Phase Oscillators Research Articles

Impacts of potential energy oscillations on the friction of graphene and BN lubricants

Abstract The frictional responses of graphene and boron nitride lubricants is studied from the perspective of the potential energy evolution. At a low normal load regime and high interface adhesion, friction can be effectively characterized by investigating the interfacial energy barrier formation process. By decomposing the energy evolution into strain and interfacial cohesive components, we find that the oscillation phase difference plays an essential role in the friction response and is controlled by the energy conversion between them. Analyses further reveal that the energy oscillations are excited by the vertical motion of the sliding asperity that induces periodic deformation and position changes in the lubrication systems. These new findings suggest the study of potential energy evolution is advantageous for understanding adhesive friction and infers the potential to leverage adhesion in 2D lubricant application through high conversion efficiency and out-of-phase oscillations between strain and cohesive energies.

Enhanced Correlation between Arousal and Infra-Slow Brain Activity in Experienced Meditators.

Meditation induces changes in the nervous system, which presumably underpin positive psychological and physiological effects. Such neural changes include alterations in the arousal fluctuation, as well as in infraslow brain activity (ISA, <0.1 Hz). Furthermore, it is known that fluctuations of arousal over time correlate with the oscillatory phase of ISA. However, whether this arousal-ISA correlation changes after meditation practices remains unanswered.; Methods: The present study aims to address this question by analyzing a publicly available electroencephalogram (EEG) dataset recorded during meditation sessions in the groups of experienced meditators and novices. The arousal fluctuation is measured by galvanic skin responses (GSR), and arousal-ISA correlations are measured by phase synchronization between GSR and EEG ISAs.; Results: While both groups exhibit arousal-ISA correlations, experienced meditators display higher correlations than novices. These increased arousal-ISA correlations in experienced meditators manifest more clearly when oscillatory phase differences between GSR and EEG ISAs are either 0 or π radians. As such, we further investigate the characteristics of these phase differences with respect to spatial distribution over the brain. We found that brain regions with the phase difference of either 0 or π radians form distinct spatial clusters, and that these clusters are spatially correlated with functional organization estimated by the principal gradient, based on functional connectivity.; Conclusions: Since increased arousal-ISA correlations reflect enhanced global organization of the central and autonomic nervous systems, our findings imply that the positive effects of meditation might be mediated by enhanced global organization of the nervous system.

Numerical study of vector solitons with the oscillatory phase backgrounds in the integrable coupled nonlinear Schrödinger equations

In this paper, we numerically investigate vector solitons with oscillatory phase backgrounds in the integrable coupled nonlinear Schrödinger equations, which are widely applied to varieties of physical contexts such as the simultaneous propagation of nonlinear optical pulses and the dynamics of two-components Bose–Einstein condensates. We develop the time-splitting Chebyshev–Galerkin method based on a transformation to accurately compute the vector soliton solutions. Compared to the finite difference method, numerical experiments show that the method with spectral accuracy and high efficiency is necessary for simulating the dynamics evolution of vector solitons. Combined with modulation instability conditions, linear stability analysis and direct numerical simulation, we reveal that the bright-dark and dark-dark solitons with various combinations of parameters under perturbations have qualitative differences. Particularly, vector solitons in unstable background with different wave numbers present distinct dynamics evolutions. The results help us to understand soliton dynamics with oscillatory phase backgrounds and the superposition between nonlinear waves.

The reset effect of attention depends on the phase of ongoing attention oscillation

The reset effect of attention depends on the phase of ongoing attention oscillation

Chimera states and eigen microstates of nonidentical power-law coupled oscillators with heterogeneous phase lag

Chimera state is a special spatiotemporal patterns where coherent and incoherent states coexist, not only related to neuronal evolution but also to diseases such as parkinson, epilepsy, and schizophrenia. In many studies of biological networks, the interaction patterns between individuals often exhibit a scale-free heavy-tailed distribution. Hence, researches into chimera state within scale-free structures may help to understand the close relationship between function and structure in biological systems. Especially in neural systems, interactions between neurons depend on both electrical and chemical signals, naturally involving heterogeneous delay effects. In this study, we introduce power-law coupling, nonidentical natural frequency, and heterogeneous phase delay into the phase oscillator model, exploring the relationship between oscillator coupled strength, power-law exponent, and the emergence of chimera state. Other important thing is that we extend the Eigen Microstate (EM) method to investigate the criticality, attempting to reveal the mechanism of chimera state emergence through the mesoscopic structure of eigen microstate. We find that the critical analysis results of the EM method, relying solely on phase data, are entirely consistent with those obtained by the mean-field method, revealing the inevitable relationship between the emergence of chimera state and the structure–power law coupling. In addition, the spatiotemporal patterns of eigen microstate provide insights into the mesoscopic structure, can be used to distinguish spatial distribution of synchronization, chimera state, and disorder state, as well as their characteristic dynamics of oscillators. This expansion research of the EM method will advance the exploration of criticality in real oscillatory systems.

Oscillations in an artificial neural network convert competing inputs into a temporal code.

The field of computer vision has long drawn inspiration from neuroscientific studies of the human and non-human primate visual system. The development of convolutional neural networks (CNNs), for example, was informed by the properties of simple and complex cells in early visual cortex. However, the computational relevance of oscillatory dynamics experimentally observed in the visual system are typically not considered in artificial neural networks (ANNs). Computational models of neocortical dynamics, on the other hand, rarely take inspiration from computer vision. Here, we combine methods from computational neuroscience and machine learning to implement multiplexing in a simple ANN using oscillatory dynamics. We first trained the network to classify individually presented letters. Post-training, we added temporal dynamics to the hidden layer, introducing refraction in the hidden units as well as pulsed inhibition mimicking neuronal alpha oscillations. Without these dynamics, the trained network correctly classified individual letters but produced a mixed output when presented with two letters simultaneously, indicating a bottleneck problem. When introducing refraction and oscillatory inhibition, the output nodes corresponding to the two stimuli activate sequentially, ordered along the phase of the inhibitory oscillations. Our model implements the idea that inhibitory oscillations segregate competing inputs in time. The results of our simulations pave the way for applications in deeper network architectures and more complicated machine learning problems.

Two-step and explosive synchronization in frequency-weighted Kuramoto model

We explore the dynamics of interacting phase oscillators in the generalized Kuramoto model with frequency-weighted couplings, focusing on the interplay of frequency distribution and network topology on the nature of transition to synchrony. We explore the impact of heterogeneity in the network topology and the frequency distribution. Our analysis includes unimodal (Gaussian, truncated Gaussian, and uniform) and bimodal frequency distributions. For a unimodal Gaussian distribution, we observe that in comparison to fully-connected network, the competition between topological and dynamical hubs hinders the transition to synchrony in the scale-free network, though explosive synchronization eventually happens. However, in the absence of very large frequencies, the transition is gradual. While uniform frequency distributions lead to explosive synchronization. In bimodal distributions, narrow distribution produce a two-step transition. In this case, central frequencies dominate the dynamics, overshadowing the topological features of the network. For wider bimodal distributions, scale-free network exhibits a gradual increase in the order parameter, whereas in fully-connected networks a first-order transition happens. These results specifically elucidate the mechanisms driving two-step and explosive synchronization in frequency-weighted Kuramoto models, offering new insights into managing synchronization phenomena in complex networks like power grids, neural systems, and social systems.

Higher-order interaction induced chimeralike state in a bipartite network.

We report higher-order coupling induced stable chimeralike state in a bipartite network of coupled phase oscillators without any time-delay in the coupling. We show that the higher-order interaction breaks the symmetry of the homogeneous synchronized state to facilitate the manifestation of symmetry breaking chimeralike state. In particular, such symmetry breaking manifests only when the pairwise interaction is attractive and higher-order interaction is repulsive, and vice versa. Further, we also demonstrate the increased degree of heterogeneity promotes homogeneous symmetric states in the phase diagram by suppressing the asymmetric chimeralike state. We deduce the low-dimensional evolution equationsfor the macroscopic order parameters using Ott-Antonsen ansatz and obtain the bifurcation curves from them using the software xppaut, which agrees very well with the simulation results. We also deduce the analytical stability conditions for the incoherent state, in-phase and out-of-phase synchronized states, which match with the bifurcation curves.

Aging transitions of multimodal oscillators in multilayer networks

When individual oscillators age and become inactive, the collective dynamics of coupled oscillators is often affected as well. Depending on the fraction of inactive oscillators or cascading failures that percolate from crucial information exchange points, the critical shift toward macroscopic inactivity in coupled oscillator networks is known as the aging transition. Here, we study this phenomenon in two overlayed square lattices that together constitute a multilayer network, whereby one layer is populated with slow Poincaré oscillators and the other with fast Rulkov neurons. Moreover, in this multimodal setup, the excitability of fast oscillators is influenced by the phase of slow oscillators that are gradually inactivated toward the aging transition in the fast layer. Through extensive numerical simulations, we find that the progressive inactivation of oscillators in the slow layer nontrivially affects the collective oscillatory activity and the aging transitions in the fast layer. Most counterintuitively, we show that it is possible for the intensity of oscillatory activity in the fast layer to progressively increase to up to 100%, even when up to 60% of units in the slow oscillatory layer are inactivated. We explain our results with a numerical analysis of collective behavior in individual layers, and we discuss their implications for biological systems. Published by the American Physical Society 2024

Circadian Rhythms in Conditioned Threat Extinction Reflect Time-of-Day Differences in Ventromedial Prefrontal Cortex Neural Processing.

Circadian rhythms in conditioned threat extinction emerge from a tissue-level circadian timekeeper, or local clock, in the ventromedial prefrontal cortex (vmPFC). Yet it remains unclear how this local clock contributes to extinction-dependent adaptations. Here we used single-unit and local field potential analyses to interrogate neural activity in the male rat vmPFC during repeated extinction sessions at different times of day. In association with superior recall of a remote extinction memory during the circadian active phase, vmPFC putative principal neurons exhibited phasic firing that was amplified for cue presentations and diminished at transitions in freezing behavior. Coupling of vmPFC gamma amplitude to the phase of low-frequency oscillations was greater during freezing than mobility, and this difference was augmented during the active phase, highlighting a time-of-day dependence in the organization of freezing- versus mobility-associated cell assemblies. Additionally, a greater proportion of vmPFC neurons were phase-locked to low-frequency oscillations during the active phase, consistent with heightened neural excitability at this time of day. Our results suggest that daily fluctuations in vmPFC excitability precipitate enhanced neural recruitment into extinction-based cell assemblies during the active phase, providing a potential mechanism by which the vmPFC local clock modulates circuit and behavioral plasticity during conditioned threat extinction.

Noncontact Measurements of Resonance of Small Round Liquid Surfaces Using Sound Wave to Determine Surface Tension.

Various methods have been developed for measuring the surface tension of liquids, and the present study proposes a new method for measuring the surface tension of liquids. A small (9 mm diameter) round liquid surface was excited by sound waves with a common speaker. Nine liquids possessing various physical properties and functional groups were employed, and three resonance frequencies (frs) were observed for each liquid in a frequency range of 20-180 Hz. The resonances were analyzed with a forced oscillation model. In addition, the amplitudes and phases of the resonance oscillations at various positions of the liquid surface were measured, and the total deformations of the liquid surface were determined. The deformation was compared with the Bessel functions, and the oscillation modes and boundary conditions were decided. Finally, proportional relationships between frs and σ0.5ρ-0.5 (σ: surface tension, ρ: density) with high correlations were obtained, which were supported by a new theoretical equation using hydrodynamics.

The phase coherence of cortical oscillations predicts dynamic changes in perceived visibility.

The phase synchronization of brain oscillations plays an important role in visual processing, perceptual awareness, and performance. Yet, the cortical mechanisms underlying modulatory effects of post-stimulus phase coherence and frequency-specific oscillations associated with different aspects of vision are still subject to debate. In this study, we aimed to identify the post-stimulus phase coherence of cortical oscillations associated with perceived visibility and contour discrimination. We analyzed electroencephalogram data from two masking experiments where target visibility was manipulated by the contrast ratio or polarity of the mask under various onset timing conditions (stimulus onset asynchronies, SOAs). The behavioral results indicated an SOA-dependent suppression of target visibility due to masking. The time-frequency analyses revealed significant modulations of phase coherence over occipital and parieto-occipital regions. We particularly identified modulations of phase coherence in the (i) 2-5Hz frequency range, which may reflect feedforward-mediated contour detection and sustained visibility; and (ii) 10-25Hz frequency range, which may be associated with suppressed visibility through inhibitory interactions between and within synchronized neural pathways. Taken together, our findings provide evidence that oscillatory phase alignments, not only in the pre-stimulus but also in the post-stimulus window, play a crucial role in shaping perceived visibility and dynamic vision.

Passive Islanding Detection of Inverter-Based Resources in a Noisy Environment

Islanding occurs when a load is energized solely by local generators and can result in frequency and voltage instability, changes in current, and poor power quality. Poor power quality can interrupt industrial operations, damage sensitive electrical equipment, and induce outages upon the resynchronization of the island with the grid. This study proposes an islanding detection method employing a Duffing oscillator to analyze voltage fluctuations at the point of common coupling (PCC) under a high-noise environment. Unlike existing methods, which overlook the noise effect, this paper mitigates noise impact on islanding detection. Power system noise in PCC measurements arises from switching transients, harmonics, grounding issues, voltage sags and swells, electromagnetic interference, and power quality issues that affect islanding detection. Transient events like lightning-induced traveling waves to the PCC can also introduce noise levels exceeding the voltage amplitude by more than seven times, thus disturbing conventional detection techniques. The noise interferes with measurements and increases the nondetection zone (NDZ), causing failed or delayed islanding detection. The Duffing oscillator nonlinear dynamics enable detection capabilities at a high noise level. The proposed method is designed to detect the PCC voltage fluctuations based on the IEEE standard 1547 through the Duffing oscillator. For the voltages beyond the threshold, the Duffing oscillator phase trajectory changes from periodic to chaotic mode and sends an islanded operation command to the inverter. The proposed islanding detection method distinguishes switching transients and faults from an islanded operation. Experimental validation of the method is conducted using a 3.6 kW PV setup.

Analysing crack evolution in wind turbine bearings using an oscillation-unified model

In wind turbine bearings subjected to oscillating motion, cracks undergoing reciprocating rolling contact loading experience more complex stress changes compared to those under constant rotational motion. However, oscillation is less explored. This study introduces an Oscillation Unified Surface-Initiated Crack Finite Element Model (OU-CFEM) to address this gap. The model is validated through mesh sensitivity analysis and Oscillation Contact Fatigue (OCF) experimental data. The OU-CFEM enables a detailed investigation into crack evolution characteristics under varying initial angles and friction coefficients. The findings reveal that crack behaviors significantly differ across different oscillation phases, except in cases involving vertically oriented cracks or fully lubricated conditions. The study highlights that larger initial angles and higher friction coefficients promote crack extension, with the initial angle playing a more critical role in crack evolution than the friction coefficient. This research provides new insights into the behavior of cracks in oscillating conditions, offering valuable contributions to the understanding of wind turbine bearing durability under such loading scenarios.

Stimulus-induced dynamical states in an adaptive network with symmetric adaptation.

We consider an adaptive network of identical phase oscillators with the symmetric adaptation rule for the evolution of the connection weights under the influence of an external force. We show that the adaptive network exhibits a plethora of self-organizing dynamical states such as thetwo-cluster state, multiantipodal clusters, splay cluster, splay chimera, forced entrained state, chimera state, bump state, coherent, and incoherent states in the two-parameter phase diagrams. The intriguing structures of the frequency clusters and instantaneous phases of the oscillators characterize the distinct self-organized synchronized and partial synchronized states. The hierarchical organization of the frequency clusters, resulting in strongly coupled subnetworks, is also evident from the dynamics of the coupling weights, where the frequency clusters are either very weakly coupled or even completely decoupled from each other. Additionally, we also deduce the stability condition for the forced entrained state.

Training coupled phase oscillators as a neuromorphic platform using equilibrium propagation

Abstract Given the rapidly growing scale and resource requirements of machine learning applications, the idea of building more efficient learning machines much closer to the laws of physics is an attractive proposition. One central question for identifying promising candidates for such neuromorphic platforms is whether not only inference but also training can exploit the physical dynamics. In this work, we show that it is possible to successfully train a system of coupled phase oscillators—one of the most widely investigated nonlinear dynamical systems with a multitude of physical implementations, comprising laser arrays, coupled mechanical limit cycles, superfluids, and exciton-polaritons. To this end, we apply the approach of equilibrium propagation, which permits to extract training gradients via a physical realization of backpropagation, based only on local interactions. The complex energy landscape of the XY/Kuramoto model leads to multistability, and we show how to address this challenge. Our study identifies coupled phase oscillators as a new general-purpose neuromorphic platform and opens the door towards future experimental implementations.

Closed-loop auditory stimulation targeting alpha and theta oscillations during REM sleep induces phase-dependent power and frequency changes.

Alpha and theta oscillations characterize the waking human electroencephalogram (EEG) and can be modulated by closed-loop auditory stimulation (CLAS). These oscillations also occur during rapid eye movement (REM) sleep, but their function here remains elusive. CLAS represents a promising tool to pinpoint how these brain oscillations contribute to brain function in humans. Here we investigate whether CLAS can modulate alpha and theta oscillations during REM sleep in a phase-dependent manner. We recorded high-density EEG during an extended overnight sleep period in 18 healthy young adults. Auditory stimulation was delivered during both phasic and tonic REM sleep in alternating 6s ON and 6s OFF windows. During the ON windows, stimuli were phase-locked to four orthogonal phases of ongoing alpha or theta oscillations detected in a frontal electrode. The phases of ongoing alpha and theta oscillations were targeted with high accuracy during REM sleep. Alpha and theta CLAS induced phase-dependent changes in power and frequency at the target location. Frequency-specific effects were observed for alpha trough (speeding up) and rising (slowing down) and theta trough (speeding up) conditions. CLAS-induced phase-dependent changes were observed during both REM sleep substages, even though auditory evoked potentials were very much reduced in phasic compared to tonic REM sleep. This study provides evidence that faster REM sleep rhythms can be modulated by CLAS in a phase-dependent manner. This offers a new approach to investigate how modulation of REM sleep oscillations affects the contribution of this vigilance state to brain function.

Resonance-induced synchronization in coupled phase oscillators with bimodal frequency distribution and periodic coupling.

Synchronization behaviors in globally coupled phase oscillators with symmetric bimodal frequency distribution and periodic coupling are studied. It is found that by a proper setting of the frequency of the periodic coupling, the synchronization propensity of the oscillators can be markedly improved. Specifically, we show that when the frequency of the periodic coupling matches the distance of the central frequencies in the distribution, the critical coupling characterizing the onset of synchronization can be substantially decreased. The mechanism behind the phenomenon of periodic-coupling-enhanced synchronization is analyzed by the methods of Ott-Antonsen ansatz and synchronization transition tree, and it is revealed that the synchronization enhancement is attributed to the resonance between the synchronization clusters and the periodic coupling.

Optimization research on control strategies for photovoltaic energy storage systems considering multi-mode operation

In this paper, a selective input/output strategy is proposed for improving the life of photovoltaic energy storage (PV-storage) virtual synchronous generator (VSG) caused by random load interference, which can sharply reduce costs of storage device. The strategy consists of two operating modes and a power coordination control method for the VSGs. Firstly, a selective VSG input strategy is proposed based on the magnitude of disturbances, a method of offline solving model equation is used for determine the VSG input time. An online method is used for matching the disturbance frequency variations, which enables a selective VSG startup method, allowing the grid to prioritize the utilization of the generator's physical inertia. Secondly, a dynamic VSG exit strategy is developed based on dynamic frequency characteristics to prevent secondary oscillations in the frequency recovery phase of the PV-storage VSG following grid disturbances. This strategy is crucial as grid variations may affect energy storage lifespan and reduce frequency recovery speed. Finally, the proposed approach is validated for correctness and effectiveness through computer simulations and semi-physical experiments using the NI-PXI + LabVIEW platform. Through the above optimization and research, the selective start of VSG is realized, the energy storage life is improved, the capacity of charge and discharge cycles is reduced by 37.82 % compared with the strategy without investment and withdrawal, and the life loss in the secondary charge and discharge process of PV-storage VSG is avoided, which is conducive to frequency recovery.

Modeling the chaotic dynamics of bubble growth under hydrodynamic interactions in pool boiling

This study seeks to understand the origins of intermittency in quantities of interest in pool boiling, such as bubble departure diameter and growth time. The intermittency of nucleation site activity due to hydrodynamic and thermal interactions with nearby nucleation sites is well-established; however, few mechanistic models have been developed that predict such intermittency. Here we assume a fluctuating pressure field at a nucleation site due to an adjacent bubble which alters bubble growth depending on the phase of the pressure oscillation with respect to the instant of bubble nucleation. The results suggest that even when a single departure frequency is assumed for nearby bubbles, its effect on the nucleation site being considered causes aperiodicity and intermittency in bubble departure quantities. The effects of pressure field phase angle, degree of superheat, and choice of force balance model on the bubble departure quantities are examined. The phase angle is shown to play a major role in determining bubble departure diameter and growth time. The departure diameter is observed to have a broad distribution, belying the assumption of a unique value. Period doubling of the ebullition cycle is observed for some conditions, a phenomenon documented by other investigators. A multifractal analysis of the time series of departure events indicates the presence of long term temporal correlations, which become weaker with increasing superheat. The second order Hurst exponent of the structure functions of departure events appears to have a universal behavior with Jakob number, independent of the choice of liquid. The Hurst exponent rises from zero to a value close to 0.5 at large superheats, suggesting a continuous transition from an ordered state to a disordered state along the boiling curve.