Nonchaotic random behaviour in the second order autonomous system

Evidence is presented for the nonchaotic random behaviour in a second-order autonomous deterministic system. This behaviour is different from chaos and strange nonchaotic attractor. The nonchaotic random behaviour is very sensitive to the initial conditions. Slight difference of the initial conditions will generate wholly different phase trajectories. This random behaviour has a transient random nature and is very similar to the coin-throwing case in the classical theory of probability. The existence of the nonchaotic random behaviour not only can be derived from the theoretical analysis, but also is proved by the results of the simulated experiments in this paper.     

Stochastic period-doubling bifurcation in biharmonic driven Dulling system with random parameter

Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally, numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations.     

The non-stationary freefield response for a moving load with a random amplitude

This paper presents a stochastic solution procedure for the calculation of the non-stationary freefield response due to a moving load with a random amplitude. In this case, a non-stationary autocorrelation function and a time-dependent spectral density are required to characterize the response at a fixed point in the freefield. The non-stationary solution is derived from the solution in the case of a moving load with a deterministic amplitude. It is shown how the deterministic solution can be calculated in an efficient way by means of integral transformation methods if the problem geometry exhibits a translational invariance in the direction of the moving load. A key ingredient is the transfer function between the source and the receiver that represents the fundamental response in the freefield due to an impulse load at a fixed location. The solution in the case of a moving load with a random amplitude is formulated in terms of the double forward Fourier transform of the non-stationary autocorrelation function. The solution procedure is illustrated with an example where the non-stationary autocorrelation function and the time-dependent standard deviation of the freefield response are computed for a moving harmonic load with a random phase shift. The results are compared with the response in the deterministic case.     

调Q激光光折变自适应光外差探测技术研究

基于光折变晶体中自泵浦与互泵浦相位共轭共存效应,利用新型光折变自适应光外差探测系统进行了调Q脉冲激光的光折变自适应光外差探测技术研究.结果表明,该系统可以用来实现单纵模调Q脉冲激光的自适应光外差探测,并可以通过提高本振光强度有效地提高外差探测灵敏度.进一步的实验和理论分析表明,对于一般的调Q脉冲激光,由于其各个纵模频谱分量之间不相关,难于实现光外差探测.     

晶体几何结构及入射角度对自抽运相位共轭特性影响的研究

基于两块不同尺寸的Cu∶KNSBN晶体自抽运相位共轭实验,研究了光折变晶体的几何结构及入射角度对自抽运相位共轭特性的影响,得到在入射位置不变化的情况下,随着入射角度的变化相位共轭光输出有最大值,几何结构不同对应的最大值不同。并从理论上分析了晶体结构及入射角度在双作用区自抽运相位共轭机理中的作用,指出几何结构、入射角度与自抽运光通道、耦合系数的关系,及在自抽运相位共轭效应中存在一个最佳入射角度,这时相位共轭光输出最大。最后,对理论上的相位共轭反射率公式进行了修正。对自抽运相位共轭实际应用中,选择最佳入射角度提供了理论和实验依据。     

Multiplexing encryption technique by combining random amplitude and phase masks

We propose and demonstrate an encryption-selectable undercover multiplexing. We encrypt and multiplex images for storage by means of a random phase mask common to every image, covered with random amplitude masks different for each image. In order to get a correct decryption of the encoded information, we have to use the appropriate random amplitude mask; otherwise fake information is recovered. We employ a phase conjugation scheme to generate the recovering wavefronts. We analyze and compare the different alternatives and degrees of complexity this combination of masks brings to enhance the security of optical encrypting techniques. We also include an analysis on the advantages and disadvantages this undercover multiplexing protocol offers. We present digital simulations to demonstrate the soundness of the proposal.     

Observation of phase conjugation of light arising from enhanced backscattering in a random medium

We measure the fundamental phase conjugation of a light field arising from enhanced backscattering in a multiple scattering medium. The measurements employ a two-window, time-resolved heterodyne method to suppress specularly reflected light and to determine the transverse Wigner function of the field, yielding joint amplitude and phase information. Using this method, a light field backscattered from an aqueous suspension of polystyrene spheres is found to reverse curvature relative to that of the incident field.     

The Discrete Evolution Model of Bak and Sneppen is Conjugate to the Classical Contact Process

Two fundamental models of critical phenomena are connected. We show that the discrete Bak–Sneppen evolution model is conjugate to the classical contact process. This holds in discrete and continuous time, on all graphs and for random as well as for deterministic choice of neighbors. Thus the extensive theory for the contact process applies to the discrete Bak–Sneppen model, too.     

Synchronization of Kuramoto oscillators in random complex networks

We study the synchronization of coupled phase oscillators in random complex networks. The topology of the networks is assumed to be vary over time. Here we mainly study the onset of global phase synchronization when the topology switches rapidly over time. We find that the results are, to some extent, different from those in deterministic situations. In particular, the synchronizability of coupled oscillators can be enhanced in ER networks and scale-free networks under fast switching, while in stochastic small-world networks such enhancement is not significant.     

含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔

讨论简谐激励作用下含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔现象.首先用Chebyshev 多项式逼近法将随机Duffing-van der Pol系统化成与其等价的确定性系统，然后通过等价确定性系统来探索该系统的倍周期分岔现象.数值模拟显示随机Duffing-van der Pol 系统与均值参数系统有着类似的倍周期分岔行为，同时指出，随机参数系统的倍周期分岔有其自身独有的特点.文中的主要数值结果表明Chebyshev 多项式逼近法是研究非线性随机参数系统动力学问题的一种有效方法. 关键词： Chebyshev多项式 随机Duffing-van der Pol系统 倍周期分岔     

大尺度光学列阵的成像特性

本文由光线光学理论出发,分析了无单元像差的光学元件大尺度列阵的成像特性,得到了较傍轴近似更普适的成像特性变换矩阵,其结果包含了列阵的傍轴近似成像理论.并进一步证明了大尺度平面列阵的成像特性只具有近似的准相位共轭特性,且只有在傍轴近似下才是较完善的准相位共轭成像.该结论与以往理论相比更接近实际,且能更好地解释迄今为止所观察到的实验结果及本文的实验结果.     

An efficient method of distinguishing chaos from noise

It is an important problem in chaos theory whether an observed irregular signal is deterministic chaotic or stochastic. We propose an efficient method for distinguishing deterministic chaotic from stochastic time series for short scalar time series. We first investigate, with the increase of the embedding dimension, the changing trend of the distance between two points which stay close in phase space. And then, we obtain the differences between Gaussian white noise and deterministic chaotic time series underlying this method. Finally, numerical experiments are presented to testify the validity and robustness of the method. Simulation results indicate that our method can distinguish deterministic chaotic from stochastic time series effectively even when the data are short and contaminated.     

Long time tails in stationary random media II: Applications

In a previous paper we developed a mode-coupling theory to describe the long time properties of diffusion in stationary, statistically homogeneous, random media. Here the general theory is applied to deterministic and stochastic Lorentz models and several hopping models. The mode-coupling theory predicts that the amplitudes of the long time tails for these systems are determined by spatial fluctuations in a coarse-grained diffusion coefficient and a coarse-grained free volume. For one-dimensional models these amplitudes can be evaluated, and the mode-coupling theory is shown to agree with exact solutions obtained for these models. For higher-dimensional Lorentz models the formal theory yields expressions which are difficult to evaluate. For these models we develop an approximation scheme based upon projecting fluctuations in the diffusion coefficient and free volume onto fluctuations in the density of scatterers.Work supported by grant No. CHE 77-16308 from the National Science Foundation and by a Nato Travel Grant.     

The Status of Determinism in Proofs of the Impossibility of a Noncontextual Model of Quantum Theory

In order to claim that one has experimentally tested whether a noncontextual ontological model could underlie certain measurement statistics in quantum theory, it is necessary to have a notion of noncontextuality that applies to unsharp measurements, i.e., those that can only be represented by positive operator-valued measures rather than projection-valued measures. This is because any realistic measurement necessarily has some nonvanishing amount of noise and therefore never achieves the ideal of sharpness. Assuming a generalized notion of noncontextuality that applies to arbitrary experimental procedures, it is shown that the outcome of a measurement depends deterministically on the ontic state of the system being measured if and only if the measurement is sharp. Hence for every unsharp measurement, its outcome necessarily has an indeterministic dependence on the ontic state. We defend this proposal against alternatives. In particular, we demonstrate why considerations parallel to Fine’s theorem do not challenge this conclusion.     

Continuous-time random walks with reset events

In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant drift: the process moves in a fixed direction between the reset events, either by the effect of the random jumps, or by the action of a deterministic bias. However, the orientation of its motion is randomly determined after each restart. As a result of these alternating dynamics, interesting properties do emerge. General formulas for the propagator as well as for two extreme statistics, the survival probability and the mean first-passage time, are also derived. The rigor of these analytical results is verified by numerical estimations, for particular but illuminating examples.     

利用谱共轭技术补偿光纤传输信号的失真

分析了谱共轭技术用于补偿光纤色散和非线性的基本原理。通过对超高斯脉冲的数值计算表明，谱共轭技术（SPC）较时域相位共轭技术（TPC）能更好地恢复波形失真。为了弥补SPC不能补偿脉冲内拉曼散射的缺点，提出将SPC和TPC结合使用的方法。将其作用于光孤子串脉冲，不仅进一步优化了整形效果，而且还能有效抑制孤子自频移。     

Deterministic walks in random environments

Deterministic walks in random environments (DWRE) occupy an intermediate position between purely random (generated by random trials) and purely deterministic (generated by deterministic dynamical systems, e.g., by maps) models of diffusion. These models combine deterministic and probabilistic features. We review general properties of DWRE and demonstrate that, to a large extent, their dynamics and their statistics can be analyzed consecutively and separately. We also show that orbits of one-dimensional walks in rigid environments with non-constant rigidity almost surely visit each site infinitely many times.     

基于随机场照射的最优微波成像

近年来,电磁计算成像的理论和技术得到了广泛的研究和发展,其中基于随机场照射的微波成像引起了诸多关注.与传统成像方法的连续波照射不同,基于随机场照射的成像方法以随机照射的方式获取多组非相关的目标散射测量值,经过反演计算就能提取散射目标体的轮廓和形状等信息.基于阵列天线理论,本文理论分析并实验验证了一种最优的二维微波成像系统,能够使用最少的天线单元实现随机照射,通过最少的测量次数完成矩阵求逆并得到重建图像.该系统主要有以下两个创新点:完全随机照射的获取和成像系统最优参数的选取.与基于超材料的成像系统相比,本文通过对1 bit相位调制器随机相位调制的方式获取随机场照射,使得每个天线单元都处于工作状态,因此整个系统的能量效率更高.此外,所述单频成像系统还具有频谱效率高、结构简单、成本低等优点,在安检、室内定位等不同场景中具有潜在的应用价值.     

Chaotic jets with multifractal space-time random walk

The problem of normal and anomalous diffusion is examined for the four-dimensional (4-D) map that arises from the problem of particle motion in a constant magnetic field and electrostatic wave packet. This 4-D map consists of two coupled 2-D maps: a standard map and a web map. The case of a weak chaos is considered. It is shown that due to the finite observation time, the particle diffusion possesses strong nonhomogeneous properties. Existence of long-living bundles of orbits with coherent propagation property is checked. These bundles are named "chaotic jets." The same name is used for a part of the trajectory if this part corresponds to long-living trapping or flight. The existence of chaotic jets depends on the topological properties of the phase space and influences the asymptotic law of transport. The particle transport can be considered as a random walk in the multifractal space-time that is produced by flights and trappings of a test particle in some area of its phase space. Levy random walk theory and its generalization for the multifractal space-time situation is considered and asymptotic laws for displacements are derived. Different intermediate asymptotics are discussed.     

Freezing of random RNA

We study secondary structures of random RNA molecules by means of a renormalized field theory based on an expansion in the sequence disorder. We show that there is a continuous phase transition from a molten phase at higher temperatures to a low-temperature glass phase. The primary freezing occurs above the critical temperature, with local islands of stable folds forming within the molten phase. The size of these islands defines the correlation length of the transition. Our results include critical exponents at the transition and in the glass phase.