined.
Emelianova, Yu.P., E-mail: yuliaem@gmail.com [Department of Electronics and Instrumentation, Saratov State Technical University, Polytechnicheskaya 77, Saratov 410054 (Russian Federation); Kuznetsov, A.P., E-mail: apkuz@rambler.ru [Kotel' nikov' s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelyenaya 38, Saratov 410019 (Russian Federation); Turukina, L.V., E-mail: lvtur@rambler.ru [Kotel' nikov' s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelyenaya 38, Saratov 410019 (Russian Federation); Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam (Germany)
2014-01-10
The dynamics of the four dissipatively coupled van der Pol oscillators is considered. Lyapunov chart is presented in the parameter plane. Its arrangement is discussed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators. Here are quasi-periodic saddle-node, Hopf and Neimark–Sacker bifurcations. The effect of increase of the threshold for the “amplitude death” regime and the possibilities of complete and partial broadband synchronization are revealed.
Lozano Soldevilla, D.; Huurne, N.P. ter; Oostenveld, R.
2016-01-01
Neuronal oscillations support cognitive processing. Modern views suggest that neuronal oscillations do not only reflect coordinated activity in spatially distributed networks, but also that there is interaction between the oscillations at different frequencies. For example, invasive recordings in an
Optimal homotopy asymptotic method for solving fractional relaxation-oscillation equation
Mohammad Hamarsheh
2015-11-01
Full Text Available In this paper, an approximate analytical solution of linear fractional relaxation-oscillation equations in which the fractional derivatives are given in the Caputo sense, is obtained by the optimal homotopy asymptotic method (OHAM. The studied OHAM is based on minimizing the residual error. The results given by OHAM are compared with the exact solutions and the solutions obtained by generalized Taylor matrix method. The reliability and efficiency of the proposed approach are demonstrated in three examples with the aid of the symbolic algebra program Maple.
Nilsson, Andreas; Zhang, Qiuxia; Styf, Jorma
2015-12-01
Patients with compartment syndromes have elevated intramuscular pressure (IMP) due to increased volume in the affected muscle. However, the accuracy of IMP as a parameter in diagnosing chronic compartment syndrome has been questioned. It has been observed that arterial pulsations create oscillations in the IMP in patients with abnormally elevated IMP. The amplitude of the IMP oscillations appears to be related to a pathogenic mechanism of elevated IMP. Therefore, the purpose of the present study was to investigate the relation between the amplitude of pulse-synchronous IMP oscillations and the absolute level of IMP with a high-end fiber-optic system in a human experimental model of abnormally elevated IMP (simulated compartment syndrome) of the leg. The hypothesis that the amplitude of the IMP oscillations is correlated to the absolute level of IMP was tested. IMP was measured at rest in the anterior tibial muscle in 12 legs of 7 healthy subjects (4 females and 3 males) with a mean age of 28 (range 23-38) years. The subject lay supine with his/her heel placed in a footrest. The foot was kept in a neutral position to avoid biased IMP readings. Measurements were performed at baseline and during 10 minutes with a model of abnormally elevated IMP (simulated compartment syndrome) applied. The abnormally elevated IMP was created by venous obstruction induced by a thigh tourniquet (65 mmHg) of a casted leg. Placement of the pressure-recording catheter was verified by sonography. The IMP increased from 4.7 (SD = 1.8) mmHg at baseline to 48.6 (SD = 7.1) mmHg when the model of elevated IMP was applied. The amplitude of the pulse-synchronous oscillations was undetectable at baseline. It increased to 3.9 (SD = 1.4) mmHg with increasing IMP when the model was applied. The amplitude of the oscillations showed a positive correlation (r = 0.59) with the absolute level of IMP. The amplitude of the pulse-synchronous IMP oscillations is correlated with the absolute
Amplitude model for beam oscillations in the main Linac of CLIC
Pfingstner, Jürgen; Schmickler, Hermann; Hofbaur, Michael
2010-01-01
To achieve the challenging goal of ultra-low emittance preservation in the main linac of CLIC, different techniques are used. The according algorithms often rely on an accurate, fast and efficient to compute model of the amplitude behavior of the beam oscillations in the beam line. In this paper such a model is developed, considering the accelerator design as well as the effect of filamentation. Filamentation is especially important, due to the high energy spread of the according beam and the large total phase advance of the lattice. Therefore a general model to describe filamentation is adapted to the properties of the beam in the main linac of CLIC. At the beginning of the linac, where made assumptions are not valid, this basic model is supported by a fit to simulation data. An accuracy evaluation of the produced data shows that the quadratic error is around 4 %. Therefore, the developed model delivers a fast and efficient procedure, to precisely predict the beam envelope behavior in the main linac of CLIC.
Surface activity and oscillation amplitudes of red giants in eclipsing binaries
Gaulme, P.; Jackiewicz, J. [Department of Astronomy, New Mexico State University, P.O. Box 30001, MSC 4500, Las Cruces, NM 88003-8001 (United States); Appourchaux, T. [Institut d' Astrophysique Spatiale, Université Paris-Sud 11 and CNRS (UMR 8617), Bâtiment 121, F-91405 Orsay cedex (France); Mosser, B., E-mail: gaulme@nmsu.edu [LESIA, CNRS, Université Pierre et Marie Curie, Université Denis Diderot, Observatoire de Paris, F-92195 Meudon cedex (France)
2014-04-10
Among the 19 red-giant stars belonging to eclipsing binary systems that have been identified in Kepler data, 15 display solar-like oscillations. We study whether the absence of mode detection in the remaining 4 is an observational bias or possibly evidence of mode damping that originates from tidal interactions. A careful analysis of the corresponding Kepler light curves shows that modes with amplitudes that are usually observed in red giants would have been detected if they were present. We observe that mode depletion is strongly associated with short-period systems, in which stellar radii account for 16%-24% of the semi-major axis, and where red-giant surface activity is detected. We suggest that when the rotational and orbital periods synchronize in close binaries, the red-giant component is spun up, so that a dynamo mechanism starts and generates a magnetic field, leading to observable stellar activity. Pressure modes would then be damped as acoustic waves dissipate in these fields.
Gierkink, S.L.J.; Wel, van der A.P.; Hoogzaad, G.; Klumperink, E.A.M.; Tuijl, van A.J.M.
1998-01-01
Spectrum measurement results of a CMOS ring oscillator are presented that show a 10 dB decrease in 1/f noise induced phase noise at a 2 dB increase in carrier power. Simple ring oscillator theory predicts that the 1/f noise induced phase noise is independent of carrier power. It is shown that an inc
Fantazzini, Paola; Galassi, Francesca [Department of Physics, University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna (Italy); Bortolotti, Villiam [Department of DICAM, University of Bologna, Viale del Risorgimento 2, 40136 Bologna (Italy); Brown, Robert J S [953 West Bonita Avenue, Claremont, CA 91711-4193 (United States); Vittur, Franco, E-mail: paola.fantazzini@unibo.it [Department of Life Sciences, University of Trieste, via Giorgeri 1, 24137 (Italy)
2011-06-15
When inverting nuclear magnetic resonance relaxation data in order to obtain quasi-continuous distributions of relaxation times for fluids in porous media, it is common practice to impose a non-negative (NN) constraint on the distributions. While this approach can be useful in reducing the effects of data distortion and/or preventing wild oscillations in the distributions, it may give misleading results in the presence of real negative amplitude components. Here, some examples of valid negative components for articular cartilage and hydrated collagen are given. Articular cartilage is a connective tissue, consisting mainly of collagen, proteoglycans and water, which can be considered, in many aspects, as a porous medium. Separate T{sub 1} relaxation data are obtained for low-mobility ('solid') macromolecular {sup 1}H and for higher-mobility ('liquid') {sup 1}H by the separation of these components in free induction decays, with {alpha} denoting the solid/liquid {sup 1}H ratio. When quasi-continuous distributions of relaxation times (T{sub 1}) of the solid and liquid signal components of cartilage or collagen are computed from experimental relaxation data without imposing the usual NN constraint, valid negative peaks may appear. The features of the distributions, in particular negative peaks, and the fact that peaks at longer times for macromolecular and water protons are at essentially the same T{sub 1}, are interpreted as the result of a magnetization exchange between these two spin pools. For the only-slightly-hydrated collagen samples, with {alpha}>1, the exchange leads to small negative peaks at short T{sub 1} times for the macromolecular component. However, for the cartilage, with substantial hydration or for a strongly hydrated collagen sample, both with {alpha}<<1, the behavior is reversed, with a negative peak for water at short times. The validity of a negative peak may be accepted (dismissed) by a high (low) cost of NN in error of fit
A 12MHz Switched-Capacitor Relaxation Oscillator with a Nearly Minimal FoM of -161dBc/Hz
Geraedts, P.F.J.; van Tuijl, Adrianus Johannes Maria; Klumperink, Eric A.M.; Wienk, Gerhardus J.M.; Nauta, Bram
2008-01-01
In this work the phase noise performance of relaxation oscillators has been analyzed resulting in simple though precise phase noise expressions. These expressions have lead to a new relaxation oscillator topology, which exploits a noise filtering technique implemented with a switched-capacitor
Pallesen, Karen Johanne; Bailey, Christopher J; Brattico, Elvira; Gjedde, Albert; Palva, J Matias; Palva, Satu
2015-01-01
Musical expertise is associated with structural and functional changes in the brain that underlie facilitated auditory perception. We investigated whether the phase locking (PL) and amplitude modulations (AM) of neuronal oscillations in response to musical chords are correlated with musical expertise and whether they reflect the prototypicality of chords in Western tonal music. To this aim, we recorded magnetoencephalography (MEG) while musicians and non-musicians were presented with common prototypical major and minor chords, and with uncommon, non-prototypical dissonant and mistuned chords, while watching a silenced movie. We then analyzed the PL and AM of ongoing oscillations in the theta (4-8 Hz) alpha (8-14 Hz), beta- (14-30 Hz) and gamma- (30-80 Hz) bands to these chords. We found that musical expertise was associated with strengthened PL of ongoing oscillations to chords over a wide frequency range during the first 300 ms from stimulus onset, as opposed to increased alpha-band AM to chords over temporal MEG channels. In musicians, the gamma-band PL was strongest to non-prototypical compared to other chords, while in non-musicians PL was strongest to minor chords. In both musicians and non-musicians the long-latency (> 200 ms) gamma-band PL was also sensitive to chord identity, and particularly to the amplitude modulations (beats) of the dissonant chord. These findings suggest that musical expertise modulates oscillation PL to musical chords and that the strength of these modulations is dependent on chord prototypicality.
Jiang, Xianan; Zhao, Ming; Maloney, Eric D.; Waliser, Duane E.
2016-10-01
Despite its pronounced impacts on weather extremes worldwide, the Madden-Julian Oscillation (MJO) remains poorly represented in climate models. Here we present findings that point to some necessary ingredients to produce a strong MJO amplitude in a large set of model simulations from a recent model intercomparison project. While surface flux and radiative heating anomalies are considered important for amplifying the MJO, their strength per unit MJO precipitation anomaly is found to be negatively correlated to MJO amplitude across these multimodel simulations. However, model MJO amplitude is found to be closely tied to a model's convective moisture adjustment time scale, a measure of how rapidly precipitation must increase to remove excess column water vapor, or alternately the efficiency of surface precipitation generation per unit column water vapor anomaly. These findings provide critical insights into key model processes for the MJO and pinpoint a direction for improved model representation of the MJO.
Relaxation oscillator-realized artificial electronic neurons, their responses, and noise
Lim, Hyungkwang; Ahn, Hyung-Woo; Kornijcuk, Vladimir; Kim, Guhyun; Seok, Jun Yeong; Kim, Inho; Hwang, Cheol Seong; Jeong, Doo Seok
2016-05-01
A proof-of-concept relaxation oscillator-based leaky integrate-and-fire (ROLIF) neuron circuit is realized by using an amorphous chalcogenide-based threshold switch and non-ideal operational amplifier (op-amp). The proposed ROLIF neuron offers biologically plausible features such as analog-type encoding, signal amplification, unidirectional synaptic transmission, and Poisson noise. The synaptic transmission between pre- and postsynaptic neurons is achieved through a passive synapse (simple resistor). The synaptic resistor coupled to the non-ideal op-amp realizes excitatory postsynaptic potential (EPSP) evolution that evokes postsynaptic neuron spiking. In an attempt to generalize our proposed model, we theoretically examine ROLIF neuron circuits adopting different non-ideal op-amps having different gains and slew rates. The simulation results indicate the importance of gain in postsynaptic neuron spiking, irrespective of the slew rate (as long as the rate exceeds a particular value), providing the basis for the ROLIF neuron circuit design. Eventually, the behavior of a postsynaptic neuron in connection to multiple presynaptic neurons via synapses is highlighted in terms of EPSP evolution amid simultaneously incident asynchronous presynaptic spikes, which in fact reveals an important role of the random noise in spatial integration.A proof-of-concept relaxation oscillator-based leaky integrate-and-fire (ROLIF) neuron circuit is realized by using an amorphous chalcogenide-based threshold switch and non-ideal operational amplifier (op-amp). The proposed ROLIF neuron offers biologically plausible features such as analog-type encoding, signal amplification, unidirectional synaptic transmission, and Poisson noise. The synaptic transmission between pre- and postsynaptic neurons is achieved through a passive synapse (simple resistor). The synaptic resistor coupled to the non-ideal op-amp realizes excitatory postsynaptic potential (EPSP) evolution that evokes postsynaptic
Witte, Herbert; Putsche, Peter; Hemmelmann, Claudia; Schelenz, Christoph; Leistritz, Lutz
2008-08-01
Low-frequency (0.5-2.5 Hz) and individually defined high-frequency (7-11 or 8-12 Hz; 11-15 or 14-18 Hz) oscillatory components of the electroencephalogram (EEG) burst activity derived from thiopental-induced burst-suppression patterns (BSP) were investigated in seven sedated patients (17-26 years old) with severe head injury. The predominant high-frequency burst oscillations (>7 Hz) were detected for each patient by means of time-variant amplitude spectrum analysis. Thereafter, the instantaneous envelope (IE) and the instantaneous frequency (IF) were computed for these low- and high-frequency bands to quantify amplitude-frequency dependencies (envelope-envelope, envelope-frequency, and frequency-frequency correlations). Time-variant phase-locking, phase synchronization, and quadratic phase couplings are associated with the observed amplitude-frequency characteristics. Additionally, these time-variant analyses were carried out for modeled burst patterns. Coupled Duffing oscillators were adapted to each EEG burst and by means of these models data-based burst simulations were generated. Results are: (1) strong envelope-envelope correlations (IE courses) can be demonstrated; (2) it can be shown that a rise of the IE is associated with an increase of the IF (only for the frequency bands 0.5-2.5 and 7-11 or 8-12 Hz); (3) the rise characteristics of all individually averaged envelope-frequency courses (IE-IF) are strongly correlated; (4) for the 7-11 or 8-12 Hz oscillation these associations are weaker and the variation between the time courses of the patients is higher; (5) for both frequency ranges a quantitative amplitude-frequency dependency can be shown because higher IE peak maxima are accompanied by stronger IF changes; (6) the time range of significant phase-locking within the 7-11 or 8-12 Hz frequency bands and of the strongest quadratic phase couplings (between 0.5-2.5 and 7-11 or 8-12 Hz) is between 0 and 1,000 ms; (7) all phase coupling characteristics of the
Nagao, Raphael; Zou, Wei; Kurths, Jürgen; Kiss, István Z.
2016-09-01
The dynamical behavior of delay-coupled networks of electrochemical reactions is investigated to explore the formation of amplitude death (AD) and the synchronization states in a parameter region around the amplitude death region. It is shown that difference coupling with odd and even numbered ring and random networks can produce the AD phenomenon. Furthermore, this AD can be restored by changing the coupling type from difference to direct coupling. The restored oscillations tend to create synchronization patterns in which neighboring elements are in nearly anti-phase configuration. The ring networks produce frozen and rotating phase waves, while the random network exhibits a complex synchronization pattern with interwoven frozen and propagating phase waves. The experimental results are interpreted with a coupled Stuart-Landau oscillator model. The experimental and theoretical results reveal that AD behavior is a robust feature of delayed coupled networks of chemical units; if an oscillatory behavior is required again, even a small amount of direct coupling could be sufficient to restore the oscillations. The restored nearly anti-phase oscillatory patterns, which, to a certain extent, reflect the symmetry of the network, represent an effective means to overcome the AD phenomenon.
Balasubramanian, Mukund; Jarrett, Delma Y; Mulkern, Robert V
2016-05-01
The aim of this study was to demonstrate that gradient-echo sampling of single spin echoes can be used to isolate the signal from trabecular bone marrow, with high-quality segmentation and surface reconstructions resulting from the application of simple post-processing strategies. Theoretical expressions of the time-domain single-spin-echo signal were used to simulate signals from bone marrow, non-bone fatty deposits and muscle. These simulations were compared with and used to interpret signals obtained by the application of the gradient-echo sampling of a spin-echo sequence to image the knee and surrounding tissues at 1.5 T. Trabecular bone marrow has a much higher reversible transverse relaxation rate than surrounding non-bone fatty deposits and other musculoskeletal tissues. This observation, combined with a choice of gradient-echo spacing that accentuates Dixon-type oscillations from chemical-shift interference effects, enabled the isolation of bone marrow signal from surrounding tissues through the use of simple image subtraction and thresholding. Three-dimensional renderings of the marrow surface were then readily generated with this approach - renderings that may prove useful for bone morphology assessment, e.g. for the measurement of femoral anteversion. In conclusion, understanding the behavior of signals from bone marrow and surrounding tissue as a function of time through a spin echo facilitates the segmentation and reconstruction of bone marrow surfaces using straightforward post-processing strategies that are typically available on modern radiology workstations.
Bisotto, I., E-mail: isabelle.bisotto@lncmi.cnrs.fr [LNCMI, UPR 3228, CNRS–INSA–UJF–UPS, BP 166, 38042 Grenoble, Cedex 9 (France); Portal, J.-C. [LNCMI, UPR 3228, CNRS–INSA–UJF–UPS, BP 166, 38042 Grenoble, Cedex 9 (France); Institut National des Sciences Appliquées, 31077 Toulouse Cedex 4 (France); Institut Universitaire de France, 75005 Paris (France); Brown, D. [Microelectronics Research Center Georgia Institute of Technology, 791 Atlantic Drive NW, Atlanta, GA 30332 (United States); Wieck, A. D. [Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, D-44780 Bochum (Germany)
2015-11-15
We present new photovoltage oscillation in a pure two dimensional electron gas (2DEG) and in the presence of circular or semicircular antidot lattices. Results were interpreted as EMPs-like photovoltage oscillations. We observed and explained the photovoltage oscillation amplitude enhancement in the presence of an antidot lattice with regard to the pure 2DEG. The microwave frequency excitation range is 139 – 350 GHz. The cyclotron and magnetoplasmon resonances take place in the magnetic field range 0.4 – 0.8 T. This original experimental condition allows edge magnetoplasmons EMPs interference like observation at low magnetic field, typically B < B{sub c} where B{sub c} is the magnetic field at which the cyclotron resonance takes place. The different oscillation periods observed and their microwave frequency dependence were discussed. For 139 and 158 GHz microwave excitation frequencies, a unique EMPs-like interference period was found in the presence of antidots whereas two periods were extracted for 295 or 350 GHz. An explanation of this effect is given taking account of strong electron interaction with antidot at low magnetic field. Indeed, electrons involved in EMPs like phenomenon interact strongly with antidots when electron cyclotron orbits are larger than or comparable to the antidot diameter.
I. Bisotto
2015-11-01
Full Text Available We present new photovoltage oscillation in a pure two dimensional electron gas (2DEG and in the presence of circular or semicircular antidot lattices. Results were interpreted as EMPs-like photovoltage oscillations. We observed and explained the photovoltage oscillation amplitude enhancement in the presence of an antidot lattice with regard to the pure 2DEG. The microwave frequency excitation range is 139 – 350 GHz. The cyclotron and magnetoplasmon resonances take place in the magnetic field range 0.4 – 0.8 T. This original experimental condition allows edge magnetoplasmons EMPs interference like observation at low magnetic field, typically B < Bc where Bc is the magnetic field at which the cyclotron resonance takes place. The different oscillation periods observed and their microwave frequency dependence were discussed. For 139 and 158 GHz microwave excitation frequencies, a unique EMPs-like interference period was found in the presence of antidots whereas two periods were extracted for 295 or 350 GHz. An explanation of this effect is given taking account of strong electron interaction with antidot at low magnetic field. Indeed, electrons involved in EMPs like phenomenon interact strongly with antidots when electron cyclotron orbits are larger than or comparable to the antidot diameter.
Karen Johanne Pallesen
Full Text Available Musical expertise is associated with structural and functional changes in the brain that underlie facilitated auditory perception. We investigated whether the phase locking (PL and amplitude modulations (AM of neuronal oscillations in response to musical chords are correlated with musical expertise and whether they reflect the prototypicality of chords in Western tonal music. To this aim, we recorded magnetoencephalography (MEG while musicians and non-musicians were presented with common prototypical major and minor chords, and with uncommon, non-prototypical dissonant and mistuned chords, while watching a silenced movie. We then analyzed the PL and AM of ongoing oscillations in the theta (4-8 Hz alpha (8-14 Hz, beta- (14-30 Hz and gamma- (30-80 Hz bands to these chords. We found that musical expertise was associated with strengthened PL of ongoing oscillations to chords over a wide frequency range during the first 300 ms from stimulus onset, as opposed to increased alpha-band AM to chords over temporal MEG channels. In musicians, the gamma-band PL was strongest to non-prototypical compared to other chords, while in non-musicians PL was strongest to minor chords. In both musicians and non-musicians the long-latency (> 200 ms gamma-band PL was also sensitive to chord identity, and particularly to the amplitude modulations (beats of the dissonant chord. These findings suggest that musical expertise modulates oscillation PL to musical chords and that the strength of these modulations is dependent on chord prototypicality.
Specific frequency bands of amplitude low-frequency oscillation encodes personality.
Wei, Luqing; Duan, Xujun; Zheng, Chunyan; Wang, Shanshan; Gao, Qing; Zhang, Zhiqiang; Lu, Guangming; Chen, Huafu
2014-01-01
The biological model of extraversion and neuroticism identified by Eysenck has stimulated increasing interest in uncovering neurobiological substrate of the two fundamental dimensions. Here we aim to explore brain disturbances underlying extraversion and neuroticism in 87 healthy individuals using fractional amplitude of low-frequency fluctuations (LFF) on resting-state functional magnetic resonance imaging. Two different frequency bands, Slow-5 (0.01-0.027 Hz) exhibiting higher power and involving larger brain regions, and Slow-4 (0.027-0.073 Hz) exhibiting less power and emerging locally, were analyzed. Our results showed a positive correlation between LFF amplitude at Slow-5 and extraversion in medial prefrontal cortex and precuneus, important portions of the default mode network, thus suggesting a link between default network activity and personality traits. LFF amplitude at Slow-5 was correlated positively with neuroticism in right posterior portion of the frontal lobe, further validating neuroticism with frontal lateralization. In addition, LFF amplitude at Slow-4 was negatively associated with extraversion and neuroticism in left hippocampus (HIP) and bilateral superior temporal cortex (STC) respectively, supporting the hypothesized (inverse) relationship between extraversion and resting arousal, also implying neural circuit underlying emotional process influencing on personality. Overall, these findings suggest the important relationships, between personality and LFF amplitude dynamic, depend on specific frequency bands.
Theissen, J; Lunkenheimer, P P; Niederer, P; Bush, E; Frieling, G; Lawin, P
1987-09-01
The pattern of intrapulmonary pressure distribution was studied during high-frequency ventilation in order to explain the inconsistent results reported in the literature. Methods. Pressure and flow velocity (hot-wire anemometry) were measured in different lung compartments: 1. In transalveolar chambers sealed to the perforated pleural surfaces of dried pig lungs; 2. In emphysema-simulating airbags sealed to the isolated bronchial trees of dried pig lungs; and 3. In transalveolar chambers sealed to the perforated pleural surfaces of freshly excised pig lungs. Results. 1. The pressure amplitudes change from one area to another and depending on the exciting frequency. 2. High-frequency oscillation is associated with an increase in pressure amplitude when the exciting frequency rises, whereas with conventional high-frequency jet ventilation the pressure amplitude is more likely to decrease with frequency. 3. During high-frequency jet ventilation the local pressure amplitude changes with the position of the tube in the trachea rather than with the exciting frequency. 4. When the volume of the measuring chamber is doubled the resulting pressure amplitude falls to half the control value. 5. The pressure amplitude and mean pressure measured in the transalveolar chamber vary more or less independently from the peak flow velocity. High-frequency ventilation is thus seen to be a frequency-dependant, inhomogeneous mode of ventilation that can essentially be homogenized by systematically changing the exciting frequency. The frequency-dependant response to different lung areas to excitation is likely to result from an intrabronchially-localized aerodynamic effect rather than the mechanical properties of the lung parenchyma.
Isaeva, Olga B.; Kuznetsov, Sergey P.; Mosekilde, Erik
2011-01-01
The paper proposes an approach to constructing feasible examples of dynamical systems with hyperbolic chaotic attractors based on the successive transfer of excitation between two pairs of self-oscillators that are alternately active. An angular variable that measures the relations of the current...
Banerjee, Tanmoy; Dutta, Partha Sharathi; Gupta, Anubhav
2015-05-01
One of the most important issues in spatial ecology is to understand how spatial synchrony and dispersal-induced stability interact. In the existing studies it is shown that dispersion among identical patches results in spatial synchrony; on the other hand, the combination of spatial heterogeneity and dispersion is necessary for dispersal-induced stability (or temporal stability). Population synchrony and temporal stability are thus often thought of as conflicting outcomes of dispersion. In contrast to the general belief, in this present study we show that mean-field dispersion is conducive to both spatial synchrony and dispersal-induced stability even in identical patches. This simultaneous occurrence of rather conflicting phenomena is governed by the suppression of oscillation states, namely amplitude death (AD) and oscillation death (OD). These states emerge through spatial synchrony of the oscillating patches in the strong-coupling strength. We present an interpretation of the mean-field diffusive coupling in the context of ecology and identify that, with increasing mean-field density, an open ecosystem transforms into a closed ecosystem. We report on the occurrence of OD in an ecological model and explain its significance. Using a detailed bifurcation analysis we show that, depending on the mortality rate and carrying capacity, the system shows either AD or both AD and OD. We also show that the results remain qualitatively the same for a network of oscillators. We identify a new transition scenario between the same type of oscillation suppression states whose geneses differ. In the parameter-mismatched case, we further report on the direct transition from OD to AD through a transcritical bifurcation. We believe that this study will lead to a proper interpretation of AD and OD in ecology, which may be important for the conservation and management of several communities in ecosystems.
Muhammad Ashfaq Ahmad; Lin Jie; Qian Yan; Ma Zhi-Min; Ma Ai-Qun; Liu Shu-Tian
2007-01-01
This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.
Study on relaxation oscillation of Er~(3+)/Yb~(3+) co-doped phosphate glass optical waveguide laser
LIU HuaDong; ZHANG XiaoXia; WU XianLi; ZHANG Qin; LIU YongZhi
2009-01-01
Based on the principle and fabrication of the optical waveguide laser, and through the configuration of the energy level of Er~(3+)/Yb~(3+) co-doped system, the time-dependent rate equations are formed and then solved by Runge-Kutta algorithm. The dynamic characteristic of the waveguide laser pumped unidirec-tionally by 980 nm LD is analyzed. The curves of the relaxation oscillation are drawn, showing that the photon number and inverted population vary alternately. The attenuation characteristic of the peak power is studied. It is gained that time constant changes with pump power, length of waveguide and the reflectivity of output mirror. Furthermore, the impact of the above three parameters on the frequency and end-time of relaxation oscillation is discussed. The frequency of relaxation oscillation is propor-tional to the pump power. Under high reflectivity conditions, the length of waveguide has a weak impact on the frequency. The end-time decreases as the three parameters increase. These features and results provide a theoretical basis for designing the Er~(3+)/Yb~(3+) co-doped phosphate optical waveguide laser.
Noise Effects on Oscillator Network of Transcription Regulators
WANG Xian-Ju; AI Bao-Quan; LIU Guo-Tao; LIU Liang-Gang
2002-01-01
Based on the model describing the regulation of the PRM operator region of λ phage proposed by Jeff Hastyet al., we study the noise effects on the oscillator network. We find that the additive noise cannot change the period andthe amplitude of the relaxation oscillator, but in the multiplicative case, the period of the relaxation oscillator increasesto a constant value with the increase of the strength of noise, and the amplitude of the relaxation oscillator also showsincreases with the increase of the strength of noise. This novel results suggest that an external multiplicative noise sourcecould be used to control gene expression.
Dussaux, A.; Rache Salles, B.; Jenkins, A. S.; Bortolotti, P.; Grollier, J.; Cros, V.; Fert, A. [Unité Mixte de Physique CNRS/Thales and Université Paris Sud 11, 1 Ave. A. Fresnel, 91767 Palaiseau (France); Grimaldi, E., E-mail: eva.grimaldi@thalesgroup.com [Unité Mixte de Physique CNRS/Thales and Université Paris Sud 11, 1 Ave. A. Fresnel, 91767 Palaiseau (France); CNES, 1 Avenue Edouard Belin, 31400 Toulouse (France); Khvalkovskiy, A. V. [Unité Mixte de Physique CNRS/Thales and Université Paris Sud 11, 1 Ave. A. Fresnel, 91767 Palaiseau (France); A.M. Prokhorov General Physics Institute of RAS, Vavilova Str. 38, 119991 Moscow (Russian Federation); Kubota, H.; Fukushima, A.; Yakushiji, K.; Yuasa, S. [National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba (Japan)
2014-07-14
We investigate the microwave response of a spin transfer vortex based oscillator in a magnetic tunnel junction with an in-plane reference layer combined with a spin valve with an out-of-plane magnetization spin polarizing layer. The main advantage of this perpendicular spin polarizer is to induce a large spin transfer force even at zero magnetic field, thus leading to a record emitted power (up to 0.6 μW) associated to a very narrow spectral linewidth of a few hundreds of kHz. The characteristics of this hybrid vortex based spin transfer nano-oscillator obtained at zero field and room temperature are of great importance for applications based on rf spintronic devices as integrated and tunable microwave source and/or microwave detector.
Yuan, Yi; Yan, Jiaqing; Ma, Zhitao; Li, Xiaoli
2016-01-01
Noninvasive focused ultrasound stimulation (FUS) can be used to modulate neural activity with high spatial resolution. Phase-amplitude coupling (PAC) between neuronal oscillations is tightly associated with cognitive processes, including learning, attention, and memory. In this study, we investigated the effect of FUS on PAC between neuronal oscillations and established the relationship between the PAC index and ultrasonic intensity. The rat hippocampus was stimulated using focused ultrasound at different spatial-average pulse-average ultrasonic intensities (3.9, 9.6, and 19.2 W/cm2). The local field potentials (LFPs) in the rat hippocampus were recorded before and after FUS. Then, we analyzed PAC between neuronal oscillations using a PAC calculation algorithm. Our results showed that FUS significantly modulated PAC between the theta (4–8 Hz) and gamma (30–80 Hz) bands and between the alpha (9–13 Hz) and ripple (81–200 Hz) bands in the rat hippocampus, and PAC increased with incremental increases in ultrasonic intensity. PMID:27499733
Yi Yuan
2016-07-01
Full Text Available Noninvasive focused ultrasound stimulation (FUS can be used to modulate neural activity with high spatial resolution. Phase-amplitude coupling (PAC between neuronal oscillations is tightly associated with cognitive processes, including learning, attention and memory. In this study, we investigated the effect of FUS on PAC between neuronal oscillations and established the relationship between the PAC index and ultrasonic intensity. The rat hippocampus was stimulated using focused ultrasound at different spatial-average pulse-average ultrasonic intensities (3.9 W/cm2, 9.6 W/cm2, and 19.2 W/cm2. The local field potentials (LFPs in the rat hippocampus were recorded before and after FUS. Then, we analyzed PAC between neuronal oscillations using a PAC calculation algorithm. Our results showed that FUS significantly modulated PAC between the theta (4-8 Hz and gamma (30-80 Hz bands and between the alpha (9-13 Hz and ripple (81-200 Hz bands in the rat hippocampus, and PAC increased with incremental increases in ultrasonic intensity.
Pierro, Michele; Sassaroli, Angelo; Bergethon, Peter R.; Ehrenberg, Bruce L.; Fantini, Sergio
2012-01-01
We have investigated the amplitude and phase of spontaneous low-frequency oscillations (LFOs) of the cerebral deoxy- and oxy-hemoglobin concentrations ([Hb] and [HbO]) in a human sleep study using near-infrared spectroscopy (NIRS). Amplitude and phase analysis was based on the analytic signal method, and phasor algebra was used to decompose measured [Hb] and [HbO] oscillations into cerebral blood volume (CBV) and flow velocity (CBFV) oscillations. We have found a greater phase lead of [Hb] vs. [HbO] LFOs during non-REM sleep with respect to the awake and REM sleep states (maximum increase in [Hb] phase lead: ~π/2). Furthermore, during non-REM sleep, the amplitudes of [Hb] and [HbO] LFOs are suppressed with respect to the awake and REM sleep states (maximum amplitude decrease: 87%). The associated cerebral blood volume and flow velocity oscillations are found to maintain their relative phase difference during sleep, whereas their amplitudes are attenuated during non-REM sleep. These results show the potential of phase-amplitude analysis of [Hb] and [HbO] oscillations measured by NIRS in the investigation of hemodynamics associated with cerebral physiology, activation, and pathological conditions. PMID:22820416
The phase of ongoing EEG oscillations predicts the amplitude of peri-saccadic mislocalization
McLelland, Douglas; Lavergne, Louisa; VanRullen, Rufin
2016-01-01
Our constant eye movements mean that updating processes, such as saccadic remapping, are essential for the maintenance of a stable spatial representation of the world around us. It has been proposed that, rather than continually update a full spatiotopic map, only the location of a few key objects is updated, suggesting that the process is linked to attention. At the same time, mounting evidence links attention to oscillatory neuronal processes. We therefore hypothesized that updating processes should themselves show oscillatory characteristics, inherited from underlying attentional processes. To test this, we carried out a combined psychophysics and EEG experiment in human participants, using a saccadic mislocalization task as a behaviourally measureable proxy for spatial updating, and simultaneously recording 64-channel EEG. We then used a time-frequency analysis to test for a correlation between oscillation phase and perceptual outcome. We found a significant phase-dependence of mislocalization in a time-frequency region from around 400 ms prior to saccade initiation and peaking at around 7 Hz, principally apparent over occipital electrodes. Thus the degree of perceived mislocalization is correlated with the phase of a theta-frequency oscillation prior to saccade onset. We conclude that spatial updating processes are indeed linked to rhythmic processes in the brain. PMID:27403937
Lum, Jordan S; Dove, Jacob D; Murray, Todd W; Borden, Mark A
2016-09-20
Lipid monolayer rheology plays an important role in a variety of interfacial phenomena, the physics of biological membranes, and the dynamic response of acoustic bubbles and drops. We show here measurements of lipid monolayer elasticity and viscosity for very small strains at megahertz frequency. Individual plasmonic microbubbles of 2-6 μm radius were photothermally activated with a short laser pulse, and the subsequent nanometer-scale radial oscillations during ring-down were monitored by optical scatter. This method provided average dynamic response measurements of single microbubbles. Each microbubble was modeled as an underdamped linear oscillator to determine the damping ratio and eigenfrequency, and thus the lipid monolayer viscosity and elasticity. Our nonisothermal measurement technique revealed viscoelastic trends for different lipid shell compositions. We observed a significant increase in surface elasticity with the lipid acyl chain length for 16 to 20 carbons, and this effect was explained by an intermolecular forces model that accounts for the lipid composition, packing, and hydration. The surface viscosity was found to be equivalent for these lipid shells. We also observed an anomalous decrease in elasticity and an increase in viscosity when increasing the acyl chain length from 20 to 22 carbons. These results illustrate the use of a novel nondestructive optical technique to investigate lipid monolayer rheology in new regimes of frequency and strain, possibly elucidating the phase behavior, as well as how the dynamic response of a microbubble can be tuned by the lipid intermolecular forces.
Non-linear Vibration of Oscillation Systems using Frequency-Amplitude Formulation
Fereidoon, A.; Ghadimi, M.; Barari, Amin
2012-01-01
In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifthorder nonlinearity for two examples using He’s Frequency Amplitude Formulation (HFAF).The effectiveness and convenience of the method is illustrated in these examples. It will be shown...... that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems....
Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it [MR-Lab, Center for Mind/Brain Science, University of Trento, Italy and Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)
2014-12-01
In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties.
Thanassoulas, C; Verveniotis, G
2010-01-01
Starting from the observation that quite often the Earth's oscillating electric field varies in amplitude, a mechanism is postulated that accounts for these observations. That mechanism is the piezoelectric one driven by the M1 and K1 tidal components. It is demonstrated how the system: piezoelectricity triggered in the lithosphere - M1 and K1 tidal components is activated and produces the amplitude modulated Earth's oscillating electric field. This procedure is linked to the strain load conditions met in the seismogenic area before the occurrence of a large EQ. Peaks of the oscillating Earth's electric field are tightly connected to the M1 peak tidal component and to the timing of the occurrence of large EQs. Typical examples from real recordings of the Earth's oscillating electric field, recorded by the ATH (Greece) monitoring site, are given in order to verify the postulated detailed piezoelectric mechanism.
Taylor-Couette flow control by amplitude variation of the inner cylinder cross-section oscillation
Oualli, Hamid; Mekadem, Mahmoud; Lebbi, Mohamed; Bouabdallah, Ahcene
2015-07-01
The hydrodynamic stability of a viscous fluid flow evolving in an annular space between a rotating inner cylinder with a periodically variable radius and an outer fixed cylinder is considered. The basic flow is axis-symmetric with two counter-rotating vortices each wavelength along the whole filled system length. The numerical simulations are implemented on the commercial Fluent software package, a finite-volume CFD code. It is aimed to make investigation of the early flow transition with assessment of the flow response to radial pulsatile motion superimposed to the inner cylinder cross-section as an extension of a previous developed work in Oualli et al. [H. Oualli, A. Lalaoua, S. Hanchi, A. Bouabdallah, Eur. Phys. J. Appl. Phys. 61, 11102 (2013)] where a comparative controlling strategy is applied to the outer cylinder. The same basic system is considered with similar calculating parameters and procedure. In Oualli et al. [H. Oualli, A. Lalaoua, S. Hanchi, A. Bouabdallah, Eur. Phys. J. Appl. Phys. 61, 11102 (2013)], it is concluded that for the actuated outer cylinder and relatively to the non-controlled case, the critical Taylor number, Tac1, characterizing the first instability onset illustrated by the piled Taylor vortices along the gap, increases substantially to reach a growing rate of 70% when the deforming amplitude is ɛ = 15%. Interestingly, when this controlling strategy is applied to the inner cylinder cross-section with a slight modification of the actuating law, this tendency completely inverts and the critical Taylor number decreases sharply from Tac1 = 41.33 to Tac1 = 17.66 for ɛ = 5%, corresponding to a reduction rate of 57%. Fundamentally, this result is interesting and can be interpreted by prematurely triggering instabilities resulting in rapid development of flow turbulence. Practically, important applicative aspects can be met in several industry areas where substantial intensification of transport phenomena (mass, momentum and heat) is
Gonzalo Martín-Vázquez
Full Text Available Fluctuations in successive waves of oscillatory local field potentials (LFPs reflect the ongoing processing of neuron populations. However, their amplitude, polarity and synaptic origin are uncertain due to the blending of electric fields produced by multiple converging inputs, and the lack of a baseline in standard AC-coupled recordings. Consequently, the estimation of underlying currents by laminar analysis yields spurious sequences of inward and outward currents. We devised a combined analytical/experimental approach that is suitable to study laminated structures. The approach was essayed on an experimental oscillatory LFP as the Schaffer-CA1 gamma input in anesthetized rats, and it was verified by parallel processing of model LFPs obtained through a realistic CA1 aggregate of compartmental units. This approach requires laminar LFP recordings and the isolation of the oscillatory input from other converging pathways, which was achieved through an independent component analysis. It also allows the spatial and temporal components of pathway-specific LFPs to be separated. While reconstructed Schaffer-specific LFPs still show spurious inward/outward current sequences, these were clearly stratified into distinct subcellular domains. These spatial bands guided the localized delivery of neurotransmitter blockers in experiments. As expected, only Glutamate but not GABA blockers abolished Schaffer LFPs when applied to the active but not passive subcellular domains of pyramidal cells. The known chemical nature of the oscillatory LFP allowed an empirical offset of the temporal component of Schaffer LFPs, such that following reconstruction they yield only sinks or sources at the appropriate sites. In terms of number and polarity, some waves increased and others decreased proportional to the concomitant inputs in native multisynaptic LFPs. Interestingly, the processing also retrieved the initiation time for each wave, which can be used to discriminate
Guillermo H Goldsztein
Full Text Available Consider a person standing on a platform that oscillates laterally, i.e. to the right and left of the person. Assume the platform satisfies Hooke's law. As the platform moves, the person reacts and moves its body attempting to keep its balance. We develop a simple model to study this phenomenon and show that the person, while attempting to keep its balance, may do positive work on the platform and increase the amplitude of its oscillations. The studies in this article are motivated by the oscillations in pedestrian bridges that are sometimes observed when large crowds cross them.
Fuqing Zhou
Full Text Available Decreases in metabolites and increased motor-related, but decreased sensory-related activation of the sensorimotor cortex (SMC have been observed in patients with cervical myelopathy (CM using advanced MRI techniques. However, the nature of intrinsic neuronal activity in the SMC, and the relationship between cerebral function and structural damage of the spinal cord in patients with CM are not fully understood. The purpose of this study was to assess intrinsic neuronal activity by calculating the regional amplitude of low frequency fluctuations (ALFF using resting-state functional MRI (rs-fMRI, and correlations with clinical and imaging indices. Nineteen patients and 19 age- and sex-matched healthy subjects underwent rs-fMRI scans. ALFF measurements were performed in the SMC, a key brain network likely to impaired or reorganized patients with CM. Compared with healthy subjects, increased amplitude of cortical low-frequency oscillations (LFO was observed in the right precentral gyrus, right postcentral gyrus, and left supplementary motor area. Furthermore, increased z-ALFF values in the right precentral gyrus and right postcentral gyrus correlated with decreased fractional anisotropy values at the C2 level, which indicated increased intrinsic neuronal activity in the SMC corresponding to the structural impairment in the spinal cord of patients with CM. These findings suggest a complex and diverging relationship of cortical functional reorganization and distal spinal anatomical compression in patients with CM and, thus, add important information in understanding how spinal cord integrity may be a factor in the intrinsic covariance of spontaneous low-frequency fluctuations of BOLD signals involved in cortical plasticity.
Nagashima, Kaori; Fournier, Damien; Birch, Aaron C.; Gizon, Laurent
2017-03-01
Context. In time-distance helioseismology, wave travel times are measured from the two-point cross-covariance function of solar oscillations and are used to image the solar convection zone in three dimensions. There is, however, also information in the amplitude of the cross-covariance function, for example, about seismic wave attenuation. Aims: We develop a convenient procedure to measure the amplitude of the cross-covariance function of solar oscillations. Methods: In this procedure, the amplitude of the cross-covariance function is linearly related to the cross-covariance function and can be measured even for high levels of noise. Results: As an example application, we measure the amplitude perturbations of the seismic waves that propagate through the sunspot in active region NOAA 9787. We can recover the amplitude variations due to the scattering and attenuation of the waves by the sunspot and associated finite-wavelength effects. Conclusions: The proposed definition of cross-covariance amplitude is robust to noise, can be used to relate measured amplitudes to 3D perturbations in the solar interior under the Born approximation, and provides independent information from the travel times.
Baudin, F; Belkacem, K; Hekker, S; Morel, T; Samadi, R; Benomar, O; Goupil, M -J; Carrier, F; Ballot, J; Deheuvels, S; De Ridder, J; Hatzes, A P; Kallinger, T; Weiss, W W
2011-01-01
Context. The advent of space-borne missions such as CoRoT or Kepler providing photometric data has brought new possibilities for asteroseismology across the H-R diagram. Solar-like oscillations are now observed in many stars, including red giants and main- sequence stars. Aims. Based on several hundred identified pulsating red giants, we aim to characterize their oscillation amplitudes and widths. These observables are compared with those of main-sequence stars in order to test trends and scaling laws for these parameters for both main-sequence stars and red giants. Methods. An automated fitting procedure is used to analyze several hundred Fourier spectra. For each star, a modeled spectrum is fitted to the observed oscillation spectrum, and mode parameters are derived. Results. Amplitudes and widths of red-giant solar-like oscillations are estimated for several hundred modes of oscillation. Amplitudes are relatively high (several hundred ppm) and widths relatively small (very few tenths of a {\\mu}Hz). Conclus...
A Design of Relaxation Oscillator with High Precision%一种高精度张弛振荡器的设计
柯志强; 张涛
2014-01-01
A relaxation oscillator with high temperature rejection characteristics is presented. This relaxation oscillator adopts the temperature compensation method of single chip relaxation oscillator,using well diffuse resistor with positive temperature coefficient to compensate. Fabricated in a 0. 35 μm CMOS process and verified by the Cadence simulation,this relaxation oscillator has only the temperature coefficient of 404í10-9/℃ in the range of-45 ℃ ~55 ℃. Also, the oscillation frequency has slim influence of the temperature change. This circuit has applied successfully in industrial control chip.%提出一种新的带温度补偿的张弛振荡器，采用正温度系数的阱电阻实现输出频率在大范围温度变化下保持稳定。该电路采用0.35μm的CMOS工艺实现，利用Cadence进行仿真验证。仿真结果显示，在-45℃~55℃范围内，该张弛振荡器的温度系数仅为404×10-9/℃。该振荡器振荡频率受温度影响很小，已经应用于工业控制类芯片中。
Relaxation and self-sustained oscillations in the time elapsed neuron network model
Pakdaman, Khashayar; Salort, Delphine
2011-01-01
The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons structured by this time. In an earlier work, based on generalized relative entropy methods, it is proved that for highly or weakly connected networks the model exhibits relaxation to the steady state and for moderately connected networks it is obtained numerical evidence of appearance of self-sustained periodic solutions. Here, we go further and, using the particular form of the model, we quantify the regime where relaxation to a stationary state occurs in terms of the network connectivity. To introduce our methodology, we first consider the case where the neurons are not connected and we give a new statement showing that total asynchronous firing of neurons appears asymptotically. In a second step, we consider the case with connections and give a low connectivity condition that...
Aulova, T V; Kravtsov, Nikolai V; Lariontsev, E G; Chekina, S N [D.V. Skobel' tsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
2012-08-31
The dynamics of solid-state ring laser (SSRL) radiation with periodic pump modulation is studied experimentally and simulated numerically in the case of parametric excitation of relaxation oscillations at the subharmonic of a modulating signal. Parametric processes are investigated by modulating the pump in two regimes of the SSRL operation: steady-state regime of unidirectional lasing and self-modulation regime of the first kind. Significant differences in the dynamics of radiation for these regimes are found. It is established that when the laser operates in the self-modulation regime, a first-order parametric instability can result in the appearance of the dynamic chaos regime. (control of laser radiation parameters)
Twin-peak quasi-periodic oscillations in X-ray binaries: clues from their amplitude and coherence
Germanà, C.; Casana, R.; Ferreira, M. M., Jr.; Gomes, A. R.
2014-10-01
Low-mass X-ray binaries (LMXBs) with either a black hole or a neutron star show power spectra characterized by several enhanced fractions of power at given frequencies, such as quasi-periodic oscillations (QPOs). Twin-peak high-frequency QPOs (HF QPOs) are typical of the orbital motion time-scale for matter orbiting within 10 r_{g} from the compact object (r_{g}=GM/c^{2} is the gravitational radius of the compact object). Thus, such modulations could arise from the energy released by accreting clumps of matter interacting with the strong gravitational field of the compact object. Twin-peak HF QPOs are characterized by their central frequency ν, root mean square amplitude (rms) and coherence Q=νΔν, where Δν is the width of the peak. Here we investigate on the characteristic behavior of the rms observed in several LMXBs. We highlight the work done by the strong tidal force as root source of the energy (rms) released by a QPO. By means of the Schwarzschild potential we estimate the maximum allowed radius of clumps of matter that can survive to tides in the inner part of the accretion disk. It turns to be R˜ 40 m for matter in an accretion disk around a 2 M_{odot} neutron star and R˜ 150 m for matter around a 10 M_{odot } black hole. The work loaded by tides on the clump of matter depends on the Schwarzschild potential shape for the given orbit. We highlight that for orbits approaching to the inner most stable circular orbit (ISCO) the changing Schwarzschild potential shape may account for the observed behavior of the energy (rms) carried by the twin-peak HF QPOs.
Higher dimensional models of cross-coupled oscillators and application to design
Elwakil, Ahmed S.
2010-06-01
We present four-dimensional and five-dimensional models for classical cross-coupled LC oscillators. Using these models, sinusoidal oscillation condition, frequency and amplitude can be found. Further, undesired behaviors such as relaxation-mode oscillations and latchup can be explained and detected. A simple graphical design procedure is also described. © 2010 World Scientific Publishing Company.
Association, partition, and surface activity in biphasic systems displaying relaxation oscillations.
Pradines, Vincent; Tadmouri, Rawad; Lavabre, Dominique; Micheau, Jean-Claude; Pimienta, Véronique
2007-11-06
Several biphasic systems giving rise to periodical Marangoni instability have been analyzed from the point of view of the physicochemical properties of the involved compounds. In each case, the compound at the origin of the oscillatory behavior has been identified: the reactant cetyltrimethylammonium bromide (CTAB) for the CTAB/picric acid (PH) system and the product of reaction dodecyl sulfate tetraalkylammonium (TAADS) for the sodium dodecyl sulfate/tetraalkylammonium bromide (SDS/TAAB) system. The properties of the latter system have been varied progressively by increasing the chain length of the tetraalkylammonium ion. Oscillations were observed whichever the direction of transfer (from water to dichloromethane and from dichloromethane to water). The comparison of the dynamic interfacial tension, recorded during transfer, to equilibrium measurements shows that the instability is favored when partition is highly in favor of the organic phase. The main criteria for the appearance of the instability are a high surface activity and a low interfacial adsorption.
Gauron, Pierre; Basarab Nicolescu [Theoretical Physics Division, Inst. de Physique Nucleaire, Paris-11 Univ., 91 - Orsay (France); Selyugin, O.V. [Lab. of Theoretical Physics, Joint Inst. for Nuclear Research, Dubna (Russian Federation)
1999-10-01
We show that the high precision dN/dt UA4/2 data at {radical} = 541 GeV are compatible with the presence of Auberson-Kinoshita-Martin (AKM) type of oscillations at very small momentum transfer. These oscillations seem to be periodic in {radical}|t|, the corresponding period being {approx_equal} 2 {center_dot}10{sup -2} GeV. The existence of such visible oscillations suggests a general mechanism of saturation of axiomatic bounds. As an illustration the consequences for extracting the parameter {rho} = ReF/ImF from dN/dt data are also discussed. (authors) 1 ref., 2 figs.
Sanderson Michael J
2006-02-01
Full Text Available Abstract Background It has been shown that the contractile state of airway smooth muscle cells (SMCs in response to agonists is determined by the frequency of Ca2+ oscillations occurring within the SMCs. Therefore, we hypothesized that the relaxation of airway SMCs induced by agents that increase cAMP results from the down-regulation or slowing of the frequency of the Ca2+ oscillations. Methods The effects of isoproterenol (ISO, forskolin (FSK and 8-bromo-cAMP on the relaxation and Ca2+ signaling of airway SMCs contracted with methacholine (MCh was investigated in murine lung slices with phase-contrast and laser scanning microscopy. Results All three cAMP-elevating agents simultaneously induced a reduction in the frequency of Ca2+ oscillations within the SMCs and the relaxation of contracted airways. The decrease in the Ca2+ oscillation frequency correlated with the extent of airway relaxation and was concentration-dependent. The mechanism by which cAMP reduced the frequency of the Ca2+ oscillations was investigated. Elevated cAMP did not affect the re-filling rate of the internal Ca2+ stores after emptying by repetitive exposure to 20 mM caffeine. Neither did elevated cAMP limit the Ca2+ available to stimulate contraction because an elevation of intracellular Ca2+ concentration induced by exposure to a Ca2+ ionophore (ionomycin or by photolysis of caged-Ca2+ did not reverse the effect of cAMP. Similar results were obtained with iberiotoxin, a blocker of Ca2+-activated K+ channels, which would be expected to increase Ca2+ influx and contraction. By contrast, the photolysis of caged-IP3 in the presence of agonist, to further elevate the intracellular IP3 concentration, reversed the slowing of the frequency of the Ca2+ oscillations and relaxation of the airway induced by FSK. This result implied that the sensitivity of the IP3R to IP3 was reduced by FSK and this was supported by the reduced ability of IP3 to release Ca2+ in SMCs in the presence of
Interlimb coupling strength scales with movement amplitude.
Peper, C Lieke E; de Boer, Betteco J; de Poel, Harjo J; Beek, Peter J
2008-05-23
The relation between movement amplitude and the strength of interlimb interactions was examined by comparing bimanual performance at different amplitude ratios (1:2, 1:1, and 2:1). For conditions with unequal amplitudes, the arm moving at the smaller amplitude was predicted to be more strongly affected by the contralateral arm than vice versa. This prediction was based on neurophysiological considerations and the HKB model of coupled oscillators. Participants performed rhythmic bimanual forearm movements at prescribed amplitude relations. After a brief mechanical perturbation of one arm, the relaxation process back to the initial coordination pattern was examined. This analysis focused on phase adaptations in the unperturbed arm, as these reflect the degree to which the movements of this arm were affected by the coupling influences stemming from the contralateral (perturbed) arm. The thus obtained index of coupling (IC) reflected the relative contribution of the unperturbed arm to the relaxation process. As predicted IC was larger when the perturbed arm moved at a larger amplitude than did the unperturbed arm, indicating that coupling strength scaled with movement amplitude. This result was discussed in relation to previous research regarding sources of asymmetry in coupling strength and the effects of amplitude disparity on interlimb coordination.
Miyake, Masataka; Hori, Daisuke; Sadachika, Norio; Feldmann, Uwe; Miura-Mattausch, Mitiko; Mattausch, Hans Jürgen; Ohguro, Tatsuya; Iizuka, Takahiro; Taguchi, Masahiko; Miyamoto, Shunsuke
Frequency dependent properties of accumulation-mode MOS varactors, which are key elements in many RF circuits, are dominated by Non-Quasi-Static (NQS) effects in the carrier transport. The circuit performances containing MOS varactors can hardly be reproduced without considering the NQS effect in MOS-varactor models. For the LC-VCO circuit as an example it is verified that frequency-tuning range and oscillation amplitude can be overestimated by over 20% and more than a factor 2, respectively, without inclusion of the NQS effect.
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. K. Sinha
Full Text Available Ionospheric scintillations of radio waves at low-latitudes are associated with electron density irregularities. These irregularities are field-aligned and can provide excitation energy all along the field line to non-local field-aligned oscillations, such as the local field line oscillations. Eigen-periods of toroidal field line oscillations at low-latitudes, computed by using the dipole magnetic field and ion distributions obtained from the International Reference Ionosphere (IRI for typical nighttime conditions, fall in the range of 20–25 s. When subjected to spectral analysis, signal strength of the radio waves recorded on the 250 MHz beacon at Pondicherry (4.5° N dip, Mumbai (13.4° N dip and Ujjain (18.6° N dip exhibit periodicities in the same range. For the single event for which simultaneous ground magnetic data were available, the geomagnetic field also oscillated at the same periodicity. The systematic presence of a significant peak in the 20–25 s range during periods of strong radio wave scintillations, and its absence otherwise suggests the possibility that field line oscillations are endogenously excited by the irregularities, and the oscillations associated with the excited field line generate the modulation characteristics of the radio waves received on the ground. The frequency of modulation is found to be much lower than the characteristic frequencies that define the main body of scintillations, and they probably correspond to scales that are much larger than the typical Fresnel scale. It is possible that the refractive mechanism associated with larger scale long-lived irregularities could be responsible for the observed phenomenon. Results of a preliminary numerical experiment that uses a sinusoidal phase irregularity in the ionosphere as a refracting media are presented. The results show that phase variations which are large enough to produce a focal plane close to the ground can reproduce features that are not
Jana Vlachová
2015-03-01
Full Text Available The stiffness of micron-sized sphere–plate contacts was studied by employing high frequency, tangential excitation of variable amplitude (0–20 nm. The contacts were established between glass spheres and the surface of a quartz crystal microbalance (QCM, where the resonator surface had been coated with either sputtered SiO2 or a spin-cast layer of poly(methyl methacrylate (PMMA. The results from experiments undertaken in the dry state and in water are compared. Building on the shifts in the resonance frequency and resonance bandwidth, the instrument determines the real and the imaginary part of the contact stiffness, where the imaginary part quantifies dissipative processes. The method is closely analogous to related procedures in AFM-based metrology. The real part of the contact stiffness as a function of normal load can be fitted with the Johnson–Kendall–Roberts (JKR model. The contact stiffness was found to increase in the presence of liquid water. This finding is tentatively explained by the rocking motion of the spheres, which couples to a squeeze flow of the water close to the contact. The loss tangent of the contact stiffness is on the order of 0.1, where the energy losses are associated with interfacial processes. At high amplitudes partial slip was found to occur. The apparent contact stiffness at large amplitude depends linearly on the amplitude, as predicted by the Cattaneo–Mindlin model. This finding is remarkable insofar, as the Cattaneo–Mindlin model assumes Coulomb friction inside the sliding region. Coulomb friction is typically viewed as a macroscopic concept, related to surface roughness. An alternative model (formulated by Savkoor, which assumes a constant frictional stress in the sliding zone independent of the normal pressure, is inconsistent with the experimental data. The apparent friction coefficients slightly increase with normal force, which can be explained by nanoroughness. In other words, contact splitting
Zhang Yushan; Liang Jianwen; Hu Yuxian
2005-01-01
Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.
I. R. Mann
Full Text Available We present magnetospheric observations of very large amplitude global scale ULF waves, from 9 and 10 December 2000 when the upstream solar wind speed exceeded 600 km/s. We characterise these ULF waves using ground-based magnetometer, radar and optical instrumentation on both the dawn and dusk flanks; we find evidence to support the hypothesis that discrete frequency field line resonances (FLRs were being driven by magnetospheric waveguide modes. During the early part of this interval, Cluster was on an outbound pass from the northern dusk side magnetospheric lobe into the magnetosheath, local-time conjugate to the Canadian sector. In situ magnetic fluctuations, observed by Cluster FGM, show evidence of quasi-periodic motion of the magnetosheath boundary layer with the same period as the ULF waves seen on the ground. Our observations represent the first simultaneous magnetometer, radar and optical observations of the characteristics of FLRs, and confirm the potential importance of ULF waves for magnetosphere-ionosphere coupling, particularly via the generation and modulation of electron precipitation into the ionosphere. The in situ Cluster measurements support the hypothesis that, during intervals of fast solar wind speed, the Kelvin-Helmholtz instability (KHI can excite magnetospheric waveguide modes which bathe the flank magnetosphere with discrete frequency ULF wave power and drive large amplitude FLRs.
Paper submitted to the special issue devoted to "Cluster: First scientific results", Ann. Geophysicae, 19, 10/11/12, 2001.
Key words. Magnetospheric physics (magnetopause, cusp and boundary layers; MHD waves and instabilities; solar wind-magnetosphere interactions
Samadi, R; Dupret, M -A; Ludwig, H -G; Baudin, F; Caffau, E; Goupil, M -J; Barban, C
2012-01-01
A growing number of solar-like oscillations has been detected in red-giant stars thanks to CoRoT and Kepler space-crafts. The seismic data gathered by CoRoT on red-giant stars allow us to test mode driving theory in different physical conditions than main-sequence stars. Using a set of 3D hydrodynamical models representative of the upper layers of sub- and red-giant stars, we compute the acoustic modes energy supply rate (Pmax). Assuming adiabatic pulsations and using global stellar models where the surface stratification comes from the 3D hydrodynamical models, mode amplitude is computed in terms of surface velocity. The latter is then converted into intensity fluctuations using either a simplified adiabatic scaling relation or a non-adiabatic one. Given L and M (the luminosity and mass respectively), the energy supply rate Pmax is found to scale as (L/M)^(2.6) for both main-sequence and red-giant stars, extending previous results by Samadi et al. (2007). The theoretical amplitudes in velocity under-estimate...
Aerts, C; Baglin, A; Degroote, P; Oreiro, R; Vuckovic, M; Smolders, K; Acke, B; Verhoelst, T; Desmet, M; Godart, M; Noels, A; Dupret, M -A; Auvergne, M; Baudin, F; Catala, C; Michel, E; Samadi, R
2010-01-01
We aim to interpret the photometric and spectroscopic variability of the luminous blue variable supergiant HD\\,50064 ($V=8.21$).CoRoT space photometry and follow-up high-resolution spectroscopy, with a time base of 137\\,d and 169\\,d, respectively, was gathered, analysed and interpreted using standard time series analysis and light curve modelling methods as well as spectral line diagnostics.The space photometry reveals one period of 37\\,d, which undergoes a sudden amplitude change with a factor 1.6. The pulsation period is confirmed in the spectroscopy, which additionally reveals metal line radial velocity values differing by $\\sim 30\\,$km\\,s$^{-1}$ depending on the spectral line and on the epoch. We estimate \\teff$\\sim$13\\,500\\,K, \\logg$\\sim$1.5 from the equivalent width of Si lines. The Balmer lines reveal that the star undergoes episodes of changing mass loss on a time scale similar to the changes in the photometric and spectroscopic variability, with an average value of $\\log\\dot{\\rm M}\\simeq-5$ (in M$_\\o...
Dähne, Sven; Meinecke, Frank C; Haufe, Stefan; Höhne, Johannes; Tangermann, Michael; Müller, Klaus-Robert; Nikulin, Vadim V
2014-02-01
Previously, modulations in power of neuronal oscillations have been functionally linked to sensory, motor and cognitive operations. Such links are commonly established by relating the power modulations to specific target variables such as reaction times or task ratings. Consequently, the resulting spatio-spectral representation is subjected to neurophysiological interpretation. As an alternative, independent component analysis (ICA) or alternative decomposition methods can be applied and the power of the components may be related to the target variable. In this paper we show that these standard approaches are suboptimal as the first does not take into account the superposition of many sources due to volume conduction, while the second is unable to exploit available information about the target variable. To improve upon these approaches we introduce a novel (supervised) source separation framework called Source Power Comodulation (SPoC). SPoC makes use of the target variable in the decomposition process in order to give preference to components whose power comodulates with the target variable. We present two algorithms that implement the SPoC approach. Using simulations with a realistic head model, we show that the SPoC algorithms are able extract neuronal components exhibiting high correlation of power with the target variable. In this task, the SPoC algorithms outperform other commonly used techniques that are based on the sensor data or ICA approaches. Furthermore, using real electroencephalography (EEG) recordings during an auditory steady state paradigm, we demonstrate the utility of the SPoC algorithms by extracting neuronal components exhibiting high correlation of power with the intensity of the auditory input. Taking into account the results of the simulations and real EEG recordings, we conclude that SPoC represents an adequate approach for the optimal extraction of neuronal components showing coupling of power with continuously changing behaviorally
Thompson, L. G.; Yao, T.; Mosley-Thompson, E.; Wu, G.; Davis, M. E.; Tian, L.; Lin, P. N.
2015-12-01
The Guliya ice cap, located in the Kunlun Mountains in the western Third Pole (TP) region near the northern limit of the southwest monsoon influence, may be the only non-polar ice field that provides detailed histories of climate and environment over the last glacial cycle. A continuous climate record from an ice core drilled in 1992 contains Eemian ice, and basal temperatures measured that year confirmed that the record was not being removed from the bottom. The δ18O record throughout Marine Isotope Stage 2 (MIS2) displays the occurrence of high-amplitude (~20‰) episodes of ~200-year periodicity, and the aerosol records suggest snow cover, regional vegetation and fire frequency that vary in synchrony. These oscillations might reflect the movement of the northernmost penetration of the monsoon precipitation through the Late Glacial Stage, which is restricted by the topographic barrier posed by the Kunlun range, and might also reflect solar-driven nonlinearities in the climate system such as sudden shifts in the jet stream. Recent model simulations suggest that glacial cooling over China was significantly amplified by stationary waves, and the Guliya MIS2 oscillations could reflect cyclical variability in these waves. These results are supported by clumped isotope thermometry of carbonates from the Chinese Loess Plateau, which indicate a 6 to 7oC decrease in Last Glacial Maximum summer temperatures. These studies will lead to a better understanding of the mechanisms driving such high-frequency, high-amplitude oscillations. A review of the 2015 Sino-American cooperative ice core drilling program on Guliya is presented. This program will serve as a flagship for the TP Environment Program, an international, multidisciplinary collaboration among professionals and students in 14 countries designed to investigate environmental changes across the TP. The rapidly warming TP contains ~46,000 glaciers that collectively hold one of Earth's largest stores of fresh water that
Long, Nguyen H.; Mavropoulos, Phivos; Zimmermann, Bernd; Heers, Swantje; Bauer, David S. G.; Blügel, Stefan; Mokrousov, Yuriy
2013-06-01
Using first-principles methods based on density-functional theory, we investigate the spin relaxation in W(001) ultrathin films. Within the framework of the Elliott-Yafet theory, we calculate the spin mixing of the Bloch states and we explicitly consider spin-flip scattering off self-adatoms. At small film thicknesses, we find an oscillatory behavior of the spin-mixing parameter and relaxation rate as a function of the film thickness, which we trace back to surface-state properties. We also analyze the Rashba effect experienced by the surface states and discuss its influence on the spin relaxation. Finally, we calculate the anisotropy of the spin-relaxation rate with respect to the polarization direction of the excited spin population relative to the crystallographic axes of the film. We find that the spin-relaxation rate can increase by as much as 27% when the spin polarization is directed out of plane, compared to the case when it is in plane. Our calculations are based on the multiple-scattering formalism of the Korringa-Kohn-Rostoker Green-function method.
Large amplitude oscillatory elongation flow
Rasmussen, Henrik K.; Laillé, Philippe; Yu, Kaijia
2008-01-01
A filament stretching rheometer (FSR) was used for measuring the elongation flow with a large amplitude oscillative elongation imposed upon the flow. The large amplitude oscillation imposed upon the elongational flow as a function of the time t was defined as epsilon(t) =(epsilon) over dot(0)t + ...
Thermal self-oscillations in radiative heat exchange
Dyakov, S. A.; Dai, J.; Yan, M.; Qiu, M.
2015-02-01
We report the effect of relaxation-type self-induced temperature oscillations in the system of two parallel plates of SiO2 and VO2 which exchange heat by thermal radiation in vacuum. The non-linear feedback in the self-oscillating system is provided by metal-insulator transition in VO2. Using the method of fluctuational electrodynamics, we show that under the action of an external laser of a constant power, the temperature of VO2 plate oscillates around its phase transition value. The period and amplitude of oscillations depend on the geometry of the structure. We found that at 500 nm vacuum gap separating bulk SiO2 plate and 50 nm thick VO2 plate, the period of self-oscillations is 2 s and the amplitude is 4 K, which is determined by phase switching at threshold temperatures of phase transition.
Putti, M; Pallecchi, I; Bernini, C; Manfrinetti, P; Palenzona, A; Affronte, M
2004-01-01
We present thermal conductivity and specific heat measurements on MgB2 and Mg-AlB2 samples. Thermal properties have been analysed by using a two-gap model in order to estimate the gap amplitudes, D(0)p and D(0)s and the intra-band scattering rates, Gss and Gpp. As a function of Al doping and disorder D(0)s rapidly decreases, while D(0)p is rather constant. Gss and Gpp are increased by the disorder, being Gpp more affected than Gss.
Norris, G; McConnell, G
2010-03-01
A novel bi-directional pump geometry that nonlinearly increases the nonlinear optical conversion efficiency of a synchronously pumped optical parametric oscillator (OPO) is reported. This bi-directional pumping method synchronizes the circulating signal pulse with two counter-propagating pump pulses within a linear OPO resonator. Through this pump scheme, an increase in nonlinear optical conversion efficiency of 22% was achieved at the signal wavelength, corresponding to a 95% overall increase in average power. Given an almost unchanged measured pulse duration of 260 fs under optimal performance conditions, this related to a signal wavelength peak power output of 18.8 kW, compared with 10 kW using the traditional single-pass geometry. In this study, a total effective peak intensity pump-field of 7.11 GW/cm(2) (corresponding to 3.55 GW/cm(2) from each pump beam) was applied to a 3 mm long periodically poled lithium niobate crystal, which had a damage threshold intensity of 4 GW/cm(2), without impairing crystal integrity. We therefore prove the application of this novel pump geometry provides opportunities for power-scaling of synchronously pumped OPO systems together with enhanced nonlinear conversion efficiency through relaxed damage threshold intensity conditions.
A. Moberg
2014-06-01
Full Text Available Practical issues arise when applying a statistical framework for unbiased ranking of alternative forced climate model simulations by comparison with climate observations from instrumental and proxy data (Part 1 in this series. Given a set of model and observational data, several decisions need to be made; e.g. concerning the region that each proxy series represents, the weighting of different regions, and the time resolution to use in the analysis. Objective selection criteria cannot be made here, but we argue to study how sensitive the results are to the choices made. The framework is improved by the relaxation of two assumptions; to allow autocorrelation in the statistical model for simulated climate variability, and to enable direct comparison of alternative simulations to test if any of them fit the observations significantly better. The extended framework is applied to a set of simulations driven with forcings for the pre-industrial period 1000–1849 CE and fifteen tree-ring based temperature proxy series. Simulations run with only one external forcing (land-use, volcanic, small-amplitude solar, or large-amplitude solar, do not significantly capture the variability in the tree-ring data – although the simulation with volcanic forcing does so for some experiment settings. When all forcings are combined (using either the small- or large-amplitude solar forcing including also orbital, greenhouse-gas and non-volcanic aerosol forcing, and additionally used to produce small simulation ensembles starting from slightly different initial ocean conditions, the resulting simulations are highly capable of capturing some observed variability. Nevertheless, for some choices in the experiment design, they are not significantly closer to the observations than when unforced simulations are used, due to highly variable results between regions. It is also not possible to tell whether the small-amplitude or large-amplitude solar forcing causes the multiple
Study on mechanism of amplitude fluctuation of dual-frequency beat in microchip Nd:YAG laser
Chen, Hao; Tan, Yidong; Zhang, Shulian; Sun, Liqun
2017-01-01
In the laser heterodyne interferometry based on the microchip Nd:YAG dual-frequency laser, the amplitude of the beat note periodically fluctuates in time domain, which leads to the instability of the measurement. On the frequency spectrums of the two mono-frequency components of the laser and their beat note, several weak sideband signals are observed on both sides of the beat note. It is proved that the sideband frequencies are associated with the relaxation oscillation frequencies of the laser. The mechanism for the relaxation oscillations inducing the occurrence of the sideband signals is theoretically analyzed, and the quantitative relationship between the intensity ratio of the beat note to the sideband signal and the level of the amplitude fluctuation is simulated with the derived mathematical model. The results demonstrate that the periodical amplitude fluctuation of the beat note is actually induced by the relaxation oscillation. And the level of the amplitude fluctuation is lower than 10% when the intensity ratio is greater than 32 dB. These conclusions are beneficial to reduce the amplitude fluctuation of the microchip Nd:YAG dual-frequency laser and improve the stability of the heterodyne interferometry.
Protostring Scattering Amplitudes
Thorn, Charles B
2016-01-01
We calculate some tree level scattering amplitudes for a generalization of the protostring, which is a novel string model implied by the simplest string bit models. These bit models produce a lightcone worldsheet which supports $s$ integer moded Grassmann fields. In the generalization we supplement this Grassmann worldsheet system with $d=24-s$ transverse coordinate worldsheet fields. The protostring corresponds to $s=24$ and the bosonic string to $s=0$. The interaction vertex is a simple overlap with no operator insertions at the break/join point. Assuming that $s$ is even we calculate the multi-string scattering amplitudes by bosonizing the Grassmann fields, each pair equivalent to one compactified bosonic field, and applying Mandelstam's interacting string formalism to a system of $s/2$ compactified and $d$ uncompactified bosonic worldsheet fields. We obtain all amplitudes for open strings with no oscillator excitations and for closed strings with no oscillator excitations and zero winding number. We then ...
Protostring scattering amplitudes
Thorn, Charles B.
2016-11-01
We calculate some tree-level scattering amplitudes for a generalization of the protostring, which is a novel string model implied by the simplest string bit models. These bit models produce a light-cone world sheet which supports s integer moded Grassmann fields. In the generalization we supplement this Grassmann world-sheet system with d =24 -s transverse coordinate world-sheet fields. The protostring corresponds to s =24 and the bosonic string to s =0 . The interaction vertex is a simple overlap with no operator insertions at the break/join point. Assuming that s is even we calculate the multistring scattering amplitudes by bosonizing the Grassmann fields, each pair equivalent to one compactified bosonic field, and applying Mandelstam's interacting string formalism to a system of s /2 compactified and d uncompactified bosonic world-sheet fields. We obtain all amplitudes for open strings with no oscillator excitations and for closed strings with no oscillator excitations and zero winding number. We then study in detail some simple special cases. Multistring processes with maximal helicity violation have much simpler amplitudes. We also specialize to general four-string amplitudes and discuss their high energy behavior. Most of these models are not covariant under the full Lorentz group O (d +1 ,1 ). The exceptions are the bosonic string whose Lorentz group is O (25 ,1 ) and the protostring whose Lorentz group is O (1 ,1 ). The models in between only enjoy an O (1 ,1 )×O (d ) spacetime symmetry.
Perturbations and quantum relaxation
Kandhadai, Adithya
2016-01-01
We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding space. We assume an initial wave function with small perturbations to the ground state. We present evidence that the trajectories are highly confined so as to preclude relaxation to equilibrium even over very long timescales. Cosmological implications are briefly discussed.
Latyshev, A V
2016-01-01
In the present work the second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane limiting half-space makes harmonious fluctuations with variable amplitude in the plane. The amplitude changes on the exponential law. The kinetic equation with model integral of collisions in the form $\\tau$-model is used. The case of diffusion reflexions of gas molecules from a wall is considered. Eigen solutions (continuous modes) of the initial kinetic equation corresponding to the continuous spectrum are searched. Properties of dispersion function are studied. It is investigated the discrete spectrum of the problem consisting of zero of the dispersion functions in the complex plane. It is shown, that number of zero of dispersion function to equally doubled index of problem coefficient. The problem coefficient is understood as the relation of boundary values of dispersion function from above and from below on the real axis. Further are eigen solutions (discrete modes) of the initial k...
Germanà, C.; Casana, R.
2015-04-01
The twin-peak high-frequency quasiperiodic oscillations (HFQPOs), observed in the power spectra of low-mass x-ray binaries, might carry relevant clues about the physics laws reigning close to a compact object. Their frequencies are typical of the orbital motion time scales a few gravitational radii away from the compact object. The aim of the manuscript is to propose an intuitive model explaining that the energy carried by the lower high-frequency quasiperiodic oscillation can be related to differences of potential energy released by clumps of plasma spiraling in a curved space-time. Our model provides estimates on both the size of clumps of matter that can survive to the strong tidal force and energy loaded by tides on the clump. We also have obtained some constrains on the mechanical properties of the plasma orbiting into the accretion disk. We note that the systematic behavior of the emitted energy as a function of the central frequency of the lower HFQPO, observed in several sources with a neutron star, might give clues related to an innermost stable bound orbit predicted by the general relativity theory in strong field regime.
Relaxation of liquid bridge after droplets coalescence
Jiangen Zheng
2016-11-01
Full Text Available We investigate the relaxation of liquid bridge after the coalescence of two sessile droplets resting on an organic glass substrate both experimentally and theoretically. The liquid bridge is found to relax to its equilibrium shape via two distinct approaches: damped oscillation relaxation and underdamped relaxation. When the viscosity is low, damped oscillation shows up, in this approach, the liquid bridge undergoes a damped oscillation process until it reaches its stable shape. However, if the viscous effects become significant, underdamped relaxation occurs. In this case, the liquid bridge relaxes to its equilibrium state in a non-periodic decay mode. In depth analysis indicates that the damping rate and oscillation period of damped oscillation are related to an inertial-capillary time scale τc. These experimental results are also testified by our numerical simulations with COMSOL Multiphysics.
Jonker, P G; Méndez, M; Van der Klis, M
2007-01-01
We have observed the ultra-compact low-mass X-ray binary (LMXB) 1A 1246-588 with the Rossi X-ray Timing Explorer (RXTE). In this manuscript we report the discovery of a kilohertz quasi-periodic oscillation (QPO) in 1A 1246-588. The kilohertz QPO was only detected when the source was in a soft high-flux state reminiscent of the lower banana branch in atoll sources. Only one kilohertz QPO peak is detected at a relatively high frequency of 1258+-2 Hz and at a single trial significance of more than 7 sigma. Kilohertz QPOs with a higher frequency have only been found on two occasions in 4U 0614+09. Furthermore, the frequency is higher than that found for the lower kilohertz QPO in any source, strongly suggesting that the QPO is the upper of the kilohertz QPO pair often found in LMXBs. The full-width at half maximum is 25+-4 Hz, making the coherence the highest found for an upper kilohertz QPO. From a distance estimate of ~6 kpc from a radius expansion burst we derive that 1A 1246-588 is at a persistent flux of ~0....
High Amplitude Secondary Mass Drive
DYCK,CHRISTOPHER WILLIAM; ALLEN,JAMES J.; HUBER,ROBERT JOHN; SNIEGOWSKI,JEFFRY J.
2000-07-06
In this paper we describe a high amplitude electrostatic drive for surface micromachined mechanical oscillators that may be suitable for vibratory gyroscopes. It is an advanced design of a previously reported dual mass oscillator (Dyck, et. al., 1999). The structure is a 2 degree-of-freedom, parallel-plate driven motion amplifier, termed the secondary mass drive oscillator (SMD oscillator). During each cycle the device contacts the drive plates, generating large electrostatic forces. Peak-to-peak amplitudes of 54 {micro}m have been obtained by operating the structure in air with an applied voltage of 11 V. We describe the structure, present the analysis and design equations, and show recent results that have been obtained, including frequency response data, power dissipation, and out-of- plane motion.
Rivolta, Davide; Heidegger, Tonio; Scheller, Bertram; Sauer, Andreas; Schaum, Michael; Birkner, Katharina; Singer, Wolf; Wibral, Michael; Uhlhaas, Peter J
2015-09-01
Hypofunctioning of the N-methyl-D-aspartate receptor (NMDA-R) has been prominently implicated in the pathophysiology of schizophrenia (ScZ). The current study tested the effects of ketamine, a dissociative anesthetic and NMDA-R antagonist, on resting-state activity recorded with magnetoencephalography (MEG) in healthy volunteers. In a single-blind cross-over design, each participant (n = 12) received, on 2 different sessions, a subanesthetic dose of S-ketamine (0.006 mg/Kg) and saline injection. MEG-data were analyzed at sensor- and source-level in the beta (13-30 Hz) and gamma (30-90 Hz) frequency ranges. In addition, connectivity analysis at source-level was performed using transfer entropy (TE). Ketamine increased gamma-power while beta-band activity was decreased. Specifically, elevated 30-90 Hz activity was pronounced in subcortical (thalamus and hippocampus) and cortical (frontal and temporal cortex) regions, whilst reductions in beta-band power were localized to the precuneus, cerebellum, anterior cingulate, temporal and visual cortex. TE analysis demonstrated increased information transfer in a thalamo-cortical network after ketamine administration. The findings are consistent with the pronounced dysregulation of high-frequency oscillations following the inhibition of NMDA-R in animal models of ScZ as well as with evidence from electroencephalogram-data in ScZ-patients and increased functional connectivity during early illness stages. Moreover, our data highlight the potential contribution of thalamo-cortical connectivity patterns towards ketamine-induced neuronal dysregulation, which may be relevant for the understanding of ScZ as a disorder of disinhibition of neural circuits.
Rivolta, Davide; Heidegger, Tonio; Scheller, Bertram; Sauer, Andreas; Schaum, Michael; Birkner, Katharina; Singer, Wolf; Wibral, Michael; Uhlhaas, Peter J.
2015-01-01
Hypofunctioning of the N-methyl-D-aspartate receptor (NMDA-R) has been prominently implicated in the pathophysiology of schizophrenia (ScZ). The current study tested the effects of ketamine, a dissociative anesthetic and NMDA-R antagonist, on resting-state activity recorded with magnetoencephalography (MEG) in healthy volunteers. In a single-blind cross-over design, each participant (n = 12) received, on 2 different sessions, a subanesthetic dose of S-ketamine (0.006mg/Kg) and saline injection. MEG-data were analyzed at sensor- and source-level in the beta (13–30 Hz) and gamma (30–90 Hz) frequency ranges. In addition, connectivity analysis at source-level was performed using transfer entropy (TE). Ketamine increased gamma-power while beta-band activity was decreased. Specifically, elevated 30–90 Hz activity was pronounced in subcortical (thalamus and hippocampus) and cortical (frontal and temporal cortex) regions, whilst reductions in beta-band power were localized to the precuneus, cerebellum, anterior cingulate, temporal and visual cortex. TE analysis demonstrated increased information transfer in a thalamo-cortical network after ketamine administration. The findings are consistent with the pronounced dysregulation of high-frequency oscillations following the inhibition of NMDA-R in animal models of ScZ as well as with evidence from electroencephalogram-data in ScZ-patients and increased functional connectivity during early illness stages. Moreover, our data highlight the potential contribution of thalamo-cortical connectivity patterns towards ketamine-induced neuronal dysregulation, which may be relevant for the understanding of ScZ as a disorder of disinhibition of neural circuits. PMID:25987642
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.
Millennial-scale stable oscillations between sea ice and convective deep water formation
Saha, Raj
2015-01-01
During the last ice age there were several quasi-periodic abrupt warming events. The climatic effects of the so-called Dansgaard-Oeschger (DO) events were felt globally, although the North Atlantic experienced the largest and most abrupt temperature anomalies. Similar but weaker oscillations also took place during the interglacial period. This paper proposes an auto-oscillatory mechanism between sea ice and convective deep water formation in the north Atlantic as the source of the persistent cycles. A simple dynamical model is constructed by coupling and slightly modifying two existing models of ocean circulation and sea ice. The model exhibits mixed mode oscillations, consisting of decadal scale small amplitude oscillations, and a large amplitude relaxation fluctuation. The decadal oscillations occur due to the insulating effect of sea ice and leads to periodic ventilation of heat from the polar ocean. Gradually an instability builds up in the polar column and results in an abrupt initiation of convection an...
Xiao-Fei Hu
2015-01-01
Full Text Available Background: Neuroimaging studies have found that functional changes exist in patients with Parkinson′s disease (PD. However, the majority of functional magnetic resonance imaging (fMRI studies in patients with PD are task-related and cross-sectional. This study investigated the functional changes observed in patients with PD, at both baseline and after 2 years, using resting-state fMRI. It further investigated the relationship between whole-brain spontaneous neural activity of patients with PD and their clinical characteristics. Methods: Seventeen patients with PD underwent an MRI procedure at both baseline and after 2 years using resting-state fMRI that was derived from the same 3T MRI. In addition, 20 age- and sex-matched, healthy controls were examined using resting-state fMRI. The fractional amplitude of low-frequency fluctuation (fALFF approach was used to analyze the fMRI data. Nonlinear registration was used to model within-subject changes over the scanning interval, as well as changes between the patients with PD and the healthy controls. A correlative analysis between the fALFF values and clinical characteristics was performed in the regions showing fALFF differences. Results: Compared to the control subjects, the patients with PD showed increased fALFF values in the left inferior temporal gyrus, right inferior parietal lobule (IPL and right middle frontal gyrus. Compared to the baseline in the 2 years follow-up, the patients with PD presented with increased fALFF values in the right middle temporal gyrus and right middle occipital gyrus while also having decreased fALFF values in the right cerebellum, right thalamus, right striatum, left superior parietal lobule, left IPL, left precentral gyrus, and left postcentral gyrus (P < 0.01, after correction with AlphaSim. In addition, the fALFF values in the right cerebellum were positively correlated with the Unified PD Rating Scale (UPDRS motor scores (r = 0.51, P < 0.05, uncorrected and
Linearization of conservative nonlinear oscillators
Belendez, A; Alvarez, M L [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E; Pascual, I [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-03-11
A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for the complete range of oscillation amplitudes. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of the technique.
João Gomes Netinho
2005-03-01
Full Text Available BACKGROUND: The rectoanal inhibitory reflex has an important rule in the fecal continence mechanism. Alterations in this reflex can be associated with compromised anal sphincteric function. AIM: To identify possible correlation between rectoanal inhibitory reflex parameters and intestinal constipation due to obstructive evacuation. PATIENTS: Sixty nine patients with intestinal constipation had been submitted to anorectal manometry. It was selected 29 patients (27 female, mean age of 42.3 (19-73 years having intestinal constipation owing to obstructive evacuation. Thirteen individuals without anorectal functional complaints (eight female, mean age 52.5 (28-73 years formed the control group. RESULTS: The mean value of resting anal pressure before rectoanal inhibitory reflex in the proximal and distal anal canals were 61.8 mm Hg and 81.7 mm Hg respectively, for the constipated patients, and 46.0 mm Hg and 64.5 mm Hg, respectively, for asymptomatic individuals. The mean pressure at the point of maximal relaxation in constipated patients was 29.0 mm Hg in the proximal anal canal, and 52.1 mm Hg in the distal anal canal, whilst in the asymptomatic group they were 17.8 mm Hg and 36.3 mm Hg, respectively. The mean percentage difference between the mean resting anal pressure and the mean point of maximal relaxation pressure in the proximal anal canal (amplitude of relaxation was 54.1% in constipated patients and 54.3% in asymptomatic individuals. In the distal anal canal it was, respectively, 35.6% in constipated patients, and 38.5% in the control group. The average recovery velocity of relaxation in the proximal anal canal was 4.06 mm/second in constipated patients and 2.98 mm/second in asymptomatic individuals, giving a significant difference between the two groups, as well as in the distal anal canal (3.9 mm/second and 2.98 mm/second, respectively CONCLUSION: The greater recovery velocity of the resting anal pressure in the proximal anal canal in
Wessendorf, K.O.
1998-07-01
This paper describes the Active-Bridge Oscillator (ABO), a new concept in high-stability oscillator design. The ABO is ab ridge-type oscillator design that is easly to design and overcomes many of the operational and design difficulties associated with standard bridge oscillator designs. The ABO will oscillate with a very stable output amplitude over a wide range of operating conditions without the use of an automatic-level-control (ALC). A standard bridge oscillator design requires an ALC to maintain the desired amplitude of oscillation. for this and other reasons, bridge oscilaltors are not used in mainstream designs. Bridge oscillators are generally relegated to relatively low-volume, high-performance applications. The Colpitts and Pierce designs are the most popular oscillators but are typically less stable than a bridge-type oscillator.
Numerical modeling of bubble dynamics in viscoelastic media with relaxation
Warnez, M. T.; Johnsen, E.
2015-06-01
Cavitation occurs in a variety of non-Newtonian fluids and viscoelastic materials. The large-amplitude volumetric oscillations of cavitation bubbles give rise to high temperatures and pressures at collapse, as well as induce large and rapid deformation of the surroundings. In this work, we develop a comprehensive numerical framework for spherical bubble dynamics in isotropic media obeying a wide range of viscoelastic constitutive relationships. Our numerical approach solves the compressible Keller-Miksis equation with full thermal effects (inside and outside the bubble) when coupled to a highly generalized constitutive relationship (which allows Newtonian, Kelvin-Voigt, Zener, linear Maxwell, upper-convected Maxwell, Jeffreys, Oldroyd-B, Giesekus, and Phan-Thien-Tanner models). For the latter two models, partial differential equations (PDEs) must be solved in the surrounding medium; for the remaining models, we show that the PDEs can be reduced to ordinary differential equations. To solve the general constitutive PDEs, we present a Chebyshev spectral collocation method, which is robust even for violent collapse. Combining this numerical approach with theoretical analysis, we simulate bubble dynamics in various viscoelastic media to determine the impact of relaxation time, a constitutive parameter, on the associated physics. Relaxation time is found to increase bubble growth and permit rebounds driven purely by residual stresses in the surroundings. Different regimes of oscillations occur depending on the relaxation time.
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.
Capture into resonance of coupled Duffing oscillators.
Kovaleva, Agnessa
2015-08-01
In this paper we investigate capture into resonance of a pair of coupled Duffing oscillators, one of which is excited by periodic forcing with a slowly varying frequency. Previous studies have shown that, under certain conditions, a single oscillator can be captured into persistent resonance with a permanently growing amplitude of oscillations (autoresonance). This paper demonstrates that the emergence of autoresonance in the forced oscillator may be insufficient to generate oscillations with increasing amplitude in the attachment. A parametric domain, in which both oscillators can be captured into resonance, is determined. The quasisteady states determining the growth of amplitudes are found. An agreement between the theoretical and numerical results is demonstrated.
Millennial-scale oscillations between sea ice and convective deep water formation
Saha, Raj
2015-11-01
During the last ice age there were several quasiperiodic abrupt warming events. The climatic effects of the so-called Dansgaard-Oeschger (D-O) events were felt globally, although the North Atlantic experienced the largest and most abrupt temperature anomalies. Similar but weaker oscillations also took place during the interglacial period. This paper proposes an auto-oscillatory mechanism between sea ice and convective deep water formation in the North Atlantic as the source of the persistent cycles. A simple dynamical model is constructed by coupling and slightly modifying two existing models of ocean circulation and sea ice. The model exhibits mixed mode oscillations, consisting of decadal-scale small-amplitude oscillations and a large-amplitude relaxation fluctuation. The decadal oscillations occur due to the insulating effect of sea ice and leads to periodic ventilation of heat from the polar ocean. Gradually, an instability builds up in the polar column and results in an abrupt initiation of convection and polar warming. The unstable convective state relaxes back to the small-amplitude oscillations from where the process repeats in a self-sustained manner. Freshwater pulses mimicking Heinrich events cause the oscillations to be grouped into packets of progressively weaker fluctuations, as observed in proxy records. Modulation of this stable oscillation mechanism by freshwater and insolation variations could account for the distribution and pacing of D-O and Bond events. Physical aspects of the system such as sea ice extent and oceanic advective flow rates could determine the characteristic 1500 year time scale of D-O events. The model results with respect to the structure of the water column in the Nordic seas during stadial and interstadial phases are in agreement with paleoproxy observations.
Finite-amplitude shear-Alfv\\'en waves do not propagate in weakly magnetized collisionless plasmas
Squire, J; Schekochihin, A A
2016-01-01
It is shown that low-collisionality plasmas cannot support linearly polarized shear-Alfv\\'en fluctuations above a critical amplitude $\\delta B_{\\perp}/B_{0} \\sim \\beta^{\\,-1/2}$, where $\\beta$ is the ratio of thermal to magnetic pressure. Above this cutoff, a developing fluctuation will generate a pressure anisotropy that is sufficient to destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, interrupting the fluctuation before any oscillation. The magnetic field lines rapidly relax into a sequence of angular zig-zag structures. Such a restrictive bound on shear-Alfv\\'en-wave amplitudes has far-reaching implications for the physics of magnetized turbulence in the high-$\\beta$ conditions prevalent in many astrophysical plasmas, as well as for the solar wind at $\\sim 1 \\mathrm{AU}$ where $\\beta \\gtrsim 1$.
Mechanical models of amplitude and frequency modulation
Bellomonte, L; Guastella, I; Sperandeo-Mineo, R M [GRIAF - Research Group on Teaching/Learning Physics, DI.F.TE.R. -Dipartimento di Fisica e Tecnologie Relative, University of Palermo, Viale delle Scienze, Edificio 18, 90128 Palermo (Italy)
2005-05-01
This paper presents some mechanical models for amplitude and frequency modulation. The equations governing both modulations are deduced alongside some necessary approximations. Computer simulations of the models are carried out by using available educational software. Amplitude modulation is achieved by using a system of two weakly coupled pendulums, whereas the frequency modulation is obtained by using a pendulum of variable length. Under suitable conditions (small oscillations, appropriate initial conditions, etc) both types of modulation result in significantly accurate and visualized simulations.
PULSE AMPLITUDE DISTRIBUTION RECORDER
Cowper, G.
1958-08-12
A device is described for automatica1ly recording pulse annplitude distribution received from a counter. The novelty of the device consists of the over-all arrangement of conventional circuit elements to provide an easy to read permanent record of the pulse amplitude distribution during a certain time period. In the device a pulse analyzer separates the pulses according to annplitude into several channels. A scaler in each channel counts the pulses and operates a pen marker positioned over a drivable recorder sheet. Since the scalers in each channel have the sanne capacity, the control circuitry permits counting of the incoming pulses until one scaler reaches capacity, whereupon the input is removed and an internal oscillator supplies the necessary pulses to fill up the other scalers. Movement of the chart sheet is initiated wben the first scaler reaches capacity to thereby give a series of marks at spacings proportional to the time required to fill the remaining scalers, and accessory equipment marks calibration points on the recorder sheet to facilitate direct reading of the number of external pulses supplied to each scaler.
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.
Grinevich, Andrey A.; Tankanag, Arina V.; Chemeris, Nikolay K.
2017-04-01
In the framework of our previous hypothesis about the participation of structural and hydrodynamic properties of the vascular bed in the formation of the 0.1-Hz component of blood flow oscillations in the human cardiovascular system and on the basis of the reduced hydrodynamic model, the role of additive stochastic perturbations of the operation of the single-chamber pump that simulates the heart was investigated. It was shown that aperiodic noise modulation of the rigidity of the walls of the pump or its valves generates low-frequency oscillations of pressure of arterial vascular bed with the spectral components at a frequency close to 0.1 Hz.
Starosvetsky, Y; Manevitch, L I
2011-04-01
An analytical investigation of nonstationary processes in a Duffing oscillator subject to biharmonic forcing, under conditions of primary resonance, is carried out. The earlier developed methodology of limiting phase trajectories (LPTs) for studying highly nonstationary regimes, characterized by intense energy exchanges between the different degrees of freedom, is successfully applied to the system under investigation. Two distinct types of LPT trajectories are described in the first part of the study. Conditions for the recurrent transitions in time from one type of LPT to another were derived in the first part of the analysis corresponding to the undamped case. An approximation of the LPT related to the higher amplitude of oscillations was derived using nonsmooth transformations. An analysis carried out in the study has revealed the necessary and sufficient conditions for excitation of relaxation oscillations exhibited by a lightly damped system. It was also demonstrated that the mechanism of relaxations may be approximated and explained by the methodology of LPTs, characterized by strong energy exchanges between the coupled oscillators or, alternatively, a single oscillator and an external source of energy. The results of analytical approximations and numerical simulations are observed to be in quite satisfactory agreement.
Amplitude metrics for cellular circadian bioluminescence reporters.
St John, Peter C; Taylor, Stephanie R; Abel, John H; Doyle, Francis J
2014-12-01
Bioluminescence rhythms from cellular reporters have become the most common method used to quantify oscillations in circadian gene expression. These experimental systems can reveal phase and amplitude change resulting from circadian disturbances, and can be used in conjunction with mathematical models to lend further insight into the mechanistic basis of clock amplitude regulation. However, bioluminescence experiments track the mean output from thousands of noisy, uncoupled oscillators, obscuring the direct effect of a given stimulus on the genetic regulatory network. In many cases, it is unclear whether changes in amplitude are due to individual changes in gene expression level or to a change in coherence of the population. Although such systems can be modeled using explicit stochastic simulations, these models are computationally cumbersome and limit analytical insight into the mechanisms of amplitude change. We therefore develop theoretical and computational tools to approximate the mean expression level in large populations of noninteracting oscillators, and further define computationally efficient amplitude response calculations to describe phase-dependent amplitude change. At the single-cell level, a mechanistic nonlinear ordinary differential equation model is used to calculate the transient response of each cell to a perturbation, whereas population-level dynamics are captured by coupling this detailed model to a phase density function. Our analysis reveals that amplitude changes mediated at either the individual-cell or the population level can be distinguished in tissue-level bioluminescence data without the need for single-cell measurements. We demonstrate the effectiveness of the method by modeling experimental bioluminescence profiles of light-sensitive fibroblasts, reconciling the conclusions of two seemingly contradictory studies. This modeling framework allows a direct comparison between in vitro bioluminescence experiments and in silico ordinary
Finite amplitude effects on drop levitation for material properties measurement
Ansari Hosseinzadeh, Vahideh; Holt, R. Glynn
2017-05-01
The method of exciting shape oscillation of drops to extract material properties has a long history, which is most often coupled with the technique of acoustic levitation to achieve non-contact manipulation of the drop sample. We revisit this method with application to the inference of bulk shear viscosity and surface tension. The literature is replete with references to a "10% oscillation amplitude" as a sufficient condition for the application of Lamb's analytical expressions for the shape oscillations of viscous liquids. Our results show that even a 10% oscillation amplitude leads to dynamic effects which render Lamb's results inapplicable. By comparison with samples of known viscosity and surface tension, we illustrate the complicating finite-amplitude effects (mode-splitting and excess dissipation associated with vorticity) that can occur and then show that sufficiently small oscillations allow us to recover the correct material properties using Lamb's formula.
On the excitation of Goodwin's oscillations
Antonova, A. O.; Reznik, S. N.; Todorov, M. D.
2014-11-01
We consider the necessary condition for excitation of long-periodic Goodwin's oscillations and short-periodic sawtooth oscillations in the Goodwin model with fixed delay in the induced investment. Also, using the method of equivalent linearization we evaluate the amplitude of steady-state oscillation.
Amplitude Modulations of Acoustic Communication Signals
Turesson, Hjalmar K.
2011-12-01
In human speech, amplitude modulations at 3 -- 8 Hz are important for discrimination and detection. Two different neurophysiological theories have been proposed to explain this effect. The first theory proposes that, as a consequence of neocortical synaptic dynamics, signals that are amplitude modulated at 3 -- 8 Hz are propagated better than un-modulated signals, or signals modulated above 8 Hz. This suggests that neural activity elicited by vocalizations modulated at 3 -- 8 Hz is optimally transmitted, and the vocalizations better discriminated and detected. The second theory proposes that 3 -- 8 Hz amplitude modulations interact with spontaneous neocortical oscillations. Specifically, vocalizations modulated at 3 -- 8 Hz entrain local populations of neurons, which in turn, modulate the amplitude of high frequency gamma oscillations. This suggests that vocalizations modulated at 3 -- 8 Hz should induce stronger cross-frequency coupling. Similar to human speech, we found that macaque monkey vocalizations also are amplitude modulated between 3 and 8 Hz. Humans and macaque monkeys share similarities in vocal production, implying that the auditory systems subserving perception of acoustic communication signals also share similarities. Based on the similarities between human speech and macaque monkey vocalizations, we addressed how amplitude modulated vocalizations are processed in the auditory cortex of macaque monkeys, and what behavioral relevance modulations may have. Recording single neuron activity, as well as, the activity of local populations of neurons allowed us to test both of the neurophysiological theories presented above. We found that single neuron responses to vocalizations amplitude modulated at 3 -- 8 Hz resulted in better stimulus discrimination than vocalizations lacking 3 -- 8 Hz modulations, and that the effect most likely was mediated by synaptic dynamics. In contrast, we failed to find support for the oscillation-based model proposing a
Marzola, Luca; Raidal, Martti
2016-11-01
Motivated by natural inflation, we propose a relaxation mechanism consistent with inflationary cosmology that explains the hierarchy between the electroweak scale and Planck scale. This scenario is based on a selection mechanism that identifies the low-scale dynamics as the one that is screened from UV physics. The scenario also predicts the near-criticality and metastability of the Standard Model (SM) vacuum state, explaining the Higgs boson mass observed at the Large Hadron Collider (LHC). Once Majorana right-handed neutrinos are introduced to provide a viable reheating channel, our framework yields a corresponding mass scale that allows for the seesaw mechanism as well as for standard thermal leptogenesis. We argue that considering singlet scalar dark matter extensions of the proposed scenario could solve the vacuum stability problem and discuss how the cosmological constant problem is possibly addressed.
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.
Grueneisen relaxation photoacoustic microscopy
Wang, Lidai; Zhang, Chi; Wang, Lihong V.
2014-01-01
The temperature-dependent property of the Grueneisen parameter has been employed in photoacoustic imaging mainly to measure tissue temperature. Here we explore this property using a different approach and develop Grueneisen-relaxation photoacoustic microscopy (GR-PAM), a technique that images non-radiative absorption with confocal optical resolution. GR-PAM sequentially delivers two identical laser pulses with a micro-second-scale time delay. The first laser pulse generates a photoacoustic signal and thermally tags the in-focus absorbers. Owing to the temperature dependence of the Grueneisen parameter, when the second laser pulse excites the tagged absorbers within the thermal relaxation time, a photoacoustic signal stronger than the first one is produced. GR-PAM detects the amplitude difference between the two co-located photoacoustic signals, confocally imaging the non-radiative absorption. We greatly improved axial resolution from 45 µm to 2.3 µm and at the same time slightly improved lateral resolution from 0.63 µm to 0.41 µm. In addition, the optical sectioning capability facilitates the measurement of the absolute absorption coefficient without fluence calibration. PMID:25379919
Possible damping model of the 6 year oscillation signal in length of day
Duan, Pengshuo; Liu, Genyou; Hu, Xiaogang; Sun, Yafei; Li, Honglei
2017-04-01
A significant 6 year oscillation signal exists in the observed length-of-day (LOD) series. We recently used normal Morlet wavelet transform method to recover this oscillation signal. The result indicates that the amplitude of this oscillation has been decreasing for the over past 50 years. Using the simulation analysis, this study further demonstrates that the above result is reliable. However, the geophysical mechanism responsible for this decrease is less clear. Here, we develop a temporal-decaying function to characterize the secular attenuation of the oscillation signal. Using the least squared method, we obtain the corresponding quality factor Q value (51.6 ± 0.4) and the damping relaxation time τ (99.2 ± 0.8 years). We find the attenuation of the 6 year oscillation signal and its Q value can be explained by previous theoretical prediction, providing constraints on the related physical parameters of the lowermost mantle. The dissipative effect of electromagnetic coupling at the core-mantle boundary is likely to be a primary factor to cause the decaying of the 6 year oscillation signal.
Holographic Relaxation of Finite Size Isolated Quantum Systems
Abajo-Arrastia, Javier; Lopez, Esperanza; Mas, Javier; Serantes, Alexandre
2014-01-01
We study holographically the out of equilibrium dynamics of a finite size closed quantum system in 2+1 dimensions, modelled by the collapse of a shell of a massless scalar field in AdS4. In global coordinates there exists a variety of evolutions towards final black hole formation which we relate with different patterns of relaxation in the dual field theory. For large scalar initial data rapid thermalization is achieved as a priori expected. Interesting phenomena appear for small enough amplitudes. Such shells do not generate a black hole by direct collapse, but quite generically an apparent horizon emerges after enough bounces off the AdS boundary. We relate this bulk evolution with relaxation processes at strong coupling which delay in reaching an ergodic stage. Besides the dynamics of bulk fields, we monitor the entanglement entropy, finding that it oscillates quasi-periodically before final equilibration. The radial position of the traveling shell is brought into correspondence with the evolution of the e...
The effect of phase stabilization of microwave oscillations in nanosecond Gunn oscillators
Konev, V. Yu.; Klimov, A. I.; Koval'chuk, O. B.; Gubanov, V. P.; Kozhevnikov, V. Yu.; Kozyrev, A. V.; Torkhov, N. A.
2013-11-01
The effect of the semiconductor structure of an oscillator diode on the phase stabilization of microwave oscillations in a nanosecond Gunn oscillator by using a modulating voltage pulse edge is investigated. Numerical simulation is employed to determine phase deviations depending on the scatter of pulseedge duration and pulse amplitude. The standard deviation of phase-delay time of microwave oscillations in the oscillator with regard to a constant level at the modulating pulse edge and the standard deviation of phase difference of microwave oscillations in two electrodynamically insulated oscillators connected in parallel to one and the same modulator have been measured.
Control of Transport-barrier relaxations by Resonant Magnetic Perturbations
Leconte, M; Garbet, X; Benkadda, S
2009-01-01
Transport-barrier relaxation oscillations in the presence of resonant magnetic perturbations are investigated using three-dimensional global fluid turbulence simulations from first principles at the edge of a tokamak. It is shown that resonant magnetic perturbations have a stabilizing effect on these relaxation oscillations and that this effect is due mainly to a modification of the pressure profile linked to the presence of both residual residual magnetic island chains and a stochastic layer.
Amplitudes, acquisition and imaging
Bloor, Robert
1998-12-31
Accurate seismic amplitude information is important for the successful evaluation of many prospects and the importance of such amplitude information is increasing with the advent of time lapse seismic techniques. It is now widely accepted that the proper treatment of amplitudes requires seismic imaging in the form of either time or depth migration. A key factor in seismic imaging is the spatial sampling of the data and its relationship to the imaging algorithms. This presentation demonstrates that acquisition caused spatial sampling irregularity can affect the seismic imaging and perturb amplitudes. Equalization helps to balance the amplitudes, and the dealing strategy improves the imaging further when there are azimuth variations. Equalization and dealiasing can also help with the acquisition irregularities caused by shot and receiver dislocation or missing traces. 2 refs., 2 figs.
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.
Photoacoustic elastic oscillation and characterization.
Gao, Fei; Feng, Xiaohua; Zheng, Yuanjin
2015-08-10
Photoacoustic imaging and sensing have been studied extensively to probe the optical absorption of biological tissue in multiple scales ranging from large organs to small molecules. However, its elastic oscillation characterization is rarely studied and has been an untapped area to be explored. In literature, photoacoustic signal induced by pulsed laser is commonly modelled as a bipolar "N-shape" pulse from an optical absorber. In this paper, the photoacoustic damped oscillation is predicted and modelled by an equivalent mass-spring system by treating the optical absorber as an elastic oscillator. The photoacoustic simulation incorporating the proposed oscillation model shows better agreement with the measured signal from an elastic phantom, than conventional photoacoustic simulation model. More interestingly, the photoacoustic damping oscillation effect could potentially be a useful characterization approach to evaluate biological tissue's mechanical properties in terms of relaxation time, peak number and ratio beyond optical absorption only, which is experimentally demonstrated in this paper.
Photoacoustic elastic oscillation and characterization
Gao, Fei; Zheng, Yuanjin
2014-01-01
Photoacoustic imaging and sensing have been studied extensively to probe the optical absorption of biological tissue in multiple scales ranging from large organs to small molecules. However, its elastic oscillation characterization is rarely studied and has been an untapped area to be explored. In literature, photoacoustic signal induced by pulsed laser is commonly modelled as a bipolar "N-shape" pulse from an optical absorber. In this paper, the photoacoustic damped oscillation is predicted and modelled by an equivalent mass-spring system by treating the optical absorber as an elastic oscillator. The photoacoustic simulation incorporating the proposed oscillation model shows better agreement with the measured signal from an elastic phantom, than conventional photoacoustic simulation model. More interestingly, the photoacoustic damping oscillation effect could potentially be a useful characterization approach to evaluate biological tissue's mechanical properties in terms of relaxation time, peak number and ra...
Collisionless Relaxation of Stellar Systems
Kandrup, H E
1998-01-01
The objective of the work summarised here has been to exploit and extend ideas from plasma physics and accelerator dynamics to formulate a unified description of collisionless relaxation that views violent relaxation, Landau damping, and phase mixing as (manifestations of) a single phenomenon. This approach embraces the fact that the collisionless Boltzmann equation (CBE), the basic object of the theory, is an infinite-dimensional Hamiltonian system, with the distribution function f playing the role of the fundamental dynamical variable, and that, interpreted appropriately, an evolution described by the other Hamiltonian system. Equilibrium solutions correspond to extremal points of the Hamiltonian subject to the constraints associated with Liouville's Theorem. Stable equilibria correspond to energy minima. The evolution of a system out of equilibrium involves (in general nonlinear) phase space oscillations which may -- or may not -- interfere destructively so as to damp away.
Collisionless Relaxation of Stellar Systems
Kandrup, Henry E.
1999-08-01
The objective of the work summarized here has been to exploit and extend ideas from plasma physics and accelerator dynamics to formulate a unified description of collisionless relaxation of stellar systems that views violent relaxation, Landau damping, and phase mixing as (manifestations of) a single phenomenon. This approach embraces the fact that the collisionless Boltzmann equation (CBE), the basic object of the theory, is an infinite-dimensional Hamiltonian system, with the distribution function f playing the role of the fundamental dynamical variable, and that, interpreted appropriately, an evolution described by the CBE is no different fundamentally from an evolution described by any other Hamiltonian system. Equilibrium solutions f0 correspond to extremal points of the Hamiltonian subject to the constraints associated with Liouville's Theorem. Stable equilibria correspond to energy minima. The evolution of a system out of equilibrium involves (in general nonlinear) phase space oscillations which may - or may not - interfere destructively so as to damp away.
Automated force controller for amplitude modulation atomic force microscopy
Miyagi, Atsushi, E-mail: atsushi.miyagi@inserm.fr, E-mail: simon.scheuring@inserm.fr; Scheuring, Simon, E-mail: atsushi.miyagi@inserm.fr, E-mail: simon.scheuring@inserm.fr [U1006 INSERM, Université Aix-Marseille, Parc Scientifique et Technologique de Luminy, 163 Avenue de Luminy, 13009 Marseille (France)
2016-05-15
Atomic Force Microscopy (AFM) is widely used in physics, chemistry, and biology to analyze the topography of a sample at nanometer resolution. Controlling precisely the force applied by the AFM tip to the sample is a prerequisite for faithful and reproducible imaging. In amplitude modulation (oscillating) mode AFM, the applied force depends on the free and the setpoint amplitudes of the cantilever oscillation. Therefore, for keeping the applied force constant, not only the setpoint amplitude but also the free amplitude must be kept constant. While the AFM user defines the setpoint amplitude, the free amplitude is typically subject to uncontrollable drift, and hence, unfortunately, the real applied force is permanently drifting during an experiment. This is particularly harmful in biological sciences where increased force destroys the soft biological matter. Here, we have developed a strategy and an electronic circuit that analyzes permanently the free amplitude of oscillation and readjusts the excitation to maintain the free amplitude constant. As a consequence, the real applied force is permanently and automatically controlled with picoNewton precision. With this circuit associated to a high-speed AFM, we illustrate the power of the development through imaging over long-duration and at various forces. The development is applicable for all AFMs and will widen the applicability of AFM to a larger range of samples and to a larger range of (non-specialist) users. Furthermore, from controlled force imaging experiments, the interaction strength between biomolecules can be analyzed.
Lisovaya E. V.; Victorova E. P.; Agafonov O. S.; Kornen N. N.; Shahray T. A.
2015-01-01
The article presents a comparative assessment and peculiarities of nuclear magnetic relaxation characteristics of rapeseed and sunflower lecithin. It was established, that lecithin’s nuclear magnetic relaxation characteristics, namely, protons’ spin-spin relaxation time and amplitudes of nuclear magnetic relaxation signals of lecithin components, depend on content of oil’s fat acids and phospholipids, contained in the lecithin. Comparative assessment of protons’ spin-spin relaxation time of r...
Coherent oscillations of electrons in tunnel-coupled wells under ultrafast intersubband excitation
Hernandez-Cabrera, A [Departamento de FIsica Basica, Universidad de La Laguna, La Laguna 38206-Tenerife, Canary Islands (Spain); Aceituno, P [Departamento de FIsica Basica, Universidad de La Laguna, La Laguna 38206-Tenerife, Canary Islands (Spain); Vasko, F T [Institute of Semiconductor Physics, NAS of Ukraine, Kiev, 252650 (Ukraine)
2004-07-28
Ultrafast intersubband excitation of electrons in tunnel-coupled wells is studied in respect of its dependence on the structure parameters, the duration of the infrared pump and the detuning frequency. The temporal dependences of the photoinduced carrier concentration and dipole moment are obtained for two cases of transitions: from the single ground state to the tunnel-coupled excited states and from the tunnel-coupled states to the single excited state. The peculiarities of dephasing and population relaxation processes are also taken into account. The nonlinear regime of the response is also considered when the splitting energy between the tunnel-coupled levels is renormalized by the photoexcited electron concentration. The dependences of the period and the amplitude of oscillations on the excitation pulse are presented with a description of the damping of the nonlinear oscillations.
Real topological string amplitudes
Narain, K. S.; Piazzalunga, N.; Tanzini, A.
2017-03-01
We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude G_{χ } , at fixed worldsheet Euler characteristic χ. This corresponds in the low-energy effective action to N=2 Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power g' = -χ + 1. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude F_g.
Magnetization Transfer Induced Biexponential Longitudinal Relaxation
Prantner, Andrew M.; Bretthorst, G. Larry; Neil, Jeffrey J.; Garbow, Joel R.; Ackerman, Joseph J.H.
2009-01-01
Longitudinal relaxation of brain water 1H magnetization in mammalian brain in vivo is typically analyzed on a per voxel basis using a monoexponential model, thereby assigning a single relaxation time constant to all 1H magnetization within a given voxel. This approach was tested by obtaining inversion recovery data from grey matter of rats at 64 exponentially-spaced recovery times. Using Bayesian probability for model selection, brain water data were best represented by a biexponential function characterized by fast and slow relaxation components. At 4.7 T, the amplitude fraction of the rapidly relaxing component is 3.4 ± 0.7 % with a rate constant of 44 ± 12 s-1 (mean ± SD; 174 voxels from 4 rats). The rate constant of the slow relaxing component is 0.66 ± 0.04 s-1. At 11.7 T, the corresponding values are 6.9 ± 0.9 %, 19 ± 5 s-1, and 0.48 ± 0.02 s-1 (151 voxels from 4 rats). Several putative mechanisms for biexponential relaxation behavior were evaluated, and magnetization transfer between bulk water protons and non-aqueous protons was determined to be the source of biexponential longitudinal relaxation. MR methods requiring accurate quantification of longitudinal relaxation may need to take this effect explicitly into account. PMID:18759367
Chemical sensor with oscillating cantilevered probe
Adams, Jesse D
2013-02-05
The invention provides a method of detecting a chemical species with an oscillating cantilevered probe. A cantilevered beam is driven into oscillation with a drive mechanism coupled to the cantilevered beam. A free end of the oscillating cantilevered beam is tapped against a mechanical stop coupled to a base end of the cantilevered beam. An amplitude of the oscillating cantilevered beam is measured with a sense mechanism coupled to the cantilevered beam. A treated portion of the cantilevered beam is exposed to the chemical species, wherein the cantilevered beam bends when exposed to the chemical species. A second amplitude of the oscillating cantilevered beam is measured, and the chemical species is determined based on the measured amplitudes.
Relativistic longitudinal non-Abelian oscillations in quark–antiquark plasma
Vishnu M Bannur
2002-10-01
We study the relativistic version of the non-Abelian, longitudinal wave in quark–antiquark plasma reported earlier by Bhat et al [Phys. Rev. D39, 649 (1989)]. We have also relaxed various approximations they made in their analysis. Both the quark and antiquark dynamics are taken in our analysis. The non-linearity arising from non-Abelian ﬁeld as well as from plasma are included. Hence it is an exact longitudinal mode in relativistic quark–antiquark plasma, relevant to the study of quark gluon plasma. We ﬁnd that earlier results are reproduced for non-relativistic and low amplitude oscillations, but are modiﬁed for relativistic or large amplitude waves. Further more, the above results are based on just four ﬁrst-order equations for gauge invariant quantities derived from gauge covariant twelve ﬁrst-order equations.
Gravitational Wave - Gauge Field Oscillations
Caldwell, R R; Maksimova, N A
2016-01-01
Gravitational waves propagating through a stationary gauge field transform into gauge field waves and back again. When multiple families of flavor-space locked gauge fields are present, the gravitational and gauge field waves exhibit novel dynamics. At high frequencies, the system behaves like coupled oscillators in which the gravitational wave is the central pacemaker. Due to energy conservation and exchange among the oscillators, the wave amplitudes lie on a multi-dimensional sphere, reminiscent of neutrino flavor oscillations. This phenomenon has implications for cosmological scenarios based on flavor-space locked gauge fields.
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.
Photonic cavity synchronization of nanomechanical oscillators.
Bagheri, Mahmood; Poot, Menno; Fan, Linran; Marquardt, Florian; Tang, Hong X
2013-11-22
Synchronization in oscillatory systems is a frequent natural phenomenon and is becoming an important concept in modern physics. Nanomechanical resonators are ideal systems for studying synchronization due to their controllable oscillation properties and engineerable nonlinearities. Here we demonstrate synchronization of two nanomechanical oscillators via a photonic resonator, enabling optomechanical synchronization between mechanically isolated nanomechanical resonators. Optical backaction gives rise to both reactive and dissipative coupling of the mechanical resonators, leading to coherent oscillation and mutual locking of resonators with dynamics beyond the widely accepted phase oscillator (Kuramoto) model. In addition to the phase difference between the oscillators, also their amplitudes are coupled, resulting in the emergence of sidebands around the synchronized carrier signal.
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.
Amplitude Modulated Sinusoidal Signal Decomposition for Audio Coding
Christensen, M. G.; Jacobson, A.; Andersen, S. V.
2006-01-01
In this paper, we present a decomposition for sinusoidal coding of audio, based on an amplitude modulation of sinusoids via a linear combination of arbitrary basis vectors. The proposed method, which incorporates a perceptual distortion measure, is based on a relaxation of a nonlinear least......-squares minimization. Rate-distortion curves and listening tests show that, compared to a constant-amplitude sinusoidal coder, the proposed decomposition offers perceptually significant improvements in critical transient signals....
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.
A simple approach to nonlinear oscillators
Ren, Zhong-Fu; He, Ji-Huan
2009-10-01
A very simple and effective approach to nonlinear oscillators is suggested. Anyone with basic knowledge of advanced calculus can apply the method to finding approximately the amplitude-frequency relationship of a nonlinear oscillator. Some examples are given to illustrate its extremely simple solution procedure and an acceptable accuracy of the obtained solutions.
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)
Mixed Mode Oscillations due to the Generalized Canard Phenomenon
Brøns, Morten; Krupa, Martin; Wechselberger, Martin
2006-01-01
Mixed mode oscillations combine features of small oscillations and large oscillations of relaxation type. We describe a mechanism for mixed mode oscillations based on the presence of canard solutions, which are trajectories passing from a stable to an unstable slow manifold. An important ingredient...... on mixed mode periodic orbits with Farey sequences of the form 1s. We also show how to generalize the context of one fast variable to an arbitrary number of fast variables....
Pietruszka, Mariusz; Haduch-Sendecka, Aleksandra
2015-04-01
The augmented growth equation introduced by Ortega is solved for the apical portion of the pollen tube as an oscillating volume, which we approach in the framework of a two-fluid model in which the two fluids represent the constant pressure and the fluctuating features of the system. Based on routine Fourier analysis, we calculate the energy spectrum of the oscillating pollen tube, and discuss the resonant frequency problem of growth rate oscillations. We also outline a descriptive model for cell wall thickness fluctuations associated with small, yet regular variations (~ 0.01 MPa) observed in turgor pressure. We propose that pressure changes must lead to the sliding of wall layers, indirectly resulting in a wave of polarization of interlayer bonds. We conclude that pollen tube wall thickness may oscillate due to local variations in cell wall properties and relaxation processes. These oscillations become evident because of low amplitude/high frequency pressure fluctuations δP being superimposed on turgor pressure P. We also show that experimentally determined turgor pressure oscillates in a strict periodical manner. A solitary frequency f0 ≈ 0.066 Hz of these (~ 0.01 MPa in magnitude) oscillations for lily pollen tubes was established by the discrete Fourier transform and Lorentz fit.
Relaxation Techniques for Health
... R S T U V W X Y Z Relaxation Techniques for Health Share: On This Page What’s the ... Bottom Line? How much do we know about relaxation techniques? A substantial amount of research has been done ...
Taylor, Tomasz R.
2017-05-01
This a pedagogical introduction to scattering amplitudes in gauge theories. It proceeds from Dirac equation and Weyl fermions to the two pivot points of current developments: the recursion relations of Britto, Cachazo, Feng and Witten, and the unitarity cut method pioneered by Bern, Dixon, Dunbar and Kosower. In ten lectures, it covers the basic elements of on-shell methods.
Quantized amplitudes in a nonlinear resonant electrical circuit
Cretin, B
2008-01-01
We present a simple nonlinear resonant analog circuit which demonstrates quantization of resonating amplitudes, for a given excitation level. The system is a simple RLC resonator where C is an active capacitor whose value is related to the current in the circuit. This variation is energetically equivalent to a variation of the potential energy and the circuit acts as a pendulum in the gravitational field. The excitation voltage, synchronously switched at the current frequency, enables electrical supply and keeping the oscillation of the system. The excitation frequency has been set to high harmonic of the fundamental oscillation so that anisochronicity can keep constant the amplitude of the circuit voltage and current. The behavior of the circuit is unusual: different stable amplitudes have been measured depending on initial conditions and excitation frequency, for the same amplitude of the excitation. The excitation frequency is naturally divided by the circuit and the ratio is kept constant without external...
Kobayashi, M; Irisawa, H
1961-10-27
The latent period of relaxation of molluscan myocardium due to anodal current is much longer than that of contraction. Although the rate and the grade of relaxation are intimately related to both the stimulus condition and the muscle tension, the latent period of relaxation remains constant, except when the temperature of the bathing fluid is changed.
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...
Synchronization of a forced self-sustained Duffing oscillator
Zanette, Damián H
2014-01-01
We study the dynamics of a mechanical oscillator with linear and cubic forces -the Duffing oscillator- subject to a feedback mechanism that allows the system to sustain autonomous periodic motion with well-defined amplitude and frequency. First, we characterize the autonomous motion for both hardening and softening nonlinearities. Then, we analyze the oscillator's synchronizability by an external periodic force. We find a regime where, unexpectedly, the frequency range where synchronized motion is possible becomes wider as the amplitude of oscillations grows. This effect of nonlinearities may find application in technological uses of mechanical Duffing oscillators -for instance, in the design of time-keeping devices at the microscale- which we briefly review.
Decay-less kink oscillations in coronal loops
Anfinogentov, S.; Nisticò, G.; Nakariakov, V. M.
2013-12-01
Context. Kink oscillations of coronal loops in an off-limb active region are detected with the Imaging Assembly Array (AIA) instruments of the Solar Dynamics Observatory (SDO) at 171 Å. Aims: We aim to measure periods and amplitudes of kink oscillations of different loops and to determinate the evolution of the oscillation phase along the oscillating loop. Methods: Oscillating coronal loops were visually identified in the field of view of SDO/AIA and STEREO/EUVI-A: the loop length was derived by three-dimensional analysis. Several slits were taken along the loops to assemble time-distance maps. We identified oscillatory patterns and retrieved periods and amplitudes of the oscillations. We applied the cross-correlation technique to estimate the phase shift between oscillations at different segments of oscillating loops. Results: We found that all analysed loops show low-amplitude undamped transverse oscillations. Oscillation periods of loops in the same active region range from 2.5 to 11 min, and are different for different loops. The displacement amplitude is lower than 1 Mm. The oscillation phase is constant along each analysed loop. The spatial structure of the phase of the oscillations corresponds to the fundamental standing kink mode. We conclude that the observed behaviour is consistent with the empirical model in terms of a damped harmonic resonator affected by a non-resonant continuously operating external force. A movie is available in electronic form at http://www.aanda.org
Weak Boson Production Amplitude Zeros; Equalities of the Helicity Amplitudes
Mamedov, F
2002-01-01
We investigate the radiation amplitude zeros exhibited by many Standard Model amplitudes for triple weak gauge boson production processes. We show that $WZ\\gamma$ production amplitudes have especially rich structure in terms of zeros, these amplitudes have zeros originating from several different sources. It is also shown that TYPE I current null zone is the special case of the equality of the specific helicity amplitudes.
Diverse routes to oscillation death in a coupled oscillator system
Suárez-Vargas, José J.; González, Jorge A.; Stefanovska, Aneta; McClintock, Peter V. E.
2010-01-01
We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in the same model, and for different numbers of coupled oscillators. Our exact analytic results enable us to generalize OD as a multiparameter-sensitive phenomenon. It can be induced, not only by changes in couplings, but also by changes in the oscillator frequencies or amplitudes. We observe synchronization transitions as a function of coupling and confirm the robustness of the phenomena in the presence of noise. Numerical and analogue simulations are in good agreement with the theory. PMID:20823952
Periods and Superstring Amplitudes
Stieberger, S
2016-01-01
Scattering amplitudes which describe the interaction of physical states play an important role in determining physical observables. In string theory the physical states are given by vibrations of open and closed strings and their interactions are described (at the leading order in perturbation theory) by a world-sheet given by the topology of a disk or sphere, respectively. Formally, for scattering of N strings this leads to N-3-dimensional iterated real integrals along the compactified real axis or N-3-dimensional complex sphere integrals, respectively. As a consequence the physical observables are described by periods on M_{0,N} - the moduli space of Riemann spheres of N ordered marked points. The mathematical structure of these string amplitudes share many recent advances in arithmetic algebraic geometry and number theory like multiple zeta values, single-valued multiple zeta values, Drinfeld, Deligne associators, Hopf algebra and Lie algebra structures related to Grothendiecks Galois theory. We review the...
Light Meson Distribution Amplitudes
Arthur, R.; Brommel, D.; Donnellan, M.A.; Flynn, J.M.; Juttner, A.; de Lima, H.Pedroso; Rae, T.D.; Sachrajda, C.T.; Samways, B.
2010-01-01
We calculated the first two moments of the light-cone distribution amplitudes for the pseudoscalar mesons ($\\pi$ and $K$) and the longitudinally polarised vector mesons ($\\rho$, $K^*$ and $\\phi$) as part of the UKQCD and RBC collaborations' $N_f=2+1$ domain-wall fermion phenomenology programme. These quantities were obtained with a good precision and, in particular, the expected effects of $SU(3)$-flavour symmetry breaking were observed. Operators were renormalised non-perturbatively and extrapolations to the physical point were made, guided by leading order chiral perturbation theory. The main results presented are for two volumes, $16^3\\times 32$ and $24^3\\times 64$, with a common lattice spacing. Preliminary results for a lattice with a finer lattice spacing, $32^3\\times64$, are discussed and a first look is taken at the use of twisted boundary conditions to extract distribution amplitudes.
Quantitative Seismic Amplitude Analysis
Dey, A. K.
2011-01-01
The Seismic Value Chain quantifies the cyclic interaction between seismic acquisition, imaging and reservoir characterization. Modern seismic innovation to address the global imbalance in hydrocarbon supply and demand requires such cyclic interaction of both feed-forward and feed-back processes. Currently, the seismic value chain paradigm is in a feed-forward mode. Modern seismic data now have the potential to yield the best images in terms of spatial resolution, amplitude accuracy, and incre...
Biased competition through variations in amplitude of gamma-oscillations.
Zeitler, M.; Fries, P.; Gielen, C.C.A.M.
2008-01-01
Experiments in visual cortex have shown that the firing rate of a neuron in response to the simultaneous presentation of a preferred and non-preferred stimulus within the receptive field is intermediate between that for the two stimuli alone (stimulus competition). Attention directed to one of the s
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A V
2015-01-01
The eikonal approximation for moderately small scattering amplitudes is considered. With the purpose of using for their numerical estimations, the formulas are derived which contain no Bessel functions, and, hence, no rapidly oscillating integrands. To obtain these formulas, the improper integrals of the first kind which contain products of the Bessel functions J_0(z) are studied. The expression with four functions J_0(z) is generalized. The expressions for the integrals with the product of five and six Bessel functions J_0(z) are also found. The known formula for the improper integral with two functions J_nu(z) is generalized for non-integer nu.
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A. V.
2016-08-01
We consider the eikonal approximation for moderately small scattering amplitudes. To find numerical estimates of these approximations, we derive formulas that contain no Bessel functions and consequently no rapidly oscillating integrands. To obtain these formulas, we study improper integrals of the first kind containing products of the Bessel functions J0(z). We generalize the expression with four functions J0(z) and also find expressions for the integrals with the product of five and six Bessel functions. We generalize a known formula for the improper integral with two functions Jυ (az) to the case with noninteger υ and complex a.
Stress relaxation in viscous soft spheres.
Boschan, Julia; Vasudevan, Siddarth A; Boukany, Pouyan E; Somfai, Ellák; Tighe, Brian P
2017-09-27
We report the results of molecular dynamics simulations of stress relaxation tests in athermal viscous soft sphere packings close to their unjamming transition. By systematically and simultaneously varying both the amplitude of the applied strain step and the pressure of the initial condition, we access both linear and nonlinear response regimes and control the distance to jamming. Stress relaxation in viscoelastic solids is characterized by a relaxation time τ* that separates short time scales, where viscous loss is substantial, from long time scales, where elastic storage dominates and the response is essentially quasistatic. We identify two distinct plateaus in the strain dependence of the relaxation time, one each in the linear and nonlinear regimes. The height of both plateaus scales as an inverse power law with the distance to jamming. By probing the time evolution of particle velocities during relaxation, we further identify a correlation between mechanical relaxation in the bulk and the degree of non-affinity in the particle velocities on the micro scale.
Carlowitz, Christian; Girg, Thomas; Ghaleb, Hatem; Du, Xuan-Quang
2017-08-01
For ultra-high speed communication systems at high center frequencies above 100 GHz, we propose a disruptive change in system architecture to address major issues regarding amplifier chains with a large number of amplifier stages. They cause a high noise figure and high power consumption when operating close to the frequency limits of the underlying semiconductor technologies. Instead of scaling a classic homodyne transceiver system, we employ repeated amplification in single-stage amplifiers through positive feedback as well as synthesizer-free self-mixing demodulation at the receiver to simplify the system architecture notably. Since the amplitude and phase information for the emerging oscillation is defined by the input signal and the oscillator is only turned on for a very short time, it can be left unstabilized and thus come without a PLL. As soon as gain is no longer the most prominent issue, relaxed requirements for all the other major components allow reconsidering their implementation concepts to achieve further improvements compared to classic systems. This paper provides the first comprehensive overview of all major design aspects that need to be addressed upon realizing a SPARS-based transceiver. At system level, we show how to achieve high data rates and a noise performance comparable to classic systems, backed by scaled demonstrator experiments. Regarding the transmitter, design considerations for efficient quadrature modulation are discussed. For the frontend components that replace PA and LNA amplifier chains, implementation techniques for regenerative sampling circuits based on super-regenerative oscillators are presented. Finally, an analog-to-digital converter with outstanding performance and complete interfaces both to the analog baseband as well as to the digital side completes the set of building blocks for efficient ultra-high speed communication.
Integrating Biosystem Models Using Waveform Relaxation
Stephen Baigent
2008-12-01
Full Text Available Modelling in systems biology often involves the integration of component models into larger composite models. How to do this systematically and efficiently is a significant challenge: coupling of components can be unidirectional or bidirectional, and of variable strengths. We adapt the waveform relaxation (WR method for parallel computation of ODEs as a general methodology for computing systems of linked submodels. Four test cases are presented: (i a cascade of unidirectionally and bidirectionally coupled harmonic oscillators, (ii deterministic and stochastic simulations of calcium oscillations, (iii single cell calcium oscillations showing complex behaviour such as periodic and chaotic bursting, and (iv a multicellular calcium model for a cell plate of hepatocytes. We conclude that WR provides a flexible means to deal with multitime-scale computation and model heterogeneity. Global solutions over time can be captured independently of the solution techniques for the individual components, which may be distributed in different computing environments.
Driven damped harmonic oscillator resonance with an Arduino
Goncalves, A. M. B.; Cena, C. R.; Bozano, D. F.
2017-07-01
In this paper we propose a simple experimental apparatus that can be used to show quantitative and qualitative results of resonance in a driven damped harmonic oscillator. The driven oscillation is made by a servo motor, and the oscillation amplitude is measured by an ultrasonic position sensor. Both are controlled by an Arduino board. The frequency of free oscillation measured was campatible with the resonance frequency that was measured.
Paradoxical stabilization of forced oscillations by strong nonlinear friction
Esirkepov, Timur Zh.; Bulanov, Sergei V.
2017-08-01
In a dissipative dynamic system driven by an oscillating force, a strong nonlinear highly oscillatory friction force can create a quasi-steady tug, which is always directed opposite to the ponderomotive force induced due to a spatial inhomogeneity of oscillations. When the friction-induced tug exceeds the ponderomotive force, the friction stabilizes the system oscillations near the maxima of the oscillation spatial amplitude of the driving force.
Amplitude death of coupled hair bundles with stochastic channel noise
Kim, Kyung-Joong
2014-01-01
Hair cells conduct auditory transduction in vertebrates. In lower vertebrates such as frogs and turtles, due to the active mechanism in hair cells, hair bundles(stereocilia) can be spontaneously oscillating or quiescent. Recently, the amplitude death phenomenon has been proposed [K.-H. Ahn, J. R. Soc. Interface, {\\bf 10}, 20130525 (2013)] as a mechanism for auditory transduction in frog hair-cell bundles, where sudden cessation of the oscillations arises due to the coupling between non-identical hair bundles. The gating of the ion channel is intrinsically stochastic due to the stochastic nature of the configuration change of the channel. The strength of the noise due to the channel gating can be comparable to the thermal Brownian noise of hair bundles. Thus, we perform stochastic simulations of the elastically coupled hair bundles. In spite of stray noisy fluctuations due to its stochastic dynamics, our simulation shows the transition from collective oscillation to amplitude death as inter-bundle coupling str...
State space modeling of Memristor-based Wien oscillator
Talukdar, Abdul Hafiz Ibne
2011-12-01
State space modeling of Memristor based Wien \\'A\\' oscillator has been demonstrated for the first time considering nonlinear ion drift in Memristor. Time dependant oscillating resistance of Memristor is reported in both state space solution and SPICE simulation which plausibly provide the basis of realizing parametric oscillation by Memristor based Wien oscillator. In addition to this part Memristor is shown to stabilize the final oscillation amplitude by means of its nonlinear dynamic resistance which hints for eliminating diode in the feedback network of conventional Wien oscillator. © 2011 IEEE.
Generalized model for Memristor-based Wien family oscillators
Talukdar, Abdul Hafiz Ibne
2012-07-23
In this paper, we report the unconventional characteristics of Memristor in Wien oscillators. Generalized mathematical models are developed to analyze four members of the Wien family using Memristors. Sustained oscillation is reported for all types though oscillating resistance and time dependent poles are present. We have also proposed an analytical model to estimate the desired amplitude of oscillation before the oscillation starts. These Memristor-based oscillation results, presented for the first time, are in good agreement with simulation results. © 2011 Elsevier Ltd.
ZHOU Zhu-Wen; M.A.LIEBERMAN; Sungjin KIM
2006-01-01
@@ We have observed relaxation oscillations in a capacitive discharge in Ar gas, connected to a peripheral ground chamber. The plasma oscillations observed from time-varying optical emission from the main discharge chamber show, for example, a high frequency (75.37kHz) relaxation oscillation, at 100mTorr and 8 W absorbed power,and a low frequency (2.72 Hz) relaxation oscillation, 100mTorr and 325 W absorbed power. Time-varying optical emission intensity and plasma density are also detected with a Langmuir probe. The theoretical result agrees well with experiments.
Intraseasonal oscillations of stratospheric ozone above Switzerland
Studer, Simone; Hocke, Klemens; Kämpfer, Niklaus
2012-01-01
GROMOS, the ground-based millimeter-wave ozone spectrometer, continuously measures the stratospheric ozone profile between the altitudes of 20 and 65 km above Bern (46°57‧N, 7°27‧E) since November 1994. Characteristics of intraseasonal oscillations of stratospheric ozone are derived from the long-term data set. Spectral analysis gives evidence for a dominant oscillation period of about 20 days in the lower and middle stratosphere during winter time. A strong 20-day wave is also found in collocated geopotential height measurements of the microwave limb sounder onboard the Aura satellite (Aura/MLS) confirming the ground-based observations of GROMOS and underlining the link between ozone and dynamics. Remarkably, the ozone series of GROMOS show an interannual variability of the strength of intraseasonal oscillations of stratospheric ozone. The interannual variability of ozone fluctuations is possibly due to influences of planetary wave forcing and the quasi-biennial oscillation (QBO) on the meridional Brewer-Dobson circulation of the middle atmosphere. In detail, time series of the mean amplitude of ozone fluctuations with periods ranging from 10 to 60 days are derived at fixed pressure levels. The mean amplitude series are regarded as a measure of the strength of intraseasonal oscillations of stratospheric ozone above Bern. After deseasonalizing the mean amplitude series, we find QBO-like amplitude modulations of the intraseasonal oscillations of ozone. The amplitudes of the intraseasonal oscillations are enhanced by a factor of 2 in 1997, 2001, 2003, and 2005. QBO-like variations of intraseasonal oscillations are also present in wind, temperature and other parameters above Bern as indicated by meteorological reanalyses of the European Centre for Medium-range Weather Forecasts (ECMWF). Further, intercomparisons of interannual variability of intraseasonal tropospheric and stratospheric oscillations are performed where the NAO index (North-Atlantic oscillation
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.
Phase-locking phenomena and excitation of damped and driven nonlinear oscillators
Shagalov, A G [Institute of Metal Physics, Ekaterinburg 620041 (Russian Federation); Rasmussen, J Juul; Naulin, V [Risoe-DTU, Building 128, PO Box 49, DK-4000 Roskilde (Denmark)], E-mail: shagalov@imp.uran.ru, E-mail: jens.juul.rasmussen@risoe.dk, E-mail: volker.naulin@risoe.dk
2009-01-30
Resonant phase-locking phenomena ('autoresonance') in the van der Pol-Duffing oscillator forced by a small amplitude periodic driving with slowly varying frequency have been studied. We show that autoresonance occurs for oscillators with sufficiently small damping, when the system may have bi-stable states. We find the range of parameters of the oscillator, the thresholds and the appropriate control paths where autoresonant excitation of high amplitude oscillations is possible.
Phase-locking phenomena and excitation of damped and driven nonlinear oscillators
Shagalov, A.G.; Juul Rasmussen, Jens; Naulin, Volker
2009-01-01
Resonant phase-locking phenomena ('autoresonance') in the van der Pol Duffing oscillator forced by a small amplitude periodic driving with slowly varying frequency have been studied. We show that autoresonance occurs for oscillators with sufficiently small damping, when the system may have bi......-stable states. We find the range of parameters of the oscillator, the thresholds and the appropriate control paths where autoresonant excitation of high amplitude oscillations is possible....
Cubication of conservative nonlinear oscillators
Belendez, Augusto; Alvarez, Mariela L [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, Elena; Pascual, Inmaculada [Departamento de Optica, FarmacologIa y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-09-15
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.
A statistical study of decaying kink oscillations detected using SDO/AIA
Goddard, C R; Nakariakov, V M; Zimovets, I V
2016-01-01
Despite intensive studies of kink oscillations of coronal loops in the last decade, a large scale statistically significant investigation of the oscillation parameters has not been made using data from the Solar Dynamics Observatory (SDO). We carry out a statistical study of kink oscillations using Extreme Ultra-Violet (EUV) imaging data from a previously compiled catalogue. We analysed 58 kink oscillation events observed by the Atmospheric Imaging Assembly (AIA) onboard SDO during its first four years of operation (2010-2014). Parameters of the oscillations, including the initial apparent amplitude, period, length of the oscillating loop, and damping are studied for 120 individual loop oscillations. Analysis of the initial loop displacement and oscillation amplitude leads to the conclusion that the initial loop displacement prescribes the initial amplitude of oscillation in general. The period is found to scale with the loop length, and a linear fit of the data cloud gives a kink speed of Ck =(1330+/-50) km ...
Chirality oscillation of primordial gravitational waves during inflation
Cai, Yong; Piao, Yun-Song
2016-01-01
We show that if the gravitational Chern-Simons term couples to a massive scalar field ($m>H$), the primordial gravitational waves (GWs) will show itself the chirality oscillation, i.e., the amplitudes of the left- and right-handed GWs modes will convert into each other and oscillate in their propagations. This oscillation will eventually develop a permanent difference of the amplitudes of both modes, which leads to nearly opposite oscillating shapes in the power spectra of the left- and right-handed primordial GWs. We discuss its implication to the CMB B-mode polarization.
Neutrino oscillations: what is magic about the "magic" baseline?
Smirnov, A Yu
2006-01-01
Physics interpretation of the ``magic'' baseline that can play important role in future oscillation experiments is given. The ``magic'' baseline coincides with the refraction length, $l_0$. The latter, in turn, approximately equals the oscillation length in matter at high energies. Therefore at the baseline $L = l_0$ the oscillation phase is $2\\pi$, and consequently, the ``solar'' amplitude of oscillations driven by the mixing angle $\\theta_{12}$ and mass splitting $\\Delta m^2_{21}$ vanishes. As a result, in the lowest order (i) the interference of amplitudes in the $\
Subthalamic nucleus phase-amplitude coupling correlates with motor impairment in Parkinson's disease
van Wijk, Bernadette C. M.; Beudel, Martijn; Jha, Ashwani; Oswal, Ashwini; Foltynie, Tom; Hariz, Marwan I.; Limousin, Patricia; Zrinzo, Ludvic; Aziz, Tipu Z.; Green, Alexander L.; Brown, Peter; Litvak, Vladimir
2016-01-01
Objective: High-amplitude beta band oscillations within the subthalamic nucleus are frequently associated with Parkinson's disease but it is unclear how they might lead to motor impairments. Here we investigate a likely pathological coupling between the phase of beta band oscillations and the amplit
Frequency stabilization by synchronization of Duffing oscillators
Zanette, Damián H.
2016-07-01
We present analytical and numerical results on the joint dynamics of two coupled Duffing oscillators with nonlinearity of opposite signs (hardening and softening). In particular, we focus on the existence and stability of synchronized oscillations where the frequency is independent of the amplitude. In this regime, the amplitude-frequency interdependence (a-f effect) —a noxious consequence of nonlinearity, which jeopardizes the use of micromechanical oscillators in the design of time-keeping devices— is suppressed. By means of a multiple time scale formulation, we find approximate conditions under which frequency stabilization is achieved, characterize the stability of the resulting oscillations, and compare with numerical solutions to the equations of motion.
Phase stabilization of nanosecond microwave oscillations in Gunn-diode-based oscillators
Konev, V. Yu.; Klimov, A. I.; Koval'chuk, O. B.; Gubanov, V. P.; Kozhevnikov, V. Yu.; Kozyrev, A. V.
2015-03-01
The "intrusion" of the phase of a Gunn-diode nanosecond microwave oscillator by applying a modulating voltage pulse is numerically simulated. The dependences of the microwave oscillation phase on the spread of the pulse rise time and modulating pulse amplitude are revealed. The standard deviation of the phase lag time in a 3-cm-range oscillator relative to a fixed level at the leading edge of the modulating phase is measured. Phase synchronization between two electrodynamically uncoupled oscillators that are simultaneously excited by a single modulator is studied experimentally.
Stable oscillation in spin torque oscillator excited by a small in-plane magnetic field
Taniguchi, Tomohiro; Tsunegi, Sumito; Kubota, Hitoshi [National Institute of Advanced Industrial Science and Technology (AIST), Spintronics Research Center, Tsukuba 305-8568 (Japan); Ito, Takahiro; Utsumi, Yasuhiro [Faculty of Engineering, Mie University, Tsu, Mie 514-8507 (Japan)
2015-08-07
Theoretical conditions to excite self-oscillation in a spin torque oscillator consisting of a perpendicularly magnetized free layer and an in-plane magnetized pinned layer are investigated by analytically solving the Landau-Lifshitz-Gilbert equation. The analytical relation between the current and oscillation frequency is derived. It is found that a large amplitude oscillation can be excited by applying a small field pointing to the direction anti-parallel to the magnetization of the pinned layer. The validity of the analytical results is confirmed by comparing with numerical simulation, showing good agreement especially in a low current region.
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.
Chaos control of parametric driven Duffing oscillators
Jin, Leisheng; Mei, Jie; Li, Lijie, E-mail: L.Li@swansea.ac.uk [College of Engineering, Swansea University, Swansea SA2 8PP (United Kingdom)
2014-03-31
Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.
Pattern formation in arrays of chemical oscillators
Neeraj Kumar Kamal
2012-05-01
We describe a simple model mimicking diffusively coupled chemical micro-oscillators. We characterize the rich variety of dynamical states emerging from the model under variation of time delay in coupling, coupling strength and boundary conditions. The spatiotemporal patterns obtained include clustering, mixed dynamics, inhomogeneous steady states and amplitude death. Further, under delay in coupling, the model yields transitions from phase to antiphase oscillations, reminiscent of that observed in experiments [M Toiya et al, J. Chem. Lett. 1, 1241 (2010)].
Chaos control of parametric driven Duffing oscillators
Jin, Leisheng; Mei, Jie; Li, Lijie
2014-03-01
Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.
Oscillation modes in the rapidly rotating Slowly Pulsating B-type star $\\bmu$ Eridani
Daszyńska-Daszkiewicz, J; Jerzykiewicz, M; Handler, G
2014-01-01
We present results of a search for identification of modes responsible for the six most significant frequency peaks detected in the rapidly rotating SPB star $\\mu$ Eridani. All published and some unpublished photometric data are used in our new analysis. The mode identification is carried out with the method developed by Daszy\\'nska-Daszkiewicz et al. employing the phases and amplitudes from multi-band photometric data and relying on the traditional approximation for the treatment of oscillations in rotating stars. Models consistent with the observed mean parameters are considered. For the five frequency peaks, the candidates for the identifications are searched amongst unstable modes. In the case of the third frequency, which is an exact multiple of the orbital frequency, this condition is relaxed. The systematic search is continued up to a harmonic degree $\\ell =6$. Determination of the angular numbers, $(\\ell,m)$, is done simultaneously with the rotation rate, $V_{\\rm rot}$, and the inclination angle, $i$,...
Influence of pulsed laser heating on morphological relaxation of surface ripples.
Khenner, M
2005-07-01
A continuum (Mullins-type) model is proposed for the nonisothermal, isotropic evolution of a crystal surface on which mass transport occurs by surface diffusion. The departure from constant temperature is assumed induced by incident pulsed radiation. It has been shown experimentally and theoretically [see, e.g., Yakunkin, High Temp. 26, 585 (1988); Yilbas and Kalyon, J. Phys. D. 34, 222 (2001)] that such a heating mode gives rise to the quasistationary regime, in which the surface temperature of a thick solid film oscillates about the mean value with the pulse repetition frequency. The implications of oscillatory driving with high frequency values on relaxation of surface ripples are examined; in particular, the traveling wave solutions with decreasing amplitude are detected numerically. Pulsed heating also results in faster smoothing of the ripple, compared to the case when the surface is at constant temperature which is same as the mean temperature in the pulsed heating mode. Impact on ripple shape is minor for ripple amplitudes considered.
Evolution of structural relaxation spectra of glycerol within the gigahertz band
Franosch, T.; Göauttze, W.; Mayr, M. R.; Singh, A. P.
1997-03-01
The structural relaxation spectra and the crossover from relaxation to oscillation dynamics, as measured by Wuttke et al. [Phys. Rev. Lett. 72, 3052 (1994)] for glycerol within the GHz band by depolarized light scattering, are described by the solutions of a schematic mode coupling theory model. The applicability of scaling laws for the discussion of the model solutions is considered.
Collisionless relaxation in beam-plasma systems
Backhaus, Ekaterina Yu. [Univ. of California, Berkeley, CA (United States)
2001-01-01
This thesis reports the results from the theoretical investigations, both numerical and analytical, of collisionless relaxation phenomena in beam-plasma systems. Many results of this work can also be applied to other lossless systems of plasma physics, beam physics and astrophysics. Different aspects of the physics of collisionless relaxation and its modeling are addressed. A new theoretical framework, named Coupled Moment Equations (CME), is derived and used in numerical and analytical studies of the relaxation of second order moments such as beam size and emittance oscillations. This technique extends the well-known envelope equation formalism, and it can be applied to general systems with nonlinear forces. It is based on a systematic moment expansion of the Vlasov equation. In contrast to the envelope equation, which is derived assuming constant rms beam emittance, the CME model allows the emittance to vary through coupling to higher order moments. The CME model is implemented in slab geometry in the absence of return currents. The CME simulation yields rms beam sizes, velocity spreads and emittances that are in good agreement with particle-in-cell (PIC) simulations for a wide range of system parameters. The mechanism of relaxation is also considered within the framework of the CME system. It is discovered that the rapid relaxation or beam size oscillations can be attributed to a resonant coupling between different modes of the system. A simple analytical estimate of the relaxation time is developed. The final state of the system reached after the relaxation is complete is investigated. New and accurate analytical results for the second order moments in the phase-mixed state are obtained. Unlike previous results, these connect the final values of the second order moments with the initial beam mismatch. These analytical estimates are in good agreement with the CME model and PIC simulations. Predictions for the final density and temperature are developed that show
Indentation load relaxation test
Hannula, S.P.; Stone, D.; Li, C.Y. (Cornell Univ., Ithaca, NY (USA))
Most of the models that are used to describe the nonelastic behavior of materials utilize stress-strain rate relations which can be obtained by a load relaxation test. The conventional load relaxation test, however, cannot be performed if the volume of the material to be tested is very small. For such applications the indentation type of test offers an attractive means of obtaining data necessary for materials characterization. In this work the feasibility of the indentation load relaxation test is studied. Experimental techniques are described together with results on Al, Cu and 316 SS. These results are compared to those of conventional uniaxial load relaxation tests, and the conversion of the load-indentation rate data into the stress-strain rate data is discussed.
Relaxation techniques for stress
... problems such as high blood pressure, stomachaches, headaches, anxiety, and depression. Using relaxation techniques can help you feel calm. These exercises can also help you manage stress and ease the effects of stress on your body.
Olivary subthreshold oscillations and burst activity revisited
Paolo eBazzigaluppi
2012-11-01
Full Text Available The inferior olive forms one of the major gateways for information that travels to the cerebellar cortex. Olivary neurons process sensory and motor signals that are subsequently relayed to Purkinje cells. The intrinsic subthreshold membrane potential oscillations of the olivary neurons are thought to be important for gating this flow of information. In vitro studies have revealed that the phase of the subthreshold oscillation determines the size of the olivary burst and may gate the information flow or encode the temporal state of the olivary network. Here, we investigated whether the same phenomenon occurred in murine olivary cells in an intact olivocerebellar system using the in vivo whole-cell recording technique. Our in vivo findings revealed that the number of wavelets within the olivary burst did not encode the timing of the spike relative to the phase of the oscillation but was related to the amplitude of the oscillation. Manipulating the oscillation amplitude by applying Harmaline confirmed the inverse relationship between the amplitude of oscillation and the number of wavelets within the olivary burst. Furthermore, we demonstrated that electrotonic coupling between olivary neurons affect this modulation of the olivary burst size. Based on these results, we suggest that the olivary burst size might reflect the expectancy of a spike to occur rather than the spike timing, and that this process requires the presence of gap junction coupling.
CHY formula and MHV amplitudes
Du, Yi-jian; Wu, Yong-shi
2016-01-01
In this paper, we study the relation between the Cachazo-He-Yuan (CHY) formula and the maximal-helicity-violating (MHV) amplitudes of Yang-Mills and gravity in four dimensions. We prove that only one special rational solution of the scattering equations found by Weinzierl support the MHV amplitudes. Namely, localized at this solution, the integrated CHY formula reproduces the Parke-Taylor formula for Yang-Mills amplitudes as well as the Hodges formula for gravitational amplitudes. This is achieved by developing techniques, in a manifestly M\\"obius covariant formalism, to explicitly compute relevant reduced Pfaffians/determinants. We observe and prove two interesting properties (or identities), which facilitate the computations. We also check that all the other $(n-3)!-1$ solutions to the scattering equations do not support the MHV amplitudes, and prove analytically that this is indeed true for the other special rational solution proposed by Weinzierl, that actually supports the anti-MHV amplitudes.
Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems
Yanchuk, S.; Wolfrum, M. [Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin (Germany); Perlikowski, P. [Division of Dynamics, Technical University of Lodz, 90-924 Lodz (Poland); Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore, Singapore 117576 (Singapore); Stefański, A.; Kapitaniak, T. [Division of Dynamics, Technical University of Lodz, 90-924 Lodz (Poland)
2015-03-15
We study the coupling induced destabilization in an array of identical oscillators coupled in a ring structure where the number of oscillators in the ring is large. The coupling structure includes different types of interactions with several next neighbors. We derive an amplitude equation of Ginzburg-Landau type, which describes the destabilization of a uniform stationary state and close-by solutions in the limit of a large number of nodes. Studying numerically an example of unidirectionally coupled Duffing oscillators, we observe a coupling induced transition to collective spatio-temporal chaos, which can be understood using the derived amplitude equations.
Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems.
Yanchuk, S; Perlikowski, P; Wolfrum, M; Stefański, A; Kapitaniak, T
2015-03-01
We study the coupling induced destabilization in an array of identical oscillators coupled in a ring structure where the number of oscillators in the ring is large. The coupling structure includes different types of interactions with several next neighbors. We derive an amplitude equation of Ginzburg-Landau type, which describes the destabilization of a uniform stationary state and close-by solutions in the limit of a large number of nodes. Studying numerically an example of unidirectionally coupled Duffing oscillators, we observe a coupling induced transition to collective spatio-temporal chaos, which can be understood using the derived amplitude equations.
Effect of relaxation on adiabatic following
Nayfeh, M.H.
1976-09-01
A solution is presented for the damped optical Bloch equations under the excitation of a smooth pulse by first deriving three independent third-order equations of the Bloch vector components. Each equation is reduced to quadratures by assuming that the logarithmic time derivative of the field amplitude is small compared to the Rabi frequency. This results in an approximate summation of the infinite-order time-dependent perturbation in the field amplitude. The relaxation-dependent induced damping of the population inversion is calculated. Also calculated are additional relaxation-dependent contributions to the intensity-dependent refractive index. The time-integrated intensity contribution tends to cause line asymmetry, which becomes, at later times, linear in ..gamma../sub 2/ when ..gamma../sub 2/ very-much-greater-than ..gamma../sub 1/ and zero when 2..gamma../sub 2/ = ..gamma../sub 1/, where ..gamma../sub 1/ and ..gamma../sub 2/ are the atomic energy and phase-changing relaxations, respectively. The dependence of the spectral broadening on pulse length, pressure, and length of the sample is discussed. (AIP)
Stability analysis and design of amplitude death induced by a time-varying delay connection
Konishi, Keiji, E-mail: konishi@eis.osakafu-u.ac.j [Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 (Japan); Kokame, Hideki; Hara, Naoyuki [Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 (Japan)
2010-01-18
The present Letter considers amplitude death in a pair of oscillators coupled by a time-varying delay connection. A linear stability analysis is used to derive the boundary curves for amplitude death in a connection parameters space. The delay time can be arbitrarily long for certain amplitude of delay variation and coupling strength. A simple systematic procedure for designing such variation and strength is provided. The theoretical results are verified by a numerical simulation.
An Analytical Approximation Method for Strongly Nonlinear Oscillators
Wang Shimin
2012-01-01
Full Text Available An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of the spring varies with the vibration amplitude for nonstationary oscillations. The varied stiffness is constructed by means of the first and second averaged derivatives of the restoring force with respect to the displacement. Then, this stiffness gives the amplitude frequency and the phase frequency characteristics of the oscillator. Various examples show that this method can be applied extensively to oscillators with nonlinear restoring force, and that the solving process is extremely simple.
Mechanical filtering in forced-oscillation of two coupled pendulums
Foulaadvand, M Ebrahim
2010-01-01
Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the amplitudes and phases of in terms of the frequency of the sinusoidal driving force. The resonance frequencies are obtained and the amplitude ratio is discussed in details. Contrary to a single oscillator, in this two-degree of freedom system four resonant frequencies, which are close to mode frequencies, appear. Within the pass-band interval the system is shown to exhibit a rich and complicated behaviour. It is shown that damping crucially affects the system properties. Under certain circumstances, the amplitude of the oscillator which is directly connected to the driving force becomes smaller than the one far from it. Particularly we show the existence of a driving frequency at which the connected oscillator's amplitude goes zero.
Amplitude dependent closest tune approach
Tomas Garcia, Rogelio; Franchi, Andrea; Maclean, Ewen Hamish; CERN. Geneva. ATS Department
2016-01-01
Recent observations in the LHC point to the existence of an amplitude dependent closest tune approach. However this dynamical behavior and its underlying mechanism remain unknown. This effect is highly relevant for the LHC as an unexpectedly closest tune approach varying with amplitude modifies the frequency content of the beam and, hence, the Landau damping. Furthermore the single particle stability would also be affected by this effect as it would modify how particles with varying amplitudes approach and cross resonances. We present analytic derivations that lead to a mechanism generating an amplitude dependent closest tune approach.
Two-temperature reaction and relaxation rates
Kolesnichenko, E.; Gorbachev, Yu.
2016-09-01
Within the method of solving the kinetic equations for gas mixtures with internal degrees of freedom developed by the authors and based on the approximate summational invariants (ASI) concept, gas-dynamic equations for a multi-temperature model for the spatially inhomogeneous case are derived. For the two-temperature case, the expressions for the non-equilibrium reaction and relaxation rates are obtained. Special attention is drawn to corresponding thermodynamic equations. Different possibilities of introducing the gas-dynamic variables related to the internal degrees of freedom are considered. One is based on the choice of quantum numbers as the ASI, while the other is based on the choice of internal (vibrational) energy as the ASI. Limits to a one-temperature situation are considered in all the cases. For the cutoff harmonic oscillator model, explicit expressions for the reaction and relaxation rates are derived.
Vibrational shear flow of anisotropic viscoelastic fluid with small amplitudes
韩式方
2008-01-01
Using the constitutive equation of co-rotational derivative type for anisotropic viscoelastic fluid-liquid crystalline(LC),polymer liquids was developed.Two relaxation times are introduced in the equation:λn represents relaxation of the normal-symmetric stress components;λs represents relaxation of the shear-unsymmetric stress components.A vibrational rotating flow in gap between cylinders with small amplitudes is studied for the anisotropic viscoelastic fluid-liquid crystalline polymer.The time-dependent constitutive equation are linearized with respect to parameter of small amplitude.For the normal-symmetric part of stress tensor analytical expression of the shear stress is obtained by the constitutive equation.The complex viscosity,complex shear modulus,dynamic and imaginary viscosities,storage modulus and loss modulus are obtained for the normal-symmetric stress case which are defined by the common shear rate.For the shear-unsymmetric stress part,two shear stresses are obtained thus two complex viscosities and two complex shear modulus(i.e.first and second one) are given by the constitutive equation which are defined by rotating shear rate introduced by author.The dynamic and imaginary viscosities,storage modulus and loss modulus are given for each complex viscosities and complex shear modulus.Using the constituive equation the rotating flow with small amplitudes in gap between two coaxial cylinders is studied.
Graviton amplitudes from collinear limits of gauge amplitudes
Stieberger, Stephan, E-mail: stephan.stieberger@mpp.mpg.de [Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München (Germany); Taylor, Tomasz R. [Department of Physics, Northeastern University, Boston, MA 02115 (United States)
2015-05-11
We express all tree-level graviton amplitudes in Einstein's gravity as the collinear limits of a linear combination of pure Yang–Mills amplitudes in which each graviton is represented by two gauge bosons, each of them carrying exactly one half of graviton's momentum and helicity.
On the Period-Amplitude and Amplitude-Period Relationships
Wilson, Robert M.; Hathaway, David H.
2008-01-01
Examined are Period-Amplitude and Amplitude-Period relationships based on the cyclic behavior of the 12-month moving averages of monthly mean sunspot numbers for cycles 0.23, both in terms of Fisher's exact tests for 2x2 contingency tables and linear regression analyses. Concerning the Period-Amplitude relationship (same cycle), because cycle 23's maximum amplitude is known to be 120.8, the inferred regressions (90-percent prediction intervals) suggest that its period will be 131 +/- 24 months (using all cycles) or 131 +/- 18 months (ignoring cycles 2 and 4, which have the extremes of period, 108 and 164 months, respectively). Because cycle 23 has already persisted for 142 months (May 1996 through February 2008), based on the latter prediction, it should end before September 2008. Concerning the Amplitude-Period relationship (following cycle maximum amplitude versus preceding cycle period), because cycle 23's period is known to be at least 142 months, the inferred regressions (90-percent prediction intervals) suggest that cycle 24's maximum amplitude will be about less than or equal to 96.1 +/- 55.0 (using all cycle pairs) or less than or equal to 91.0 +/- 36.7 (ignoring statistical outlier cycle pairs). Hence, cycle 24's maximum amplitude is expected to be less than 151, perhaps even less than 128, unless cycle pair 23/24 proves to be a statistical outlier.
Nonlinear amplitude dynamics in flagellar beating
Oriola, David; Casademunt, Jaume
2016-01-01
The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive crosslinkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatiotemporal dynamics of dynein populations and flagell...
Measurements of Tune Shifts with Amplitude at LEP
Müller, A S
1999-01-01
The beam orbit system of the LEP electron-positron collider is able to store the beam position over 1000 turns following a deflection by a horizontal kicker. A precise analysis of such 1000-turn data for many beam position monitors was used to study the dependence of the tune on the horizontal amplitude. The horizontal tune shift with amplitude was determined from the decay of the beam oscillation for various LEP optics. This parameter turned out to be an important issue for the LEP high energy optics.
Source-Space Cross-Frequency Amplitude-Amplitude Coupling in Tinnitus
Oliver Zobay
2015-01-01
Full Text Available The thalamocortical dysrhythmia (TCD model has been influential in the development of theoretical explanations for the neurological mechanisms of tinnitus. It asserts that thalamocortical oscillations lock a region in the auditory cortex into an ectopic slow-wave theta rhythm (4–8 Hz. The cortical area surrounding this region is hypothesized to generate abnormal gamma (>30 Hz oscillations (“edge effect” giving rise to the tinnitus percept. Consequently, the model predicts enhanced cross-frequency coherence in a broad range between theta and gamma. In this magnetoencephalography study involving tinnitus and control cohorts, we investigated this prediction. Using beamforming, cross-frequency amplitude-amplitude coupling (AAC was computed within the auditory cortices for frequencies (f1,f2 between 2 and 80 Hz. We find the AAC signal to decompose into two distinct components at low (f1,f230 Hz frequencies, respectively. Studying the correlation of AAC with several key covariates (age, hearing level (HL, tinnitus handicap and duration, and HL at tinnitus frequency, we observe a statistically significant association between age and low-frequency AAC. Contrary to the TCD predictions, however, we do not find any indication of statistical differences in AAC between tinnitus and controls and thus no evidence for the predicted enhancement of cross-frequency coupling in tinnitus.
Pair creation and plasma oscillations.
Prozorkevich, A. V.; Vinnik, D. V.; Schmidt, S. M.; Hecht, M. B.; Roberts, C. D.
2000-12-15
We describe aspects of particle creation in strong fields using a quantum kinetic equation with a relaxation-time approximation to the collision term. The strong electric background field is determined by solving Maxwell's equation in tandem with the Vlasov equation. Plasma oscillations appear as a result of feedback between the background field and the field generated by the particles produced. The plasma frequency depends on the strength of the initial background fields and the collision frequency, and is sensitive to the necessary momentum-dependence of dressed-parton masses.
Analytical approximations for stick-slip vibration amplitudes
Thomsen, Jon Juel; Fidlin, A.
2003-01-01
The classical "mass-on-moving-belt" model for describing friction-induced vibrations is considered, with a friction law describing friction forces that first decreases and then increases smoothly with relative interface speed. Approximate analytical expressions are derived for the conditions......, the amplitudes, and the base frequencies of friction-induced stick¿slip and pure-slip oscillations. For stick¿slip oscillations, this is accomplished by using perturbation analysis for the finite time interval of the stick phase, which is linked to the subsequent slip phase through conditions of continuity...... and periodicity. The results are illustrated and tested by time-series, phase plots and amplitude response diagrams, which compare very favorably with results obtained by numerical simulation of the equation of motion, as long as the difference in static and kinetic friction is not too large....
Closed string amplitudes as single-valued open string amplitudes
Stieberger, Stephan, E-mail: stephan.stieberger@mpp.mpg.de [Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München (Germany); Taylor, Tomasz R. [Department of Physics, Northeastern University, Boston, MA 02115 (United States)
2014-04-15
We show that the single trace heterotic N-point tree-level gauge amplitude A{sub N}{sup HET} can be obtained from the corresponding type I amplitude A{sub N}{sup I} by the single-valued (sv) projection: A{sub N}{sup HET}=sv(A{sub N}{sup I}). This projection maps multiple zeta values to single-valued multiple zeta values. The latter represent a subclass of multiple zeta values originating from single-valued multiple polylogarithms at unity. Similar relations between open and closed string amplitudes or amplitudes of different string vacua can be established. As a consequence the α{sup ′}-expansion of a closed string amplitude is dictated by that of the corresponding open string amplitude. The combination of single-valued projections, Kawai–Lewellen–Tye relations and Mellin correspondence reveal a unity of all tree-level open and closed superstring amplitudes together with the maximally supersymmetric Yang–Mills and supergravity theories.
Pulse Sequence Shaper For Radiospectroscopy And Relaxation Methods In NQR
Bobalo Yuriy
2015-09-01
Full Text Available A pulse sequence shaper for the pursuance of the research using a wide spectrum of radiospectroscopy and relaxation methods in NQR is proposed. The distinctive feature of this product is its implementation with the application of a multi-functional programmable frequency synthesizer suitable for high-speed amplitude and phase manipulations.
OSCILLATION-DRIVEN MAGNETOSPHERIC ACTIVITY IN PULSARS
Lin, Meng-Xiang; Xu, Ren-Xin; Zhang, Bing, E-mail: linmx97@gmail.com, E-mail: r.x.xu@pku.edu.cn, E-mail: zhang@physics.unlv.edu [Department of Astronomy, School of Physics, Peking University, Beijing 100871 (China)
2015-02-01
We study the magnetospheric activity in the polar cap region of pulsars under stellar oscillations. The toroidal oscillation of the star propagates into the magnetosphere, which provides additional voltage due to unipolar induction, changes Goldreich-Julian charge density from the traditional value due to rotation, and hence influences particle acceleration. We present a general solution of the effect of oscillations within the framework of the inner vacuum gap model and consider three different inner gap modes controlled by curvature radiation, inverse Compton scattering, and two-photon annihilation, respectively. With different pulsar parameters and oscillation amplitudes, one of three modes would play a dominant role in defining the gap properties. When the amplitude of oscillation exceeds a critical value, mode changing occurs. Oscillations also lead to a change of the size of the polar cap. As applications, we show the inner gap properties under oscillations in both normal pulsars and anomalous X-ray pulsars/soft gamma-ray repeaters (AXPs/SGRs). We interpret the onset of radio emission after glitches/flares in AXPs/SGRs as due to oscillation-driven magnetic activities in these objects, within the framework of both the magnetar model and the solid quark star model. Within the magnetar model, radio activation may be caused by the enlargement of the effective polar cap angle and the radio emission beam due to oscillation, whereas within the solid quark star angle, it may be caused by activation of the pulsar inner gap from below the radio emission death line due to an oscillation-induced voltage enhancement. The model can also explain the glitch-induced radio profile change observed in PSR J1119–6127.
Relaxation time estimation in surface NMR
Grunewald, Elliot D.; Walsh, David O.
2017-03-21
NMR relaxation time estimation methods and corresponding apparatus generate two or more alternating current transmit pulses with arbitrary amplitudes, time delays, and relative phases; apply a surface NMR acquisition scheme in which initial preparatory pulses, the properties of which may be fixed across a set of multiple acquisition sequence, are transmitted at the start of each acquisition sequence and are followed by one or more depth sensitive pulses, the pulse moments of which are varied across the set of multiple acquisition sequences; and apply processing techniques in which recorded NMR response data are used to estimate NMR properties and the relaxation times T.sub.1 and T.sub.2* as a function of position as well as one-dimensional and two-dimension distributions of T.sub.1 versus T.sub.2* as a function of subsurface position.
Relaxation time estimation in surface NMR
Grunewald, Elliot D.; Walsh, David O.
2017-03-21
NMR relaxation time estimation methods and corresponding apparatus generate two or more alternating current transmit pulses with arbitrary amplitudes, time delays, and relative phases; apply a surface NMR acquisition scheme in which initial preparatory pulses, the properties of which may be fixed across a set of multiple acquisition sequence, are transmitted at the start of each acquisition sequence and are followed by one or more depth sensitive pulses, the pulse moments of which are varied across the set of multiple acquisition sequences; and apply processing techniques in which recorded NMR response data are used to estimate NMR properties and the relaxation times T.sub.1 and T.sub.2* as a function of position as well as one-dimensional and two-dimension distributions of T.sub.1 versus T.sub.2* as a function of subsurface position.
Nonlinear oscillations in a unijunction transistor (UJT) circuit
Zielinski, John
2005-10-01
Phenomena such as plasma wavesootnotetextT Tsuru, Nonlinear resonance phenomena of elect. plasma oscillations by beam modulation, J. Phys. Soc. Japan, 40, 548, 1976. and oscillations in electric circuits which employ a plasma componentootnotetextM Wendt, I Axnas, S Torven, Amplitude collapse of nonlinear double-layer oscillations, Phys. Rev. E, 57, 4638, 1998. can be described by a differential equation with nonlinear dissipative and restoring force terms. The UJT oscillator circuit developed by Koepke and HartleyootnotetextME Koepke, DM Hartley, Experimental verification of periodic pulling in a nonlinear electronic oscillator, Phys. Rev. A, 44, 6877, 1991 is also described by a similar equation. During the past year efforts have been made to understand the following aspects of this circuit's operation: 1) Determining conditions which lead to oscillation onset and termination (amplitude collapse). 2) Analytic and numerical modeling. 3) Characterizing the capacitances associated with the emitter-base junctions. 4) Exploring the relationship between this circuit and astable multivibrators.
Quantum correlation in degenerate optical parametric oscillators with mutual injections
Takata, Kenta
2015-01-01
We theoretically and numerically study the quantum dynamics of two degenerate optical parametric oscillators with mutual injections. The cavity mode in the optical coupling path between the two oscillator facets is explicitly considered. Stochastic equations for the oscillators and mutual injection path based on the positive $P$ representation are derived. The system of two gradually pumped oscillators with out-of-phase mutual injections are simulated, and their quantum states are investigated. When the incoherent loss of the oscillators other than the mutual injections is small, the squeezed quadratic amplitudes $\\hat{p}$ in the oscillators are positively correlated near the oscillation threshold. It indicates finite quantum correlation, and the entanglement between the intracavity subharmonic fields. When with a small loss of the injection path, each oscillator around the phase transition point forms macroscopic superposition for a small pump noise. It suggests that the low-loss injection path works as a sq...
Crystalline Undulator with a Small Amplitude and a Short Period
Kostyuk, Andriy
2012-01-01
The crystalline undulator is a single crystal with periodically bent crystallographic planes. If ultrarelativistic charged particles channel through such a crystal, they emit hard radiation of undulator type. A crystalline undulator with a bending amplitude smaller than the distance between the bent planes and a bending period shorter than the period of channeling oscillations is proposed. Heretofore, it was believed that such a range of bending parameters was unsuitable for a crystalline und...
A new analytical approximation to the Duffing-harmonic oscillator
Fesanghary, M. [Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803 (United States); Pirbodaghi, T. [School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., 11365-9567 Tehran (Iran, Islamic Republic of); Asghari, M. [School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., 11365-9567 Tehran (Iran, Islamic Republic of)], E-mail: asghari@sharif.edu; Sojoudi, H. [Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803 (United States)
2009-10-15
In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations.
Andrews, D. J.; Cowley, S. W. H.; Dougherty, M. K.; Lamy, L.; Provan, G.; Southwood, D. J.
2012-04-01
We investigate the evolution of the properties of planetary period magnetic field oscillations observed by the Cassini spacecraft in Saturn's magnetosphere over the interval from late 2004 to early 2011, spanning equinox in mid-2009. Oscillations within the inner quasi-dipolar region (L ≤ 12) consist of two components of close but distinct periods, corresponding essentially to the periods of the northern and southern Saturn kilometric radiation (SKR) modulations. These give rise to modulations of the combined amplitude and phase at the beat period of the two oscillations, from which the individual oscillation amplitudes and phases (and hence periods) can be determined. Phases are also determined from northern and southern polar oscillation data when available. Results indicate that the southern-period amplitude declines modestly over this interval, while the northern-period amplitude approximately doubles to become comparable with the southern-period oscillations during the equinox interval, producing clear effects in pass-to-pass oscillation properties. It is also shown that the periods of the two oscillations strongly converge over the equinox interval, such that the beat period increases significantly from ˜20 to more than 100 days, but that they do not coalesce or cross during the interval investigated, contrary to recent reports of the behavior of the SKR periods. Examination of polar oscillation data for similar beat phase effects yields a null result within a ˜10% upper limit on the relative amplitude of northern-period oscillations in the south and vice versa. This result strongly suggests a polar origin for the two oscillation periods.
Thoke, Henrik Seir; Tobiesen, Asger; Brewer, Jonathan R.
2015-01-01
We detected very strong coupling between the oscillating concentration of ATP and the dynamics of intracellular water during glycolysis in Saccharomyces cerevisiae. Our results indicate that: i) dipolar relaxation of intracellular water is heterogeneous within the cell and different from dilute...... conditions, ii) water dipolar relaxation oscillates with glycolysis and in phase with ATP concentration, iii) this phenomenon is scale-invariant from the subcellular to the ensemble of synchronized cells and, iv) the periodicity of both glycolytic oscillations and dipolar relaxation are equally affected by D...
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 ...
ENTRAINMENT OF THE BREATHING RHYTHM OF THE CARP BY IMPOSED OSCILLATION OF THE GILL ARCHES
DEGRAAF, PJF; ROBERTS, BL
1991-01-01
Artificial oscillation imposed onto the gill arches could modify the respiratory rhythm in the carp Cyprinus carpio. The degree of modification depended upon the frequency and amplitude of the applied movement. Oscillation at frequencies close to the spontaneous respiratory rhythm and at amplitudes
The effect of consumption delay on the excitation of Goodwin's oscillations
Antonova, A. O.; Reznik, S. N.; Todorov, M. D.
2014-11-01
We investigate the influence of the consumption delay in Godwin's model of the business cycle on the excitation of the Goodwin oscillation, its amplitude and period. We show that the amplitudes of the oscillations of income, consumption and induced investment fall with the increasing the consumption delay.
Sound-Triggered Collapse of Stably Oscillating Low-Mass Cores in a Two-Phase Interstellar Medium
Zhang, Ui-Han; Chiueh, Tzihong
2015-01-01
Inspired by Barnard 68, a Bok globule, that undergoes stable oscillations, we perform multi-phase hydrodynamic simulations to analyze the stability of Bok globules. We show that a high-density soft molecular core, with an adiabatic index $\\gamma$ = 0.7 embedded in a warm isothermal diffuse gas, must have a small density gradient to retain the stability. Despite being stable, the molecular core can still collapse spontaneously as it will relax to develop a sufficiently large density gradient after tens of oscillations, or a few $10^7$ years. However, during its relaxation, the core may abruptly collapse triggered by the impingement of small-amplitude, long-wavelength ($\\sim$ 6 $-$ 36 pc) sound waves in the warm gas. This triggered collapse mechanism is similar to a sonoluminescence phenomenon, where underwater ultrasounds can drive air bubble coalescence. The collapse configuration is found to be different from both inside-out and outside-in models of low-mass star formation; nonetheless the mass flux is close...
Molecular Relaxation in Liquids
Bagchi, Biman
2012-01-01
This book brings together many different relaxation phenomena in liquids under a common umbrella and provides a unified view of apparently diverse phenomena. It aligns recent experimental results obtained with modern techniques with recent theoretical developments. Such close interaction between experiment and theory in this area goes back to the works of Einstein, Smoluchowski, Kramers' and de Gennes. Development of ultrafast laser spectroscopy recently allowed study of various relaxation processes directly in the time domain, with time scales going down to picosecond (ps) and femtosecond (fs
Time course of corticospinal excitability and intracortical inhibition just before muscle relaxation
Tomotaka eSuzuki
2016-01-01
Full Text Available Using transcranial magnetic stimulation (TMS, we investigated how short-interval intracortical inhibition (SICI was involved with transient motor cortex excitability changes observed just before the transition from muscle contraction to muscle relaxation. Ten healthy participants performed a simultaneous relaxation task of the ipsilateral finger and foot, relaxing from 10% of their maximal voluntary contraction force after the go signal. In the simple reaction time paradigm, single or paired TMS pulses were randomly delivered after the go signal, and motor evoked potentials were recorded from the right first dorsal interosseous muscle. We analyzed the time course prior to the estimated relaxation reaction time, defined here as the onset of voluntary relaxation. SICI decreased in the 80–100 ms before relaxation reaction time, and motor evoked potentials were significantly greater in amplitude in the 60–80 ms period before relaxation reaction time than in the other intervals in single-pulse trials. TMS pulses did not effectively increase relaxation reaction time. These results show that cortical excitability in the early stage, before muscle relaxation, plays an important role in muscle relaxation control. SICI circuits may vary between decreased and increased activation to continuously maintain muscle relaxation during or after a relaxation response. With regard to motor cortex excitability dynamics, we suggest that SICI also dynamically changes throughout the muscle relaxation process.
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...
Determining the Strength of an Electromagnet through Damped Oscillations
Thompson, Michael; Leung, Chi Fan
2011-01-01
This article describes a project designed to extend sixth-form pupils looking to further their knowledge and skill base in physics. This project involves a quantitative analysis of the decaying amplitude of a metal plate oscillating in a strong magnetic field; the decay of the amplitude is used to make estimates of the strength of the magnetic…
Nanzai, Ben; Funazaki, Tomohisa; Igawa, Manabu
2010-09-16
This study of self-oscillation was conducted using a new three-phase liquid membrane system of ethanol aqueous solution, benzyl alcohol solution with nonionic surfactant, and pure water. Relations of the initial ethanol concentration to the oscillation amplitude and frequency, and to the induction period before oscillations were investigated. The oscillation amplitude is independent of the initial ethanol concentration, but the frequency and the induction period are related to it. The oscillation frequency increased concomitantly with the increased ethanol initial concentration, but the induction period before the electrical oscillations decreased with increasing concentration. To estimate the influence of ethanol diffusion on the electrical oscillations, the ethanol concentration in each phase was measured using separate experiments after different durations of oscillation. The diffusion coefficient was calculated using Fick's second law. Results show successful estimation of the threshold for oscillations. The threshold is defined in terms of the ethanol concentration at the interface between the benzyl alcohol phase and the pure water phase.
Oscillation of large air bubble cloud
Bae, Y.Y.; Kim, H.Y.; Park, J.K. [Korea Atomic Energy Research Inst., Daejeon (Korea, Republic of)
2001-07-01
The behavior of a large air bubble cloud, which is generated by the air discharged from a perforated sparger, is analyzed by solving Rayleigh-Plesset equation, energy equations and energy balance equation. The equations are solved by Runge-Kutta integration and MacCormack finite difference method. Initial conditions such as driving pressure, air volume, and void fraction strongly affect the bubble pressure amplitude and oscillation frequency. The pool temperature has a strong effect on the oscillation frequency and a negligible effect on the pressure amplitude. The polytropic constant during the compression and expansion processes of individual bubbles ranges from 1.0 to 1.4, which may be attributed to the fact that small bubbles oscillated in frequencies different from their resonance. The temperature of the bubble cloud rapidly approaches the ambient temperature, as is expected from the polytropic constants being between 1.0 and 1.4. (authors)
Calibrating oscillation response of a piezo-stage using optical tweezers.
Zhou, Jin-Hua; Li, Di; Hu, Xin-Yao; Zhong, Min-Cheng; Wang, Zi-Qiang; Gong, Lei; Liu, Wei-Wei; Li, Yin-Mei
2015-09-21
In optical tweezers, a piezo-stage (PZT) is widely used to precisely position samples for force clamp, calibrating optical trap and stretching DNA. For a trapped bead in solution, the oscillation response of PZT is vital for all kinds of applications. A coupling ratio, actual amplitude to nominal amplitude, can be calibrated by power spectral density during sinusoidal oscillations. With oscillation frequency increasing, coupling ratio decreases in both x- and y-directions, which is also confirmed by the calibration with light scattering of scanning two aligned beads on slide. Those oscillation responses are related with deformability of chamber and the intrinsic characteristics of PZT. If we take nominal amplitude as actual amplitude for sinusoidal oscillations at 50 Hz, the amplitude is overestimated ~2 times in x-direction and ~3 times in y-direction. That will lead to huge errors for subsequent calibrations.
State resolved vibrational relaxation modeling for strongly nonequilibrium flows
Boyd, Iain D.; Josyula, Eswar
2011-05-01
Vibrational relaxation is an important physical process in hypersonic flows. Activation of the vibrational mode affects the fundamental thermodynamic properties and finite rate relaxation can reduce the degree of dissociation of a gas. Low fidelity models of vibrational activation employ a relaxation time to capture the process at a macroscopic level. High fidelity, state-resolved models have been developed for use in continuum gas dynamics simulations based on computational fluid dynamics (CFD). By comparison, such models are not as common for use with the direct simulation Monte Carlo (DSMC) method. In this study, a high fidelity, state-resolved vibrational relaxation model is developed for the DSMC technique. The model is based on the forced harmonic oscillator approach in which multi-quantum transitions may become dominant at high temperature. Results obtained for integrated rate coefficients from the DSMC model are consistent with the corresponding CFD model. Comparison of relaxation results obtained with the high-fidelity DSMC model shows significantly less excitation of upper vibrational levels in comparison to the standard, lower fidelity DSMC vibrational relaxation model. Application of the new DSMC model to a Mach 7 normal shock wave in carbon monoxide provides better agreement with experimental measurements than the standard DSMC relaxation model.
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.
Scattering amplitudes in gauge theories
Henn, Johannes M
2014-01-01
At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum ...
Positive Amplitudes In The Amplituhedron
Arkani-Hamed, Nima; Trnka, Jaroslav
2014-01-01
The all-loop integrand for scattering amplitudes in planar N = 4 SYM is determined by an "amplitude form" with logarithmic singularities on the boundary of the amplituhedron. In this note we provide strong evidence for a new striking property of the superamplitude, which we conjecture to be true to all loop orders: the amplitude form is positive when evaluated inside the amplituhedron. The statement is sensibly formulated thanks to the natural "bosonization" of the superamplitude associated with the amplituhedron geometry. However this positivity is not manifest in any of the current approaches to scattering amplitudes, and in particular not in the cellulations of the amplituhedron related to on-shell diagrams and the positive grassmannian. The surprising positivity of the form suggests the existence of a "dual amplituhedron" formulation where this feature would be made obvious. We also suggest that the positivity is associated with an extended picture of amplituhedron geometry, with the amplituhedron sitting...
Model selection for amplitude analysis
Guegan, Baptiste; Stevens, Justin; Williams, Mike
2015-01-01
Model complexity in amplitude analyses is often a priori under-constrained since the underlying theory permits a large number of amplitudes to contribute to most physical processes. The use of an overly complex model results in reduced predictive power and worse resolution on unknown parameters of interest. Therefore, it is common to reduce the complexity by removing from consideration some subset of the allowed amplitudes. This paper studies a data-driven method for limiting model complexity through regularization during regression in the context of a multivariate (Dalitz-plot) analysis. The regularization technique applied greatly improves the performance. A method is also proposed for obtaining the significance of a resonance in a multivariate amplitude analysis.
Parametrization of the driven betatron oscillation
R. Miyamoto
2008-08-01
Full Text Available An AC dipole is a magnet which produces a sinusoidally oscillating dipole field and excites coherent transverse beam oscillations in a synchrotron. By observing this driven coherent oscillation, the linear optical parameters can be directly measured at locations of the beam position monitors. The driven oscillations induced by an AC dipole will generate a phase space ellipse which differs from that of free oscillations. If not properly accounted for, this difference can lead to misinterpretations of the actual optical parameters, for instance, 6% or more in the cases of the Tevatron, RHIC, or LHC. This paper shows that the effect of an AC dipole on the observed linear optics is identical to that of a thin lens quadrupole. By introducing a new amplitude function to describe this new phase space ellipse, the motion produced by an AC dipole becomes easier to interpret. The introduction of this new amplitude function also helps measurements of the normal Courant-Snyder parameters based on beam position data taken under the influence of an AC dipole. This new parametrization of driven oscillations is presented and is used to interpret data taken in the FNAL Tevatron using an AC dipole.
Autoresonance versus localization in weakly coupled oscillators
Kovaleva, Agnessa; Manevitch, Leonid I.
2016-04-01
We study formation of autoresonance (AR) in a two-degree of freedom oscillator array including a nonlinear (Duffing) oscillator (the actuator) weakly coupled to a linear attachment. Two classes of systems are studied. In the first class of systems, a periodic force with constant (resonance) frequency is applied to a nonlinear oscillator (actuator) with slowly time-decreasing stiffness. In the systems of the second class a nonlinear time-invariant oscillator is subjected to an excitation with slowly increasing frequency. In both cases, the attached linear oscillator and linear coupling are time-invariant, and the system is initially engaged in resonance. This paper demonstrates that in the systems of the first type AR in the nonlinear actuator entails oscillations with growing amplitudes in the linear attachment while in the system of the second type energy transfer from the nonlinear actuator is insufficient to excite high-energy oscillations of the attachment. It is also shown that a slow change of stiffness may enhance the response of the actuator and make it sufficient to support oscillations with growing energy in the attachment even beyond the linear resonance. Explicit asymptotic approximations of the solutions are obtained. Close proximity of the derived approximations to exact (numerical) results is demonstrated.
Intrinsic correlation between β-relaxation and spatial heterogeneity in a metallic glass
Zhu, F.; Nguyen, H. K.; Song, S. X.; Aji, Daisman P. B.; Hirata, A.; Wang, H.; Nakajima, K.; Chen, M. W.
2016-01-01
β-relaxation has long been attributed to localized motion of constituent molecules or atoms confined to isolated regions in glasses. However, direct experimental evidence to support this spatially heterogeneous scenario is still missing. Here we report the evolution of nanoscale structural heterogeneity in a metallic glass during β-relaxation by utilizing amplitude-modulation dynamic atomic force microscopy. The successive degeneration of heterogeneity during β-relaxation can be well described by the Kohlrausch–Williams–Watts equation. The characteristic relaxation time and activation energy of the heterogeneity evolution are in accord with those of excess enthalpy release by β-relaxation. Our study correlates β-relaxation with nanoscale spatial heterogeneity and provides direct evidence on the structural origins of β-relaxation in metallic glasses. PMID:27158084
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....
Zampetoulas, Vasileios; Lurie, David J.; Broche, Lionel M.
2017-09-01
T1 relaxation times can be measured at a range of magnetic field strengths by Fast Field-Cycling (FFC) NMR relaxometry to provide T1-dispersion curves. These are valuable tools for the investigation of material properties as they provide information about molecular dynamics non-invasively. However, accessing information at fields below 230 μT (10 kHz proton Larmor frequency) requires careful correction of unwanted environmental magnetic fields. In this work a novel method is proposed that compensates for the environmental fields on a FFC-NMR relaxometer and extends the acquisition of Nuclear Magnetic Relaxation Dispersion profiles to 2.3 μT (extremely low field region), with direct application in the study of slow molecular motions. Our method is an improvement of an existing technique, reported by Anoardo and Ferrante in 2003, which exploits the non-adiabatic behaviour of the magnetisation in rapidly-varying magnetic fields and makes use of the oscillation of the signal amplitude to estimate the field strength. This increases the accuracy in measuring the environmental fields and allows predicting the optimal correction values by applying simple equations to fit the data acquired. Validation of the method is performed by comparisons with well-known dispersion curves obtained from polymers and benzene.
Numerical simulations of transverse oscillations in radiatively cooling coronal loops
Magyar, N; Marcu, A
2015-01-01
We aim to study the influence of radiative cooling on the standing kink oscillations of a coronal loop. Using the FLASH code, we solved the 3D ideal magnetohydrodynamic equations. Our model consists of a straight, density enhanced and gravitationally stratified magnetic flux tube. We perturbed the system initially, leading to a transverse oscillation of the structure, and followed its evolution for a number of periods. A realistic radiative cooling is implemented. Results are compared to available analytical theory. We find that in the linear regime (i.e. low amplitude perturbation and slow cooling) the obtained period and damping time are in good agreement with theory. The cooling leads to an amplification of the oscillation amplitude. However, the difference between the cooling and non-cooling cases is small (around 6% after 6 oscillations). In high amplitude runs with realistic cooling, instabilities deform the loop, leading to increased damping. In this case, the difference between cooling and non-cooling...
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)
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 $\
Linear oscillation of gas bubbles in a viscoelastic material under ultrasound irradiation
Hamaguchi, Fumiya; Ando, Keita
2015-11-01
Acoustically forced oscillation of spherical gas bubbles in a viscoelastic material is studied through comparisons between experiments and linear theory. An experimental setup has been designed to visualize bubble dynamics in gelatin gels using a high-speed camera. A spherical gas bubble is created by focusing an infrared laser pulse into (gas-supersaturated) gelatin gels. The bubble radius (up to 150 μm) under mechanical equilibrium is controlled by gradual mass transfer of gases across the bubble interface. The linearized bubble dynamics are studied from the observation of spherical bubble oscillation driven by low-intensity, planar ultrasound driven at 28 kHz. It follows from the experiment for an isolated bubble that the frequency response in its volumetric oscillation was shifted to the high frequency side and its peak was suppressed as the gelatin concentration increases. The measurement is fitted to the linearized Rayleigh-Plesset equation coupled with the Voigt constitutive equation that models the behavior of linear viscoelastic solids; the fitting yields good agreement by tuning unknown values of the viscosity and rigidity, indicating that more complex phenomena including shear thinning, stress relaxation, and retardation do not play an important role for the small-amplitude oscillations. Moreover, the cases for bubble-bubble and bubble-wall systems are studied. The observed interaction effect on the linearized dynamics can be explained as well by a set of the Rayleigh-Plesset equations coupled through acoustic radiation among these systems. This suggests that this experimental setup can be applied to validate the model of bubble dynamics with more complex configuration such as a cloud of bubbles in viscoelastic materials.
Linear oscillation of gas bubbles in a viscoelastic material under ultrasound irradiation
Hamaguchi, Fumiya; Ando, Keita, E-mail: kando@mech.keio.ac.jp [Department of Mechanical Engineering, Keio University, Yokohama 223-8522 (Japan)
2015-11-15
Acoustically forced oscillation of spherical gas bubbles in a viscoelastic material is studied through comparisons between experiments and linear theory. An experimental setup has been designed to visualize bubble dynamics in gelatin gels using a high-speed camera. A spherical gas bubble is created by focusing an infrared laser pulse into (gas-supersaturated) gelatin gels. The bubble radius (up to 150 μm) under mechanical equilibrium is controlled by gradual mass transfer of gases across the bubble interface. The linearized bubble dynamics are studied from the observation of spherical bubble oscillation driven by low-intensity, planar ultrasound driven at 28 kHz. It follows from the experiment for an isolated bubble that the frequency response in its volumetric oscillation was shifted to the high frequency side and its peak was suppressed as the gelatin concentration increases. The measurement is fitted to the linearized Rayleigh–Plesset equation coupled with the Voigt constitutive equation that models the behavior of linear viscoelastic solids; the fitting yields good agreement by tuning unknown values of the viscosity and rigidity, indicating that more complex phenomena including shear thinning, stress relaxation, and retardation do not play an important role for the small-amplitude oscillations. Moreover, the cases for bubble-bubble and bubble-wall systems are studied. The observed interaction effect on the linearized dynamics can be explained as well by a set of the Rayleigh–Plesset equations coupled through acoustic radiation among these systems. This suggests that this experimental setup can be applied to validate the model of bubble dynamics with more complex configuration such as a cloud of bubbles in viscoelastic materials.
... For Consumers Consumer Information by Audience For Women Hair Dye and Hair Relaxers Share Tweet Linkedin Pin it More sharing ... products. If you have a bad reaction to hair dyes and relaxers, you should: Stop using the ...
The Detection of Phase Amplitude Coupling during Sensory Processing
Robert A. Seymour
2017-09-01
Full Text Available There is increasing interest in understanding how the phase and amplitude of distinct neural oscillations might interact to support dynamic communication within the brain. In particular, previous work has demonstrated a coupling between the phase of low frequency oscillations and the amplitude (or power of high frequency oscillations during certain tasks, termed phase amplitude coupling (PAC. For instance, during visual processing in humans, PAC has been reliably observed between ongoing alpha (8–13 Hz and gamma-band (>40 Hz activity. However, the application of PAC metrics to electrophysiological data can be challenging due to numerous methodological issues and lack of coherent approaches within the field. Therefore, in this article we outline the various analysis steps involved in detecting PAC, using an openly available MEG dataset from 16 participants performing an interactive visual task. Firstly, we localized gamma and alpha-band power using the Fieldtrip toolbox, and extracted time courses from area V1, defined using a multimodal parcelation scheme. These V1 responses were analyzed for changes in alpha-gamma PAC, using four common algorithms. Results showed an increase in alpha (7–13 Hz–gamma (40–100 Hz PAC in response to the visual grating stimulus, though specific patterns of coupling were somewhat dependent upon the algorithm employed. Additionally, post-hoc analyses showed that these results were not driven by the presence of non-sinusoidal oscillations, and that trial length was sufficient to obtain reliable PAC estimates. Finally, throughout the article, methodological issues and practical guidelines for ongoing PAC research will be discussed.
CPGs control method using a new oscillator in robotic fish
无
2010-01-01
A new oscillator is presented in this paper based on our pervious oscillator (Zhang’s oscillator). Using this new oscillator, a bionic neural control system, the central pattern generators (CPGs) control system, is built. This control system has a two-level form. To validate the function of this new oscillator and the control system, simulations and experiments were both carried out, a simple robotic fish was built with three joints, and the results showed that the new oscillator can be used in startup and stop control mode, angle offset control mode and amplitude changing control mode. The new oscillator can be used in bionic CPGs control area with a simple form, and may be a new progress in bionic control.
An analytical formulation for phase noise in MEMS oscillators.
Agrawal, Deepak; Seshia, Ashwin
2014-12-01
In recent years, there has been much interest in the design of low-noise MEMS oscillators. This paper presents a new analytical formulation for noise in a MEMS oscillator encompassing essential resonator and amplifier nonlinearities. The analytical expression for oscillator noise is derived by solving a second-order nonlinear stochastic differential equation. This approach is applied to noise modeling of an electrostatically addressed MEMS resonator-based square-wave oscillator in which the resonator and oscillator circuit nonlinearities are integrated into a single modeling framework. By considering the resulting amplitude and phase relations, we derive additional noise terms resulting from resonator nonlinearities. The phase diffusion of an oscillator is studied and the phase diffusion coefficient is proposed as a metric for noise optimization. The proposed nonlinear phase noise model provides analytical insight into the underlying physics and a pathway toward the design optimization for low-noise MEMS oscillators.
Magnus approximation in neutrino oscillations
Acero, Mario A.; Aguilar-Arevalo, Alexis A.; D'Olivo, J. C.
2011-04-01
Oscillations between active and sterile neutrinos remain as an open possibility to explain some anomalous experimental observations. In a four-neutrino (three active plus one sterile) mixing scheme, we use the Magnus expansion of the evolution operator to study the evolution of neutrino flavor amplitudes within the Earth. We apply this formalism to calculate the transition probabilities from active to sterile neutrinos with energies of the order of a few GeV, taking into account the matter effect for a varying terrestrial density.
Computing Maximally Supersymmetric Scattering Amplitudes
Stankowicz, James Michael, Jr.
This dissertation reviews work in computing N = 4 super-Yang--Mills (sYM) and N = 8 maximally supersymmetric gravity (mSUGRA) scattering amplitudes in D = 4 spacetime dimensions in novel ways. After a brief introduction and overview in Ch. 1, the various techniques used to construct amplitudes in the remainder of the dissertation are discussed in Ch. 2. This includes several new concepts such as d log and pure integrand bases, as well as how to construct the amplitude using exactly one kinematic point where it vanishes. Also included in this chapter is an outline of the Mathematica package on shell diagrams and numerics.m (osdn) that was developed for the computations herein. The rest of the dissertation is devoted to explicit examples. In Ch. 3, the starting point is tree-level sYM amplitudes that have integral representations with residues that obey amplitude relations. These residues are shown to have corresponding residue numerators that allow a double copy prescription that results in mSUGRA residues. In Ch. 4, the two-loop four-point sYM amplitude is constructed in several ways, showcasing many of the techniques of Ch. 2; this includes an example of how to use osdn. The two-loop five-point amplitude is also presented in a pure integrand representation with comments on how it was constructed from one homogeneous cut of the amplitude. On-going work on the two-loop n-point amplitude is presented at the end of Ch. 4. In Ch. 5, the three-loop four-point amplitude is presented in the d log representation and in the pure integrand representation. In Ch. 6, there are several examples of four- through seven-loop planar diagrams that illustrate how considerations of the singularity structure of the amplitude underpin dual-conformal invariance. Taken with the previous examples, this is additional evidence that the structure known to exist in the planar sector extends to the full theory. At the end of this chapter is a proof that all mSUGRA amplitudes have a pole at
Scattering Amplitudes in Gauge Theories
Schubert, Ulrich
2014-01-01
This thesis is focused on the development of new mathematical methods for computing multi-loop scattering amplitudes in gauge theories. In this work we combine, for the first time, the unitarity-based construction for integrands, and the recently introduced integrand-reduction through multivariate polynomial division. After discussing the generic features of this novel reduction algorithm, we will apply it to the one- and two-loop five-point amplitudes in ${\\cal N}=4$ sYM. The integrands of the multiple-cuts are generated from products of tree-level amplitudes within the super-amplitudes formalism. The corresponding expressions will be used for the analytic reconstruction of the polynomial residues. Their parametric form is known a priori, as derived by means of successive polynomial divisions using the Gr\\"obner basis associated to the on-shell denominators. The integrand reduction method will be exploited to investigate the color-kinematic duality for multi-loop ${\\cal N}=4$ sYM scattering amplitudes. Our a...
Cyanohydrin reactions enhance glycolytic oscillations in yeast
Hald, Bjørn Olav; Nielsen, Astrid Gram; Tortzen, Christian
2015-01-01
Synchronous metabolic oscillations can be induced in yeast by addition of glucose and removal of extracellular acetaldehyde (ACAx). Compared to other means of ACAx removal, cyanide robustly induces oscillations, indicating additional cyanide reactions besides ACA to lactonitrile conversion. Here......, (13)C NMR is used to confirm our previous hypothesis, that cyanide directly affects glycolytic fluxes through reaction with carbonyl-containing compounds. Intracellularly, at least 3 cyanohydrins were identified. Extracellularly, all signals could be identified and lactonitrile was found to account...... for ~66% of total cyanide removal. Simulations of our updated computational model show that intracellular cyanide reactions increase the amplitude of oscillations and that cyanide addition lowers [ACA] instantaneously. We conclude that cyanide provides the following means of inducing global oscillations...
The Origin of Type I Spicule Oscillations
Jess, D B; Christian, D J; Mathioudakis, M; Keys, P H; Keenan, F P
2011-01-01
We use images of high spatial and temporal resolution, obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope, to reveal how the generation of transverse waves in Type I spicules is a direct result of longitudinal oscillations occurring in the photosphere. Here we show how pressure oscillations, with periodicities in the range 130 - 440 s, manifest in small-scale photospheric magnetic bright points, and generate kink waves in the Sun's outer atmosphere with transverse velocities approaching the local sound speed. Through comparison of our observations with advanced two-dimensional magneto-hydrodynamic simulations, we provide evidence for how magnetoacoustic oscillations, generated at the solar surface, funnel upwards along Type I spicule structures, before undergoing longitudinal-to-transverse mode conversion into waves at twice the initial driving frequency. The resulting kink modes are visible in chromospheric plasma, with periodicities of 65 -220 s, and amplitud...
Oscillations in SIRS model with distributed delays
Gonçalves, S.; Abramson, G.; Gomes, M. F. C.
2011-06-01
The ubiquity of oscillations in epidemics presents a long standing challenge for the formulation of epidemic models. Whether they are external and seasonally driven, or arise from the intrinsic dynamics is an open problem. It is known that fixed time delays destabilize the steady state solution of the standard SIRS model, giving rise to stable oscillations for certain parameters values. In this contribution, starting from the classical SIRS model, we make a general treatment of the recovery and loss of immunity terms. We present oscillation diagrams (amplitude and period) in terms of the parameters of the model, showing how oscillations can be destabilized by the shape of the distributions of the two characteristic (infectious and immune) times. The formulation is made in terms of delay equations which are both numerically integrated and linearized. Results from simulations are included showing where they support the linear analysis and explaining why not where they do not. Considerations and comparison with real diseases are presented along.
Detecting Friedel oscillations in ultracold Fermi gases
Riechers, Keno; Hueck, Klaus; Luick, Niclas; Lompe, Thomas; Moritz, Henning
2017-09-01
Investigating Friedel oscillations in ultracold gases would complement the studies performed on solid state samples with scanning-tunneling microscopes. In atomic quantum gases interactions and external potentials can be tuned freely and the inherently slower dynamics allow to access non-equilibrium dynamics following a potential or interaction quench. Here, we examine how Friedel oscillations can be observed in current ultracold gas experiments under realistic conditions. To this aim we numerically calculate the amplitude of the Friedel oscillations which are induced by a potential barrier in a 1D Fermi gas and compare it to the expected atomic and photonic shot noise in a density measurement. We find that to detect Friedel oscillations the signal from several thousand one-dimensional systems has to be averaged. However, as up to 100 parallel one-dimensional systems can be prepared in a single run with present experiments, averaging over about 100 images is sufficient.
Kinetic Actviation Relaxation Technique
Béland, Laurent Karim; El-Mellouhi, Fedwa; Joly, Jean-François; Mousseau, Normand
2011-01-01
We present a detailed description of the kinetic Activation-Relaxation Technique (k-ART), an off-lattice, self-learning kinetic Monte Carlo algorithm with on-the-fly event search. Combining a topological classification for local environments and event generation with ART nouveau, an efficient unbiased sampling method for finding transition states, k-ART can be applied to complex materials with atoms in off-lattice positions or with elastic deformations that cannot be handled with standard KMC approaches. In addition to presenting the various elements of the algorithm, we demonstrate the general character of k-ART by applying the algorithm to three challenging systems: self-defect annihilation in c-Si, self-interstitial diffusion in Fe and structural relaxation in amorphous silicon.
Nonlinear fractional relaxation
A Tofighi
2012-04-01
We deﬁne a nonlinear model for fractional relaxation phenomena. We use -expansion method to analyse this model. By studying the fundamental solutions of this model we ﬁnd that when → 0 the model exhibits a fast decay rate and when → ∞ the model exhibits a power-law decay. By analysing the frequency response we ﬁnd a logarithmic enhancement for the relative ratio of susceptibility.
Kondo Breakdown and Quantum Oscillations in SmB_{6}.
Erten, Onur; Ghaemi, Pouyan; Coleman, Piers
2016-01-29
Recent quantum oscillation experiments on SmB_{6} pose a paradox, for while the angular dependence of the oscillation frequencies suggest a 3D bulk Fermi surface, SmB_{6} remains robustly insulating to very high magnetic fields. Moreover, a sudden low temperature upturn in the amplitude of the oscillations raises the possibility of quantum criticality. Here we discuss recently proposed mechanisms for this effect, contrasting bulk and surface scenarios. We argue that topological surface states permit us to reconcile the various data with bulk transport and spectroscopy measurements, interpreting the low temperature upturn in the quantum oscillation amplitudes as a result of surface Kondo breakdown and the high frequency oscillations as large topologically protected orbits around the X point. We discuss various predictions that can be used to test this theory.
Direct observation of coherent energy transfer in nonlinear micromechanical oscillators
Chen, Changyao; Zanette, Damián H.; Czaplewski, David A.; Shaw, Steven; López, Daniel
2017-05-01
Energy dissipation is an unavoidable phenomenon of physical systems that are directly coupled to an external environmental bath. In an oscillatory system, it leads to the decay of the oscillation amplitude. In situations where stable oscillations are required, the energy dissipated by the vibrations is usually compensated by replenishment from external energy sources. Consequently, if the external energy supply is removed, the amplitude of oscillations start to decay immediately, since there is no means to restitute the energy dissipated. Here, we demonstrate a novel dissipation engineering strategy that can support stable oscillations without supplying external energy to compensate losses. The fundamental intrinsic mechanism of resonant mode coupling is used to redistribute and store mechanical energy among vibrational modes and coherently transfer it back to the principal mode when the external excitation is off. To experimentally demonstrate this phenomenon, we exploit the nonlinear dynamic response of microelectromechanical oscillators to couple two different vibrational modes through an internal resonance.
Direct observation of coherent energy transfer in nonlinear micromechanical oscillators.
Chen, Changyao; Zanette, Damián H; Czaplewski, David A; Shaw, Steven; López, Daniel
2017-05-26
Energy dissipation is an unavoidable phenomenon of physical systems that are directly coupled to an external environmental bath. In an oscillatory system, it leads to the decay of the oscillation amplitude. In situations where stable oscillations are required, the energy dissipated by the vibrations is usually compensated by replenishment from external energy sources. Consequently, if the external energy supply is removed, the amplitude of oscillations start to decay immediately, since there is no means to restitute the energy dissipated. Here, we demonstrate a novel dissipation engineering strategy that can support stable oscillations without supplying external energy to compensate losses. The fundamental intrinsic mechanism of resonant mode coupling is used to redistribute and store mechanical energy among vibrational modes and coherently transfer it back to the principal mode when the external excitation is off. To experimentally demonstrate this phenomenon, we exploit the nonlinear dynamic response of microelectromechanical oscillators to couple two different vibrational modes through an internal resonance.
Factorization of Chiral String Amplitudes
Huang, Yu-tin; Yuan, Ellis Ye
2016-01-01
We re-examine a closed-string model defined by altering the boundary conditions for one handedness of two-dimensional propagators in otherwise-standard string theory. We evaluate the amplitudes using Kawai-Lewellen-Tye factorization into open-string amplitudes. The only modification to standard string theory is effectively that the spacetime Minkowski metric changes overall sign in one open-string factor. This cancels all but a finite number of states: As found in earlier approaches, with enough supersymmetry (e.g., type II) the tree amplitudes reproduce those of the massless truncation of ordinary string theory. However, we now find for the other cases that additional fields, formerly thought to be auxiliary, describe new spin-2 states at the two adjacent mass levels (tachyonic and tardyonic). The tachyon is always a ghost, but can be avoided in the heterotic case.
Factorization of chiral string amplitudes
Huang, Yu-tin; Siegel, Warren; Yuan, Ellis Ye
2016-09-01
We re-examine a closed-string model defined by altering the boundary conditions for one handedness of two-dimensional propagators in otherwise-standard string theory. We evaluate the amplitudes using Kawai-Lewellen-Tye factorization into open-string amplitudes. The only modification to standard string theory is effectively that the spacetime Minkowski metric changes overall sign in one open-string factor. This cancels all but a finite number of states: as found in earlier approaches, with enough supersymmetry (e.g., type II) the tree amplitudes reproduce those of the massless truncation of ordinary string theory. However, we now find for the other cases that additional fields, formerly thought to be auxiliary, describe new spin-2 states at the two adjacent mass levels (tachyonic and tardyonic). The tachyon is always a ghost, but can be avoided in the heterotic case.
Shape of Pion Distribution Amplitude
Radyushkin, Anatoly
2009-11-01
A scenario is investigated in which the leading-twist pion distribution amplitude $\\varphi_\\pi (x)$ is approximated by the pion decay constant $f_\\pi$ for all essential values of the light-cone fraction $x$. A model for the light-front wave function $\\Psi (x, k_\\perp)$ is proposed that produces such a distribution amplitude and has a rapidly decreasing (exponential for definiteness) dependence on the light-front energy combination $ k_\\perp^2/x(1-x)$. It is shown that this model easily reproduces the fit of recent large-$Q^2$ BaBar data on the photon-pion transition form factor. Some aspects of scenario with flat pion distribution amplitude are discussed.
Nonsinglet pentagons and NMHV amplitudes
A.V. Belitsky
2015-07-01
Full Text Available Scattering amplitudes in maximally supersymmetric gauge theory receive a dual description in terms of the expectation value of the super Wilson loop stretched on a null polygonal contour. This makes the analysis amenable to nonperturbative techniques. Presently, we elaborate on a refined form of the operator product expansion in terms of pentagon transitions to compute twist-two contributions to NMHV amplitudes. To start with, we provide a novel derivation of scattering matrices starting from Baxter equations for flux-tube excitations propagating on magnon background. We propose bootstrap equations obeyed by pentagon form factors with nonsinglet quantum numbers with respect to the R-symmetry group and provide solutions to them to all orders in 't Hooft coupling. These are then successfully confronted against available perturbative calculations for NMHV amplitudes to four-loop order.
Model of flicker noise effects on phase noise in oscillators
Centurelli, Francesco; Ercolani, Alessandro; Tommasino, Pasquale; Trifiletti, Alessandro
2003-05-01
Phase noise models that describe the near-carrier spectrum in an accurate but insightful way are needed, to better optimize the oscillator design. In this paper we present a model to describe the effect of flicker noise sources on the phase noise of an oscillator, that can be applied both to linear oscillators and to nonlinear structures like relaxation and ring oscillators, so extending previous works that considered only the effect of the flicker noise superimposed to the control voltage of a VCO. In the phase noise of an oscillator we can separate the effect of high frequency noise sources, that can be described by a short-time-constant system, and the effect of low frequency noises (mostly flicker sources), described by a system with time constants much slower than the oscillation period. Flicker noise has been considered to cause a change in the circuit bias point; this bias point change can be mapped in a shift of the oscillation frequency by exploiting Barkhausen conditions (for linear oscillators) or obtaining this link by simulations. The power spectral density of the oscillator can then be obtained as the probability distribution of the oscillation frequency, starting from the flicker noise probability distribution. If the effect of high frequency noise sources is also taken into account, the overall oscillator spectrum can be obtained as a convolution of the spectrum due to flicker sources with the Lorentzian-shaped spectrum due to white noise sources, in analogy with the description of inhomogeneous broadening of laser linewidth.
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.
Numerical investigation of phase relationships in an oscillating sessile drop
Korenchenko, A. E.; Malkova, J. P.
2015-10-01
Forced linear oscillations of a viscous drop placed on a horizontal surface vibrating in perpendicular direction are investigated. The problem is solved for two cases: (1) constant contact angle, and (2) pinned contact line. Phase-frequency and amplitude-frequency characteristics of oscillations of the drop apex are found for the first axisymmetrical mode of oscillations. The independence of the difference of oscillation phases of the drop apex and the substrate on fluid density, viscosity, surface tension, and drop size as well as on presence or absence of the gravity force was demonstrated.
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.
A fast determination method for transverse relaxation of spin-exchange-relaxation-free magnetometer.
Lu, Jixi; Qian, Zheng; Fang, Jiancheng
2015-04-01
We propose a fast and accurate determination method for transverse relaxation of the spin-exchange-relaxation-free (SERF) magnetometer. This method is based on the measurement of magnetic resonance linewidth via a chirped magnetic field excitation and the amplitude spectrum analysis. Compared with the frequency sweeping via separate sinusoidal excitation, our method can realize linewidth determination within only few seconds and meanwhile obtain good frequency resolution. Therefore, it can avoid the drift error in long term measurement and improve the accuracy of the determination. As the magnetic resonance frequency of the SERF magnetometer is very low, we include the effect of the negative resonance frequency caused by the chirp and achieve the coefficient of determination of the fitting results better than 0.998 with 95% confidence bounds to the theoretical equation. The experimental results are in good agreement with our theoretical analysis.
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....
Vibrational resonance in the Morse oscillator
K Abirami; S Rajasekar; M A F Sanjuan
2013-07-01
The occurrence of vibrational resonance is investigated in both classical and quantum mechanical Morse oscillators driven by a biharmonic force. The biharmonic force consists of two forces of widely different frequencies and with $ \\gg $. In the damped and biharmonically driven classical Morse oscillator, by applying a theoretical approach, an analytical expression is obtained for the response amplitude at the low-frequency . Conditions are identified on the parameters for the occurrence of resonance. The system shows only one resonance and moreover at resonance the response amplitude is 1/ where is the coefficient of linear damping. When the amplitude of the high-frequency force is varied after resonance the response amplitude does not decay to zero but approaches a nonzero limiting value. It is observed that vibrational resonance occurs when the sinusoidal force is replaced by a square-wave force. The occurrence of resonance and antiresonance of transition probability of quantum mechanical Morse oscillator is also reported in the presence of the biharmonic external field.
Multivariate Time Series Decomposition into Oscillation Components.
Matsuda, Takeru; Komaki, Fumiyasu
2017-08-01
Many time series are considered to be a superposition of several oscillation components. We have proposed a method for decomposing univariate time series into oscillation components and estimating their phases (Matsuda & Komaki, 2017 ). In this study, we extend that method to multivariate time series. We assume that several oscillators underlie the given multivariate time series and that each variable corresponds to a superposition of the projections of the oscillators. Thus, the oscillators superpose on each variable with amplitude and phase modulation. Based on this idea, we develop gaussian linear state-space models and use them to decompose the given multivariate time series. The model parameters are estimated from data using the empirical Bayes method, and the number of oscillators is determined using the Akaike information criterion. Therefore, the proposed method extracts underlying oscillators in a data-driven manner and enables investigation of phase dynamics in a given multivariate time series. Numerical results show the effectiveness of the proposed method. From monthly mean north-south sunspot number data, the proposed method reveals an interesting phase relationship.
Probing Brownian relaxation in water-glycerol mixtures using magnetic hyperthermia
Nemala, Humeshkar; Milgie, Michael; Wadehra, Anshu; Thakur, Jagdish; Naik, Vaman; Naik, Ratna
2013-03-01
Generation of heat by magnetic nanoparticles in the presence of an external oscillating magnetic field is known as magnetic hyperthermia (MHT). This heat is generated by two mechanisms: the Neel relaxation and Brownian relaxation. While the internal spin relaxation of the nanoparticles known as Neel relaxation is largely dependent on the magnetic properties of the nanoparticles, the physical motion of the particle or the Brownian relaxation is largely dependent on the viscous properties of the carrier liquid. The MHT properties of dextran coated iron oxide nanoparticles have been investigated at a frequency of 400KHz. To understand the influence of Brownian relaxation on heating, we probe the MHT properties of these ferrofluids in water-glycerol mixtures of varying viscosities. The heat generation is quantified using the specific absorption rate (SAR) and its maximum at a particular temperature is discussed with reference to the viscosity.
Employing Helicity Amplitudes for Resummation
Moult, Ian; Tackmann, Frank J; Waalewijn, Wouter J
2015-01-01
Many state-of-the-art QCD calculations for multileg processes use helicity amplitudes as their fundamental ingredients. We construct a simple and easy-to-use helicity operator basis in soft-collinear effective theory (SCET), for which the hard Wilson coefficients from matching QCD onto SCET are directly given in terms of color-ordered helicity amplitudes. Using this basis allows one to seamlessly combine fixed-order helicity amplitudes at any order they are known with a resummation of higher-order logarithmic corrections. In particular, the virtual loop amplitudes can be employed in factorization theorems to make predictions for exclusive jet cross sections without the use of numerical subtraction schemes to handle real-virtual infrared cancellations. We also discuss matching onto SCET in renormalization schemes with helicities in $4$- and $d$-dimensions. To demonstrate that our helicity operator basis is easy to use, we provide an explicit construction of the operator basis, as well as results for the hard m...
Scattering amplitudes in gauge theories
Henn, Johannes M. [Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Plefka, Jan C. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2014-03-01
First monographical text on this fundamental topic. Course-tested, pedagogical and self-contained exposition. Includes exercises and solutions. At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.
Employing Helicity Amplitudes for Resummation
Moult, I.; Stewart, I.W.; Tackmann, F.J.; Waalewijn, W.J.
2015-01-01
Many state-of-the-art QCD calculations for multileg processes use helicity amplitudes as their fundamental ingredients. We construct a simple and easy-to-use helicity operator basis in soft-collinear effective theory (SCET), for which the hard Wilson coefficients from matching QCD onto SCET are dire
Extracting amplitudes from photoproduction data
Workman, R. L.
2011-09-01
We consider the problems associated with amplitude extraction, from meson photoproduction data, over the first resonance regions. The notion of a complete experiment has motivated the FROST program at Jefferson Lab. Exercises applied to pion photoproduction data illustrate the problems to be confronted in any attempt to extract underlying resonance signals from these data (without introducing a model for the resonant process).
Breaking of Large Amplitude Electron Plasma Wave in a Maxwellian Plasma
Mukherjee, Arghya
2016-01-01
The determination of maximum possible amplitude of a coherent longitudinal plasma oscillation/wave is a topic of fundamental importance in non-linear plasma physics. The amplitudes of these large amplitude plasma waves is limited by a phenomena called wave breaking which may be induced by several non-linear processes. It was shown by Coffey [T. P. Coffey, Phys. Fluids 14, 1402 (1971)] using a "water-bag" distribution for electrons that, in a warm plasma the maximum electric field amplitude and density amplitude implicitly depend on the electron temperature, known as Coffey's limit. In this paper, the breaking of large amplitude freely running electron plasma wave in a homogeneous warm plasma where electron's velocity distribution is Maxwellian has been studied numerically using 1D Particle in Cell (PIC) simulation method. It is found that Coffey's propagating wave solutions, which was derived using a "water-bag" distribution for electrons, also represent propagating waves in a Maxwellian plasma. Coffey's wave...
The vertical oscillations of coupled magnets
Kewei, Li; Jiahuang, Lin; Yang, Kang Zi; Liang, Samuel Yee Wei; Wong Say Juan, Jeremias
2011-07-01
The International Young Physicists' Tournament (IYPT) is a worldwide, annual competition for high school students. This paper is adapted from the winning solution to Problem 14, Magnetic Spring, as presented in the final round of the 23rd IYPT in Vienna, Austria. Two magnets were arranged on top of each other on a common axis. One was fixed, while the other could move vertically. Various parameters of interest were investigated, including the effective gravitational acceleration, the strength, size, mass and geometry of the magnets, and damping of the oscillations. Despite its simplicity, this setup yielded a number of interesting and unexpected relations. The first stage of the investigation was concerned only with the undamped oscillations of small amplitudes, and the period of small amplitude oscillations was found to be dependent only on the eighth root of important magnet properties such as its strength and mass. The second stage sought to investigate more general oscillations. A numerical model which took into account magnet size, magnet geometry and damping effects was developed to model the general oscillations. Air resistance and friction were found to be significant sources of damping, while eddy currents were negligible.
The vertical oscillations of coupled magnets
Li Kewei; Lin Jiahuang; Kang Zi Yang [Raffles Institution, 1 Raffles Institution Lane, Singapore 575954 (Singapore); Liang, Samuel Yee Wei [Anglo-Chinese School Independent, 121 Dover Road, Singapore 139650 (Singapore); Juan, Jeremias Wong Say, E-mail: likewei92@gmail.com [NUS High School of Mathematics and Science, 20 Clementi Avenue 1, Singapore 129957 (Singapore)
2011-07-15
The International Young Physicists' Tournament (IYPT) is a worldwide, annual competition for high school students. This paper is adapted from the winning solution to Problem 14, Magnetic Spring, as presented in the final round of the 23rd IYPT in Vienna, Austria. Two magnets were arranged on top of each other on a common axis. One was fixed, while the other could move vertically. Various parameters of interest were investigated, including the effective gravitational acceleration, the strength, size, mass and geometry of the magnets, and damping of the oscillations. Despite its simplicity, this setup yielded a number of interesting and unexpected relations. The first stage of the investigation was concerned only with the undamped oscillations of small amplitudes, and the period of small amplitude oscillations was found to be dependent only on the eighth root of important magnet properties such as its strength and mass. The second stage sought to investigate more general oscillations. A numerical model which took into account magnet size, magnet geometry and damping effects was developed to model the general oscillations. Air resistance and friction were found to be significant sources of damping, while eddy currents were negligible.
Miwadinou, C H; Monwanou, A V; Orou, J B Chabi
2013-01-01
This paper considers nonlinear dynamics of plasma oscillations modeled by a forced modified Van der Pol-Duffing oscillator. These plasma oscillations are described by a nonlinear differential equation of the form $ \\ddot{x}+ \\epsilon (1 +{x}^{2}){\\dot{x}} + x+ \\alpha \\epsilon{x}{\\dot{x}} + {\\beta}x^{2}+\\gamma x^{3}= F\\cos{\\Omega t}.$ The amplitudes of the forced harmonic, superharmonic and subharmonic oscillatory states are obtained using the harmonic balance technique and the multiple time scales methods. Bifurcation sequences displayed by the model for each type of oscillatory states are performed numerically through the fourth order Runge- Kutta scheme. The influences of the differents parameters and of amplitude of external forced have been found.
Basin stability measure of different steady states in coupled oscillators.
Rakshit, Sarbendu; Bera, Bidesh K; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-04-05
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis.
Basin stability measure of different steady states in coupled oscillators
Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-01-01
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis. PMID:28378760
LC Oscillator Driver for Safety Critical Applications
Horsky, Pavel
2011-01-01
A CMOS harmonic signal LC oscillator driver for automotive applications working in a harsh environment with high safety critical requirements is described. The driver can be used with a wide range of external components parameters (LC resonance network of a sensor). Quality factor of the external LC network can vary two decades. Amplitude regulation of the driver is digitally controlled and the DAC is constructed as exponential with piece-wise-linear (PWL) approximation. Low current consumption for high quality resonance networks is achieved. Realized oscillator is robust, used in safety critical application and has low EMC emissions.
Effect of joint mobilization on the H Reflex amplitude in people with spasticity
Pérez Parra, Julio Ernesto; Henao Lema, Claudia Patricia
2011-01-01
Objective: To determine the effect of ankle joint mobilization on the H reflex amplitude of thesoleus muscle in people with spasticity. Materials and methods: A quasi-experimental study withcrossover design and simple masking was conducted in 24 randomized subjects to initiate thecontrol or experimental group. Traction and rhythmic oscillation were applied for five minutesto the ankle joint. H wave amplitude changes of Hoffmann reflex (electrical equivalent of themonosynaptic spinal reflex) w...
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.
Slow Intramolecular Vibrational Relaxation Leads to Long-Lived Excited-State Wavepackets.
Rafiq, Shahnawaz; Scholes, Gregory D
2016-09-01
Broadband optical pump and compressed white light continuum probe were used to measure the transient excited-state absorption, ground-state bleach, and stimulated emission signals of cresyl violet solution in methanol. Amplitude oscillations caused by wavepacket motion in the ground and excited electronic states were analyzed. It was found that vibrational coherences in the excited state persist for more than the experimental waiting time window of 6 ps, and the strongest mode had a dephasing time constant of 2.4 ps. We hypothesize the dephasing of the wavepacket in the excited state is predominantly caused by intramolecular vibrational relaxation (IVR). Slow IVR indicates weak mode-mode coupling and therefore weak anharmonicity of the potential of this vibration. Thus, the initially prepared vibrational wavepacket in the excited state is not significantly perturbed by nonadiabatic coupling to other electronic states, and hence the diabatic and adiabatic representations of the system are essentially identical within the Born-Oppenheimer approximation. The wavepacket therefore evolves with time in an almost harmonic potential, slowly dephased by IVR and the pure vibrational decoherence. The consistency in the position of node (phase change in the wavepacket) in the excited-state absorption and stimulated emission signals without undergoing any frequency shift until the wavepacket is completely dephased conforms to the absence of any reactive internal conversion.
Thermal self-oscillations in radiative heat exchange
Dyakov, Sergey; Yan, Min; Qiu, Min
2014-01-01
We report the effect of relaxation-type self-induced temperature oscillations in the system of two parallel plates of SiO$_2$ and VO$_2$ which exchange heat by thermal radiation in vacuum. The nonlinear feedback in the self-oscillating system is provided by metal-insulator transition in VO$_2$. Using the method of fluctuational electrodynamics we show that under the action of external laser of a constant power, the temperature of VO$_2$ plate oscillates around its phase transition value.
Relaxation and resonances in fluctuating dielectric systems
Garcia-Colin, L. S.; del Castillo, L. F.
1989-09-01
In this paper we show how the ideas behind extended irreversible thermodynamics are used to generate a systematic treatment of the relaxation and resonance phenomena in the propagation and absorption of electromagnetic energy in dielectric materials in a nonequilibrium state. Two cases are discussed: the first, in which the forced oscillations arising from the correlation between the fluctuations of the polarization vector and the electric field are neglected, and the second, in which this term is taken into account. In both cases we show how the main equations serve to make a connection between the macroscopic approach followed here and a number of results obtained for both, gases and polar liquids using molecular models. The results obtained here are compared with previous work on this problem, and new effects arising from the second case are pointed out.
Gauge and Gravity Amplitude Relations
Carrasco, John Joseph M
2015-01-01
In these lectures I talk about simplifications and universalities found in scattering amplitudes for gauge and gravity theories. In contrast to Ward identities, which are understood to arise from familiar symmetries of the classical action, these structures are currently only understood in terms of graphical organizational principles, such as the gauge-theoretic color-kinematics duality and the gravitational double-copy structure, for local representations of multi-loop S-matrix elements. These graphical principles make manifest new relationships in and between gauge and gravity scattering amplitudes. My lectures will focus on arriving at such graphical organizations for generic theories with examples presented from maximal supersymmetry, and their use in unitarity-based multi-loop integrand construction.
Infrared singularities in QCD amplitudes
Gardi, Einan
2009-01-01
We review recent progress in determining the infrared singularity structure of on-shell scattering amplitudes in massless gauge theories. We present a simple ansatz where soft singularities of any scattering amplitude of massless partons, to any loop order, are written as a sum over colour dipoles, governed by the cusp anomalous dimension. We explain how this formula was obtained, as the simplest solution to a newly-derived set of equations constraining the singularity structure to all orders. We emphasize the physical ideas underlying this derivation: the factorization of soft and collinear modes, the special properties of soft gluon interactions, and the notion of the cusp anomaly. Finally, we briefly discuss potential multi-loop contributions going beyond the sum-over-dipoles formula, which cannot be excluded at present.
Pulse amplitude modulated chlorophyll fluorometer
Greenbaum, Elias; Wu, Jie
2015-12-29
Chlorophyll fluorometry may be used for detecting toxins in a sample because of changes in micro algae. A portable lab on a chip ("LOAC") based chlorophyll fluorometer may be used for toxin detection and environmental monitoring. In particular, the system may include a microfluidic pulse amplitude modulated ("PAM") chlorophyll fluorometer. The LOAC PAM chlorophyll fluorometer may analyze microalgae and cyanobacteria that grow naturally in source drinking water.
Gamma oscillations in human primary somatosensory cortex reflect pain perception.
Joachim Gross
2007-05-01
Full Text Available Successful behavior requires selection and preferred processing of relevant sensory information. The cortical representation of relevant sensory information has been related to neuronal oscillations in the gamma frequency band. Pain is of invariably high behavioral relevance and, thus, nociceptive stimuli receive preferred processing. Here, by using magnetoencephalography, we show that selective nociceptive stimuli induce gamma oscillations between 60 and 95 Hz in primary somatosensory cortex. Amplitudes of pain-induced gamma oscillations vary with objective stimulus intensity and subjective pain intensity. However, around pain threshold, perceived stimuli yielded stronger gamma oscillations than unperceived stimuli of equal stimulus intensity. These results show that pain induces gamma oscillations in primary somatosensory cortex that are particularly related to the subjective perception of pain. Our findings support the hypothesis that gamma oscillations are related to the internal representation of behaviorally relevant stimuli that should receive preferred processing.
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.
The roles of cortical oscillations in sustained attention.
Clayton, Michael S; Yeung, Nick; Cohen Kadosh, Roi
2015-04-01
We rely on sustained attention to protect task performance against fatigue and distraction. Time-related variations in attention correlate with amplitude changes of specific cortical oscillations. However, the ways in which these oscillations might support sustained attention, how these oscillations are controlled, and the extent to which they influence one another remain unclear. We address this issue by proposing an oscillatory model of sustained attention. Within this framework, sustained attention relies on frontomedial theta oscillations, inter-areal communication via low-frequency phase synchronisation, and selective excitation and inhibition of cognitive processing through gamma and alpha oscillations, respectively. Sustained attention also relies on interactions between these oscillations across attention-related brain networks.
Drop oscillation and mass transfer in alternating electric fields
Carleson, T.E.
1992-06-24
In certain cases droplet direct contact heat transfer rates can be significantly enhanced by the application of an alternating electric field. This field can produce shape oscillations in a droplet which will enhance mixing. The theoretical evaluation of the effect of the interaction of the field with drop charge on the hydrodynamics has been completed for small amplitude oscillations. Previous work with a zero order perturbation method was followed up with a first order perturbation method to evaluate the effect of drop distortion on drop charge and field distribution. The first order perturbation results show secondary drop oscillations of four modes and two frequencies in each mode. The most significant secondary oscillation has the same mode and frequency as the second mode oscillation predicted from the first order perturbation work. The resonant frequency of all oscillations decrease with increasing electric field strength and drop charge. Work is currently underway to evaluate the heat transfer enhancement from an applied alternating electric field.
Artifacts correction for T1rho imaging with constant amplitude spin-lock
Chen, Weitian
2017-01-01
T1rho imaging with constant amplitude spin-lock is prone to artifacts in the presence of B1 RF and B0 field inhomogeneity. Despite significant technological progress, improvements on the robustness of constant amplitude spin-lock are necessary in order to use it for routine clinical practice. This work proposes methods to simultaneously correct for B1 RF and B0 field inhomogeneity in constant amplitude spin-lock. By setting the maximum B1 amplitude of the excitation adiabatic pulses equal to the expected constant amplitude spin-lock frequency, the spins become aligned along the effective field throughout the spin-lock process. This results in T1rho-weighted images free of artifacts, despite the spatial variation of the effective field caused by B1 RF and B0 field inhomogeneity. When the pulse is long, the relaxation effect during the adiabatic half passage may result in a non-negligible error in the mono-exponential relaxation model. A two-acquisition approach is presented to solve this issue. Simulation, phantom, and in-vivo scans demonstrate the proposed methods achieve superior image quality compared to existing methods, and that the two-acquisition method is effective in resolving the relaxation effect during the adiabatic half passage.
All-Multiplicity Amplitudes with Massive Scalars
Forde, D; Forde, Darren; Kosower, David A.
2005-01-01
We compute two infinite series of tree-level amplitudes with a massive scalar pair and an arbitrary number of gluons. We provide results for amplitudes where all gluons have identical helicity, and amplitudes with one gluon of opposite helicity. These amplitudes are useful for unitarity-based one-loop calculations in nonsupersymmetric gauge theories generally, and QCD in particular.
Noise effect on the dynamics and synchronization of saline oscillator's model
Fokou Kenfack, W.; Siewe Siewe, M.; Kofane, T. C.
2017-02-01
The effects of noisy flows on the dynamics and synchronization of the saline oscillator's model are studied. To this aim, we first of all take the noisy perturbations into account in our recent mathematical model of coupled saline oscillators in the form of an additive noise. We next study, through numerical simulations, the effects of the noisy perturbations on the relaxation oscillations and the bifurcation of the oscillatory mode of a sole oscillator. Lastly, the effects of noise on the synchronization of the oscillatory behaviors observed in several coupled cups are investigated through numerical simulations. We find that noises of low intensity synchronize with the internal periodicity of the system and have as effect the shortening of the relaxation time of oscillations. Also, we show that noise has as major effect, to overcome the region of "dead" dynamical behavior. Accounting for noise is useful to reproduce some of the experimental findings in the sense that noises break the identity of coupled identical oscillators.
Attainable conditions and exact invariant for the time-dependent harmonic oscillator
Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)
2006-09-22
The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.
Electron-phonon relaxation time in ultrathin tungsten silicon film
Sidorova, M; Korneev, A; Chulkova, G; Korneeva, Yu; Mikhailov, M; Devizenko, Yu; Kozorezov, A; Goltsman, G
2016-01-01
Using amplitude-modulated absorption of sub-THz radiation (AMAR) method, we studied electron-phonon relaxation in thin disordered films of tungsten silicide. We found a response time ~ 800 ps at critical temperature Tc = 3.4 K, which scales as minus 3 in the temperature range from 1.8 to 3.4 K. We discuss mechanisms, which can result in a strong phonon bottle-neck effect in a few nanometers thick film and yield a substantial difference between the measured time, characterizing response at modulation frequency, and the inelastic electron-phonon relaxation time. We estimate the electron-phonon relaxation time to be in the range ~ 100-200 ps at 3.4 K.
Identification of parameters in amplitude equations describing coupled wakes
Fullana, J M; Zaleski, S; Le Gal, P; Fullana, Jose Maria; Rossi, Maurice; Zaleski, Stephane; Le Gal, Patrice
1996-01-01
We study the flow behind an array of equally spaced parallel cylinders. A system of Stuart-Landau equations with complex parameters is used to model the oscillating wakes. Our purpose is to identify the 6 scalar parameters which most accurately reproduce the experimental data of Chauve and Le Gal [{Physica D {\\bf 58}}, pp 407--413, (1992)]. To do so, we perform a computational search for the minimum of a distance \\calj. We define \\calj as the sum-square difference of the data and amplitudes reconstructed using coupled equations. The search algorithm is made more efficient through the use of a partially analytical expression for the gradient \
Photoinduced Enhancement of the Charge Density Wave Amplitude
Singer, A.; Patel, S. K. K.; Kukreja, R.; Uhlíř, V.; Wingert, J.; Festersen, S.; Zhu, D.; Glownia, J. M.; Lemke, H. T.; Nelson, S.; Kozina, M.; Rossnagel, K.; Bauer, M.; Murphy, B. M.; Magnussen, O. M.; Fullerton, E. E.; Shpyrko, O. G.
2016-07-01
Symmetry breaking and the emergence of order is one of the most fascinating phenomena in condensed matter physics. It leads to a plethora of intriguing ground states found in antiferromagnets, Mott insulators, superconductors, and density-wave systems. Exploiting states of matter far from equilibrium can provide even more striking routes to symmetry-lowered, ordered states. Here, we demonstrate for the case of elemental chromium that moderate ultrafast photoexcitation can transiently enhance the charge-density-wave (CDW) amplitude by up to 30% above its equilibrium value, while strong excitations lead to an oscillating, large-amplitude CDW state that persists above the equilibrium transition temperature. Both effects result from dynamic electron-phonon interactions, providing an efficient mechanism to selectively transform a broad excitation of the electronic order into a well-defined, long-lived coherent lattice vibration. This mechanism may be exploited to transiently enhance order parameters in other systems with coupled degrees of freedom.
Crystalline Undulator with a Small Amplitude and a Short Period
Kostyuk, Andriy
2012-01-01
The crystalline undulator is a single crystal with periodically bent crystallographic planes. If ultrarelativistic charged particles channel through such a crystal, they emit hard radiation of undulator type. A crystalline undulator with a bending amplitude smaller than the distance between the bent planes and a bending period shorter than the period of channeling oscillations is proposed. Heretofore, it was believed that such range of the bending parameters was unsuitable for a crystalline undulator. This point of view is refuted. In fact, the undulator with a small amplitude and a short period is far superior to what was proposed previously. It requires much lower beam energy for production of photons of the same frequency. Such an undulator allows for a larger effective number of undulator periods. It is predicted to emit intense undulator radiation with a narrow spectral distribution and lower and softer background.
Amplitude modulation control of escape from a potential well
Chacón, R. [Departamento de Física Aplicada, Escuela de Ingenierías Industriales, Universidad de Extremadura, Apartado Postal 382, E-06006 Badajoz (Spain); Martínez García-Hoz, A. [Departamento de Física Aplicada, Escuela Universitaria Politécnica, Universidad de Castilla-La Mancha, E-13400 Almadén (Ciudad Real) (Spain); Miralles, J.J. [Departamento de Física Aplicada, Escuela de Ingenieros Industriales, Universidad de Castilla-La Mancha, E-02071 Albacete (Spain); Martínez, P.J. [Departamento de Física Aplicada, E.I.N.A., Universidad de Zaragoza, E-50018 Zaragoza (Spain); Instituto de Ciencia de Materiales de Aragón, CSIC – Universidad de Zaragoza, E-50009 Zaragoza (Spain)
2014-03-01
We demonstrate the effectiveness of periodic amplitude modulations in controlling (suppressing and enhancing) escape from a potential well through the universal model of a damped Helmholtz oscillator subjected to an external periodic excitation (the escape-inducing excitation) whose amplitude is periodically modulated (the escape-controlling excitation). Analytical and numerical results show that this multiplicative control works reliably for different subharmonic resonances between the two periodic excitations involved, and that its effectiveness is comparable to those of different methods of additive control. Additionally, we demonstrate the robustness of the multiplicative control against the presence of low-intensity Gaussian noise. -- Highlights: •Multiplicative control of escape from a potential well has been demonstrated. •Theoretical predictions are obtained from a Melnikov analysis. •It has been shown the robustness of the multiplicative control against noise.
Molecular dynamics simulation of amplitude modulation atomic force microscopy.
Hu, Xiaoli; Egberts, Philip; Dong, Yalin; Martini, Ashlie
2015-06-12
Molecular dynamics (MD) simulations were used to model amplitude modulation atomic force microscopy (AM-AFM). In this novel simulation, the model AFM tip responds to both tip-substrate interactions and to a sinusoidal excitation signal. The amplitude and phase shift of the tip oscillation observed in the simulation and their variation with tip-sample distance were found to be consistent with previously reported trends from experiments and theory. These simulation results were also fit to an expression enabling estimation of the energy dissipation, which was found to be smaller than that in a corresponding experiment. The difference was analyzed in terms of the effects of tip size and substrate thickness. Development of this model is the first step toward using MD to gain insight into the atomic-scale phenomena that occur during an AM-AFM measurement.
Crisis in Amplitude Control Hides in Multistability
Li, Chunbiao; Sprott, Julien Clinton; Xing, Hongyan
2016-12-01
A crisis of amplitude control can occur when a system is multistable. This paper proposes a new chaotic system with a line of equilibria to demonstrate the threat to amplitude control from multistability. The new symmetric system has two coefficients for amplitude control, one of which is a partial amplitude controller, while the other is a total amplitude controller that simultaneously controls the frequency. The amplitude parameter rescales the basins of attraction and triggers a state switch among different states resulting in a failure of amplitude control to the desired state.
Calculation of multi-loop superstring amplitudes
Danilov, G. S.
2016-12-01
The multi-loop interaction amplitudes in the closed, oriented superstring theory are obtained by the integration of local amplitudes. The local amplitude is represented by a sum over the spinning string local amplitudes. The spinning string local amplitudes are given explicitly through super-Schottky group parameters and through interaction vertex coordinates on the (1| 1) complex, non-split supermanifold. The obtained amplitudes are free from divergences. They are consistent with the world-sheet spinning string symmetries. The vacuum amplitude vanishes along with 1-, 2- and 3-point amplitudes of massless states. The vanishing of the above-mentioned amplitude occurs after the integration of the corresponding local amplitude has been performed over the super-Schottky group limiting points and over interaction vertex coordinate, except for those (3| 2) variables which are fixed due to SL(2)-symmetry.
Magnetoviscosity and relaxation in ferrofluids
Felderhof
2000-09-01
The increase in viscosity of a ferrofluid due to an applied magnetic field is discussed on the basis of a phenomenological relaxation equation for the magnetization. The relaxation equation was derived earlier from irreversible thermodynamics, and differs from that postulated by Shliomis. The two relaxation equations lead to a different dependence of viscosity on magnetic field, unless the relaxation rates are related in a specific field-dependent way. Both planar Couette flow and Poiseuille pipe flow in parallel and perpendicular magnetic field are discussed. The entropy production for these situations is calculated and related to the magnetoviscosity.
Rupp, Wolf; Simon, Karl-Heinz; Bohnert, Michael
2009-01-01
Complete relaxation can be achieved by floating in a darkened, sound-proof relaxation tank filled with salinated water kept at body temperature. Under these conditions, meditation exercises up to self-hypnosis may lead to deep relaxation with physical and mental revitalization. A user manipulated his tank, presumably to completely cut off all optical and acoustic stimuli and accidentally also covered the ventilation hole. The man was found dead in his relaxation tank. The findings suggested lack of oxygen as the cause of death.
Energy substrates that fuel fast neuronal network oscillations
Lukas V. Galow
2014-12-01
Full Text Available Fast neuronal network oscillations in the gamma-frequency band (30-100 Hz provide a fundamental mechanism of complex neuronal information processing in the hippocampus and neocortex of mammals. Gamma oscillations have been implicated in higher brain functions such as sensory perception, motor activity and memory formation. The oscillations emerge from precise synapse interactions between excitatory principal neurons such as pyramidal cells and inhibitory GABAergic interneurons, and they are associated with high energy expenditure. However, both energy substrates and metabolic pathways that are capable to power cortical gamma oscillations have been less defined. Here, we investigated the energy sources fueling persistent gamma oscillations in the CA3 subfield of organotypic hippocampal slice cultures of the rat. This preparation permits superior oxygen supply as well as fast application of glucose, glycolytic metabolites or drugs such as glycogen phosphorylase inhibitor during extracellular recordings of the local field potential. Our findings are: (i gamma oscillations persist in the presence of glucose (10 mmol/L for greater than 60 minutes in slice cultures while (ii lowering glucose levels (2.5 mmol/L significantly reduces the amplitude of the oscillation. (iii Gamma oscillations are absent at low concentration of lactate (2 mmol/L. (iv Gamma oscillations persist at high concentration (20 mmol/L of either lactate or pyruvate, albeit showing significant reductions in the amplitude. (v The breakdown of glycogen significantly delays the decay of gamma oscillations during glucose deprivation. However, when glucose is present, the turnover of glycogen is not essential to sustain gamma oscillations. Our study shows that fast neuronal network oscillations can be fueled by different energy-rich substrates, with glucose being most effective.
Energy substrates that fuel fast neuronal network oscillations.
Galow, Lukas V; Schneider, Justus; Lewen, Andrea; Ta, Thuy-Truc; Papageorgiou, Ismini E; Kann, Oliver
2014-01-01
Fast neuronal network oscillations in the gamma-frequency band (30--100 Hz) provide a fundamental mechanism of complex neuronal information processing in the hippocampus and neocortex of mammals. Gamma oscillations have been implicated in higher brain functions such as sensory perception, motor activity, and memory formation. The oscillations emerge from precise synapse interactions between excitatory principal neurons such as pyramidal cells and inhibitory GABAergic interneurons, and they are associated with high energy expenditure. However, both energy substrates and metabolic pathways that are capable to power cortical gamma oscillations have been less defined. Here, we investigated the energy sources fueling persistent gamma oscillations in the CA3 subfield of organotypic hippocampal slice cultures of the rat. This preparation permits superior oxygen supply as well as fast application of glucose, glycolytic metabolites or drugs such as glycogen phosphorylase inhibitor during extracellular recordings of the local field potential. Our findings are: (i) gamma oscillations persist in the presence of glucose (10 mmol/L) for greater than 60 min in slice cultures while (ii) lowering glucose levels (2.5 mmol/L) significantly reduces the amplitude of the oscillation. (iii) Gamma oscillations are absent at low concentration of lactate (2 mmol/L). (iv) Gamma oscillations persist at high concentration (20 mmol/L) of either lactate or pyruvate, albeit showing significant reductions in the amplitude. (v) The breakdown of glycogen significantly delays the decay of gamma oscillations during glucose deprivation. However, when glucose is present, the turnover of glycogen is not essential to sustain gamma oscillations. Our study shows that fast neuronal network oscillations can be fueled by different energy-rich substrates, with glucose being most effective.
Influence of nonlinearities on the power output of the Self-Oscillating Fluidic Heat Engine (SOFHE)
Tessier-Poirier, A.; Monin, T.; Léveillé, E.; Formosa, F.; Monfray, S.; Fréchette, L. G.
2016-11-01
In this paper, it is shown that two non-linearities drive the oscillations amplitude and the potential power density of the Self-Oscillating Fluidic Heat Engine (SOFHE). This new type of engine converts thermal energy into mechanical energy by producing self-sustained oscillations of a liquid column from a continuous heat source to power wireless sensors from waste heat. The underlying theoretical modeling shows that the pressure and the temperature nonlinearities limit the final oscillations amplitude, hence its achievable power density.
About zeros of some oscillations with dynamic friction
Nicolae MARCOV
2014-04-01
Full Text Available Consider a second order differential non-linear equation having free boundary value conditions. Let be a solution having infinity of unknown zeros. The integral of energy gives the implicit correlation between the successive modules of the extreme values of oscillation. The method of successive approximations transforms this correlation into an algorithmic correlation. The decreasing sequence of the modules or local amplitudes converges to zero. For the local amplitude of oscillation inside the interval of two successive zeros, the length of the interval is a sum of two improper integrals. In order to obtain the values of these integrals, it is necessary to use series expansions. If the coefficient of dynamic friction is small and the amplitude reached a low enough value, then the polynomial functions are given for the numerical calculus of distances between zeros of the oscillation.
Relaxing Behavioural Inheritance
Nuno Amálio
2013-05-01
Full Text Available Object-oriented (OO inheritance allows the definition of families of classes in a hierarchical way. In behavioural inheritance, a strong version, it should be possible to substitute an object of a subclass for an object of its superclass without any observable effect on the system. Behavioural inheritance is related to formal refinement, but, as observed in the literature, the refinement constraints are too restrictive, ruling out many useful OO subclassings. This paper studies behavioural inheritance in the context of ZOO, an object-oriented style for Z. To overcome refinement's restrictions, this paper proposes relaxations to the behavioural inheritance refinement rules. The work is presented for Z, but the results are applicable to any OO language that supports design-by-contract.
Parametrically Driven Nonlinear Oscillators with an Impurity
张卓; 唐翌
2002-01-01
By virtue of the method of multiple scales, we study a chain of parametrically driven nonlinear oscillators with a mass impurity. An equation is presented to describe the nonlinear wave of small amplitude in the chain.In our derivation, the equation is applicable to any eigenmode of coupled pendulum. Our result shows that a nonpropagation soliton emerges as the lowest or highest eigenmode of coupled pendulum is excited, and the impurity tends to pin the nonpropagation soliton excitation.
Diffraction method of vocal chord oscillation sensing
Kuzmin, Sergey Y.; Tuchin, Valery V.
1996-04-01
A method of small-amplitude biovibrations detection is presented in the paper. The method uses a dependence of properties of speckle-structures formed by focused coherent light field diffraction from rough surfaces on the statistics and movement parameters of the surface. With the help of computer modeling the different components of skin surface vibration were analyzed and their influence on speckles dynamics was studied. Human vocal chord oscillations spectrum was monitored using the developed technique.
Combustion Oscillations,Extinction and Control
2007-11-02
counterflow jets using a combination of hot - wire anemometry and laser Doppler velocimetry. The single frequency oscillations will be created by a...slightly heated and using pairs of parallel cold wires of 0.5 micron in diameter. Bulk strain rate and frequency and amplitude of the imposed periodic...characterised by short residence times. The model was first formulated to account for molecular diffusion and turbulent convection and its ability to
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.
High fidelity modeling of thermal relaxation and dissociation of oxygen
Andrienko, Daniil A., E-mail: daniila@umich.edu; Boyd, Iain D. [Department of Aerospace Engineering, University of Michigan, 1320 Beal Ave., Ann Arbor, Michigan 48108 (United States)
2015-11-15
A master equation study of vibrational relaxation and dissociation of oxygen is conducted using state-specific O{sub 2}–O transition rates, generated by extensive trajectory simulations. Both O{sub 2}–O and O{sub 2}–O{sub 2} collisions are concurrently simulated in the evolving nonequilibrium gas system under constant heat bath conditions. The forced harmonic oscillator model is incorporated to simulate the state-to-state relaxation of oxygen in O{sub 2}–O{sub 2} collisions. The system of master equations is solved to simulate heating and cooling flows. The present study demonstrates the importance of atom-diatom collisions due to the extremely efficient energy randomization in the intermediate O{sub 3} complex. It is shown that the presence of atomic oxygen has a significant impact on vibrational relaxation time at temperatures observed in hypersonic flow. The population of highly-excited O{sub 2} vibrational states is affected by the amount of atomic oxygen when modeling the relaxation under constant heat bath conditions. A model of coupled state-to-state vibrational relaxation and dissociation of oxygen is also discussed.
Suzuki, Tomotaka; Sugawara, Kenichi; Ogahara, Kakuya; Higashi, Toshio
2016-01-01
Using transcranial magnetic stimulation (TMS), we investigated how short-interval intracortical inhibition (SICI) was involved with transient motor cortex (M1) excitability changes observed just before the transition from muscle contraction to muscle relaxation. Ten healthy participants performed a simultaneous relaxation task of the ipsilateral finger and foot, relaxing from 10% of their maximal voluntary contraction (MVC) force after the go signal. In the simple reaction time (RT) paradigm, single or paired TMS pulses were randomly delivered after the go signal, and motor evoked potentials (MEPs) were recorded from the right first dorsal interosseous (FDI) muscle. We analyzed the time course prior to the estimated relaxation reaction time (RRT), defined here as the onset of voluntary relaxation. SICI decreased in the 80-100 ms before RRT, and MEPs were significantly greater in amplitude in the 60-80 ms period before RRT than in the other intervals in single-pulse trials. TMS pulses did not effectively increase RRT. These results show that cortical excitability in the early stage, before muscle relaxation, plays an important role in muscle relaxation control. SICI circuits may vary between decreased and increased activation to continuously maintain muscle relaxation during or after a relaxation response. With regard to M1 excitability dynamics, we suggest that SICI also dynamically changes throughout the muscle relaxation process.
Time Course of Corticospinal Excitability and Intracortical Inhibition Just before Muscle Relaxation
Suzuki, Tomotaka; Sugawara, Kenichi; Ogahara, Kakuya; Higashi, Toshio
2016-01-01
Using transcranial magnetic stimulation (TMS), we investigated how short-interval intracortical inhibition (SICI) was involved with transient motor cortex (M1) excitability changes observed just before the transition from muscle contraction to muscle relaxation. Ten healthy participants performed a simultaneous relaxation task of the ipsilateral finger and foot, relaxing from 10% of their maximal voluntary contraction (MVC) force after the go signal. In the simple reaction time (RT) paradigm, single or paired TMS pulses were randomly delivered after the go signal, and motor evoked potentials (MEPs) were recorded from the right first dorsal interosseous (FDI) muscle. We analyzed the time course prior to the estimated relaxation reaction time (RRT), defined here as the onset of voluntary relaxation. SICI decreased in the 80–100 ms before RRT, and MEPs were significantly greater in amplitude in the 60–80 ms period before RRT than in the other intervals in single-pulse trials. TMS pulses did not effectively increase RRT. These results show that cortical excitability in the early stage, before muscle relaxation, plays an important role in muscle relaxation control. SICI circuits may vary between decreased and increased activation to continuously maintain muscle relaxation during or after a relaxation response. With regard to M1 excitability dynamics, we suggest that SICI also dynamically changes throughout the muscle relaxation process. PMID:26858619
Oscillation-Based Test Applied to a Wideband CCII
Pablo Petrashin
2017-01-01
Full Text Available Oscillation-based testing (OBT has been proven to be a simple, yet effective VLSI test for numerous circuit types. This paper investigates, for the first time, the application of OBT verification for second generation current conveyors (CCIIs. The OBT is formed by connecting the CCII into a simple Wien bridge oscillator and monitoring both the amplitude and frequency of oscillation. The fault detection rate, taking into account both the open and short circuit fault simulation analyses, indicates 96.34% fault coverage using a combination of amplitude and frequency output sensing in all technology corners. The only nondetected faults are short circuits between VDD and VSS, which can be detected using other techniques such as IDDQ testing. This method is found to be sensitive to resistor and capacitor process variation in the Wien bridge oscillator, but mitigating test steps are proposed.
Simulations of Oscillating Hydrofoils in Array Configurations
Franck, Jennifer; Simeski, Filip; Spaulding, Arianne
2016-11-01
The vortex and wake interactions of multiple oscillating foils are investigated computationally for energy harvesting applications. Oscillating with high pitch and heave amplitudes to maximize power production, the elliptical-shaped foils generate large coherent vortices at the leading and trailing edge, which are shed downstream to create a large highly structured wake of vortices with alternating sign. Downstream foils oscillate within the large organized wake at a relative phase angle to the lead foil such that power efficiency is optimized. When placed directly downstream of one another, the optimal phase of a second foil is to avoid interactions with the first foil's wake, generating less than half of the total power of the first foil. However, when placed in a staggered configuration the downstream foil has an increase in efficiency through constructive vortex-foil interactions. Funded by ARPAe.
Thermal explosion in oscillating ambient conditions
Novozhilov, Vasily
2016-07-01
Thermal explosion problem for a medium with oscillating ambient temperature at its boundaries is considered. This is a new problem in thermal explosion theory, not previously considered in a distributed system formulation, but important for combustion and fire science. It describes autoignition of wide range of fires (such as but not limited to piles of biosolids and other organic matter; storages of munitions, explosives, propellants) subjected to temperature variations, such as seasonal or day/night variation. The problem is considered in formulation adopted in classical studies of thermal explosion. Critical conditions are determined by frequency and amplitude of ambient temperature oscillations, as well as by a number of other parameters. Effects of all the parameters on critical conditions are quantified. Results are presented for the case of planar symmetry. Development of thermal explosion in time is also considered, and a new type of unsteady thermal explosion development is discovered where thermal runaway occurs after several periods of temperature oscillations within the medium.
Fourier series expansion for nonlinear Hamiltonian oscillators.
Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac
2010-06-01
The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.
Nonlinear Dynamics of A Damped Magnetic Oscillator
Kim, S Y
1999-01-01
We consider a damped magnetic oscillator, consisting of a permanent magnet in a periodically oscillating magnetic field. A detailed investigation of the dynamics of this dissipative magnetic system is made by varying the field amplitude $A$. As $A$ is increased, the damped magnetic oscillator, albeit simple looking, exhibits rich dynamical behaviors such as symmetry-breaking pitchfork bifurcations, period-doubling transitions to chaos, symmetry-restoring attractor-merging crises, and saddle-node bifurcations giving rise to new periodic attractors. Besides these familiar behaviors, a cascade of ``resurrections'' (i.e., an infinite sequence of alternating restabilizations and destabilizations) of the stationary points also occurs. It is found that the stationary points restabilize (destabilize) through alternating subcritical (supercritical) period-doubling and pitchfork bifurcations. We also discuss the critical behaviors in the period-doubling cascades.
Cao, Yongsheng; Osadchiy, Alexey Vladimirovich; Xin, Xiangjun;
2010-01-01
We propose a new method of recognizing spectral amplitude code by using optical coherent detection with a frequency swept local light source oscillator. Our proposed method offer a substantial simplification in terms of required components to built optical label processing units with enhanced...
A Closed form Solution for Nonlinear Oscillators’ Frequencies Using Amplitude-Frequency Formulation
Barari, Amin; Kimiaeifar, Amin; Nejad, M.G
2012-01-01
an analytical approach with a closed form expression for system response would be very useful in different applications. Some analytical techniques have been presented in the literature for the solution of strong nonlinear oscillators as well as approximate and numerical solutions. In this paper, Amplitude...
Theoretical Study of Amplitude Modulation Application during Radio Frequency Electrocoagulation
V. A. Karpuhin
2015-01-01
Full Text Available This article concerns the investigation results of influence of the amplitude-modulated acting signal parameters on the thermoelectric characteristics of biological tissues for a specified geometry of the working electrode section during RF mono-polar electrocoagulation. The geometric model ‘electrode - a biological tissue’ was suggested to study the distribution of power and temperature fields in biological tissue during mono-polar coagulation. The model of biological tissue is represented as a cylinder and the needle electrode is an ellipsoid immersed in the biological tissue. The heat and quasi-electrostatics equations are used as a mathematical model. These equations are solved in Comsol Multiphysics environment.As a result, we have got the following findings: the technique of calculating parameters of the PAM acting signal which has a fixed carrier frequency for the needle electrode of a specified geometry and the immersion depth in biological tissues is suggested. Parameters of PAM signal are determined for this electrode geometry. These parameters provide a 60 ... 80°C heating range of biological tissues near the working part of the tool for different amplitudes of acting signal during RF coagulation. It has been found out that both the temperature and the relaxation frequency of biological tissue depend on exposure time for the needle electrode of a specified geometry and immersion depth of the working part of tool into biological tissue.It is shown that the relaxation frequency of the biological tissue, subjected to the radiofrequency pulses, linearly depends on its heating temperature and can be used as a numerical criterion for maintaining the specified temperature conditions. It is found that the relaxation frequency of the biological tissue depends on the contact area of the tool working part and biological tissues. To reduce this dependence it is necessary to provide automatic current control of the output action.
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...
Observation of oscillatory radial electric field relaxation in a helical plasma
Alonso, J A; Calvo, I; Velasco, J L; Perfilov, S; Chmyga, A; Eliseev, L G; Krupnik, L I; Estrada, T; Kleiber, R; McCarthy, K J; Melnikov, A V; Monreal, P; Parra, F I; Zhezhera, A I
2016-01-01
Measurements of the relaxation of a zonal electrostatic potential perturbation in a non-axisymmetric magnetically confined plasma are presented. A sudden perturbation of the plasma equilibrium is induced by the injection of a cryogenic hydrogen pellet in the TJ-II stellarator, which is observed to be followed by a damped oscillation in the electrostatic potential. The waveform of the relaxation is consistent with theoretical calculations of zonal potential relaxation in a non-axisymmetric magnetic geometry. The turbulent transport properties of a magnetic confinement configuration are expected to depend on the features of the collisionless damping of zonal flows, of which the present letter is the first direct observation.
Magnetic relaxation in anisotropic magnets
Lindgård, Per-Anker
1971-01-01
The line shape and the kinematic and thermodynamic slowing down of the critical and paramagnetic relaxation in axially anisotropic materials are discussed. Kinematic slowing down occurs only in the longitudinal relaxation function. The thermodynamic slowing down occurs in either the transverse or...
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.
Aschwanden, Markus J
2011-01-01
A detailed analysis of a coronal loop oscillation event is presented, using data from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) for the first time. The loop oscillation event occurred on 2010 Oct 16, 19:05-19:35 UT, was triggered by an M2.9 GOES-class flare, located inside a highly inclined cone of a narrow-angle CME. This oscillation event had a number of unusual features: (i) Excitation of kink-mode oscillations in vertical polarization (in the loop plane); (ii) Coupled cross-sectional and density oscillations with identical periods; (iii) no detectable kink amplitude damping over the observed duration of four kink-mode periods ($P=6.3$ min); (iv) multi-loop oscillations with slightly ($\\approx 10%$) different periods; and (v) a relatively cool loop temperature of $T\\approx 0.5$ MK. We employ a novel method of deriving the electron density ratio external and internal to the oscillating loop from the ratio of Alfv\\'enic speeds deduced from the flare trigger delay and...
Constraints on neutrinoless double $\\beta$ decay from neutrino oscillation experiments
Bilenky, S M; Monteno, M
1997-01-01
We show that, in the framework of a general model with mixing of three Majorana neutrinos and a neutrino mass hierarchy, the results of the Bugey and Krasnoyarsk reactor neutrino oscillation experiments imply strong limitations for the effective Majorana mass || that characterizes the amplitude of neutrinoless double beta decay. We obtain further limitations on || from the data of the atmospheric neutrino experiments. We discuss the possible implications of the results of the future long baseline neutrino oscillation experiments for neutrinoless double beta decay.
Electromagnetic emission of a strongly charged oscillating droplet
Grigor'ev, A. I.; Kolbneva, N. Yu.; Shiryaeva, S. O.
2016-08-01
Analytical expressions for electric field in the vicinity of an oscillating strongly charged droplet of nonviscous conducting liquid and intensity of electromagnetic radiation are derived in the linear approximation with respect to perturbation amplitude of the droplet surface. Order-of-magnitude estimations of the radiation intensity are presented. The intensity of electromagnetic radiation of a ball lightning that can be simulated using a charged droplet is not related to the surface oscillations.
Theory of a resonance oscillator with relay interaction
Alekseev, G. A.; Mikhailov, V. I.; Pivovarova, A. G.
A theoretical analysis is presented of an open-resonator oscillator the operation of which is based on the relay interaction of a broad ribbon-shaped electron beam with the spatial harmonic of the HF field of the resonator. Relations of the general theory of oscillator excitation are used to investigate the dependence of the output characteristics on the parameters of the problem, assuming the distribution of HF amplitude to be uniform along the periodic structure.
Super Bloch Oscillation in a PT symmetric system
Turker, Z
2016-01-01
Wannier-Stark ladder in a PT symmetric system is generally complex that leads to amplified/damped Bloch oscillation. We show that a non-amplified wave packet oscillation with very large amplitude can be realized in a non-Hermitian tight binding lattice if certain conditions are satisfied. We show that pseudo PT symmetry guarantees the reality of the quasi energy spectrum in our system.
Time Series Decomposition into Oscillation Components and Phase Estimation.
Matsuda, Takeru; Komaki, Fumiyasu
2017-02-01
Many time series are naturally considered as a superposition of several oscillation components. For example, electroencephalogram (EEG) time series include oscillation components such as alpha, beta, and gamma. We propose a method for decomposing time series into such oscillation components using state-space models. Based on the concept of random frequency modulation, gaussian linear state-space models for oscillation components are developed. In this model, the frequency of an oscillator fluctuates by noise. Time series decomposition is accomplished by this model like the Bayesian seasonal adjustment method. Since the model parameters are estimated from data by the empirical Bayes' method, the amplitudes and the frequencies of oscillation components are determined in a data-driven manner. Also, the appropriate number of oscillation components is determined with the Akaike information criterion (AIC). In this way, the proposed method provides a natural decomposition of the given time series into oscillation components. In neuroscience, the phase of neural time series plays an important role in neural information processing. The proposed method can be used to estimate the phase of each oscillation component and has several advantages over a conventional method based on the Hilbert transform. Thus, the proposed method enables an investigation of the phase dynamics of time series. Numerical results show that the proposed method succeeds in extracting intermittent oscillations like ripples and detecting the phase reset phenomena. We apply the proposed method to real data from various fields such as astronomy, ecology, tidology, and neuroscience.
Stationary Large Amplitude Dynamics of the Finite Chain of Harmonically Coupled Pendulums
Smirnov, Valeri V
2016-01-01
We present an analytical description of the large-amplitude stationary oscillations of the finite discrete system of harmonically-coupled pendulums without any restrictions to their amplitudes (excluding a vicinity of $\\pi$). Although this model has numerous applications in different fields of physics it was studied earlier in the infinite limit only. The developed approach allows to find the dispersion relations for arbitrary amplitudes of the nonlinear normal modes. We underline that the long-wavelength approximation, which is described by well- known sine-Gordon equation leads to inadequate zone structure for the amplitude order of $\\pi/2$ even if the chain is long enough. The extremely complex zone structure at the large amplitudes corresponds to lot of resonances between nonlinear normal modes even with strongly different wave numbers. Due to complexity of the dispersion relations the more short wavelength modes can possess the smaller frequencies. The numerical simulation of the dynamics of the finite-l...
Chimera distribution amplitudes for the pion and the longitudinally polarized ρ-meson
Stefanis, N.G., E-mail: stefanis@tp2.ruhr-uni-bochum.de [Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Pimikov, A.V., E-mail: pimikov@theor.jinr.ru [Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Russian Federation); Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, 730000 (China)
2016-01-15
Using QCD sum rules with nonlocal condensates, we show that the distribution amplitude of the longitudinally polarized ρ-meson may have a shorttailed platykurtic profile in close analogy to our recently proposed platykurtic distribution amplitude for the pion. Such a chimera distribution de facto amalgamates the broad unimodal profile of the distribution amplitude, obtained with a Dyson–Schwinger equations-based computational scheme, with the suppressed tails characterizing the bimodal distribution amplitudes derived from QCD sum rules with nonlocal condensates. We argue that pattern formation, emerging from the collective synchronization of coupled oscillators, can provide a single theoretical scaffolding to study unimodal and bimodal distribution amplitudes of light mesons without recourse to particular computational schemes and the reasons for them.
Chimera distribution amplitudes for the pion and the longitudinally polarized $\\rho$-meson
Stefanis, N G
2016-01-01
Using QCD sum rules with nonlocal condensates, we show that the distribution amplitude of the longitudinally polarized $\\rho$-meson may have a shorttailed platykurtic profile in close analogy to our recently proposed platykurtic distribution amplitude for the pion. Such a chimera distribution de facto amalgamates the broad unimodal profile of the distribution amplitude, obtained with a Dyson-Schwinger equations-based computational scheme, with the suppressed tails characterizing the bimodal distribution amplitudes derived from QCD sum rules with nonlocal condensates. We argue that pattern formation, emerging from the collective synchronization of coupled oscillators, can provide a single theoretical scaffolding to study unimodal and bimodal distribution amplitudes of light mesons without recourse to particular computational schemes and the reasons for them.
Amplitude recruitment of cochlear potential
LI Xingqi; SUN Wei; SUN Jianhe; YU Ning; JIANG Sichang
2001-01-01
Intracellular recordings were made from outer hair cells (OHC) and the cochlear microphonics (CM) were recorded from scala media (SM) in three turn of guinea pig cochlea,the compound action potential (CAP) were recorded at the round window (RW) before and after the animal were exposed to white noise. The results suggest that the nonlinear properties with “saduration” of Input/output (I/O) function of OHC AC recepter potential and CM were founded; the nonlinear properties with “Low”, “Platean” and “high” of CAP also were investigated. After explosion, the threshold shift of CAP has about 10 dB. The I/O of OHC responses and CM were changed in a linearizing (i.e., nonlinearity loss), the “platean” of I/O CAP disappeared and the growth rate of CAP amplitude were larger than before explosion. The response amplitude recruitment of OHC appears to result from reduction in gain (i.e., hearing loss); It was due to the nonlinear growth function of OHC receptor potentials was changed in linearzing that the basilar membrance motion was changed in linearizing. Since intensity coding in the inner ear depends on an interactions of nonlinear basilar membrance and nerve fibers. So that it must lead to a linearizing of CAP as input responses.
Damping of nonlinear standing kink oscillations: a numerical study
Magyar, N
2016-01-01
We aim to study the standing fundamental kink mode of coronal loops in the nonlinear regime, investigating the changes in energy evolution in the cross-section and oscillation amplitude of the loop which are related to nonlinear effects, in particular to the development of the Kelvin-Helmholtz instability (KHI). We run idea, high-resolution three-dimensional (3D) magnetohydrodynamics (MHD) simulations, studying the influence of the initial velocity amplitude and the inhomogeneous layer thickness. We model the coronal loop as a straight, homogeneous magnetic flux tube with an outer inhomogeneous layer, embedded in a straight, homogeneous magnetic field. We find that, for low amplitudes which do not allow for the KHI to develop during the simulated time, the damping time agrees with the theory of resonant absorption. However, for higher amplitudes, the presence of KHI around the oscillating loop can alter the loop's evolution, resulting in a significantly faster damping than predicted by the linear theory in so...
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.
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.
Excitation and evolution of finite-amplitude plasma wave
Hou, Y. W.; Wu, Y. C., E-mail: yican.wu@fds.org.cn [Key Laboratory of Neutronics and Radiation Safety, Institute of Nuclear Energy Safety Technology, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); Chen, M. X. [School of Electronic Science and Applied Physics, Hefei University of Technology, Hefei, Anhui 230009 (China); Yu, M. Y., E-mail: myyu@zju.edu.cn [Institute for Fusion Theory and Simulation and Department of Physics, Zhejiang University, Hangzhou 310027 (China); Institute for Theoretical Physics I, Ruhr University, D-44780 Bochum (Germany); Wu, B. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui 230031 (China)
2015-12-15
The evolution of a small spatially periodic perturbation in the electron velocity distribution function in collisionless plasma is reconsidered by numerically solving the Vlasov and Poisson equations. The short as well as long time behaviors of the excited oscillations and damping/modulation are followed. In the small but finite-amplitude excited plasma wave, resonant electrons become trapped in the wave potential wells and their motion affects the low-velocity electrons participating in the plasma oscillations, leading to modulation of the latter at an effective trapping frequency. It is found that the phase space of the resonant and low-velocity electrons becomes chaotic, but then self-organization takes place but remains fine-scale chaotic. It is also found that as long as particles are trapped, there is only modulation and no monotonic damping of the excited plasma wave. The modulation period/amplitude increases/decreases as the magnitude of the initial disturbance is reduced. For the initial and boundary conditions used here, linear Landau damping corresponds to the asymptotic limit of the modulation period becoming infinite, or no trapping of the resonant electrons.
Large-amplitude ULF waves at high latitudes
Guido, T.; Tulegenov, B.; Streltsov, A. V.
2014-11-01
We present results from the statistical study of ULF waves detected by the fluxgate magnetometer in Gakona, Alaska during several experimental campaigns conducted at the High Frequency Active Auroral Research Program (HAARP) facility in years 2011-2013. We analyzed frequencies of ULF waves recorded during 26 strongly disturbed geomagnetic events (substorms) and compared them with frequencies of ULF waves detected during magnetically quiet times. Our analysis demonstrates that the frequency of the waves carrying most of the power in almost all these events is less than 1 mHz. We also analyzed data from the ACE satellite, measuring parameters of the solar wind in the L1 Lagrangian point between Earth and Sun, and found that in several occasions there is a strong correlation between oscillations of the magnetic field in the solar wind and oscillations detected on the ground. We also found several cases when there is no correlation between signals detected on ACE and on the ground. This finding suggests that these frequencies correspond to the fundamental eigenfrequency of the coupled magnetosphere-ionosphere system, and the amplitude of these waves can reach significant magnitude when the system is driven by the external driver (for example, the solar wind) with this particular frequency. When the frequency of the driver does not match the frequency of the system, the waves still are observed, but their amplitudes are much smaller.
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.
Stress relaxation experiments on a lamellar polystyrene-polyisoprene diblock copolymer melt
Holmqvist, P.; Castelletto, V.; Hamley, I.W.;
2001-01-01
via dynamic light scattering experiments. The slowest relaxation process may be related to the shear-induced orientation of the lamellae. It is shown that time-strain separability G(t, gamma)= G(t)h(gamma) can be applied, and the damping function h(gamma) is consistent with a strongly strain......The non-linear rheology of the lamellar phase of a polystyrene-polyisoprene diblock copolymer is studied by oscillatory shear experiments. The relaxation of the shear modulus, G(t, gamma) is studied as a function of strain amplitude, gamma, up to large amplitude strains, gamma = 100%. The decay...
Chishty, Wajid Ali
between combustor acoustic and heat release and also between combustor acoustics and air through-flow were found to exist. The impact of high amplitude limit-cycle pressure on droplet breakdown under very low mean airflow and the localized effects of forced primary fuel modulations on heat release were also investigated. The non-reacting flow experiments were conducted to study the spray behavior under the presence of an acoustic field. An isothermal acoustic rig was specially fabricated, where the pressure oscillations were generated using an acoustic driver. Phase Doppler Anemometry was used to measure the droplet velocities and sizes under varying acoustic forcing conditions and spray feed pressures. Measurements made at different locations in the spray were related to these variations in mean and unsteady inputs. The droplet velocities were found to show a second order response to acoustic forcing with the cut-off frequency equal to the relaxation time corresponding to mean droplet size. It was also found that under acoustic forcing the droplets migrate radially away from the spray centerline and show oscillatory excursions in their movement. Modeling efforts were undertaken to gain physical insights of spray dynamics under the influence of acoustic forcing and to explain the experimental findings. The radial migration of droplets and their oscillatory movement were validated. The flame characteristics in the two unstable regimes and the transition between them were explained. It was found that under certain acoustic and mean air-flow condition, bands of high droplet densities were formed which resulted in diffusion type group burning of droplets. It was also shown that very high acoustic amplitudes cause secondary breakup of droplets.
Facilitation of epileptic activity during sleep is mediated by high amplitude slow waves.
Frauscher, Birgit; von Ellenrieder, Nicolás; Ferrari-Marinho, Taissa; Avoli, Massimo; Dubeau, François; Gotman, Jean
2015-06-01
Epileptic discharges in focal epilepsy are frequently activated during non-rapid eye movement sleep. Sleep slow waves are present during this stage and have been shown to include a deactivated ('down', hyperpolarized) and an activated state ('up', depolarized). The 'up' state enhances physiological rhythms, and we hypothesize that sleep slow waves and particularly the 'up' state are the specific components of non-rapid eye movement sleep that mediate the activation of epileptic activity. We investigated eight patients with pharmaco-resistant focal epilepsies who underwent combined scalp-intracerebral electroencephalography for diagnostic evaluation. We analysed 259 frontal electroencephalographic channels, and manually marked 442 epileptic spikes and 8487 high frequency oscillations during high amplitude widespread slow waves, and during matched control segments with low amplitude widespread slow waves, non-widespread slow waves or no slow waves selected during the same sleep stages (total duration of slow wave and control segments: 49 min each). During the slow waves, spikes and high frequency oscillations were more frequent than during control segments (79% of spikes during slow waves and 65% of high frequency oscillations, both P ∼ 0). The spike and high frequency oscillation density also increased for higher amplitude slow waves. We compared the density of spikes and high frequency oscillations between the 'up' and 'down' states. Spike and high frequency oscillation density was highest during the transition from the 'up' to the 'down' state. Interestingly, high frequency oscillations in channels with normal activity expressed a different peak at the transition from the 'down' to the 'up' state. These results show that the apparent activation of epileptic discharges by non-rapid eye movement sleep is not a state-dependent phenomenon but is predominantly associated with specific events, the high amplitude widespread slow waves that are frequent, but not
Noisy transcription factor NF-¿B oscillations stabilize and sensitize cytokine signaling in space
Gangstad, S.W.; Feldager, C.W.; Juul, Jeppe Søgaard;
2013-01-01
NF-¿B is a major transcription factor mediating inflammatory response. In response to a pro-inflammatory stimulus, it exhibits a characteristic response - a pulse followed by noisy oscillations in concentrations of considerably smaller amplitude. NF-¿B is an important mediator of cellular...... amplitude has not been addressed. We use a cellular automaton model to address these issues in the context of spatially distributed communicating cells. We find that noisy secondary oscillations stabilize concentric wave patterns, thus improving signal quality. Furthermore, both lower secondary amplitude...... as well as noise in the oscillation period might be working against chronic inflammation, the state of self-sustained and stimulus-independent excitations. Our findings suggest that the characteristic irregular secondary oscillations of lower amplitude are not accidental. On the contrary, they might have...
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.
Induced two-body scattering resonances from a square-well potential with oscillating depth
Hudson Smith, D.
2016-03-01
In systems of ultracold atoms, pairwise interactions can be resonantly enhanced by a new mechanism which does not rely upon a magnetic Feshbach resonance. In this mechanism, interactions are controlled by tuning the frequency of an oscillating parallel component of the magnetic field close to the Bohr frequency for the transition to a two-atom bound state. The real part of the s-wave scattering length a has a resonance as a function of the oscillation frequency near the Bohr frequency. The resonance parameters can be controlled by varying the amplitude of the oscillating field. The amplitude also controls the imaginary part of a which arises predominantly because the oscillating field converts atom pairs into molecules. For the case of a shallow bound state in the scattering channel, the dimensionless resonance parameters are universal functions of the dimensionless oscillation amplitude.
Shen, Yuandeng [Yunnan Observatories, Chinese Academy of Sciences, Kunming 650011 (China); Liu, Ying D. [State Key Laboratory of Space Weather, Chinese Academy of Sciences, Beijing 100190 (China); Chen, P. F. [Key Laboratory of Modern Astronomy and Astrophysics, School of Astronomy and Space Science, Nanjing University, Nanjing 210093 (China); Ichimoto, Kiyoshi, E-mail: ydshen@ynao.ac.cn [Kwasan and Hida Observatories, Kyoto University, Yamashina-ku, Kyoto 607-8471 (Japan)
2014-11-10
We present the first stereoscopic and Doppler observations of simultaneous transverse oscillations of a prominence and a filament and longitudinal oscillation of another filament launched by a single shock wave. Using Hα Doppler observations, we derive the three-dimensional oscillation velocities at different heights along the prominence axis. The results indicate that the prominence has a larger oscillation amplitude and damping time at higher altitude, but the periods at different heights are the same (i.e., 13.5 minutes). This suggests that the prominence oscillates like a linear vertical rigid body with one end anchored on the Sun. One of the filaments shows weak transverse oscillation after the passing of the shock, which is possibly due to the low altitude of the filament and the weakening (due to reflection) of the shock wave before the interaction. Large-amplitude longitudinal oscillation is observed in the other filament after the passing of the shock wave. The velocity amplitude and period are about 26.8 km s{sup –1} and 80.3 minutes, respectively. We propose that the orientation of a filament or prominence relative to the normal vector of the incoming shock should be an important factor for launching transverse or longitudinal filament oscillations. In addition, the restoring forces of the transverse prominence are most likely due to the coupling of gravity and magnetic tension of the supporting magnetic field, while that for the longitudinal filament oscillation is probably the resultant force of gravity and magnetic pressure.
Relations Between Helicity Coupling Amplitude and L-S Coupling Amplitude
WU Ning; RUAN Tu-Nan
2001-01-01
Relations between helicity coupling amplitude and L-S coupling amplitude are discussed. The equivalence condition for these two kinematic analysis methods and the limitations of the L-S coupling amplitude are also studied in this paper.``
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
Holonomy-flux spinfoam amplitude
Perini, Claudio
2012-01-01
We introduce a holomorphic representation for the Lorentzian EPRL spinfoam on arbitrary 2-complexes. The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mour\\~ao-Thiemann heat kernel coherent state transform. The new variables are classical holonomy-flux phase space variables $(h,X)\\simeq \\mathcal T^*SU(2)$ of Hamiltonian loop quantum gravity prescribing the holonomies of the Ashtekar connection $A=\\Gamma + \\gamma K$, and their conjugate gravitational fluxes. For small heat kernel `time' the spinfoam amplitude is peaked on classical space-time geometries, where at most countably many curvatures are allowed for non-zero Barbero-Immirzi parameter. We briefly comment on the possibility to use the alternative flipped classical limit.
Constructing Amplitudes from Their Soft Limits
Boucher-Veronneau, Camille; Larkoski, Andrew J.; /SLAC
2011-12-09
The existence of universal soft limits for gauge-theory and gravity amplitudes has been known for a long time. The properties of the soft limits have been exploited in numerous ways; in particular for relating an n-point amplitude to an (n-1)-point amplitude by removing a soft particle. Recently, a procedure called inverse soft was developed by which 'soft' particles can be systematically added to an amplitude to construct a higher-point amplitude for generic kinematics. We review this procedure and relate it to Britto-Cachazo-Feng-Witten recursion. We show that all tree-level amplitudes in gauge theory and gravity up through seven points can be constructed in this way, as well as certain classes of NMHV gauge-theory amplitudes with any number of external legs. This provides us with a systematic procedure for constructing amplitudes solely from their soft limits.
Constructing amplitudes from their soft limits
Boucher-Veronneau, Camille; Larkoski, Andrew J.
2011-09-01
The existence of universal soft limits for gauge-theory and gravity amplitudes has been known for a long time. The properties of the soft limits have been exploited in numerous ways; in particular for relating an n-point amplitude to an ( n - 1)-point amplitude by removing a soft particle. Recently, a procedure called inverse soft was developed by which "soft" particles can be systematically added to an amplitude to construct a higher-point amplitude for generic kinematics. We review this procedure and relate it to Britto-Cachazo-Feng-Witten recursion. We show that all tree-level amplitudes in gauge theory and gravity up through seven points can be constructed in this way, as well as certain classes of NMHV gauge-theory amplitudes with any number of external legs. This provides us with a systematic procedure for constructing amplitudes solely from their soft limits.
Self-exited gas oscillations in Helmholtz resonator type combustor
Larionov, V. M.; Saifullin, E. R.; Semenova, E. V.
2016-01-01
When the length of the resonance tube is much less and order of the acoustic wavelength is studied. Experimental set-up with a multiport burner is considered. The "energy balance" method is used to calculate the frequency and amplitude of the gas oscillations. The results of measurements and calculations show that increasing the length of the resonance tube causes the excitation oscillation with a first lower frequency. Further, there are no oscillations. When the length of the resonance tube becomes the order of the wavelength, the second resonant frequency is excited. The calculation results are in good agreement with the experimental data.
Investigation of acoustic streaming patterns around oscillating sharp edges
Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco
2014-01-01
Oscillating sharp edges have been employed to achieve rapid and homogeneous mixing in microchannels using acoustic streaming. Here we use a perturbation approach to study the flow around oscillating sharp edges in a microchannel. This work extends prior experimental studies to numerically characterize the effect of various parameters on the acoustically induced flow. Our numerical results match well with the experimental results. We investigated multiple device parameters such as the tip angle, oscillation amplitude, and channel dimensions. Our results indicate that, due to the inherent nonlinearity of acoustic streaming, the channel dimensions could significantly impact the flow patterns and device performance.
Oscillation effects upon film boiling from a sphere.
Schmidt, W. E.; Witte, L. C.
1972-01-01
Heat transfer rates from a silver-plated copper sphere, 0.75 in. in diameter, were studied by high speed photography during oscillations of the sphere in saturated liquid nitrogen and Freon-11. The oscillation frequencies ranged from zero to 13 Hz, and the amplitude-to-diameter ratio varied from zero to 2.67. The sphere was supported by a thin-walled stainless steel tube and carried a thermocouple attached near the lower stagnation point. A Fastax WF-3 16mm movie camera was used at about 2000 frames/sec. The differences in the vapor removal process at lower and higher oscillation frequencies are discussed.
Plasmonic Bloch oscillations in cylindrical metal-dielectric waveguide arrays.
Shiu, Ruei-Cheng; Lan, Yung-Chiang; Chen, Chin-Min
2010-12-01
This study investigates plasmonic Bloch oscillations (PBOs) in cylindrical metal-dielectric waveguide arrays (MDWAs) by performing numerical simulations and theoretical analyses. Optical conformal mapping is used to transform cylindrical MDWAs into equivalent chirped structures with permittivity and permeability gradients across the waveguide arrays, which is caused by the curvature of the cylindrical waveguide. The PBOs are attributed to the transformed structure. The period of oscillation increases with the wavelength of the incident Gaussian beam. However, the amplitude of oscillation is almost independent of wavelength.
Linear oscillations of a drop in uniform alternating electric fields
Yang, Wenrui; Carleson, T.E.
1990-10-01
Oscillations of a conducting drop immersed in a dielectric fluid in an alternating electric field has been modelled in order to understand the enhancement of the transport processes by the electric field. Numerical solutions for oscillation amplitude, velocity distribution, resonant frequency and streamlines were obtained. The effects of viscosity and density on the resonant frequency and the velocity distribution were investigated. It was found that the resonant frequency of viscous fluids was always smaller than the free oscillation frequency of the same droplet. The predicted scanning frequency response curve and the streamlines agree well with the experimental observations.
A Note on Loop Amplitudes in QED
Brandhuber, Andreas; Vincon, Massimiliano
2009-01-01
We consider the two-loop four-point amplitude in N=2 super QED, and show that there exists an approximate recursive structure similar to that captured by the ABDK/BDS ansatz for MHV amplitudes in N=4 super Yang-Mills. Furthermore, we present a simple relation between the box coefficients of one-loop photon MHV amplitudes in (super) QED, and sums of box coefficients of one-loop MHV amplitudes in (super) Yang-Mills.
Qamar, Adnan
2017-06-28
Mass transport and fluid dynamics characteristics in the vicinity of an oscillating cylindrical fiber with an imposed pulsatile inflow condition are computationally investigated in the present study. The work is motivated by a recently proposed design modification to the Total Artificial Lung (TAL) device, which is expected to provide better gas exchange. Navier–Stokes computations, coupled with convection–diffusion equation are performed to assess flow dynamics and mass transport behavior around the oscillating fiber. The oscillations and the pulsatile free stream velocity are represented by two sinusoidal functions. The resulting non-dimensional parameters are Keulegan–Carpenter number (KC), Schmidt number (Sc), Reynolds number (Re), pulsatile inflow amplitude (), and amplitude of cylinder oscillation (). Results are computed for , Sc = 1000, Re = 5 and 10, and 0.7 and 0.25 5.25. The pulsatile inflow parameters correspond to the flow velocities found in human pulmonary artery while matching the operating TAL Reynolds number. Mass transport from the surface of the cylinder to the bulk fluid is found to be primarily dependent on the size of surface vortices created by the movement of the cylinder. Time-averaged surface Sherwood number (Sh) is dependent on the amplitude and KC of cylinder oscillation. Compared to the fixed cylinder case, a significant gain up to 380% in Sh is achieved by oscillating the cylinder even at the small displacement amplitude (AD = 0.75D). Moreover, with decrease in KC the oscillating cylinder exhibits a lower drag amplitude compared with the fixed cylinder case. Inflow pulsation amplitude has minor effects on the mass transport characteristics. However, an increase in results in an increase in the amplitude of the periodic drag force on the cylinder. This rise in the drag amplitude is similar to that measured for the fixed cylinder case. Quantifications of shear stress distribution in the bulk fluid suggest that the physiological
Can Black Hole Relax Unitarily?
Solodukhin, S. N.
2005-03-01
We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex quasi-normal modes. We discuss two ways of modifying the semiclassical black hole geometry to maintain unitarity: the (fractal) brick wall and the worm-hole modification. In the latter case the entropy comes out correctly as well.
Can Black Hole Relax Unitarily?
Solodukhin, Sergey N.
2004-01-01
We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex quasi-normal modes. We discuss two ways of modifying the semiclassical black hole geometry to maintain unitarity: the (fractal) brick wall and the...
Can Black Hole Relax Unitarily?
Solodukhin, S N
2004-01-01
We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex quasi-normal modes. We discuss two ways of modifying the semiclassical black hole geometry to maintain unitarity: the (fractal) brick wall and the worm-hole modification. In the latter case the entropy comes out correctly as well.
Grosse-Wentrup, Moritz; Schölkopf, Bernhard
2014-10-01
Objective. Brain-computer interface (BCI) systems are often based on motor- and/or sensory processes that are known to be impaired in late stages of amyotrophic lateral sclerosis (ALS). We propose a novel BCI designed for patients in late stages of ALS that only requires high-level cognitive processes to transmit information from the user to the BCI. Approach. We trained subjects via EEG-based neurofeedback to self-regulate the amplitude of gamma-oscillations in the superior parietal cortex (SPC). We argue that parietal gamma-oscillations are likely to be associated with high-level attentional processes, thereby providing a communication channel that does not rely on the integrity of sensory- and/or motor-pathways impaired in late stages of ALS. Main results. Healthy subjects quickly learned to self-regulate gamma-power in the SPC by alternating between states of focused attention and relaxed wakefulness, resulting in an average decoding accuracy of 70.2%. One locked-in ALS patient (ALS-FRS-R score of zero) achieved an average decoding accuracy significantly above chance-level though insufficient for communication (55.8%). Significance. Self-regulation of gamma-power in the SPC is a feasible paradigm for brain-computer interfacing and may be preserved in late stages of ALS. This provides a novel approach to testing whether completely locked-in ALS patients retain the capacity for goal-directed thinking.
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.
Analysis of friction self-oscillations of a drilling string with the exponential law of resistance
Belokobylskiy, S.V.; Prokopov, V.K.
1982-01-01
An analysis of the friction self-oscillations in the drilling string based on the exponential law of resistance with. A spasmodic law of resistance was obtained from it as a particular case. It is indicated that for definite parameters, the amplitude of self-oscillations with expoential law of resistance exceeds the scope of oscillations with spasmodic law. Dependences were constructed for the period of self-oscillations and time for motion from these parameters. Dangerous modes of friction self-oscillations were defined.
Magnetic oscillations driven by the spin Hall effect in 3-terminal magnetic tunnel junction devices.
Liu, Luqiao; Pai, Chi-Feng; Ralph, D C; Buhrman, R A
2012-11-02
We show that a direct current in a tantalum microstrip can induce steady-state magnetic oscillations in an adjacent nanomagnet through spin torque from the spin Hall effect (SHE). The oscillations are detected electrically via a magnetic tunnel junction (MTJ) contacting the nanomagnet. The oscillation frequency can be controlled using the MTJ bias to tune the magnetic anisotropy. In this 3-terminal device, the SHE torque and the MTJ bias therefore provide independent controls of the oscillation amplitude and frequency, enabling new approaches for developing tunable spin torque nano-oscillators.
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.
Detection of forced oscillations in power systems with multichannel methods
Follum, James D. [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
2015-09-30
The increasing availability of high fidelity, geographically dispersed measurements in power systems improves the ability of researchers and engineers to study dynamic behaviors in the grid. One such behavior that is garnering increased attention is the presence of forced oscillations. Power system engineers are interested in forced oscillations because they are often symptomatic of the malfunction or misoperation of equipment. Though the resulting oscillation is not always large in amplitude, the root cause may be serious. In this report, multi-channel forced oscillation detection methods are developed. These methods leverage previously developed detection approaches based on the periodogram and spectral-coherence. Making use of geographically distributed channels of data is shown to improved detection performance and shorten the delay before an oscillation can be detected in the online environment. Results from simulated and measured power system data are presented.
Controlling chaos with localized heterogeneous forces in oscillator chains.
Chacón, Ricardo
2006-10-01
The effects of decreasing the impulse transmitted by localized periodic pulses on the chaotic behavior of homogeneous chains of coupled nonlinear oscillators are studied. It is assumed that when the oscillators are driven synchronously, i.e., all driving pulses transmit the same impulse, the chains display chaotic dynamics. It is shown that decreasing the impulse transmitted by the pulses of the two free end oscillators results in regularization with the whole array exhibiting frequency synchronization, irrespective of the chain size. A maximum level of amplitude desynchrony as the pulses of the two end oscillators narrow is typically found, which is explained as the result of two competing universal mechanisms: desynchronization induced by localized heterogeneous pulses and oscillation death of the complete chain induced by drastic decreasing of the impulse transmitted by such localized pulses. These findings demonstrate that decreasing the impulse transmitted by localized external forces can suppress chaos and lead to frequency-locked states in networks of dissipative systems.
Optimal operating points of oscillators using nonlinear resonators.
Kenig, Eyal; Cross, M C; Villanueva, L G; Karabalin, R B; Matheny, M H; Lifshitz, Ron; Roukes, M L
2012-11-01
We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for complete phase noise elimination. We apply the method to a feedback oscillator which employs a high Q weakly nonlinear resonator and provide explicit parameter values for which the feedback phase noise is completely eliminated and others for which there is no amplitude-phase noise conversion. We then establish an operational mode of the oscillator which optimizes its performance by diminishing the feedback noise in both quadratures, thermal noise, and quality factor fluctuations. We also study the spectrum of the oscillator and provide specific results for the case of 1/f noise sources.
Human gamma oscillations during slow wave sleep.
Mario Valderrama
Full Text Available Neocortical local field potentials have shown that gamma oscillations occur spontaneously during slow-wave sleep (SWS. At the macroscopic EEG level in the human brain, no evidences were reported so far. In this study, by using simultaneous scalp and intracranial EEG recordings in 20 epileptic subjects, we examined gamma oscillations in cerebral cortex during SWS. We report that gamma oscillations in low (30-50 Hz and high (60-120 Hz frequency bands recurrently emerged in all investigated regions and their amplitudes coincided with specific phases of the cortical slow wave. In most of the cases, multiple oscillatory bursts in different frequency bands from 30 to 120 Hz were correlated with positive peaks of scalp slow waves ("IN-phase" pattern, confirming previous animal findings. In addition, we report another gamma pattern that appears preferentially during the negative phase of the slow wave ("ANTI-phase" pattern. This new pattern presented dominant peaks in the high gamma range and was preferentially expressed in the temporal cortex. Finally, we found that the spatial coherence between cortical sites exhibiting gamma activities was local and fell off quickly when computed between distant sites. Overall, these results provide the first human evidences that gamma oscillations can be observed in macroscopic EEG recordings during sleep. They support the concept that these high-frequency activities might be associated with phasic increases of neural activity during slow oscillations. Such patterned activity in the sleeping brain could play a role in off-line processing of cortical networks.
Dysrhythmias of the respiratory oscillator
Paydarfar, David; Buerkel, Daniel M.
1995-03-01
refractory periods. The same system can be perturbed to a state in which amplitude of oscillation is attenuated or abolished. We have characterized critical perturbations which induce transitions between these two states, giving rise to patterns of dysrhythmic activity that are similar to those seen in the experiments. We illustrate the importance of noise in initiation and termination of rhythm, comparable to normal respiratory rhythm intermixed with spontaneous dysrhythmias. In the BvP system the incidence and duration of dysrhythmia is shown to be strongly influenced by the level of noise. These studies should lead to greater understanding of rhythmicity and integrative responses of the respiratory control system, and provide insight into disturbances in control mechanisms that cause apnea and aspiration in clinical disease states.
An experimental investigation of low-frequency noise in 8-mm-band Gunn-diode oscillators
Kravtsov, I. A.; Malyshev, V. M.; Meshcheriakov, A. V.
1989-07-01
The noise characteristics of Ka-band Gunn oscillators are studied. The dependences of the frequency fluctuations on the SWR and load phases are analyzed. A comparison of the noise characteristics of Ka- and X-band Gunn oscillators shows that their fluctuation levels are about the same if they are calculated at the same oscillation frequency. The amplitude fluctuation is 10 dB lower in Ka-band oscillators.
Pressure oscillations in a chemical garden
Pantaleone, J.; Toth, A.; Horvath, D.; Rosefigura, L.; Morgan, W.; Maselko, J.
2009-05-01
When soluble metal salts are placed in a silicate solution, chemical gardens grow. These gardens are treelike structures formed of long thin hollow tubes. The growth is driven by the increase in internal pressure from osmosis. One particular case is examined here, calcium chloride in a solution of sodium trisilicate. We directly measure the internal pressure of a silicate garden as it grows via a series of relaxation oscillations. From these observations we deduce the stresses in the membrane and discuss how they influence the growth of tubes. Also we estimate the critical stress and the average Young’s modulus for the silicate garden’s membrane.
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.
Spontaneous Oscillations in an Active Matter System
Hayes, Robert; Tsang, Boyce; Granick, Steve
Active matter (which consumes energy to move about) can organize into dynamic structures more interesting than those possible at steady-state. Here we show spontaneous periodic self-assembly in a simple three-component system of water, oil phase, and surfactant at constant room temperature, with emphasis on one model system. Benchtop experiments show that liquid crystal oil droplets spontaneously and collectively oscillate like a `beating heart' for several hours; contract, relax, and subsequently re-contract in a petri dish at a rate of a few `beats' per minute. These oscillations, emergent from the cooperative interaction of the three components, are driven by the competition between positive and negative feedback processes. This illustration of feedback in action reveals a new way to program self-assembled structures to vary with time.
Halim NAGEM FILHO
1997-04-01
Full Text Available Trinta e sete amalgamadores considerados novos e usados, de cinco marcas comerciais, foram avaliados comparando-os em relação à freqüência de oscilação e à sua possível influência no "creep" do amálgama. Não existiu diferença significante para o número de revoluções por minuto. O pistilo permitiu uma trituração mais eficiente e rápida, ocasionou o aumento da temperatura de trituração e proporcionou um amálgama de menor "creep".Thirty seven used and new amalgamators of five different commercial brands were compared for the frequency of oscillation they produce in order to verify a possible relationship between frequency and creep of the amalgam. No significant differences in frequency were observed; yet the use of the pestle alone allowed a quicker, more efficient trituration under increased temperature, and it produced an amalgam with lower creep.
Roiban, Radu; Spradlin, Marcus; Volovich, Anastasia
2011-11-01
oscillator. In the much more complicated realm of four-dimensional quantum field theories, developments over the past several years have led to the extremely exciting, and already partially realized, prospect of completely solving SYM theory (at least in the planar approximation). This alone is a thrilling prospect for theorists, but the great interest in this subject stems in particular from the fact that this is not some obscure field theory but rather a gauge theory, and hence a close cousin of QCD. As reviewed in several of the articles in this issue, many of the insights and methods developed for SYM theory can be applied, with suitable care, to arbitrary gauge theories. It has occasionally been noted that the study of amplitudes is an experimental science in which expressions for, or empirically observed properties of, various scattering amplitudes serve as the 'data' to be collected and analyzed. The rapid pace of progress is made possible in part by the fact that new data is often available at the click of a mouse. The articles in this issue offer testament to the riches which have been discovered hiding in these data, and there is no doubt that more rewards await theorists with the ambition to seek them out.
An Exact Relaxation of Clustering
Mørup, Morten; Hansen, Lars Kai
2009-01-01
of clustering problems such as the K-means objective and pairwise clustering as well as graph partition problems, e.g., for community detection in complex networks. In particular we show that a relaxation to the simplex can be given for which the extreme solutions are stable hard assignment solutions and vice......Continuous relaxation of hard assignment clustering problems can lead to better solutions than greedy iterative refinement algorithms. However, the validity of existing relaxations is contingent on problem specific fuzzy parameters that quantify the level of similarity between the original...... versa. Based on the new relaxation we derive the SR-clustering algorithm that has the same complexity as traditional greedy iterative refinement algorithms but leading to significantly better partitions of the data. A Matlab implementation of the SR-clustering algorithm is available for download....
The relaxation & stress reduction workbook
Davis, Martha; Eshelman, Elizabeth Robbins; McKay, Matthew
2008-01-01
"The Relaxation & Stress Reduction Workbook broke new ground when it was first published in 1980, detailing easy, step-by-step techniques for calming the body and mind in an increasingly overstimulated world...
Tsunami Focusing and Leading Amplitude
Kanoglu, U.
2016-12-01
Tsunamis transform substantially through spatial and temporal spreading from their source region. This substantial spreading might result unique maximum tsunami wave heights which might be attributed to the source configuration, directivity, the waveguide structures of mid-ocean ridges and continental shelves, focusing and defocusing through submarine seamounts, random focusing due to small changes in bathymetry, dispersion, and, most likely, combination of some of these effects. In terms of the maximum tsunami wave height, after Okal and Synolakis (2016 Geophys. J. Int. 204, 719-735), it is clear that dispersion would be one of the reasons to drive the leading wave amplitude in a tsunami wave train. Okal and Synolakis (2016), referring to this phenomenon as sequencing -later waves in the train becoming higher than the leading one, considered Hammack's (1972, Ph.D. Dissertation, Calif. Inst. Tech., 261 pp) formalism, in addition to LeMéhauté and Wang's (1995 Water waves generated by underwater explosion, World Scientific, 367 pp), to evaluate linear dispersive tsunami propagation from a circular plug uplifted on an ocean of constant depth. They identified transition distance, as the second wave being larger, performing parametric study for the radius of the plug and the depth of the ocean. Here, we extend Okal and Synolakis' (2016) analysis to an initial wave field with a finite crest length and, in addition, to a most common tsunami initial wave form of N-wave (Tadepalli and Synolakis, 1994 Proc. R. Soc. A: Math. Phys. Eng. Sci. 445, 99-112). First, we investigate the focusing feature in the leading-depression side, which enhance tsunami wave height as presented by Kanoglu et al. (2013 Proc. R. Soc. A: Math. Phys. Eng. Sci. 469, 20130015). We then discuss the results in terms of leading wave amplitude presenting a parametric study and identify a simple relation for the transition distance. The solution presented here could be used to better analyze dispersive
无
2010-01-01
The advance in the wide-area measurement system (WAMS) is driving the power system to the trend of wide-area monitoring and control.The Prony method is usually used for low frequency oscillation online identification.However,the identified amplitude and phase information is not sufficiently used.In this paper,the amplitude is adopted to detect the occurrence of the oscillation and to obtain the mode observability of the sites.The phase is adopted to identify the oscillation generator grouping and to obtain the mode shapes.The time varying characteristics of low frequency oscillations are studied.The behaviors and the characters of low frequency oscillations are displayed by dynamic visual techniques.Demonstrations on the "11.9" low frequency oscillation of the Guizhou Power Grid substantiate the feasibility and the validation of the proposed methods.
Contribution of synchrotron oscillation to spill ripple in RF-knockout slow-extraction
Furukawa, T.; Noda, K.
2005-02-01
We have studied the effect of synchrotron oscillations on the spill ripple in RF-knockout extraction, in order to investigate the ripple component of the synchrotron-oscillation frequency and to suppress this component. By using a simplified model of RF-knockout extraction and the simulation, it was found that the following conditions are essential for suppressing the spill ripple including the component of the synchrotron-oscillation frequency: (1) sufficient amplitude of the synchrotron oscillation and (2) uniform distribution in longitudinal phase-space. In the experiment at the Heavy Ion Medical Accelerator in Chiba (HIMAC) synchrotron, the debunch-recapture was carried out before the extraction to obtain the larger oscillation amplitude and the uniform distribution in the longitudinal phase-space. In this article, the contribution of the synchrotron oscillation to the spill ripple is described in detail.
Cross-frequency coupling of brain oscillations in studying motivation and emotion.
Schutter, Dennis J L G; Knyazev, Gennady G
2012-03-01
Research has shown that brain functions are realized by simultaneous oscillations in various frequency bands. In addition to examining oscillations in pre-specified bands, interactions and relations between the different frequency bandwidths is another important aspect that needs to be considered in unraveling the workings of the human brain and its functions. In this review we provide evidence that studying interdependencies between brain oscillations may be a valuable approach to study the electrophysiological processes associated with motivation and emotional states. Studies will be presented showing that amplitude-amplitude coupling between delta-alpha and delta-beta oscillations varies as a function of state anxiety and approach-avoidance-related motivation, and that changes in the association between delta-beta oscillations can be observed following successful psychotherapy. Together these studies suggest that cross-frequency coupling of brain oscillations may contribute to expanding our understanding of the neural processes underlying motivation and emotion.
Relaxation Dynamics in Heme Proteins.
Scholl, Reinhard Wilhelm
A protein molecule possesses many conformational substates that are likely arranged in a hierarchy consisting of a number of tiers. A hierarchical organization of conformational substates is expected to give rise to a multitude of nonequilibrium relaxation phenomena. If the temperature is lowered, transitions between substates of higher tiers are frozen out, and relaxation processes characteristic of lower tiers will dominate the observational time scale. This thesis addresses the following questions: (i) What is the energy landscape of a protein? How does the landscape depend on the environment such as pH and viscosity, and how can it be connected to specific structural parts? (ii) What relaxation phenomena can be observed in a protein? Which are protein specific, and which occur in other proteins? How does the environment influence relaxations? (iii) What functional form best describes relaxation functions? (iv) Can we connect the motions to specific structural parts of the protein molecule, and are these motions important for the function of the protein?. To this purpose, relaxation processes after a pressure change are studied in carbonmonoxy (CO) heme proteins (myoglobin-CO, substrate-bound and substrate-free cytochrome P450cam-CO, chloroperoxidase-CO, horseradish peroxidase -CO) between 150 K and 250 K using FTIR spectroscopy to monitor the CO bound to the heme iron. Two types of p -relaxation experiments are performed: p-release (200 to ~eq40 MPa) and p-jump (~eq40 to 200 MPa) experiments. Most of the relaxations fall into one of three groups and are characterized by (i) nonexponential time dependence and non-Arrhenius temperature dependence (FIM1( nu), FIM1(Gamma)); (ii) exponential time dependence and non-Arrhenius temperature dependence (FIM0(A_{i}to A_{j})); exponential time dependence and Arrhenius temperature dependence (FIMX( nu)). The influence of pH is studied in myoglobin-CO and shown to have a strong influence on the substate population of the
Energy Partition Oscillator and Necessary and Sufficient Conditions of Energy Localization
Pilipchuk V.N.
2012-07-01
Full Text Available A strongly nonlinear conservative oscillator describing the dynamics of energy partition between two identical linearly coupled Duffing oscillators is introduced and analyzed. Temporal shapes of such oscillator are close to harmonic when the initial energy disbalance between the interacting Duffing oscillators is relatively small. However the oscillator becomes strongly nonlinear as the amplitude of energy exchange increases. It is shown nevertheless that the oscillator is exactly solvable and, as a result, the entire first order averaging system, describing the dynamics of coupled Duffing oscillators, admits exact analytical solution. Based on the first integral of the energy partition oscillator, necessary and sufficient conditions of energy localization are obtained in terms of the initial states of original system.
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.
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...
Negative magnetic relaxation in superconductors
Krasnoperov E.P.
2013-01-01
Full Text Available It was observed that the trapped magnetic moment of HTS tablets or annuli increases in time (negative relaxation if they are not completely magnetized by a pulsed magnetic field. It is shown, in the framework of the Bean critical-state model, that the radial temperature gradient appearing in tablets or annuli during a pulsed field magnetization can explain the negative magnetic relaxation in the superconductor.
Sinusoidal oscillators and waveform generators using modern electronic circuit building blocks
Senani, Raj; Singh, V K; Sharma, R K
2016-01-01
This book serves as a single-source reference to sinusoidal oscillators and waveform generators, using classical as well as a variety of modern electronic circuit building blocks. It provides a state-of-the-art review of a large variety of sinusoidal oscillators and waveform generators and includes a catalogue of over 600 configurations of oscillators and waveform generators, describing their relevant design details and salient performance features/limitations. The authors discuss a number of interesting, open research problems and include a comprehensive collection of over 1500 references on oscillators and non-sinusoidal waveform generators/relaxation oscillators. Offers readers a single-source reference to everything connected to sinusoidal oscillators and waveform generators, using classical as well as modern electronic circuit building blocks; Provides a state-of-the-art review of a large variety of sinusoidal oscillators and waveform generators; Includes a catalog of over 600 configurations of oscillato...
Low-frequency oscillations of a cylinder in a viscous fluid
Amin, Norsarahaida
1988-05-01
The flow induced by a circular cylinder oscillating in a viscous fluid when the amplitude of the oscillation is small and the frequecy is low is considered. This solution, obtained by the method of matched asymptotic expansions, is compared with the solution obtained from an Oseen approximation to the governing equations by Andres and Ingard (1953).