Synchronization Regime Research Articles

Vortex-induced vibrations of two mechanically coupled circular cylinders with asymmetrical stiffness in side-by-side arrangements

Vortex-induced vibrations of two mechanically coupled circular cylinders with asymmetrical stiffness in side-by-side arrangements are numerically investigated in a uniform flow at a low Reynolds number of 100. The oscillation system is restricted to the cross-flow direction, giving rise to a coupled two-degree-of-freedom response. Attention is placed on the two cylinders with a center-to-center gap ratio of 4 and a mass ratio of 10. The flow dynamics are described by the two-dimensional incompressible Navier–Stokes equations and resolved by the Characteristic-Based-Split finite element method. The stiffness of the first spring that connects the lower cylinder to the wall is chosen such that the vortex-induced vibration of the associated single cylinder with the same stiffness undergoes a pre-synchronization (state A), synchronization (state B) and post-synchronization (state C), respectively. In each state, the stiffness of the second spring connecting the lower and upper cylinders is varied to cover both synchronization and de-synchronization regimes. Numerical results show that the mechanically coupled system locks on the first-mode natural frequency in state A, while on the second-mode natural frequency in states B and C. In such a lock-in regime, the amplitude ratios of the two oscillating and coupled cylinders collapse well onto the corresponding first or second free-vibration mode. The overall coupling mechanism is further explained in terms of the hydrodynamic coefficients, frequency characteristics, wake patterns and effective added mass, quantifying the associated fluid-structure interactions against those governing a single-degree-of-freedom, single-cylinder system.

Nonlinear Cyclotron Resonance Absorber for a Microwave Subnanosecond Pulse Generator Powered by a Helical-Waveguide Gyrotron Traveling-Wave Tube

A well-known principle for periodical production of high-power ultrashort optical pulses is related to passive mode locking realized when a saturable absorber is incorporated into the laser resonator. A similar effect can be implemented in two-section electronic oscillators comprising an amplifier and a saturable absorber, which should be applicable in the microwave frequency band and suitable for high-power operation. In this paper, we analyze in detail the possibility of realizing a saturable absorber based on cyclotron resonance interaction in the regular waveguide with initially rectilinear electron beam, when saturation is caused by the relativistic dependence of the gyrofrequency on electron energy. Maximum contrast between the absorption of a high-power signal and of a weak signal is achieved in the group synchronism regime when the particle velocity is close to the wave's group velocity. Within the frame of a time-domain self-consistent model, we demonstrate that when such an absorber is installed in the feedback loop of an electron generator powered by existing Ka-band helical-waveguide gyrotron traveling-wave tube, periodical generation of subnanosecond pulses can be provided with peak power up to several hundred kW and sub-GHz repetition frequency. We discuss the influence of deviation from the group synchronism regime on the parameters of generated pulses. Experimental feasibility of the considered scheme is verified based on three-dimensional particle-in-cell simulations.

Population dynamics and life history traits of Daphnia magna across thermal regimes of environments

The consequences of raising temperatures have been intensively studied by biologists and ecologists for the past few decades. However, current climatic changes also include many anomalous weather events, such as intra-seasonal heatwaves followed by immediate decreases in temperature. In this study, the responses of population development and life history traits to different thermal regimes were investigated. The freshwater water flea Daphnia magna (Cladocera, Crustacea) was used as a model organism. Daphnia magna populations were monitored under temperature regimes of warm (25 °C), cold (5 °C), synchronous (gradual changes between 25 °C and 5 °C) or stochastic (random changes between 25 °C and 5 °C). Population size of D. magna populations decreased with unpredictability of thermal conditions; the highest density of D. magna was found in the warm environment and the lowest density in the stochastic environment. Thermal regime had significant impact on the prevalence of asexual and sexual reproduction of D. magna. Under a synchronous regime, an accumulation of asexual reproduction was observed during cold episodes; this was followed by a phase of population disturbance, manifesting itself in high fluctuations of asexual reproduction and a pattern of sexual reproduction typical of a cold regime. Under a stochastic regime, the population disturbances were observed throughout the duration of the experiment. Daily observations of individual life history traits revealed that the development of populations under different thermal regimes resulted from the regime-specific survivability of neonates. Population development was also affected by the frequency of reproduction, which consisted of the number of broods carried per lifetime. The results indicate that not only temperature but also shifts in thermal conditions have an important influence on individual life history traits and population dynamics of D. magna. It is important to consider the effects of shifts in water temperature on demographic and individual traits simultaneously because the impact of thermal changes on population traits can be modified by individual life histories.

Fractal brain dynamics: from Mandelbrot to marmosets.

Fractal brain dynamics: from Mandelbrot to marmosets.

Magnetic Actuation of Surface Walkers: The Effects of Confinement and Inertia.

Driven by a magnetic field, the rotation of a particle near a wall can be rectified into a net translation. The particles thus actuated, or surface walkers, are a kind of active colloid that finds application in biology and microfluidics. Here, we investigate the motion of spherical surface walkers confined between two walls using simulations based on the immersed-boundary lattice Boltzmann method. The degree of confinement and the nature of the confining walls (slip vs no-slip) significantly affect a particle's translational speed and can even reverse its translational direction. When the rotational Reynolds number Reω is larger than 1, inertia effects reduce the critical frequency of the magnetic field, beyond which the sphere can no longer follow the external rotating field. The reduction of the critical frequency is especially pronounced when the sphere is confined near a no-slip wall. As Reω increases beyond 1, even when the sphere can still rotate in the synchronous regime, its translational Reynolds number ReT no longer increases linearly with Reω and even decreases when Reω exceeds ∼10.

Self-Organized Synchronization of Phonon Lasers.

Self-organized synchronization is a ubiquitous collective phenomenon, in which each unit adjusts their rhythms to achieve synchrony through mutual interactions. The optomechanical systems, due to their inherently engineerable nonlinearities, provide an ideal platform to study self-organized synchronization. Here, we demonstrate the self-organized synchronization of phonon lasers in a two-membrane-in-the-middle optomechanical system. The probe of each individual membrane enables us to monitor the real-time transient dynamics of synchronization, which reveals that the system enters into the synchronization regime via a torus birth bifurcation line. The phase-locking phenomenon and the transition between in-phase and antiphase regimes are directly observed. Moreover, such a system greatly facilitates the controllable synchronous states, and consequently a phononic memory is realized by tuning the system parameters. This result is an important step towards the future studies of many-body collective behaviors in multiresonator optomechanics with long distances, and might find potential applications in quantum information processing and complex networks.

Steady states of non-axial dipolar rods driven by rotating fields.

We investigate a two-dimensional system of magnetic colloids with anisotropic geometry (rods) subjected to an oscillating external magnetic field. The structural and dynamical properties of the steady states are analyzed, by means of Langevin dynamics simulations, as a function of the misalignment of the intrinsic magnetic dipole moment of the rods with respect to their axial direction, and also in terms of the strength and rotation frequency of an external magnetic field. The misalignment of the dipole relative to their axial direction is inspired by recent studies, and this is extremely relevant in the microscopic aggregation states of the system. The dynamical response of the magnetic rods to the external magnetic field is strongly affected by such a misalignment. Concerning the synchronization between the magnetic rods and the direction of the external magnetic field, we define three distinct regimes of synchronization. A set of steady states diagrams are presented, showing the magnitude and rotation frequency intervals in which the distinct self-organized structures are observed.

Метод определения характеристик перемежающейся обобщенной синхронизации на основе расчета локальных показателей Ляпунова

Method for the laminar and turbulent phase detection in coupled dynamical systems being near the boundary of the generalized synchronization regime based on the calculation of local Lyapunov exponents has been proposed. The efficiency of the method has been testified using the systems with unidirectional coupling allowing the analysis of intermittency by the auxiliary system approach. The results of both methods have been compared with each other, a good agreement between them has been obtained.

Корректность определения характеристик перемежающейся обобщенной синхронизации при использовании только одной переменной ведомой и вспомогательной систем

Method for detection of characteristic phases of behavior in the intermittent generalized synchronization regime based on the use of an auxiliary system is considered. It is found that for the correct determination of the type of intermittency realized in the system, it is sufficient to use the only one variable characterizing the state of this system.

Dynamics of disordered heterogeneous chains of phase oscillators

We study the problem of robustness of synchronous states to disorder in the chain of phase oscillators with local coupling. The study combines a numerical determination of the existence and stability of synchronous states with an analytical investigation of the role of the phase shift and the level of disorder in the natural frequencies in the destruction of synchrony. We show that the presence of the phase shift facilitates robustness of the synchronous regime, at least up to its certain threshold value.

On the onset of bifurcation and nonlinear characterization of vortex-induced vibrations under varying initial conditions

We perform numerical simulations to investigate the hysteresis phenomenon near the bifurcation points of the synchronization region leading to vortex-induced vibrations. We characterize the response using nonlinear dynamics tools. We find an unstable region at both ends of the synchronization regime where the response depends on initial conditions. Unlike previous studies, the focus of the current research is to analyze the effect of the structure’s initial condition on the VIV response. We vary the initial velocity of the cylinder and observe the response of transverse displacement and lift coefficient as a function of Reynolds number. We observe that in the pre-synchronous and synchronous regimes, the cylinder response is always period-1 at cylinder’s natural frequency. However, in the post-synchronous regime, the response is period-n where $$n > 1$$. Thus, bifurcation diagrams depicts the variation of the onset of synchronization and its spectrum over the range of Reynolds number.

Experimental research on vortex-induced vibrations of flexible circular cylinders at low Reynolds number: revealing atypical branches

This study presents the experimental results of 31 cantilevered flexible circular cylinders, subjected to vortex-induced vibrations, with different materials, diameters and lengths. Diameter and length ranges are 1.56 mm ≤ D ≤ 3.19 mm and 30 cm ≤ L ≤ 40 cm, respectively. Tested materials are aluminum, bronze, copper and stainless steel. A total of 1905 experimental points were obtained and processed with the Particle Velocimetry technique. A Matlab code was developed to obtain the maximum amplitude for several Reynolds number through the synchronization regime. Reynolds number range is 75 ≤ Re ≤ 1050. Results illustrate the existence of four different groups corresponding to different maximum amplitude behaviors. As some of these behaviors are not yet reported in the literature, each branch is distinguished and explained in detail. One group presents two local maximum amplitudes and the global maximum is not located in the initial branch as usually expected. In order to classify all the groups, several parameters were analyzed. The slope of reduced velocity vs Reynolds number resulted in the best parameter. This parameter, and therefore the classification of a given cylinder, can be predicted through a 2D polynomial linear fit by knowing only the L/D and mass damping ratios.

On Synchronous, Asynchronous, and Randomized Best-Response Schemes for Stochastic Nash Games

In this paper, we consider a stochastic Nash game in which each player minimizes a parameterized expectation-valued convex objective function. In deterministic regimes, proximal best-response (BR) schemes have been shown to be convergent under a suitable spectral property associated with the proximal BR map. However, a direct application of this scheme to stochastic settings requires obtaining exact solutions to stochastic optimization problems at each iteration. Instead, we propose an inexact generalization of this scheme in which an inexact solution to the BR problem is computed in an expected-value sense via a stochastic approximation (SA) scheme. On the basis of this framework, we present three inexact BR schemes: (i) First, we propose a synchronous inexact BR scheme where all players simultaneously update their strategies. (ii) Second, we extend this to a randomized setting where a subset of players is randomly chosen to update their strategies while the other players keep their strategies invariant. (iii) Third, we propose an asynchronous scheme, where each player chooses its update frequency while using outdated rival-specific data in updating its strategy. Under a suitable contractive property on the proximal BR map, we proceed to derive almost sure convergence of the iterates to the Nash equilibrium (NE) for (i) and (ii) and mean convergence for (i)–(iii). In addition, we show that for (i)–(iii), the generated iterates converge to the unique equilibrium in mean at a linear rate with a prescribed constant rather than a sublinear rate. Finally, we establish the overall iteration complexity of the scheme in terms of projected stochastic gradient (SG) steps for computing an [Formula: see text]-NE2 (or [Formula: see text]-NE∞) and note that in all settings, the iteration complexity is [Formula: see text], where [Formula: see text] in the context of (i), and c > 0 represents the positive cost of randomization in (ii) and asynchronicity and delay in (iii). Notably, in the synchronous regime, we achieve a near-optimal rate from the standpoint of solving stochastic convex optimization problems by SA schemes. The schemes are further extended to settings where players solve two-stage stochastic Nash games with linear and quadratic recourse. Finally, preliminary numerics developed on a multiportfolio investment problem and a two-stage capacity expansion game support the rate and complexity statements.

Climate clusters of Eurasia against the background of global climate change

In this paper we suggest a solution to the problem of identifying the patterns of climate system transformations against the background of global climate change by means of studying changes in the pattern of climate classifications. We present an implementation of the objective classification method using an algorithm proposed by us for the territory of Eurasia for two different time intervals corresponding to global temperature trends. The results of applying our approach to temperature series measured at 485 weather stations in Eurasia from 1955 to 2016 are presented. The classification algorithm is based on comparing changes in the phases of the temperature series. A comparative analysis is performed to show changes in the temperature synchronization regime against the background of climate warming and changes in the structure of climate classes as well. The Russian Arctic and Subarctic, South Western Siberia, as well as stations located in mountainous regions of Eurasia, have shown high sensitivity to the changing climate. We believe that our approach will allow the formation of a general view on the phenomenon under study. This approach can be useful for the analysis of observational data, analytical transformations, and climate modelling.

Observation of Arnold Tongues in Coupled Soliton Kerr Frequency Combs.

We demonstrate various regimes of synchronization in systems of two coupled cavity soliton-based Kerr frequency combs. We show subharmonic, harmonic, and harmonic-ratio synchronization of coupled microresonators, and reveal their dynamics in the form of Arnold tongues, structures that are ubiquitous in nonlinear dynamical systems. Our experimental results are well corroborated by numerical simulations based on coupled Lugiato-Lefever equations. This Letter illustrates the newfound degree of flexibility in synchronizing Kerr combs across a wide range of comb spacings and could find applications in time and frequency metrology, spectroscopy, microwave photonics, optical communications, and astronomy.

Master-slave synchronization of hyperchaotic systems through a linear dynamic coupling.

The development of synchronization strategies for dynamical systems is an important research activity that can be applied in several different fields from locomotion control of multilimbed structures to secure communication. In the presence of chaotic systems, synchronization is more difficult to accomplish and there are different techniques that can be adopted. In this paper we considered a master-slave topology where the coupling mechanism is realized through a second-order linear dynamical system. This control scheme, recently applied to chaotic systems, is here analyzed in the presence of hyperchaotic dynamics that represent a more challenging scenario. The possibility to reach a complete synchronization and the range of allowable coupling strength is investigated comparing the effects of the dynamical coupling with a standard configuration characterized by a static gain. This methodology is also applied to weighted networks to reach synchronization regimes otherwise not obtainable with a static coupling.

Flow-induced oscillations of three tandem circular cylinders in a two-dimensional flow

Flow-induced oscillations of three identical circular cylinders, arranged in tandem configuration, are studied via two-dimensional finite element computations. Cylinders are mounted on elastic supports in the streamwise and transverse directions. Each downstream cylinder is placed at a distance of 5 diameters (5D) from its immediate upstream neighbor. Nondimensional mass ( m∗) of 2, and zero damping (ξ) are considered. Simulations are performed with the objective of understanding dynamic response of cylinders, as they are subject to wake interference, at constant Reynolds number, Re=150, and for varying reduced velocity (U∗) in the range of U∗=2−14. Similar to the behavior of an isolated cylinder at low Re, oscillation response of the upstream body exhibits initial excitation and lower lock-in regimes. However, for both the downstream cylinders, depending on their amplitude and frequency responses, the synchronization regime of U∗ can be categorized into three distinct regions: initial excitation, upper and lower lock-in regions. First downstream cylinder undergoes gradual transition between initial excitation and upper region, whereas the second downstream body exhibits this transition in two phases, which are separated by a periodic oscillation response regime. Upper lock-in region is characterized by periodic oscillations, while amplitude is modulated in the lower region. Only 2S shedding mode is observed for all the U∗ considered.

Synchronization and temporal nonreciprocity of optical microresonators via spontaneous symmetry breaking

Synchronization is of importance in both fundamental and applied physics, but its demonstration at the micro/nanoscale is mainly limited to low-frequency oscillations such as mechanical resonators. We report the synchronization of two coupled optical microresonators, in which the high-frequency resonances in the optical domain are aligned with reduced noise. It is found that two types of synchronization regimes emerge with either the first- or second-order transition, both presenting a process of spontaneous symmetry breaking. In the second-order regime, the synchronization happens with an invariant topological character number and a larger detuning than that of the first-order case. Furthermore, an unconventional hysteresis behavior is revealed for a time-dependent coupling strength, breaking the static limitation and the temporal reciprocity. The synchronization of optical microresonators offers great potential in reconfigurable simulations of many-body physics and scalable photonic devices on a chip.

Exploring the Phase-Locking Mechanisms Yielding Delayed and Anticipated Synchronization in Neuronal Circuits.

Synchronization is one of the brain mechanisms allowing the coordination of neuronal activity required in many cognitive tasks. Anticipated Synchronization (AS) is a specific type of out-of-phase synchronization that occurs when two systems are unidirectionally coupled and, consequently, the information is transmitted from the sender to the receiver, but the receiver leads the sender in time. It has been shown that the primate cortex could operate in a regime of AS as part of normal neurocognitive function. However it is still unclear what is the mechanism that gives rise to anticipated synchronization in neuronal motifs. Here, we investigate the synchronization properties of cortical motifs on multiple scales and show that the internal dynamics of the receiver, which is related to its free running frequency in the uncoupled situation, is the main ingredient for AS to occur. For biologically plausible parameters, including excitation/inhibition balance, we found that the phase difference between the sender and the receiver decreases when the free running frequency of the receiver increases. As a consequence, the system switches from the usual delayed synchronization (DS) regime to an AS regime. We show that at three different scales, neuronal microcircuits, spiking neuronal populations and neural mass models, both the inhibitory loop and the external current acting on the receiver mediate the DS-AS transition for the sender-receiver configuration by changing the free running frequency of the receiver. Therefore, we propose that a faster internal dynamics of the receiver system is the main mechanism underlying anticipated synchronization in brain circuits.

Stability analysis of a paramagnetic spheroid in a precessing field

Stability analysis of paramagnetic prolate and oblate spheroidal particle in precessing magnetic field is studied. Bifurcation diagram is calculated analytically in dependence of magnetic field frequency and precession angle. The direction of particle in synchronous regime is calculated. Rotational dynamics and mean rotational frequency in asynchronous regime is found. Obtained theoretical model gives possibility to calculate analytically dynamics of the particle in limiting case (when motion is periodic). Theoretically obtained models were compared with experimental results of rod like particle dynamics in precessing magnetic field. Experimental results are in good agreement with proposed theory.