Lyapunov function for the Kuramoto model of nonlinearly coupled oscillators

A Lyapunov function for the phase-locked state of the Kuramoto model of non-linearly coupled oscillators is presented. It is also valid for finite-range interactions and allows the introduction of thermodynamic formalism such as ground states and universality classes. For the Kuramoto model, a minimum of the Lyapunov function corresponds to a ground state of a system with frustration: the interaction between the oscillators,XY spins, is ferromagnetic, whereas the random frequencies induce random fields which try to break the ferromagnetic order, i.e., global phase locking. The ensuing arguments imply asymptotic stability of the phase-locked state (up to degeneracy) and hold for any probability distribution of the frequencies. Special attention is given to discrete distribution functions. We argue that in this case a perfect locking on each of the sublattices which correspond to the frequencies results, but that a partial locking of some but not all sublattices is not to be expected. The order parameter of the phase-locked state is shown to have a strictly positive lower bound (r 1/2), so that a continuous transition to a nonlocked state with vanishing order parameter is to be excluded.     

Phase synchronization and its transition in two coupled bursting neurons: theoretical and numerical analysis

It is crucially important to study different synchronous regimes in coupled neurons because different regimes may correspond to different cognitive and pathological states. In this paper, phase synchronization and its transitions are discussed by means of theoretical and numerical analyses. In two coupled modified Morris--Lecar neurons with a gap junction, we show that the occurrence of phase synchronization can be investigated from the dynamics of phase equation, and the analytical synchronization condition is derived. By defining the phase of spike and burst, the transitions from burst synchronization to spike synchronization and then toward nearly complete synchronization can be identified by bifurcation diagrams, the mean frequency difference and time series of neurons. The simulation results suggest that the synchronization of bursting activity is a multi-time-scale phenomenon and the phase synchronization deduced by the phase equation is actually spike synchronization.     

Parameter-dependent synchronization transition of coupled neurons with co-existing spiking and bursting

A firing pattern transition is simulated in the Leech neuron model, firstly from bursting to co-existence of spiking and bursting and then to spiking. The attraction domain of spiking and bursting for three different parameter values are calculated. Synchronization transition processes of two coupled Leech neurons, one is bursting and the other the co-existing spiking, are simulated for the three parameters. The three synchronization processes appear similar as the coupling strength increases, beginning from non-synchronization to complete synchronization through a complex dynamical procedure, but their detailed processes are different depending on the parameter values. The transition procedure is complex and the complete synchronization is in bursting for larger parameter values, while the process is simple with complete synchronization of spiking for smaller values. The potential relationship between complete synchronization and the attraction domain is also discussed. The results are instructive to understanding the synchronization behaviors of the coupled neuronal system with co-existing attractors.     

Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses

The minimal two-dimensional model of bursting neuronal dynamics is used to study the influence of time-delay on the properties of synchronization of bursting neurons. Generic properties of bursting and dependence of the stability of synchronization on the time-lag and the strength of coupling are described, and compared with the two common types of synaptical coupling, i.e., time-delayed chemical and electrical synapses.     

振幅耦合动态网络中相邻结点间的相同步

研究用适当的量化指标来刻画动态网络的相同步,为此定义了新的量化指标:相邻结点的网络平均锁相值和网络平均相频差.动态网络结点选择的是多旋转中心的Lorenz混沌振子,对Lorenz系统进行柱面坐标变换,用振幅耦合方法构造动态网络.分别对星形网络和小世界网络进行了仿真计算,结果表明随着耦合强度的增大,网络中相邻结点的两个系统之间存在相同步现象,而且相同步行为与定义的量化指标之间存在较准确的对应关系.     

Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses

The minimal two-dimensional model of bursting neuronal dynamics is used to study the influence of time-delay on the properties of synchronization of bursting neurons. Generic properties of bursting and dependence of the stability of synchronization on the time-lag and the strength of coupling are described, and compared with the two common types of synaptical coupling, i.e., time-delayed chemical and electrical synapses.     

Stability of incoherence in a population of coupled oscillators

We analyze a mean-field model of coupled oscillators with randomly distributed frequencies. This system is known to exhibit a transition to collective oscillations: for small coupling, the system is incoherent, with all the oscillators running at their natural frequencies, but when the coupling exceeds a certain threshold, the system spontaneously synchronizes. We obtain the first rigorous stability results for this model by linearizing the Fokker-Planck equation about the incoherent state. An unexpected result is that the system has pathological stability properties: the incoherent state is unstable above threshold, butneutrally stable below threshold. We also show that the system is singular in the sense that its stability properties are radically altered by infinitesimal noise.     

Berry Phase of Composite System Induced by Time-Dependent Interaction

The Berry phase in a composite system induced by the time-dependent interaction is discussed. We choose two coupled spin-1/2 systems as the composite system： one of the subsystems is subjected to a static magnetic field, and the coupling parameters between two spins are controllable in time. We show that the time-dependent interaction can induce the Berry phase in a similar way as that a spin-1/2 system （qubit） is driven by an effective time-dependent magnetic field. Furthermore, using two consecutive cycles with opposite directions of both the static magnetic field as well as opposite signs of the coupling parameters, a nontrivial two-qubit unitary transformation purely based on Berry phases can be constructed.     

Acoustic measurements of the infinitesimal phase response curve from a sounding organ pipe

The infinitesimal phase response curve (iPRC) of an organ pipe was measured using two types of external forcing, namely, sinusoidal and pulse forcing. Although the measured iPRCs exhibited different shapes because of the difficulty in realizing ideal pulses in acoustic experiments, the spectral structures agreed between both methods. Both measurements indicated that an external sound, which matched the pipe's second resonance, could most effectively induce frequency locking. Acoustically, this may be considered as a consequence of the pipe's open end. Our study is of significant importance in understanding the characteristics of frequency locking among organ pipes.     

耦合哈密顿系统中测度同步的研究

测度同步现象是耦合哈密顿系统的一种重要性质.对规则系统和混沌系统的测度同步性 质作了深入研究，重点讨论了耦合哈密顿系统处于混沌状态时，系统测度同步的特点及系统 的相位关系.提出了一种定量判断测度同步的简单方法，考虑了高斯白噪声对系统中测度同 步性质的影响. 关键词： 耦合哈密顿系统 测度同步 相锁定 高斯白噪声     

改进的单次散射相函数解析表达式

单次散射相函数对电磁辐射传输模拟过程的准确性和计算效率有重要的影响.基于电磁散射与辐射传输中的基本理论,对单次散射相函数的解析表达式进行了研究,提出了一种新的单次散射相函数解析表达式.比较了单个粒子的Henyey-Greenstein相函数、Henyey-Greenstein*相函数与新的相函数随角度的分布,发现新的散射相函数提高了后向散射峰值,可以更合理地描述单个粒子的散射特性.按三种气溶胶粒子谱分布模式计算了Henyey-Greenstein*相函数和新的相函数对应的数值结果,并与多分散系Mie散射相函数进行对比,发现新的相函数提高了与多分散系Mie散射相函数的符合程度.研究表明,对于大角度(大于90°)后向散射,新的相函数与Mie散射相函数均方根差较小的占73.3%,高于Henyey-Greenstein*相函数的26.7%,证明了新的相函数可以显著提高后向散射峰值.新的相函数对准确模拟辐射传输过程具有重要意义.     

Photon--photon interactions with inner coupled double-cavity

This paper describes the interaction between two spatial modes of the optical fields with a single atom trapped inner coupled double-cavity. Theoretical derivation and numerical simulation with the experimental available parameters show that photon-photon switching and π phase shift of single photons may be achieved with current experimental technology. As the probe and control fields are in different spatial modes, the system is superior for implementing cavity QED-based photonic quantum networks.     

Induced modification of the geometric phase of a qubit coupled to an XY spin chain by Dzyaloshinsky-Moriya interaction

We consider a qubit symmetrically and transversely coupled to an XY spin chain with Dzyaloshinsky-Moriya(DM) interaction in the presence of a transverse magnetic field.An analytical expression for the geometric phase of the qubit is obtained in the weak coupling limit.We find that the modification of the geometrical phase induced by the spin chain environment is greatly enhanced by DM interaction in the weak coupling limit around the quantum phase transition point of the spin chain.     

Ac response of a coupled double quantum dot

The effect of phase-breaking process on the ac response of a coupled double quantum dot is studied in this paper based on the nonequilibrium Green function formalism. A general expression is derived for the ac current in the presence of electron--phonon interaction. The ac conductance is numerically computed and the results are compared with those in [Anatram M P and Datta S 1995 Phys. Rev. B 51 7632]. Our results reveal that the inter-dot electron tunnelling interplays with that between dots and electron reservoirs, and contributes prominently to the ac current when inter-dot tunnelling coupling is much larger than the tunnelling coupling between dots and electron reservoirs. In addition, the phase-breaking process is found to have a significant effect on the ac transport through the coupled double dot.     

相对论返波管注入锁相的数值模拟

给出了一种基于梯形慢波结构的相对论返波管结构,并采用2.5维全电磁PIC粒子模拟软件对其前端注入锁相进行了模拟研究。注入功率从二极管区注入相对论返波管中,注入功率50 kW,注入比$48.3dB时,返波管输出的相位抖动在±20°范围内,并拟合了返波管相位抖动与注入功率之间关系,给出了判断返波管相位抖动大小的经验公式。注入功率提高至120 MW,注入比$14.5 dB时,注入信号对相对论返波管输出的频率实现了牵引。     

Rhythm dynamics of complex neuronal networks with mixed bursting neurons

The spatiotemporal order and rhythm dynamics of a complex neuronal network with mixed bursting neurons are studied in this paper. A quantitative characteristic, the width factor, is introduced to describe the rhythm dynamics of an individual neuron, and the average width factor is used to characterize the rhythm dynamics of a neuronal network. An r parameter is introduced to denote the ratio of the short bursting neurons in the network. Then we investigate the effect of the ratio on the rhythm dynamics of the neuronal network. The critical value of r is derived, and the neurons in the network always remain short bursting when the r ratio is larger than the critical value.     

相对论返波管注入锁相的数值模拟

给出了一种基于梯形慢波结构的相对论返波管结构,并采用2.5维全电磁PIC粒子模拟软件对其前端注入锁相进行了模拟研究。注入功率从二极管区注入相对论返波管中,注入功率50 kW,注入比－48.3 dB时,返波管输出的相位抖动在20范围内,并拟合了返波管相位抖动与注入功率之间关系,给出了判断返波管相位抖动大小的经验公式。注入功率提高至120 MW,注入比－14.5 dB时,注入信号对相对论返波管输出的频率实现了牵引。     

JMCT光子-电子耦合输运模拟计算研究

为满足光子-电子耦合输运应用模拟需求,自主研发了JMCT光子-电子耦合输运功能,并实现了多种光电耦合输运处理方式,以便满足不同的工程需求。利用光子-电子耦合输运典型算例验证了JMCT光子-电子耦合输运功能的正确性,并应用到了探测器响应函数模拟、闪光照相模拟计算中,表明JMCT在实验核物理、核分析技术应用等方面发挥着越来越重要的作用。     

Decoherence dynamics of a charge qubit coupled to the noise bath

By virtue of the canonical quantization method, we present a quantization scheme for a charge qubit based on the superconducting quantum interference device (SQUID), taking the self-inductance of the loop into account. Under reasonable short-time approximation, we study the effect of decoherence in the ohmic case by employing the response function and the norm. It is confirmed that the decoherence time, which depends on the parameters of the circuit components, the coupling strength, and the temperature, can be as low as several picoseconds, so there is enough time to record the information.     

Effect of coupling between passenger compartment and trunk of a car on coupled system natural frequencies using acoustic frequency response function

Conventional numerical techniques, used to study the acoustics of a car passenger cabin, treat the cabin as an isolated cavity excited by the cavity boundaries. Realistically, other cavity volumes such as the trunk communicate with the cabin through the holes in the parcel shelf of the car. An extended acoustic model of a car is formed by the cavity volumes of the passenger compartment and the trunk as well as air leakages through the holes provided for electrical devices and ventilation on the parcel shelf. In this study, the dynamic influence of air leakages between the passenger and trunk compartments on the first and second coupled system modes was investigated experimentally using acoustic frequency response function. The response to the acoustic excitation was measured for four different configurations of trim and holes of the parcel shelf. The natural frequencies of the first and second coupled system modes increased with increasing holes size with and without the trim of the parcel shelf. The experimental results were in good agreement with the reported results of coupling effects of double cavities connected by a neck. In the low frequency region since the wavelength is longer compared to the holes dimension, these holes act as point sources.