Synchronization of coupled oscillators on small-world networks

We investigate the synchronous dynamics of Kuramoto oscillators and van der Pol oscillators on Watts-Strogatz type small-world networks. The order parameters to characterize macroscopic synchronization are calculated by numerical integration. We focus on the difference between frequency synchronization and phase synchronization. In both oscillator systems, the critical coupling strength of the phase order is larger than that of the frequency order for the small-world networks. The critical coupling strength for the phase and frequency synchronization diverges as the network structure approaches the regular one. For the Kuramoto oscillators, the behavior can be described by a power-law function and the exponents are obtained for the two synchronizations. The separation of the critical point between the phase and frequency synchronizations is found only for small-world networks in the theoretical models studied.     

Current theoretical approaches to collective behavior of dislocations

Plastic deformation is a highly dissipative process that induces a variety of patterns such as the cell structure in multislip conditions, the matrix structure and the persistent slip bands in cyclic deformation, as also the static and propagating bands in constant strain rate conditions. The diversity and the complexity of these patterns with length scales ranging from nanometers all the way to millimeters level, and time scales ranging from picoseconds to a few hours, pose serious challenges for modeling the collective behavior of dislocations. While a large body of knowledge has accumulated on the mechanics of dislocations and their interactions for a long time, describing such patterns has been slow mainly due to lack of methods to deal with the collective behavior of dislocations. The purpose of this review is to present the rich variety of dislocation patterns observed in different deformation conditions along with the recent advances in modeling using borrowed techniques traditionally used in condensed matter physics. These can be classified as statistical and dynamical approaches. The review begins with a summary of different types of patterns and their characterization. Appropriate background material is provided both in terms of basic dislocation mechanisms and theoretical methods. The latter includes the Langevin and distribution function approaches, and a host of standard dynamical methods such as the Ginzburg–Landau approach, methods of characterization of chaos and slow manifold analysis. Statistical models for the cell structure and persistent slip bands are based on Langevin dynamics and distribution function theoretic approaches. Of the dynamical models, the first set addresses the slowly emerging matrix structure and persistent slip bands. The second set of models is devoted to the study of a type of propagative instability called the Portevin–Le Chatelier effect. Generic features of the instability addressed include bistability, negative strain rate sensitivity of the flow stress, different types of bands, the dynamics and statistics of stress drops, and their characterization. Three different models all of which are dynamical in nature are discussed. While these models are quite different with regard to their frameworks, what they seek to describe and the levels of sophistication undertaken, these models capture a good variety of the observed features. The review ends with a summary and outlook.     

History Marginalization Improves Forecasting in Variational Recurrent Neural Networks

Deep probabilistic time series forecasting models have become an integral part of machine learning. While several powerful generative models have been proposed, we provide evidence that their associated inference models are oftentimes too limited and cause the generative model to predict mode-averaged dynamics. Mode-averaging is problematic since many real-world sequences are highly multi-modal, and their averaged dynamics are unphysical (e.g., predicted taxi trajectories might run through buildings on the street map). To better capture multi-modality, we develop variational dynamic mixtures (VDM): a new variational family to infer sequential latent variables. The VDM approximate posterior at each time step is a mixture density network, whose parameters come from propagating multiple samples through a recurrent architecture. This results in an expressive multi-modal posterior approximation. In an empirical study, we show that VDM outperforms competing approaches on highly multi-modal datasets from different domains.     

Analytic analysis of irregular discrete universes

In this work we investigate the dynamics of cosmological models with spherical topology containing up to 600 Schwarzschild black holes arranged in an irregular manner. We solve the field equations by tessellating the 3-sphere into eight identical cells, each having a single edge which is shared by all cells. The shared edge is enforced to be locally rotationally symmetric, thereby allowing for solving the dynamics to high accuracy along this edge. Each cell will then carry an identical (up to parity) configuration which can however have an arbitrarily random distribution. The dynamics of such models is compared to that of previous works on regularly distributed black holes as well as with the standard isotropic dust models of the FLRW type. The irregular models are shown to have richer dynamics than that of the regular models. The randomization of the distribution of the black holes is done both without bias and also with a certain clustering bias. The geometry of the initial configuration of our models is shown to be qualitatively different from the regular case in the way it approaches the isotropic model.     

最优速度模型与元胞自动机模型的比较研究

用解析分析与数值仿真的手段研究了一种典型的车辆跟驰模型(OV模型)与元胞自动机模型(NS模型)之间的区别与联系.首先通过对模型规则的分析,证明了确定NS模型是OV模型的一种离散形式.随后针对两模型更复杂的具体形式,通过数值仿真的手段进行了模型的密度-流量关系与模型在开放边界下的动态特性的研究.实验结果表明,从现象来看,OV模型与NS模型具有非常近似的性质,但两种模型的机制不相同,并且各自具有不能相互替代的优势.为交通流模型的使用和改进提供了参考.     

Nonequilibrium dynamics of ultracold Fermi superfluids

The aim of this mini review is to survey the literature on the study of nonequilibrium dynamics of Fermi superfluids in the BCS and BEC limits, both in the single channel and dual channel cases. The focus is on mean field approaches to the dynamics, with specific attention drawn to the dynamics of the Ginzburg-Landau order parameters of the Fermi and composite Bose fields, as well as on the microscopic dynamics of the quantum degrees of freedom. The two approaches are valid approximations in two different time scales of the ensuing dynamics. The system is presumed to evolve during and/or after a quantum quench in the parameter space. The quench can either be an impulse quench with virtually instantaneous variation, or a periodic variation between two values. The literature for the order parameter dynamics, described by the time-dependent Ginzburg-Landau equations, is reviewed, and the works of the author in this area highlighted. The mixed phase regime in the dual channel case is also considered, and the dual order parameter dynamics of Fermi-Bose mixtures reviewed. Finally, the nonequilibrium dynamics of the microscopic degrees of freedom for the superfluid is reviewed for the self-consistent and non self-consistent cases. The dynamics of the former can be described by the Bogoliubov de-Gennes equations with the equilibrium BCS gap equation continued in time and self -consistently coupled to the BdG dynamics. The latter is a reduced BCS problem and can be mapped onto the dynamics of Ising and Kitaev models. This article reviews the dynamics of both impulse quenches in the Feshbach detuning, as well as periodic quenches in the chemical potential, and highlights the author’s contributions in this area of research.     

非圆化磨耗激励下高速列车转向架区域噪声边频带产生机理及影响

该文通过对车辆噪声和车轮非圆化磨耗开展跟踪测试和分析,发现存在车轮非圆化磨耗的列车在运行过程中,其转向架区域噪声窄带频谱上会出现了以非圆化磨耗激励频率为中心,以过轨枕频率为间隔等间距分布的噪声峰值(即噪声边频带).这使得车轮非圆化磨耗不仅会影响其激励频率处的列车轨道结构的振动和噪声,还会对其他频段的噪声产生重要影响.为...     

Coupled disease–behavior dynamics on complex networks: A review

It is increasingly recognized that a key component of successful infection control efforts is understanding the complex, two-way interaction between disease dynamics and human behavioral and social dynamics. Human behavior such as contact precautions and social distancing clearly influence disease prevalence, but disease prevalence can in turn alter human behavior, forming a coupled, nonlinear system. Moreover, in many cases, the spatial structure of the population cannot be ignored, such that social and behavioral processes and/or transmission of infection must be represented with complex networks. Research on studying coupled disease–behavior dynamics in complex networks in particular is growing rapidly, and frequently makes use of analysis methods and concepts from statistical physics. Here, we review some of the growing literature in this area. We contrast network-based approaches to homogeneous-mixing approaches, point out how their predictions differ, and describe the rich and often surprising behavior of disease–behavior dynamics on complex networks, and compare them to processes in statistical physics. We discuss how these models can capture the dynamics that characterize many real-world scenarios, thereby suggesting ways that policy makers can better design effective prevention strategies. We also describe the growing sources of digital data that are facilitating research in this area. Finally, we suggest pitfalls which might be faced by researchers in the field, and we suggest several ways in which the field could move forward in the coming years.     

Linear and nonlinear vibrations analysis of viscoelastic sandwich beams

In this paper, numerical models are proposed for linear and nonlinear vibrations analyses of viscoelastic sandwich beams with various viscoelastic frequency dependent laws using the finite element based solution. Real and various complex eigenmodes approaches are investigated as Galerkin bases. Based on harmonic balance method, simplified and general approaches are developed for nonlinear vibration analysis. Analytical frequency-amplitude and phase-amplitude relationships are elaborated based on the numerically computed complex eigenmodes. The equivalent loss factors and frequencies as well as the forced harmonic response and phase curves are performed for sandwich beams with various boundary conditions and frequency dependent viscoelastic laws.     

Precipitate growth in concentrated binary alloys: a comparison between kinetic Monte Carlo simulations,cluster dynamics and the classical theory

The numerical modelling of concentrated alloy precipitation kinetics remains a challenge at all scales. At the microscopic scale, kinetic Monte Carlo (KMC) simulations can cope with nucleation and early growth whatever the solute concentration may be; it cannot, however, address coarsening. At the mesoscopic scale, the advantage of cluster dynamics (CD) is its ability to describe the whole kinetics of precipitation but lacks of reliability for nucleation in concentrated alloys. Finally, analytical models are preferred at the macroscopic scale for their simplicity, their flexibility and their ability to be incorporated within more general approaches, to predict mechanical properties, for instance. The present work aims at examining the ability of CD and classical analytical models to describe the growth of an isolated precipitate in a concentrated binary alloy, by comparison with KMC simulations taken as the reference.     

Coupled Electromagnetic-Dynamic Modeling and Bearing Fault Characteristics of Induction Motors considering Unbalanced Magnetic Pull

Induction motors are complex energy conversion systems across the domains of dynamics, electricity, and magnetism. Most existing models mainly consider unidirectional coupling, such as the effect of dynamics on electromagnetic properties, or the effect of unbalanced magnetic pull on dynamics, while in practice it should be a bidirectional coupling effect. The bidirectionally coupled electromagnetic-dynamics model is beneficial to the analysis of induction motor fault mechanisms and characteristics. This paper proposes a coupled electromagnetic-dynamic modeling method that introduces unbalanced magnetic pull. By using the rotor velocity, air gap length, and unbalanced magnetic pull as the coupling parameters, the coupled simulation of the dynamic and electromagnetic models can be effectively realized. Simulation results for bearing faults show that the introduction of magnetic pull induces a more complex dynamic behavior of the rotor, which in turn leads to modulation in the vibration spectrum. The fault characteristics can be found in the frequency domain of the vibration and current signals. Through the comparison between simulation and experimental results, the effectiveness of the coupled modeling approach and the frequency domain characteristics caused by the unbalanced magnetic pull are verified. The proposed model can help to obtain a variety of information that is difficult to measure in reality and can also serve as a technical basis for further research on nonlinear characteristics and chaos in induction motors.     

Hot Scatterers and Tracers for the Transfer of Heat in Collisional Dynamics

We introduce stochastic models for the transport of heat in systems described by local collisional dynamics. The dynamics consists of tracer particles moving through an array of hot scatterers describing the effect of heat baths at fixed temperatures. Those models have the structure of Markov renewal processes. We study their ergodic properties in details and provide a useful formula for the cumulant generating function of the time integrated energy current. We observe that out of thermal equilibrium, the generating function is not analytic. When the set of temperatures of the scatterers is fixed by the condition that in average no energy is exchanged between the scatterers and the system, different behaviours may arise. When the tracer particles are allowed to travel freely through the whole array of scatterers, the temperature profile is linear. If the particles are locked in between scatterers, the temperature profile becomes nonlinear. In both cases, the thermal conductivity is interpreted as a frequency of collision between tracers and scatterers.     

Transverse shear deformability in the dynamics of thin-walled composite beams: consistency of different approaches

The aim of this work is to describe an analysis of the transverse shear deformability in the dynamics of thin-walled composite beams. Some thin-walled-composite-beam models, which are derived by means of different approaches (principle of virtual works and principle of Hellinger-Reissner among others), show substantial discrepancies due to the employment of different constitutive equations based on the aforementioned approaches. In the following paragraphs a comparison of different schemes and hypotheses related to constitutive equations for thin-walled composite beams is performed.     

Vibrations of single- and double-walled carbon nanotubes with layerwise boundary conditions: A molecular dynamics study

In the present work, the vibration characteristics of single- and double-walled carbon nanotubes under various layerwise boundary conditions at different lengths are investigated. This is accomplished by the use of molecular dynamics simulations based on the Tersoff-Brenner and Lennard-Jones potential energy functions. The effects of initial tensile and compressive strains on the resonant frequency of carbon nanotubes are also taken into consideration. From the results generated, it is observed that the natural frequency of carbon nanotubes is strongly dependent on their boundary conditions especially when tubes are shorter in length. The natural frequency and its dependence on tube end conditions reduce by increasing the tube length. The natural frequency of DWCNTs lies between those of the constituent inner and outer SWCNTs and is nearer to those of the outer one. It is further observed that the natural frequency is highly sensitive to tensile and compressive strains. The frequency shift occurring in the presence of small initial strains is positive for tensile strains and negative for compressive strains. The results obtained provide valuable information for calibrating the small scaling parameter of the nonlocal models for the vibration problem of carbon nanotubes.     

Many-neighbour interaction and non-locality in traffic models

The optimal-velocity model, as proposed by Bando et al. [1], shows unrealistic values of the acceleration for various optimal-velocity functions [2,3]. We discuss different approaches of how to correct this problem. Multiple look-ahead (many-neighbour interaction) models are the most promising candidates in reducing accelerations and decelerations to realistic values. We focus on two such models and, in particular, their linear stability and how these affect the vehicle dynamics and wave solutions. As found earlier [4], multiple look-ahead models reproduce many real flow features, and our results further support the necessity of this ansatz. However, the problem of non-locality arises when they are transformed into the corresponding continuum model. We discuss three methods of how to interpret many-neighbour interaction in macroscopic models.Received: 27 March 2004, Published online: 12 July 2004PACS: 45.70.Vn Granular models of complex systems; traffic flow - 89.90. + n Other topics in areas of applied and interdisciplinary physics - 47.50. + d Non-Newtonian fluid flows     

On the equivalence of the parallel channel and the correlated cluster relaxation models

The question of the origins of nonexponential relaxation is addressed in terms of the probabilistic approach to relaxation. The interconnection between two differently rooted probabilistic models, i.e., between the parallel channel and the correlated cluster models, is presented. We show that clearly different probabilistic origins yield in both approaches a well-defined class of universally valid two-power-law responses with the stretched-exponential and exponential decay laws as special cases. The equivalence of both models indicates that variations in the local environment of the relaxing configurational units (parallel channel relaxation) can provide a basis for self-similar relaxation dynamics without the need for hierarchically constrained dynamics (correlated clusters relaxation).     

Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics

Kinetically constrained lattice models of glasses introduced by Kob and Andersen (KA) are analyzed. It is proved that only two behaviors are possible on hypercubic lattices: either ergodicity at all densities or trivial non-ergodicity, depending on the constraint parameter and the dimensionality. But in the ergodic cases, the dynamics is shown to be intrinsically cooperative at high densities giving rise to glassy dynamics as observed in simulations. The cooperativity is characterized by two length scales whose behavior controls finite-size effects: these are essential for interpreting simulations. In contrast to hypercubic lattices, on Bethe lattices KA models undergo a dynamical (jamming) phase transition at a critical density: this is characterized by diverging time and length scales and a discontinuous jump in the long-time limit of the density autocorrelation function. By analyzing generalized Bethe lattices (with loops) that interpolate between hypercubic lattices and standard Bethe lattices, the crossover between the dynamical transition that exists on these lattices and its absence in the hypercubic lattice limit is explored. Contact with earlier results are made via analysis of the related Fredrickson--Andersen models, followed by brief discussions of universality, of other approaches to glass transitions, and of some issues relevant for experiments.