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The synchronization of multiple oscillators serves as the central mechanism for maintaining stable circadian rhythms in physiology and behavior. Aging and disease can disrupt synchronization, leading to changes in the periodicity of circadian activities. While our understanding of the circadian clock under synchronization has advanced significantly, less is known about its behavior outside synchronization, which can also fall within a predictable domain. These states not only impact the stability of the rhythms but also modulate the period length. In C57BL/6 mice, aging, diseases, and removal of peripheral circadian oscillators often result in lengthened behavioral circadian periods. Here, we show that these changes can be explained by a surprisingly simple mathematical relationship: the frequency is the reciprocal of the period, and its distribution becomes skewed when the period distribution is symmetric. The synchronized frequency of a population in the skewed distribution and the macroscopic frequency of combined oscillators differ, accounting for some of the atypical circadian period outputs observed in networks without synchronization. Building on this finding, we investigate the dynamics of circadian outputs in the context of aging and disease, where synchronization is weakened.

In present work, the double and triple-frequency synchronization behaviors of a vibrating mechanical system with two different driving frequencies, driven by three reversed rotating exciters, are investigated by theory, numeric, and experiment. Based on Lagrange’s equations, the dynamic model corresponding to vibrating machine is proposed and motion differential equations are constructed. The Bogoliubov standard formal equations for three exciters are established, by introducing the asymptotic method, in which the synchronization problem is converted into that of the existence and stability of zero-valued solution of the average differential equations. The synchronization criterion of satisfying the synchronous operation is deduced. According to the Routh–Hurwitz criterion, the stability criterion of the synchronous states is achieved analytically. Based on the obtained theory results, the stability characteristics of the system, are numerically discussed in detail, including the stability ability coefficients and stable phase differences. Finally, simulations and experiments under the condition of two different driving frequencies, are performed to further examine the validity of the theoretical and numerical qualitative results. The present work can provide a theoretical reference for designing some new types of the vibrating machines with adjustable frequencies and motion trajectories.

Generally, the synchronization studies on two or multiple exciters are preconditioned by being a single frequency, while the multiple-frequency synchronization problems in a vibrating system, including double-frequency and triple-frequency, are less considered, which are also very significant in engineering. This paper attempts to solve this issue by considering a dynamical model with an isolation frame, driven by the four exciters. The synchronization for the four exciters and its stability under the double-frequency and triple-frequency conditions are studied in detail. Firstly, the mathematical modeling of the system is established, and the corresponding motion differential equations are derived. Using the asymptotic method and the average method, yields the theoretical condition of implementing multiple-frequency synchronization, and the theoretical condition for stability of the system complies with the Routh–Hurwitz criterion. The dynamic characteristics of the system, including stable phase differences, stability abilities, responses of the system, and relative motion relationship, are qualitatively discussed by numeric. Finally, simulations are performed by applying a Runge–Kutta program to validate the theoretical and numerical qualitative results. It is shown that, by reasonably matching the key parameters of the system, the stronger, stable, and valuable motion states of vibrating machines, including vibration amplitudes, frequencies, and motion trajectory, can be realized, which are exactly the desires in engineering.

This paper proposes a free-space time–frequency phase (TFP)-synchronization transmission architecture based on optoelectronic hybrid technology, addressing the high-precision TFP synchronization and high-speed communication requirements between mobile platforms in distributed collaborative positioning and other applications. The proposed scheme utilizes symmetric free-space optical (FSO) links to effectively suppress drift errors, integrating the high bandwidth of optical links and the high stability of microwave links, enabling one-to-many networking synchronization between mobile platforms. The system adopts optical wireless transmission technology based on pseudo-code regenerative ranging, integrating 1.5 Gbps high-speed data transmission with high-precision TFP-synchronization functionality. An experimental system consisting of a main station and two auxiliary stations was established in an outdoor mobile platform scenario. Experimental results show that while achieving high-speed communication, the frequency synchronization precision is 0.0131 ppb, frequency stability is in the order of 10−10@1 s, and phase synchronization precision is approximately 3.56°. The system achieves time synchronization precision at the picosecond level. The proposed technology is highly suitable for high-precision synchronization communication in scenarios lacking fiber-optic infrastructure, effectively fulfilling rigorous requirements in mobile platform applications such as distributed collaborative positioning.

Purpose This study aims to investigate the dynamic co-movement and interconnection among 69 security investment indices in China using the multi-time scale framework. Design/methodology/approach The authors first use the multiple coherence analysis method to exhibit the degree of relationships among the variables under study. In addition, the wavelet multiple correlation and wavelet multiple cross-correlation analyses are used to examine the time-frequency synchronization interdependence structure among the variables. Findings From the empirical findings, one may infer less opportunity for portfolio diversification at higher time scales. Obviously, at these scales, the authors find that the 69 Chinese investment indices generate a simple security investment class, as indicated by higher interconnection between the indices. Research limitations/implications Further research can increase the sample size to re-investigate the empirical relationship for security investment indices. Practical implications In the nutshell, the results demonstrate the potential for Chinese investors to invest in security investment indices to earn from portfolio diversification at lower time frequencies. The Chinese investment market indices under study yield further opportunities of portfolio diversification toward the short-term investors than the long-term investors. Originality/value To the best of the authors’ knowledge, this is the first paper to examine the dynamic co-movement and interconnection for security investment indices in China.

The dynamics of power-grid networks is becoming an increasingly active area of research within the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on simplifying assumptions that can be either difficult to assess or not fully justified for realistic applications. Here we perform a comprehensive comparative analysis of three leading models recently used to study synchronization dynamics in power-grid networks-a fundamental problem of practical significance given that frequency synchronization of all power generators in the same interconnection is a necessary condition for a power grid to operate. We show that each of these models can be derived from first principles within a common framework based on the classical model of a generator, thereby clarifying all assumptions involved. This framework allows us to view power grids as complex networks of coupled second-order phase oscillators with both forcing and damping terms. Using simple illustrative examples, test systems, and real power-grid datasets, we study the inherent frequencies of the oscillators as well as their coupling structure, comparing across the different models. We demonstrate, in particular, that if the network structure is not homogeneous, generators with identical parameters need to be modeled as non-identical oscillators in general. We also discuss an approach to estimate the required (dynamical) system parameters that are unavailable in typical power-grid datasets, their use for computing the constants of each of the three models, and an open-source MATLAB toolbox that we provide for these computations.

This study presents a current decomposition technique based on a novel instantaneous power theory for better power quality and reliability of a dc-grid based wind energy conversion system (WECS) used on a poultry farm. The proposed approach also offers adequate control for the parallel operation of multiple distributed generations independent of the requirement of voltage and frequency synchronisation. In addition to that, a 17-level hybrid cascaded multilevel inverter is considered and integrated by utilising a three-level flying capacitor inverter and cascading it with three floating capacitor H-bridges. The presence of single dc-link voltage facilitates the back to back operation with a reduced dv/dt ratio, common-mode voltage variation, and operations under varying load power factors and modulation index. Moreover, for attaining better power management especially in the islanded mode of operation, the battery energy storage device is incorporated. The proposed WECS has been tested through MATLAB/Simulink software simulation under various conditions to facilitate better power quality, increase the flexibility and reliability in the micro-grid operation.

Nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for analysing the structure and function of molecules, and for performing three-dimensional imaging of their spin densities. At the heart of NMR spectrometers is the detection of electromagnetic radiation, in the form of a free induction decay signal 1 , generated by nuclei precessing around an applied magnetic field. Whereas conventional NMR requires signals from 10 12 or more nuclei, recent advances in sensitive magnetometry 2 , 3 have dramatically lowered the required number of nuclei to a level where a few or even individual nuclear spins can be detected 4 – 6 . It is unclear whether continuous detection of the free induction decay can still be applied at the single-spin level, or whether quantum back-action (the effect that a detector has on the measurement itself) modifies or suppresses the NMR response. Here we report the tracking of single nuclear spin precession using periodic weak measurements 7 – 9 . Our experimental system consists of nuclear spins in diamond that are weakly interacting with the electronic spin of a nearby nitrogen vacancy centre, acting as an optically readable meter qubit. We observe and minimize two important effects of quantum back-action: measurement-induced decoherence 10 and frequency synchronization with the sampling clock 11 , 12 . We use periodic weak measurements to demonstrate sensitive, high-resolution NMR spectroscopy of multiple nuclear spins with a priori unknown frequencies. Our method may provide a useful route to single-molecule NMR 13 , 14 at atomic resolution. Periodic weak measurements of just a few carbon-13 nuclear spins in diamond demonstrate sensitive, high-resolution nuclear magnetic resonance spectroscopy at the molecular level.

This study presents a fully distributed control paradigm for secondary control of islanded AC microgrid (MG). The proposed method addresses both voltage and frequency restoration for inverter-based distributed generators (DGs). The MG system has droop controlled DG units with predominantly inductive transmission lines and different communication topologies. The restoration scheme is fully distributed in nature, and the DGs need to communicate with their neighbours using a sparse communication network. The proposed control scheme is efficient to provide quick restoration of the voltage and frequency whilst accurate power-sharing is achieved despite disturbances. Further, convergence and stability analysis of the proposed control scheme is presented. The proposed algorithm avoids the need for a central controller and complex communication structure thereby reducing the computational burden and the risk of single-point-failure. The performance of the proposed control scheme has been verified considering variations in load and communication topologies and link delay by pursuing an extensive simulation study in MATLAB/SimPowerSystem toolbox. The proposed control scheme supports plug-and-play demand and scalability of MG network. The proposed control scheme is also compared with the neighbourhood tracking error based distributed control scheme and observed that the former exhibit faster convergence and accurate performance despite disturbances in MG network.

To provide a ground-based experimental reference for free-space optical time-frequency synchronization in future space applications, this paper investigates the impact of beam drift and dynamic link-state variations on free-space laser links. A bidirectional free-space laser time-frequency synchronization and ranging system is established and the synchronization process is uniformly modeled. An improved Kalman filtering method based on innovation consistency is proposed in which a strong tracking mechanism enhances adaptability to model mismatch and abnormal observations; at the same time, an adaptive observation noise modeling strategy based on online statistical estimation characterizes the time-varying noise properties of free-space optical links. Experimental validation is conducted using an equivalent free-space laser link of approximately 321 m. The results show that the proposed method improves the time synchronization accuracy from 78.32 ps to 45.64 ps, corresponding to an enhancement of about 41%. In terms of time stability, the time deviation (TDEV) is reduced from 7.14×10-11 s to 4.33×10-11 s at an averaging time of τ=1 s, and from 4.20×10-12 s to 7.01×10-13 s at τ=800 s. For ranging performance, the system achieves an average measured distance of 321.56 m with a ranging standard deviation of 15.2 mm. These results demonstrate that the proposed approach enables high-precision and stable state estimation for integrated free-space laser time-frequency synchronization and ranging systems.