Directed transport of modulated structures in the Frenkel–Kontorova model with a pulsating coupling

We study the directed transport of commensurate and incommensurate modulated phases of the Frenkel–Kontorova model by (parametric driving) periodic pulsed variation of the nearest-neighbor coupling in the dissipative limit of the dynamics. We obtain that a directed current flow appears as the amplitude of the pulsating coupling C increases above a threshold coupling C_th. This threshold coupling depends on the average interspacing ω between the oscillators displaying singularities as the system becomes commensurable with the underlying lattice. By making use of the discommensuration theory of modulated phases we obtain that the dependence of the directed current on ω is a piecewise linear function with integer slope. Numerical results confirm these predictions.     

Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons

The dynamics of two coupled piece-wise linear one-dimensional monostable maps is investigated. The single map is associated with Poincare section of the FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to the appearance of chaotic attractor. The attractor exists in an invariant region of phase space bounded by the manifolds of the saddle fixed point and the saddle periodic point. The oscillations from the chaotic attractor have a spike-burst shape with anti-phase synchronized spiking.     

Passive mode-locking by use of waveguide arrays

A novel mode-locking technique is presented in which the intensity-dependent spatial coupling dynamics of a waveguide array is used to achieve temporal mode-locking in a passive optical fiber laser. By use of the discrete, nearest-neighbor spatial coupling of the waveguide array, low-intensity light can be transferred to the neighboring waveguides and ejected (attenuated) from the laser cavity. In contrast, higher-intensity light is self-focused in the waveguide and remains largely unaffected. Numerical studies of this pulse shaping mechanism (intensity discrimination) show that using current waveguide arrays and standard optical fiber technology produces stable and robust mode-locked soliton-like pulses.     

Lens Design: Global Optimization with Escape Function

The technique of using the ‘escape function’ for global optimization in lens design is described. This includes how to identify two solutions as independent; the threshold value for this criterion can be chosen to determine how to explore local solutions—rough or fine. Choice of appropriate values for two parameters in the escape function is most important, since this will affect the efficiency of the automatic global optimization process. There are two problems, i.e. giving default values at the beginning of the design, and determining a default rule to change them when the escape is unsuccessful. The latter was solved by assuming a ‘saddle path’ as the best route to escape. An exact solution for the former was not found, but a hint for finding a second best solution is shown based on the statistical study of local minima.     

温度对光纤准直器的角度偏移影响分析

通过对光纤准直器准直失配,即离轴耦合、偏角耦合、间距耦合三种情况的耦合损耗进行分析,发现角度偏移对耦合效率影响最大.实验中随着温度周期性的变化,光斑位置也出现了有一定规律性的变化.实验通过确定光斑位置的变化量从而求出鞍型和拱型支承架在温度循环时的角度偏移为519 μrad和395 μrad,并导致了0.944 dB和0.718 dB的耦合损耗;在温度冲击时的角度偏移为986 μrad和138 μrad,并导致了1.793 dB和0.251 dB的耦合损耗.实验结果表明拱型支承架在两种不同的温度变化情况下均优于鞍型支承架.     

Dynamics and thermodynamics of rotators interacting with both long- and short-range couplings

The effect of nearest-neighbor coupling on the thermodynamic and dynamical properties of the ferromagnetic Hamiltonian mean field model (HMF) is studied. For a range of antiferromagnetic nearest-neighbor coupling, a canonical first-order transition is observed, and the canonical and microcanonical ensembles are non-equivalent. In studying the relaxation time of non-equilibrium states it is found that as in the HMF model, a class of non-magnetic states is quasi-stationary, with an algebraic divergence of their lifetime with the number of degrees of freedom N. The lifetime of metastable states is found to increase exponentially with N as expected.     

Local waiting time fluctuations along a randomly pinned crack front

The propagation of an interfacial crack along a heterogeneous weak plane of a transparent Plexiglas block is followed using a high resolution fast camera. We show that the fracture front dynamics is governed by local and irregular avalanches with very large size and velocity fluctuations. We characterize the intermittent dynamics observed, i.e., the local pinnings and depinnings of the crack front by measuring the local waiting time fluctuations along the crack front during its propagation. The deduced local front line velocity distribution exhibits a power law behavior, P(v) alpha v-eta with eta=2.55+/-0.15, for velocities v larger than the average front speed . The burst size distribution is also a power law, P(S) alpha S-gamma with gamma=1.7+/-0.1. Above a characteristic length scale of disorder Ld approximately 15 microm, the avalanche clusters become anisotropic providing an estimate of the roughness exponent of the crack front line, H=0.66.     

Phase coexistence induced by a defensive reaction in a cellular automaton traffic flow model

Traffic flow modeling is an elusive example for the emergence of complexity in dynamical systems of interacting objects. In this work, we introduce an extension of the Nagel-Schreckenberg (NaSch) model of vehicle traffic flow that takes into account a defensive driver’s reaction. Such a mechanism acts as an additional nearest-neighbor coupling. The defensive reaction dynamical rule consists in reducing the driver’s velocity in response to deceleration of the vehicle immediately in front of it whenever the distance is smaller than a security minimum. This new mechanism, when associated with the random deceleration rule due to fluctuations, considerably reduces the mean velocity by adjusting the distance between the vehicles. It also produces the emergence of bottlenecks along the road on which the velocity is much lower than the road mean velocity. Besides the two standard phases of the NaSch model corresponding to the free flow and jammed flow, the present model also exhibits an intermediate phase on which these two flow regimes coexist, as it indeed occurs in real traffics. These findings are consistent with empirical results as well as with the general three-phase traffic theory.     

耦合振子系统的多稳态同步分析

本文讨论了一维闭合环上Kuramoto相振子在非对称耦合作用下同步区域出现的多定态现象. 研究发现在振子数N≤3情形下系统不会出现多态现象, 而N≥4多振子系统则呈现规律的多同步定态. 我们进一步对耦合振子系统中出现的多定态规律及定态稳定性进行了理论分析, 得到了定态渐近稳定解. 数值模拟多体系统发现同步区特征和理论描述相一致. 研究结果显示在绝热条件下随着耦合强度的减小, 系统从不同分支的同步态出发最终会回到同一非同步态. 这说明, 耦合振子系统在非同步区由于运动的遍历性而只具有单一的非同步态, 在发生同步时由于遍历性破缺会产生多个同步定态的共存现象.     

Structure and dynamics of liquid MgO under high pressure

Microstructure, dynamics, and diffusion mechanism in liquid MgO have been studied by molecular dynamics simulation. Models consisting of 2000 atoms were constructed under a wide range of pressure and at a temperature of 3800 K. The local structure is analyzed through the coordination number distribution and topology statistics of coordination units (basic structural units) MgO _x (x=2, 3, 4, 5, 6, 7). As regards the structural dynamics, the nearest-neighbor atomic exchange among coordination units, spatially heterogeneous dynamics, clustering, and structural stability (lifetime of basic structural units) are investigated in detail. Investigation of structural dynamics allows us to gain insight into various important atomic (molecular) properties and to clarify the diffusion mechanism in liquid MgO under high pressure.     

交变磁场下海森堡链中首尾粒子的纠缠动力学

本文研究了各向异性自旋12海森堡链中首尾粒子的纠缠动力学,其中外磁场和最近邻耦合是周期性调制的。在特定的外磁场调制频率和外磁场振幅下,将会出现纠缠共振。在某些特定频率下,最大纠缠可以在相当大的振幅范围内保持最大值。因此,可以通过外界磁场来调控纠缠。     

Synchronizability of chaotic logistic maps in delayed complex networks

We study a network of coupled logistic maps whose interactions occur with a certain distribution of delay times. The local dynamics is chaotic in the absence of coupling and thus the network is a paradigm of a complex system. There are two regimes of synchronization, depending on the distribution of delays: when the delays are sufficiently heterogeneous the network synchronizes on a steady-state (that is unstable for the uncoupled maps); when the delays are homogeneous, it synchronizes in a time-dependent state (that is either periodic or chaotic). Using two global indicators we quantify the synchronizability on the two regimes, focusing on the roles of the network connectivity and the topology. The connectivity is measured in terms of the average number of links per node, and we consider various topologies (scale-free, small-world, star, and nearest-neighbor with and without a central hub). With weak connectivity and weak coupling strength, the network displays an irregular oscillatory dynamics that is largely independent of the topology and of the delay distribution. With heterogeneous delays, we find a threshold connectivity level below which the network does not synchronize, regardless of the network size. This minimum average number of neighbors seems to be independent of the delay distribution. We also analyze the effect of self-feedback loops and find that they have an impact on the synchronizability of small networks with large coupling strengths. The influence of feedback, enhancing or degrading synchronization, depends on the topology and on the distribution of delays.     

Tailoring steep density profile with unstable points

The mesoscopic properties of a plasma in a cylindrical magnetic field are investigated from the view point of test-particle dynamics. When the system has enough time and spatial symmetries, a Hamiltonian of a test particle is completely integrable and can be reduced to a single degree of freedom Hamiltonian for each initial state. The reduced Hamiltonian sometimes has unstable fixed points (saddle points) and associated separatrices. To choose among available dynamically compatible equilibrium states of the one particle density function of these systems we use a maximum entropy principle and discuss how the unstable fixed points affect the density profile or a local pressure gradient, and are able to create a steep profile that improves plasma confinement.     

Synchronization,stickiness effects and intermittent oscillations in coupled nonlinear stochastic networks

Long distance reactive and diffusive coupling is introduced in a spatially extended nonlinear stochastic network of interacting particles. The network serves as a substrate for Lotka-Volterra dynamics with 3rd order nonlinearities. If the network includes only local nearest neighbour interactions, the system organizes into a number of local asynchronous oscillators. It is shown that (a) Introduction of all-to-all coupling in the network leads the system into global, center-type, conservative oscillations as dictated by the mean-field dynamics. (b) Introduction of reactive coupling to the network leads the system to intermittent oscillations where the trajectories stick for short times in bounded regions of space, with subsequent jumps between different bounded regions. (c) Introduction of diffusive coupling to the system does not alter the dynamics for small values of the diffusive coupling p_diff, while after a critical value p_diff ^c the system synchronizes into a limit cycle with specific frequency, deviating non-trivially from the mean-field center-type behaviour. The frequency of the limit cycle oscillations depends on the reaction rates and on the diffusion coupling. The amplitude σ of the limit cycle depends on the control parameter p_diff.     

Front Propagation Dynamics with Exponentially-Distributed Hopping

We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as typified by the A+B → 2A reaction. We find that the effect of fluctuations is especially pronounced at small hopping rates. Fluctuations are treated heuristically via a density cutoff in the reaction rate. We then consider the case of propagating up a reaction rate gradient. The effect of fluctuations here is pronounced, with the front velocity increasing without limit with increasing bulk particle density. The rate of increase is faster than in the case of a reaction-gradient with nearest-neighbor hopping. We derive analytic expressions for the front velocity dependence on bulk particle density. Computer simulations are performed to confirm the analytical results.     

Characteristics of in-out intermittency in delay-coupled FitzHugh–Nagumo oscillators

We analyze a pair of delay-coupled FitzHugh–Nagumo oscillators exhibiting in-out intermittency as a part of the generating mechanism of extreme events. We study in detail the characteristics of in-out intermittency and identify the invariant subsets involved – a saddle fixed point and a saddle periodic orbit – neither of which are chaotic as in the previously reported cases of in-out intermittency. Based on the analysis of a periodic attractor possessing in-out dynamics, we can characterize the approach to the invariant synchronization manifold and the spiralling out to the saddle periodic orbit with subsequent ejection from the manifold. Due to the striking similarities, this analysis of in-out dynamics also explains in-out intermittency     

Transitions to Long-Resident States in Coupled Chaotic Oscillators

The behaviour of coupled chaotic oscillators before complete synchronization is investigated. Long-time residence of trajectories appears besides one of the saddle foci. The tendency that orbits of the two oscillators get closer becomes faster with the increasing coupling strength. The diffusion of phase difference between the two oscillators is first enhanced and then suppressed. There are exact correspondences among these phenomena. The mechanism of these correspondences is explored. These phenomena uncover the route to synchronization of coupled chaotic oscillators.     

On propagation failure in one- and two-dimensional excitable media

We present a nonperturbative technique to study pulse dynamics in excitable media. The method is used to study propagation failure in one-dimensional and two-dimensional excitable media. In one-dimensional media we describe the behavior of pulses and wave trains near the saddle node bifurcation, where propagation fails. The generalization of our method to two dimensions captures the point where a broken front (or finger) starts to retract. We obtain approximate expressions for the pulse shape, pulse velocity, and scaling behavior. The results are compared with numerical simulations and show good agreement.