Multi-scale continuum mechanics: from global bifurcations to noise induced high-dimensional chaos

Many mechanical systems consist of continuum mechanical structures, having either linear or nonlinear elasticity or geometry, coupled to nonlinear oscillators. In this paper, we consider the class of linear continua coupled to mechanical pendula. In such mechanical systems, there often exist several natural time scales determined by the physics of the problem. Using a time scale splitting, we analyze a prototypical structural-mechanical system consisting of a planar nonlinear pendulum coupled to a flexible rod made of linear viscoelastic material. In this system both low-dimensional and high-dimensional chaos is observed. The low-dimensional chaos appears in the limit of small coupling between the continua and oscillator, where the natural frequency of the primary mode of the rod is much greater than the natural frequency of the pendulum. In this case, the motion resides on a slow manifold. As the coupling is increased, global motion moves off of the slow manifold and high-dimensional chaos is observed. We present a numerical bifurcation analysis of the resulting system illustrating the mechanism for the onset of high-dimensional chaos. Constrained invariant sets are computed to reveal a process from low-dimensional to high-dimensional transitions. Applications will be to both deterministic and stochastic bifurcations. Practical implications of the bifurcation from low-dimensional to high-dimensional chaos for detection of damage as well as global effects of noise will also be discussed.     

From local to global spatiotemporal chaos in a cardiac tissue model

Two kinds of chaos can occur in cardiac tissue, chaotic meander of a single intact spiral wave and chaotic spiral wave breakup. We studied these behaviors in a model of two-dimensional cardiac tissue based on the Luo-Rudy I action potential model. In the chaotic meander regime, chaos is spatially localized to the core of the spiral wave. When persistent spiral wave breakup occurs, there is a transition from local to global spatiotemporal chaos.     

Predicting missing links via local information

Missing link prediction in networks is of both theoretical interest and practical significance in modern science. In this paper, we empirically investigate a simple framework of link prediction on the basis of node similarity. We compare nine well-known local similarity measures on six real networks. The results indicate that the simplest measure, namely Common Neighbours, has the best overall performance, and the Adamic-Adar index performs second best. A new similarity measure, motivated by the resource allocation process taking place on networks, is proposed and shown to have higher prediction accuracy than common neighbours. It is found that many links are assigned the same scores if only the information of the nearest neighbours is used. We therefore design another new measure exploiting information on the next nearest neighbours, which can remarkably enhance the prediction accuracy.     

Community detection using global and local structural information

Community detection is of considerable importance for understanding both the structure and function of complex networks. In this paper, we introduced the general procedure of the community detection algorithms using global and local structural information, where the edge betweenness and the local similarity measures respectively based on local random walk dynamics and local cyclic structures were used. The algorithms were tested on artificial and real-world networks. The results clearly show that all the algorithms have excellent performance in the tests and the local similarity measure based on local random walk dynamics is superior to that based on local cyclic structures.     

Transfer information remotely via noise entangled coherent channels

A simple scheme of quantum teleportation is introduced to investigate the possibility of remotely transfer unknown tripartite state by using a multipartite entangled coherent state. A theoretical technique is introduced to generate maximum entangled coherent states and a generalized teleportation protocol is introduced. The fidelity of the teleported state increases significantly when increasing the number of modes in the case of large noise, whereas it shows the opposite behavior in the case of small noise.     

Localization estimation and global vs. local information measures

The maximum entropy principle is one of the great ideas of the last 50 years, with a multitude of applications in many areas of science. Its main ingredient is an information measure. We show that global and local information measures provide different types of physical information, which requires handling them with some care. The concomitant differences are illustrated with reference to the problem of localization in phase space, placing emphasis on some details of the smoothing of Wigner functions, as described in [G. Manfredi, M.R. Feix, Phys. Rev. E 62 (2000) 4665]. Our discussion is made in terms of a special version of Fisher's information measure, called the shift-invariant one.     

Communication with chemical chaos in the presence of noise

We use control of chaos to encode information into the oscillations of the Belousov-Zhabotinsky reaction. An arbitrary binary message is encoded by forcing the chaotic oscillations to follow a specified trajectory. The information manipulating control requires only small perturbations to vary the binary message. In this paper we extend our recent theoretical work [Bollt and Dolnik, Phys. Rev. E 64, 1196 (1990)] by introducing a new and simplified encoding technique which can be utilized in the presence of experimental noise. We numerically and theoretically study several practical aspects of controlling symbol dynamics including: modeling noisy time-series, learning underlying symbol dynamics, and evaluation of derivatives for control by observing system responses to an intelligent and deliberate sequence of input parameter variations. All of the modeling techniques incorporated here are ultimately designed to learn and control symbol dynamics of experimental data known only as an observed time-series; the simulation assumes no global model. We find that noise affects reliability of encoding information and may cause coding errors. But, if the level of noise is confined to relatively small values, which are achievable in experiments, the control mechanism is robust to the noise. Thus we can still produce a desired symbolic code. However, scarce errors in encoding may occur due to rare but large fluctuations. These errors may be corrected during the decoding process by a variation of the filtering technique suggested by Rosa et al. [Phys. Rev. Lett. 78, 1247 (1997)]. (c) 1998 American Institute of Physics.     

Defect-mediated turbulence in systems with local deterministic chaos

Defect-mediated turbulence is shown to exist in media where the underlying local dynamics is deterministically chaotic. While many of the characteristics of defect-mediated turbulence, such as the exponential decay of correlations and a squared Poissonian distribution for the number of defects, are identical to those seen in oscillatory media, the fluctuations in the number of defects differ significantly. The power spectra suggest the existence of underlying correlations that lead to a different and nonuniversal scaling structure in chaotic media.     

Communicating with noise: How chaos and noise combine to generate secure encryption keys

An approach for the secure transmission of encrypted messages using chaos and noise is presented in this paper. The method is based on the synchronization of certain types of chaotic oscillators in response to a common noise input. This allows two distant oscillators to generate identical output which can be used as a key for encryption and decryption of a message signal. The noiselike synchronizing input-which contains no message information-is communicated to identical oscillators in the transmitter and the receiver over a public channel. The encrypted message is also sent over a public channel, while the key is never transmitted at all. The chaotic nature of the oscillators which generate the key and the randomness of the signal driving the process combine to make the recovery of the key by an eavesdropper extremely difficult. We evaluate system performance with respect to security and robustness and show that a robust and secure system can be obtained. (c) 1998 American Institute of Physics.     

Universal local versus unified global scaling laws in the statistics of seismicity

The unified scaling law for earthquakes, proposed by Bak, Christensen, Danon and Scanlon, is shown to hold worldwide, as well as for areas as diverse as Japan, New Zealand, Spain or New Madrid. The scaling functions that account for the rescaled recurrence-time probability densities show a power-law behavior for long times, with a universal exponent about (minus) 2.2. Another decreasing power law governs short times, but with an exponent that may change from one area to another. This is in contrast with a local, time-homogenized version of Bak et al.'s procedure, which seems to present a universal scaling behavior.     

Coupled maps with local and global interactions

A coupled map lattice model with both local and global couplings is studied as a simple example of hierarchical pattern dynamics with different length scales of interactions. Several phases are classified according to domain structures, degree of chaotic dynamics, distribution function, and power spectra. In particular, a cascade process of formation and collapse of bubbles is found in some parameter regime. The state is characterized by spatiotemporal power-law correlation and few positive Lyapunov exponents. In a two-dimensional case, the state leads to a characteristic spatiotemporal pattern that may be regarded as a dynamic extension of a Turing pattern. The possible relevance to natural patterns is also discussed. (c) 2000 American Institute of Physics.     

Adaptive active contours based on local and global intensity information for image segmentation

This paper proposes a new formulation of active contours in the partial differential equation (PDE) framework. The evolution equation consists of two terms: a force term and a regularization term that smoothes the level set function. The proposed model can handle intensity inhomogeneity by integrating the local and global intensity information into the force term. Moreover, the level set function can be initialized to any bounded function (e.g., a constant function), thus completely eliminating the need of initial contours. Experimental results show that the proposed model can effectively and quickly segment many synthesized and real images, especially for images with intensity inhomogeneity.     

Type-I intermittency with noise versus eyelet intermittency

In this Letter we compare the characteristics of two types of the intermittent behavior (type-I intermittency in the presence of noise and eyelet intermittency taking place in the vicinity of the chaotic phase synchronization boundary) supposed hitherto to be different phenomena. We show that these effects are the same type of dynamics observed under different conditions. The correctness of our conclusion is confirmed by the consideration of different sample systems, such as quadratic map, Van der Pol oscillator and Rössler system. Consideration of the problem concerning the upper boundary of the intermittent behavior also confirms the validity of the statement on the equivalence of type-I intermittency in the presence of noise and eyelet intermittency observed in the onset of phase synchronization.     

Compensating the noise of a communication channel via asymmetric encoding of quantum information

An asymmetric preparation of the quantum states sent through a noisy channel can enable a new way to monitor and actively compensate the channel noise. The paradigm of such an asymmetric treatment of quantum information is the Bennett 1992 protocol, in which the counts in the two separate bases are in direct connection with the channel noise. Using this protocol as a guiding example, we show how to correct the phase drift of a communication channel without using reference pulses, interruptions of the quantum transmission, or public data exchanges.     

Symbolic synchronization and the detection of global properties of coupled dynamics from local information

We study coupled dynamics on networks using symbolic dynamics. The symbolic dynamics is defined by dividing the state space into a small number of regions (typically 2), and considering the relative frequencies of the transitions between those regions. It turns out that the global qualitative properties of the coupled dynamics can be classified into three different phases based on the synchronization of the variables and the homogeneity of the symbolic dynamics. Of particular interest is the homogeneous unsynchronized phase, where the coupled dynamics is in a chaotic unsynchronized state, but exhibits qualitative similar symbolic dynamics at all the nodes in the network. We refer to this dynamical behavior as symbolic synchronization. In this phase, the local symbolic dynamics of any arbitrarily selected node reflects global properties of the coupled dynamics, such as qualitative behavior of the largest Lyapunov exponent and phase synchronization. This phase depends mainly on the network architecture, and only to a smaller extent on the local chaotic dynamical function. We present results for two model dynamics, iterations of the one-dimensional logistic map and the two-dimensional Henon map, as local dynamical function.     

基于局部和全局信息的自适应水平集图像分割

针对仅采用局部或全局信息无法快速准确分割灰度不均匀图像的问题,提出了一种基于局部和全局信息的自适应水平集图像分割模型。首先,利用图像局部信息和全局信息建立局部能量项和全局能量项,并且利用演化曲线轮廓内外小邻域的灰度均值差作为自变量,建立了权重函数模型,实现了局部能量项和全局能量项之间权重的自适应调整,提高了模型分割灰度不均匀图像的效率和准确性。其次,提出了一种新的能量惩罚项,避免了水平集函数的重新初始化,增强了数值计算的稳定性。最后,为验证模型的优越性,将模型与CV模型、LBF模型和LGIF模型进行了对比,并通过分割时间、迭代次数以及相似度等指标对分割结果进行了客观、定量分析。最终结果表明:该模型不但对初始轮廓具有较高鲁棒性,而且对灰度不均匀图像具有较高的分割准确性与分割效率。     

基于局部和全局信息的自适应水平集图像分割

针对仅采用局部或全局信息无法快速准确分割灰度不均匀图像的问题,提出了一种基于局部和全局信息的自适应水平集图像分割模型。首先,利用图像局部信息和全局信息建立局部能量项和全局能量项,并且利用演化曲线轮廓内外小邻域的灰度均值差作为自变量,建立了权重函数模型,实现了局部能量项和全局能量项之间权重的自适应调整,提高了模型分割灰度不均匀图像的效率和准确性。其次,提出了一种新的能量惩罚项,避免了水平集函数的重新初始化,增强了数值计算的稳定性。最后,为验证模型的优越性,将模型与CV模型、LBF模型和LGIF模型进行了对比,并通过分割时间、迭代次数以及相似度等指标对分割结果进行了客观、定量分析。最终结果表明:该模型不但对初始轮廓具有较高鲁棒性,而且对灰度不均匀图像具有较高的分割准确性与分割效率。     

Annoyance with aircraft noise in local recreational areas and the recreationists' noise situation at home

Few socioacoustic studies have examined the effect of noise on outdoor recreationists. Most studies concentrate on one setting of the everyday life of a noise-exposed population, which mainly has been the residential setting. This article relates annoyance with aircraft noise in outdoor recreational areas to the recreationists' noise situation at home. In conjunction with the relocation of the main airport of Norway in 1998, field studies were conducted before and after the change in one area near the old airport (1930 survey respondents), and one area near the new airport (1001 survey respondents). Multivariate linear regression analyses of the relationship between annoyance and aircraft noise exposure (LAeq for the aircraft events) in the recreational areas were conducted, controlled for noise annoyance at home, or aircraft noise exposure at home, the situation (before/ after the change), context- and demographic variables. People more highly annoyed at home tended to be more annoyed than others while in the recreational areas. A significant effect of aircraft noise exposure at home on annoyance in the recreational setting was not found. More research is warranted regarding the relationship between noise exposure at home and outdoor recreational demands.     

Dynamic systems with chaos as a medium for information storage and processing

The possibility of using nonlinear systems with complex dynamics for information processing is demonstrated. The principles of information storage and retrieval using stable cycles of one-dimensional maps are described. The possibility of realization by neural networks and applications to text processing are discussed.Institute of Radio-Electronics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 8, pp. 1003–1019, August, 1994.     

From unweighted to weighted networks with local information

In this paper, we analyze an evolving model with local information which can generate a class of networks by choosing different values of the parameter p. The model introduced exhibits the transition from unweighted networks to weighted networks because the distribution of the edge weight can be widely tuned. With the increase in the local information, the degree correlation of the network transforms from assortative to disassortative. We also study the distribution of the degree, strength and edge weight, which all show crossover between exponential and scale-free. Finally, an application of the proposed model to the study of the synchronization is considered. It is concluded that the synchronizability is enhanced when the heterogeneity of the edge weight is reduced.