Wiener Index, Diameter, and Stretch Factor of a Weighted Planar Graph in Subquadratic Time
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
We solve three open problems: the existence of subquadratic time algorithms for computing the Wiener index (sum of APSP distances) and the diameter (maximum distance between any vertex pair) of a planar graph with non-negative edge weights and the stretch factor of a plane geometric graph (maximum...... over all pairs of distinct vertices of the ratio between the graph distance and the Euclidean distance between the two vertices). More specifically, we show that the Wiener index and diameter can be found in O(n^2*(log log n)^4/log n) worst-case time and that the stretch factor can be found in O(n^2...
Computataion of conditional wiener integrals by the composite approximation formulae with weight
Energy Technology Data Exchange (ETDEWEB)
Lobanov, Y.Y.; Shakhbagyan, R.R.; Sidorova, O.V.; Zhidkov, E.P.
1988-01-01
New approximation formulae with weight for the functional integrals with conditional Wiener measure are derived. The formulae are exact on a class of polynomial functionals of a given degree. The convergence of approximations to the exact value of integral is proved, the estimate of the remainder is obtained. The results are illustrated with numerical examples. The advantages of the formulae over lattice Monte Carlo method are demonstrated in computation of some quantities in Euclidean quantum mechanics. 16 refs., 4 figs., 3 tabs.
Reduced Wiener Chaos representation of random fields via basis adaptation and projection
Energy Technology Data Exchange (ETDEWEB)
Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu [Department of Mathematics, University of Southern California, Los Angeles, CA 90089 (United States); Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089 (United States); Ghanem, Roger G., E-mail: ghanem@usc.edu [Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089 (United States)
2017-07-15
A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.
2012-01-01
In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler et al., "Topological chaos and periodic braiding of almost-cyclic sets," Phys. Rev. Lett. 106, 114101 (2011)]. In this co...
New distributions over Wiener and Euclidean spaces
Institute of Scientific and Technical Information of China (English)
P. Imkeller; 严加安
1996-01-01
Let (H, B, u) be an abstract Wiener space. New spaces of test functionals and distributions having kernels of the chaos decomposition in (Hn,n>0) are constructed. Their counterparts over Rm are completely characterized in terms of the H-transform.
Path and semimartingale properties of chaos processes
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas; Graversen, Svend-Erik
2010-01-01
The present paper characterizes various properties of chaos processes which in particular include processes where all time variables admit a Wiener chaos expansion of a fixed finite order. The main focus is on the semimartingale property, p-variation and continuity. The general results obtained a...
Generalizations of Wiener polarity index and terminal Wiener index
Ilic, Aleksandar
2011-01-01
In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. We introduce a generalized Wiener polarity index $W_k (G)$ as the number of unordered pairs of vertices $\\{u, v\\}$ of $G$ such that the shortest distance $d (u, v)$ between $u$ and $v$ is $k$. For $k = 3$, we get standard Wiener polarity index. Furthermore, we generalize the terminal Wiener index $TW_k (G)$ as the sum of distances between all pairs of vertices of degree $k$. For $k = 1$, we get standard terminal Wiener index. In this paper we describe a linear time algorithm for computing these indices for trees and partial cubes, and characterize extremal trees maximizing the generalized Wiener polarity index and generalized terminal Wiener index among all trees of given order $n$.
Adaptive wiener image restoration kernel
Yuan, Ding
2007-06-05
A method and device for restoration of electro-optical image data using an adaptive Wiener filter begins with constructing imaging system Optical Transfer Function, and the Fourier Transformations of the noise and the image. A spatial representation of the imaged object is restored by spatial convolution of the image using a Wiener restoration kernel.
Hideaki Yanagisawa
2014-01-01
The SEIQoL-DW (Schedule for the Evaluation of Individual Quality of Life-Direct Weighting) method may be misused because of lack of confirmation by scientific theory. It is compared with the representative chaos equation. Y (n + 1) = p [1 – Y (n)] Y (n) The Z (m) axis is perpendicular to the "p" and Y (n) axes. Z (m + 1) = p [1 – Z (m)] Z (m) From both equations, a three dimensional logistic map is imagined. [Y (n + 1) / Z (m + 1)] = [1 – Y (n)] Y (n) / [1 – Z (m)] Z (m) Acc...
PC analysis of stochastic differential equations driven by Wiener noise
Le Maitre, Olivier
2015-03-01
A polynomial chaos (PC) analysis with stochastic expansion coefficients is proposed for stochastic differential equations driven by additive or multiplicative Wiener noise. It is shown that for this setting, a Galerkin formalism naturally leads to the definition of a hierarchy of stochastic differential equations governing the evolution of the PC modes. Under the mild assumption that the Wiener and uncertain parameters can be treated as independent random variables, it is also shown that the Galerkin formalism naturally separates parametric uncertainty and stochastic forcing dependences. This enables us to perform an orthogonal decomposition of the process variance, and consequently identify contributions arising from the uncertainty in parameters, the stochastic forcing, and a coupled term. Insight gained from this decomposition is illustrated in light of implementation to simplified linear and non-linear problems; the case of a stochastic bifurcation is also considered.
Energy Technology Data Exchange (ETDEWEB)
Luo, Shaohua [School of Automation, Chongqing University, Chongqing 400044 (China); Department of Mechanical Engineering, Chongqing Aerospace Polytechnic, Chongqing, 400021 (China); Wu, Songli [Department of Mechanical Engineering, Chongqing Aerospace Polytechnic, Chongqing, 400021 (China); Gao, Ruizhen [School of Automation, Chongqing University, Chongqing 400044 (China)
2015-07-15
This paper investigates chaos control for the brushless DC motor (BLDCM) system by adaptive dynamic surface approach based on neural network with the minimum weights. The BLDCM system contains parameter perturbation, chaotic behavior, and uncertainty. With the help of radial basis function (RBF) neural network to approximate the unknown nonlinear functions, the adaptive law is established to overcome uncertainty of the control gain. By introducing the RBF neural network and adaptive technology into the dynamic surface control design, a robust chaos control scheme is developed. It is proved that the proposed control approach can guarantee that all signals in the closed-loop system are globally uniformly bounded, and the tracking error converges to a small neighborhood of the origin. Simulation results are provided to show that the proposed approach works well in suppressing chaos and parameter perturbation.
Luo, Shaohua; Wu, Songli; Gao, Ruizhen
2015-07-01
This paper investigates chaos control for the brushless DC motor (BLDCM) system by adaptive dynamic surface approach based on neural network with the minimum weights. The BLDCM system contains parameter perturbation, chaotic behavior, and uncertainty. With the help of radial basis function (RBF) neural network to approximate the unknown nonlinear functions, the adaptive law is established to overcome uncertainty of the control gain. By introducing the RBF neural network and adaptive technology into the dynamic surface control design, a robust chaos control scheme is developed. It is proved that the proposed control approach can guarantee that all signals in the closed-loop system are globally uniformly bounded, and the tracking error converges to a small neighborhood of the origin. Simulation results are provided to show that the proposed approach works well in suppressing chaos and parameter perturbation.
Trace Operators on Wiener Amalgam Spaces
Jayson Cunanan; Yohei Tsutsui
2016-01-01
The paper deals with trace operators of Wiener amalgam spaces using frequency-uniform decomposition operators and maximal inequalities, obtaining sharp results. Additionally, we provide the embeddings between standard and anisotropic Wiener amalgam spaces.
Condensed Extended Hyper-Wiener Index
Institute of Scientific and Technical Information of China (English)
LI Xin-Hua; Abraham F. Jalbout; JI Zhi
2008-01-01
According to the definitions of molecular connectivity and hyper-Wiener index, a novel set of hyper-Wiener indexes (Dn, mDn) were defined and named as condensed extended hyper-Wiener index, the potential usefulness of which in QSAR/QSPR is evaluated by its correlation with a number of C3-C8 alkanes as well as by a favorable comparison with models based on molecular connectivity index and overall Wiener index.
Equiseparability on Terminal Wiener Index
DEFF Research Database (Denmark)
Deng, Xiaotie; Zhang, Jie
2012-01-01
The aim of this work is to explore the properties of the terminal Wiener index, which was recently proposed by Gutman et al. (2004) [3], and to show the fact that there exist pairs of trees and chemical trees which cannot be distinguished by using it. We give some general methods for constructing...
A change of scale formula for Wiener integrals on abstract Wiener spaces
Directory of Open Access Journals (Sweden)
Il Yoo
1994-01-01
Full Text Available In this paper we obtain a change of scale formula for Wiener integrals on abstract Wiener spaces. This formula is shown to hold for many classes of functions of interest in Feynman integration theory and quantum mechanics.
On Wiener polarity index of bicyclic networks
Ma, Jing; Shi, Yongtang; Wang, Zhen; Yue, Jun
2016-01-01
Complex networks are ubiquitous in biological, physical and social sciences. Network robustness research aims at finding a measure to quantify network robustness. A number of Wiener type indices have recently been incorporated as distance-based descriptors of complex networks. Wiener type indices are known to depend both on the network’s number of nodes and topology. The Wiener polarity index is also related to the cluster coefficient of networks. In this paper, based on some graph transformations, we determine the sharp upper bound of the Wiener polarity index among all bicyclic networks. These bounds help to understand the underlying quantitative graph measures in depth.
Zhang, Yanjun; Zhao, Yu; Fu, Xinghu; Xu, Jinrui
2016-10-01
A novel particle swarm optimization algorithm based on adaptive inertia weight and chaos optimization is proposed for extracting the features of Brillouin scattering spectra. Firstly, the adaptive inertia weight parameter of the velocity is introduced to the basic particle swarm algorithm. Based on the current iteration number of particles and the adaptation value, the algorithm can change the weight coefficient and adjust the iteration speed of searching space for particles, so the local optimization ability can be enhanced. Secondly, the logical self-mapping chaotic search is carried out by using the chaos optimization in particle swarm optimization algorithm, which makes the particle swarm optimization algorithm jump out of local optimum. The novel algorithm is compared with finite element analysis-Levenberg Marquardt algorithm, particle swarm optimization-Levenberg Marquardt algorithm and particle swarm optimization algorithm by changing the linewidth, the signal-to-noise ratio and the linear weight ratio of Brillouin scattering spectra. Then the algorithm is applied to the feature extraction of Brillouin scattering spectra in different temperatures. The simulation analysis and experimental results show that this algorithm has a high fitting degree and small Brillouin frequency shift error for different linewidth, SNR and linear weight ratio. Therefore, this algorithm can be applied to the distributed optical fiber sensing system based on Brillouin optical time domain reflection, which can effectively improve the accuracy of Brillouin frequency shift extraction.
Wiener Filter Estimation of Transfer Functions
Kessel, Robert
2004-01-01
The use of a Wiener filter estimate for the linear transfer function can significantly improve the description of behavioral dynamics. This report presents a two-pass, Monte-Carlo-based algorithm that is well suited to repeated-trials local average measurements. The Wiener filter transfer functions strongly suppress noise artifacts as well as…
Adaptive control of Hammerstein-Wiener nonlinear systems
Zhang, Bi; Hong, Hyokchan; Mao, Zhizhong
2016-07-01
The Hammerstein-Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein-Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.
Energy Technology Data Exchange (ETDEWEB)
Mueller, B.
1997-09-22
The report contains viewgraphs on the following: ergodicity and chaos; Hamiltonian dynamics; metric properties; Lyapunov exponents; KS entropy; dynamical realization; lattice formulation; and numerical results.
Institute of Scientific and Technical Information of China (English)
龙敏; 谭丽
2011-01-01
Using chaos-based weight variation of Huffman tree,an image/video encryption algorithm is proposed in this paper. In the process of the entropy coding,DC coefficients are encrypted by the weight variation of Huffman tree with the double Logistic chaos and AC coefficients are encrypted by the indexes of codeword. The security,complexity and compression ration of the algorithm are analyzed. Simulation results show that this algorithm has no impact on the compression efficiency and has low complexity,high security and good real-time property. Therefore,it is suitable for real-time image on the network.%提出一种采用混沌权值变异的Huff man树的图像加密算法.此算法在熵编码过程中,以基本的Huffman树为标准,利用双耦合混沌序列1对DC系数进行树的结构未变异、路径值变异的加密；再利用双耦合混沌序列2对AC系数进行码字序号的加密.论文对算法进行了仿真,并对安全性、计算复杂度、压缩比性能进行了分析.实验结果表明,该算法基本上不影响压缩效率,且计算复杂度低、安全性高和实时性好,可用于网络上的图像服务.
Zhang, Rui; Cavalcante, Hugo L. D. de S.; Gao, Zheng; Gauthier, Daniel J.; Socolar, Joshua E. S.; Adams, Matthew M.; Lathrop, Daniel P.
2009-01-01
We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultra-wide-band, extending from dc to beyond 2 GHz. The observed behavior is reproduced qualitatively using an autonomously updating Boolean model with signal propagation times that depend on the recent history of the gates and filtering of pulses of short duration, whose presence is confirmed experimentally. Electronic Boolean chaos may fin...
The Wiener maximum quadratic assignment problem
Cela, Eranda; Woeginger, Gerhard J
2011-01-01
We investigate a special case of the maximum quadratic assignment problem where one matrix is a product matrix and the other matrix is the distance matrix of a one-dimensional point set. We show that this special case, which we call the Wiener maximum quadratic assignment problem, is NP-hard in the ordinary sense and solvable in pseudo-polynomial time. Our approach also yields a polynomial time solution for the following problem from chemical graph theory: Find a tree that maximizes the Wiener index among all trees with a prescribed degree sequence. This settles an open problem from the literature.
On Wiener index of graph complements
Directory of Open Access Journals (Sweden)
Jaisankar Senbagamalar
2014-06-01
Full Text Available Let $G$ be an $(n,m$-graph. We say that $G$ has property $(ast$ if for every pair of its adjacent vertices $x$ and $y$, there exists a vertex $z$, such that $z$ is not adjacent to either $x$ or $y$. If the graph $G$ has property $(ast$, then its complement $overline G$ is connected, has diameter 2, and its Wiener index is equal to $binom{n}{2}+m$, i.e., the Wiener index is insensitive of any other structural details of the graph $G$. We characterize numerous classes of graphs possessing property $(ast$, among which are trees, regular, and unicyclic graphs.
Multicenter Wiener indices and their applications
Directory of Open Access Journals (Sweden)
Gutman Ivan
2015-01-01
Full Text Available The Wiener index W can be viewed as a molecular structure descriptor composed of increments representing interactions between pairs of atoms. A generalization of the W are the Steiner-Wiener indices kW, k=3,4,.... In the quantity Wk, interactions between k-tuples of atoms play role, based on the concept of Steiner distance. It is shown that the term W+λWk provides an approximation for the boiling points of alkanes better than W itself. The best such approximation is obtained for k=7.
BV-capacities on Wiener Spaces and Regularity of the Maximum of the Wiener Process
Trevisan, Dario
2012-01-01
We define a capacity C on abstract Wiener spaces and prove that, for any u with bounded variation, the total variation measure |Du| is absolutely continuous with respect to C: this enables us to extend the usual rules of calculus in many cases dealing with BV functions. As an application, we show that, on the classical Wiener space, the random variable sup_{0\\leqt\\leqT} W_t admits a measure as second derivative, whose total variation measure is singular w.r.t. the Wiener measure.
LINEAR ISOMETRIC NON-ANTICIPATIVE TRANSFORMATIONS OF WIENER PROCESS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The necessary and sufficient conditions are given so that a non-anticipative transformation in Hilbert space is isometric. In terms of second order Wiener process, these conditions assure that a non-anticipative transformation of Wiener process is a Wiener process, too.
Convergence of Symmetric Diffusions on Wiener Spaces
Institute of Scientific and Technical Information of China (English)
A.Posilicano; T.S.Zhang
2004-01-01
In this paper,we study the distorted Ornstein-Uhlenbeck processes associated with given densities on an abstract Wiener space.We prove that the laws of distorted Ornstein-Uhlenbeck processes converge in total variation norm if the densities converge in Sobolev space D 1/2.
Oracle Wiener filtering of a Gaussian signal
Babenko, A.; Belitser, E.N.
2011-01-01
We study the problem of filtering a Gaussian process whose trajectories, in some sense, have an unknown smoothness β0 from the white noise of small intensity . If we knew the parameter β0, we would use the Wiener filter which has the meaning of oracle. Our goal is now to mimic the oracle, i.e., cons
Banerjee, S; Grebogi, C; Banerjee, Soumitro; Yorke, James A.; Grebogi, Celso
1998-01-01
It has been proposed to make practical use of chaos in communication, in enhancing mixing in chemical processes and in spreading the spectrum of switch-mode power suppies to avoid electromagnetic interference. It is however known that for most smooth chaotic systems, there is a dense set of periodic windows for any range of parameter values. Therefore in practical systems working in chaotic mode, slight inadvertent fluctuation of a parameter may take the system out of chaos. We say a chaotic attractor is robust if, for its parameter values there exists a neighborhood in the parameter space with no periodic attractor and the chaotic attractor is unique in that neighborhood. In this paper we show that robust chaos can occur in piecewise smooth systems and obtain the conditions of its occurrence. We illustrate this phenomenon with a practical example from electrical engineering.
Waelbroeck, H
1999-01-01
We propose a theory of deterministic chaos for discrete systems, based on their representations in symbolic history spaces Ømega. These are spaces of semi-infinite sequences, as the one-sided shift spaces, but endowed with a more general topology which we call a semicausal topology. We show that define metrical properties, including the correlation dimension of the attractor. Examples are considered: Asymmetric neural networks and random cellular automata are not chaotic. A neural network model with memory, on the other hand, does appear to be an example of discrete chaos.
Some Remarks on Distributional Chaos for Linear Operators
Institute of Scientific and Technical Information of China (English)
TIAN GENG; Hou BING-ZHE; Ji You-qing
2011-01-01
In this paper,we consider some properties for bounded linear operators concerning distributional chaos.Norm-unimodality of bounded linear operators implies distributional chaos.Some properties such as similarity and spectra description for norm-unimodal operators are considered.The existence of distributional chaos in nest algebra is also proved.In addition,we obtain a sufficient and necessary condition of distributional chaos for a class of operators,which contains unilateral backward weighted shift operators.
IDENTIFICATION FOR WIENER SYSTEMS WITH INTERNAL NOISE
Institute of Scientific and Technical Information of China (English)
Qijiang SONG; Hanfu CHEN
2008-01-01
This paper considers identification of Wiener systems for which the internal variables and output are corrupted by noises. When the internal noise is a sequence of independent and identically distributed (iid) Gaussian random variables, by the Weierstrass transformation (WT) the system under consideration turns to be a Wiener system without internal noise. The nonlinear part of the latter is nothing else than the WT of the nonlinear function of the original system, while the linear subsystem is the same for both systems before and after WT. Under reasonable conditions, the recursive identification algorithms are proposed for the transformed Wiener system, and strong consistency for the estimates is established. By using the inverse WT the nonparametric estimates for the nonlinearity of the original system are derived, and they are strongly consistent if the nonlinearity in the original system is a polynomial. Similar results also hold in the case where the internal noise is non-Gaussian. Simulation results are fully consistent with the theoretical analysis.
The Average Widths of Sobolev-Wiener Classes and Besov-Wiener Classes
Institute of Scientific and Technical Information of China (English)
Gui Qiao XU; Yong Ping LIU
2004-01-01
This paper concerns the problem of average σ-width of Sobolev Wiener classes Wrpq(Rd),Wrpq(M, Rd), and Besov-Wiener classes Srpqθb(Rd), SrpqθB( Rd), Srpqθb(M, Rd), SrpqθB( Rd) in the metric Lq(Rd) for 1 ≤ q ≤ p ≤∞. The weak asymptotic results concerning the average linear widths, the average Bernstein widths and the infinite-dimensional Gel'fand widths are obtained, respectively.
On Modelling of Nonlinear Systems and Phenomena with the Use of Volterra and Wiener Series
Directory of Open Access Journals (Sweden)
Andrzej Borys
2015-03-01
Full Text Available This is a short tutorial on Volterra and Wiener series applications to modelling of nonlinear systems and phenomena, and also a survey of the recent achievements in this area. In particular, we show here how the philosophies standing behind each of the above theories differ from each other. On the other hand, we discuss also mathematical relationships between Volterra and Wiener kernels and operators. Also, the problem of a best approximation of large-scale nonlinear systems using Volterra operators in weighted Fock spaces is described. Examples of applications considered are the following: Volterra series use in description of nonlinear distortions in satellite systems and their equalization or compensation, exploiting Wiener kernels to modelling of biological systems, the use of both Volterra and Wiener theories in description of ocean waves and in magnetic resonance spectroscopy. Moreover, connections between Volterra series and neural network models, and also input-output descriptions of quantum systems by Volterra series are discussed. Finally, we consider application of Volterra series to solving some nonlinear problems occurring in hydrology, navigation, and transportation.
An isoperimetric inequality for the Wiener sausage
Peres, Yuval
2011-01-01
Let $(\\xi(s))_{s\\geq 0}$ be a standard Brownian motion in $d\\geq 1$ dimensions and let $(D_s)_{s \\geq 0}$ be a collection of open sets in $\\R^d$. For each $s$, let $B_s$ be a ball centered at 0 with $\\vol(B_s) = \\vol(D_s)$. We show that $\\E[\\vol(\\cup_{s \\leq t}(\\xi(s) + D_s))] \\geq \\E[\\vol(\\cup_{s \\leq t}(\\xi(s) + B_s))]$, for all $t$. In particular, this implies that the expected volume of the Wiener sausage increases when a drift is added to the Brownian motion.
Wiener-E Index and Wiener-O Index of Extended Two Stars Trees%扩展双星树的 Wiener-E 指标和 Wiener-O 指标
Institute of Scientific and Technical Information of China (English)
赵雯雯; 刘昊; 温芳卿; 景翔宇
2014-01-01
The double star graph T(n)n1 ,n2 is a kind of graphs that includes a path whose length is n-1 and two ports with n1 and n2 pendant edges separately .This paper studys the similar Wiener index of the double star graph based on its structure and gives the computational formula of Wiener‐E index and Wiener‐O index for them .%扩展双星树（T（n）n1，n2）是 n－1长路径的两端点分别联结 n1条悬挂边和 n2条悬挂边所得到的图。论文根据扩展双星树的结构特征，研究了扩展双星树的类Wiener指数，给出了一般计算公式。
Distributed chaos and isotropic turbulence
Bershadskii, A
2015-01-01
Power spectrum of the distributed chaos can be represented by a weighted superposition of the exponential functions which is converged to a stretched exponential $\\exp-(k/k_{\\beta})^{\\beta }$. An asymptotic theory has been developed in order to estimate the value of $\\beta$ for the isotropic turbulence. This value has been found to be $\\beta =3/4$. Excellent agreement has been established between this theory and the data of direct numerical simulations not only for the velocity field but also for the passive scalar and energy dissipation fields. One can conclude that the isotropic turbulence emerges from the distributed chaos.
Controlling chaos with simple limiters
Corron; Pethel; Hopper
2000-04-24
New experimental results demonstrate that chaos control can be accomplished using controllers that are very simple relative to the system being controlled. Chaotic dynamics in a driven pendulum and a double scroll circuit are controlled using an adjustable, passive limiter-a weight for the pendulum and a diode for the circuit. For both experiments, multiple unstable periodic orbits are selectively controlled using minimal perturbations. These physical examples suggest that chaos control can be practically applied to a much wider array of important problems than initially thought possible.
Segal-Bargmann Transform and Paley-Wiener Theorems on $M(2)$
Indian Academy of Sciences (India)
E K Narayanan; Suparna Sen
2010-04-01
We study the Segal–Bargmann transform on $M(2)$. The range of this transform is characterized as a weighted Bergman space. In a similar fashion Poisson integrals are investigated. Using a Gutzmer’s type formula we characterize the range as a class of functions extending holomorphically to an appropriate domain in the complexification of $M(2)$. We also prove a Paley–Wiener theorem for the inverse Fourier transform.
Sharp bounds and normalization of Wiener-type indices.
Directory of Open Access Journals (Sweden)
Dechao Tian
Full Text Available Complex networks abound in physical, biological and social sciences. Quantifying a network's topological structure facilitates network exploration and analysis, and network comparison, clustering and classification. A number of Wiener type indices have recently been incorporated as distance-based descriptors of complex networks, such as the R package QuACN. Wiener type indices are known to depend both on the network's number of nodes and topology. To apply these indices to measure similarity of networks of different numbers of nodes, normalization of these indices is needed to correct the effect of the number of nodes in a network. This paper aims to fill this gap. Moreover, we introduce an f-Wiener index of network G, denoted by Wf(G. This notion generalizes the Wiener index to a very wide class of Wiener type indices including all known Wiener type indices. We identify the maximum and minimum of Wf(G over a set of networks with n nodes. We then introduce our normalized-version of f-Wiener index. The normalized f-Wiener indices were demonstrated, in a number of experiments, to improve significantly the hierarchical clustering over the non-normalized counterparts.
Pradas, Marc; Pumir, Alain; Huber, Greg; Wilkinson, Michael
2017-07-01
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion should be refined. Despite their overall intrinsic instability, trajectories may be very strongly convergent in phase space over extremely long periods, as revealed by our investigation of a simple chaotic system (a realistic model for small bodies in a turbulent flow). We establish that this strong convergence is a multi-facetted phenomenon, in which the clustering is intense, widespread and balanced by lacunarity of other regions. Power laws, indicative of scale-free features, characterize the distribution of particles in the system. We use large-deviation and extreme-value statistics to explain the effect. Our results show that the interpretation of the ‘butterfly effect’ needs to be carefully qualified. We argue that the combination of mixing and clustering processes makes our specific model relevant to understanding the evolution of simple organisms. Lastly, this notion of convergent chaos, which implies the existence of conditions for which uncertainties are unexpectedly small, may also be relevant to the valuation of insurance and futures contracts.
interaction randomly perturbed by wiener processes
Directory of Open Access Journals (Sweden)
Anatoli V. Skorokhod
2003-01-01
Full Text Available Infinite systems of stochastic differential equations for randomly perturbed particle systems in Rd with pairwise interacting are considered. For gradient systems these equations are of the form dxk(t=Fk(ttd+σdwk(t and for Hamiltonian systems these equations are of the form dx˙k(t=Fk(ttd+σdwk(t. Here xk(t is the position of the kth particle, x˙k(t is its velocity, Fk=−∑j≠kUx(xk(t−xj(t, where the function U:Rd→R is the potential of the system, σ>0 is a constant, {wk(t,k=1,2,…} is a sequence of independent standard Wiener processes.
Markov chain approach to identifying Wiener systems
Institute of Scientific and Technical Information of China (English)
ZHAO WenXiao; CHEN HanFu
2012-01-01
Identification of the Wiener system composed of an infinite impulse response (IIR) linear subsystem followed by a static nonlinearity is considered.The recursive estimates for unknown coefficients of the linear subsystem and for the values of the nonlinear function at any fixed points are given by the stochastic approximation algorithms with expanding truncations (SAAWET).With the help of properties of the Markov chain connected with the linear subsystem,all estimates derived in the paper are proved to be strongly consistent.In comparison with the existing results on the topic,the method presented in the paper simplifies the convergence analysis and requires weaker conditions.A numerical example is given,and the simulation results are consistent with the theoretical analysis.
Indian Academy of Sciences (India)
S J Bhatt; H V Dedania
2003-05-01
Let be a continuous function on the unit circle , whose Fourier series is -absolutely convergent for some weight on the set of integers $\\mathcal{Z}$. If is nowhere vanishing on , then there exists a weight on $\\mathcal{Z}$ such that 1/ had -absolutely convergent Fourier series. This includes Wiener's classical theorem. As a corollary, it follows that if is holomorphic on a neighbourhood of the range of , then there exists a weight on $\\mathcal{Z}$ such that $\\varphi\\circ f$ has -absolutely convergent Fourier series. This is a weighted analogue of Lévy's generalization of Wiener's theorem. In the theorems, and are non-constant if and only if is non-constant. In general, the results fail if or is required to be the same weight .
Quantum signatures of chaos or quantum chaos?
Energy Technology Data Exchange (ETDEWEB)
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu [St. Petersburg State University (Russian Federation)
2016-11-15
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.
Discrete nature of multivariate Paley-Wiener space
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Eoff proves that the univariate Paley-Wiener space Bπ,p(R) is isomorphic to the discrete Hardy space Hp(R), 0
Wiener space Bπ,p(Rn), if p=1. In this paper, we continue our research and prove that the multivariate Paley-Wiener space Bπ,p(Rn) is isomorphic to the discrete Hardy space Hp(Rn), 0
An Algorithm for Optimally Fitting a Wiener Model
Directory of Open Access Journals (Sweden)
Lucas P. Beverlin
2011-01-01
Full Text Available The purpose of this work is to present a new methodology for fitting Wiener networks to datasets with a large number of variables. Wiener networks have the ability to model a wide range of data types, and their structures can yield parameters with phenomenological meaning. There are several challenges to fitting such a model: model stiffness, the nonlinear nature of a Wiener network, possible overfitting, and the large number of parameters inherent with large input sets. This work describes a methodology to overcome these challenges by using several iterative algorithms under supervised learning and fitting subsets of the parameters at a time. This methodology is applied to Wiener networks that are used to predict blood glucose concentrations. The predictions of validation sets from models fit to four subjects using this methodology yielded a higher correlation between observed and predicted observations than other algorithms, including the Gauss-Newton and Levenberg-Marquardt algorithms.
Variational Splines and Paley--Wiener Spaces on Combinatorial Graphs
Pesenson, Isaac
2011-01-01
Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator onG. The existence and uniqueness of interpolating variational splines on a graph is shown. As an application of variational splines, the paper presents a reconstruction algorithm of Paley-Wiener functions on graphs from their uniqueness sets.
Variational Splines and Paley--Wiener Spaces on Combinatorial Graphs
Pesenson, Isaac
2011-01-01
Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator onG. The existence and uniqueness of interpolating variational splines on a graph is shown. As an application of variational splines, the paper presents a reconstruction algorithm of Paley-Wiener functions on graphs from their uniqueness sets.
WIENER INDEX AND HOSOYA POLYNOMIAL OF FIBONACCI AND LUCAS CUBES
Klavzar, Sandi; Mollard, Michel
2011-01-01
In the language of mathematical chemistry, Fibonacci cubes can be defined as the resonance graphs of fibonacenes. Lucas cubes form a symmetrization of Fibonacci cubes and appear as resonance graphs of cyclic polyphenantrenes. In this paper it is proved that the Wiener index of Fibonacci cubes can be written as the sum of products of four Fibonacci numbers which in turn yields a closed formula for the Wiener index of Fibonacci cubes. Asymptotic behavior of the average distance of Fibonacci cub...
Approximations of the Wiener sausage and its curvature measures
Rataj, Jan; Meschenmoser, Daniel; 10.1214/09-AAP596
2009-01-01
A parallel neighborhood of a path of a Brownian motion is sometimes called the Wiener sausage. We consider almost sure approximations of this random set by a sequence of random polyconvex sets and show that the convergence of the corresponding mean curvature measures holds under certain conditions in two and three dimensions. Based on these convergence results, the mean curvature measures of the Wiener sausage are calculated numerically by Monte Carlo simulations in two dimensions. The corresponding approximation formulae are given.
Poisson process Fock space representation, chaos expansion and covariance inequalities
Last, Guenter
2009-01-01
We consider a Poisson process $\\eta$ on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of $\\eta$. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener-Ito chaos expansion. We apply these results to extend well-known variance inequalities for homogeneous Poisson processes on the line to the general Poisson case. The Poincare inequality is a special case. Further applications are covariance identities for Poisson processes on (strictly) ordered spaces and Harris-FKG-inequalities for monotone functions of $\\eta$.
Mammograms restoration by using Wiener filter
Energy Technology Data Exchange (ETDEWEB)
Dakovic, M., E-mail: mdakovic@gmail.com; Mijovic, S. [University of Montenegro, Faculty of Natural Sciences and Mathematics, Dž. Vašingtona bb, 20000 Podgorica (Montenegro); Ivanović, S. [Clinical Center of Montenegro, 20000 Podgorica (Montenegro)
2016-03-25
Restoration of digital mammograms, as a pre-processing tool, using deconvolution procedures, is analysed. It implies, knowing Modulation Transfer Function (MTF) of the mammography device and the estimation of the mammogram’s noise. Wiener filter is used, as the most objective in mammograms restoration by deconvolution. Using MATLAB program the deconvolution procedures are conducted in two ways with different level of approximation. The first method approximates the noise/signal power ratio by a constant and the second method uses autocorrelation functions of the noise and signals. Abilities and limitations of the methods are analysed and checked by using the raw images of the bar-pattern due to better visualisation of the obtained results. The raw images are obtained at a Computed Radiography (CR) mammography device in Clinical Centre in Podgorica. It is found that quality of the restored image highly depends of knowledge of type and magnitude of noise. In the both methods spatial resolution of the restored images are improved, but much better in a case where autocorrelation functions of the noise and signal are used. This procedure is proposed as an objective pre-processing tool to put back imperfectness of mammography devices.
The Average Errors for Hermite Interpolation on the 1-Fold Integrated Wiener Space
Institute of Scientific and Technical Information of China (English)
Guiqiao XU; Jingrui NING
2012-01-01
For the weighted approximation in Lp-norm,the authors determine the weakly asymptotic order for the p-average errors of the sequence of Hermite interpolation based on the Chebyshev nodes on the 1-fold integrated Wiener space.By this result,it is known that in the sense of information-based complexity,if permissible information functionals are Hermite data,then the p-average errors of this sequence are weakly equivalent to those of the corresponding sequence of the minimal p-average radius of nonadaptive information.
Erçetin, Şefika; Tekin, Ali
2014-01-01
The present work investigates global politics and political implications of social science and management with the aid of the latest complexity and chaos theories. Until now, deterministic chaos and nonlinear analysis have not been a focal point in this area of research. This book remedies this deficiency by utilizing these methods in the analysis of the subject matter. The authors provide the reader a detailed analysis on politics and its associated applications with the help of chaos theory, in a single edited volume.
Quantum Chaos and Statistical Mechanics
Srednicki, Mark
1994-01-01
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
Physical white chaos generation
Wang, Anbang; Wang, Bingjie; Li, Lei; Zhang, Mingjiang; Zhang, Wendong
2014-01-01
Physical chaos is a fascinating prospect for high-speed data security by serving as a masking carrier or a key source, but suffers from a colored spectrum that divulges system's intrinsic oscillations and degrades randomness. Here, we demonstrate that physical chaos with a white spectrum can be achieved by the optical heterodyning of two delayed-feedback lasers. A white chaotic spectrum with 1-dB fluctuation in a band of 11 GHz is experimentally obtained. The white chaos also has a perfect delta-like autocorrelation function and a high dimensionality of greater than 10, which makes chaos reconstruction extremely difficult and thus improves security.
Spano, Mark
1997-04-01
The publication by Ott, Grebogi and Yorke(E. Ott, C. Grebogi and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).) of their theory of chaos control in 1990 led to an explosion of experimental work applying their theory to mechanical systems and electronic circuits, lasers and chemical reactors, and heart and brain tissue, to name only a few. In this talk the basics of chaos control as implemented in a simple mechanical system will be described, as well as extensions of the method to biological applications. Finally, current advances in the field, including the maintenance of chaos and the control of high dimensional chaos, will be discussed.
Cosmology, Epistemology and Chaos
Unno, Wasaburo
1992-03-01
We may consider the following three fundamental epistemological questions concerning cosmology. Can cosmology at last understand the origin of the universe? Can computers at last create? Can life be formed at last synthetically? These questions are in some sense related to the liar paradox containing the self-reference and, therefore, may not be answered by recursive processes in finite time. There are, however, various implications such that the chaos may break the trap of the self- reference paradox. In other words, Goedel's incompleteness theorem would not apply to chaos, even if the chaos can be generated by recursive processes. Internal relations among cosmology, epistemology and chaos must be investigated in greater detail
Identification of Stochastic Wiener Systems using Indirect Inference
2015-01-01
We study identification of stochastic Wiener dynamic systems using so-called indirect inference. The main idea is to first fit an auxiliary model to the observed data and then in a second step, often by simulation, fit a more structured model to the estimated auxiliary model. This two-step procedure can be used when the direct maximum-likelihood estimate is difficult or intractable to compute. One such example is the identification of stochastic Wiener systems, i.e.,~linear dynamic systems wi...
高维Wiener sausage 的强逼近%Strong approximation of high dimensional Wiener sausage
Institute of Scientific and Technical Information of China (English)
王艳清
2011-01-01
本文研究了四维及四维以上的Wiener sausage的体积,得到它们可以由一维Brown运动强逼近.作为应用,推出了弱收敛和重对数率.%In this paper, we study the volume of Wiener sausage in Rd ford ≥ 4. We obtain that it can be strongly approximated by a one-dimensional standard Brownian motion. As an application, we give the weak convergence and laws of the iterated logarithm.
The Wiener-Khinchin theorem and recurrence quantification
Energy Technology Data Exchange (ETDEWEB)
Zbilut, Joseph P. [Department of Molecular Biophysics and Physiology, Rush University Medical Center, 1653 W. Congress, Chicago, IL 60612 (United States)], E-mail: jzbilut@rush.edu; Marwan, Norbert [Potsdam Institute for Climate Impact Research (PIK), 14412 Potsdam (Germany)
2008-10-27
The Wiener-Khinchin theorem states that the power spectrum is the Fourier transform of the autocovariance function. One form of the autocovariance function can be obtained through recurrence quantification. We show that the advantage of defining the autocorrelation function with recurrences can demonstrate higher dimensional dynamics.
Scientific Works by Wiener and Lévy After Brown
Hida, Takeyuki
2008-07-01
Brownian motion was recognized as a scientific research object by R. Brown in 1827, and then many scientists studied the motion within science. Two famous mathematicians, N. Wiener and P. Lévy, studied Browniam motion mainly in mathematics. We appreciate their works and would like to note that their results play very important role in the study of biological phenomena.
Average widths of anisotropic Besov-Wiener classes
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper concerns the problem of average σ-K width and average σ-L width of some anisotropic Besov-Wiener classes Srp q θb(Rd) and Srp q θB(Rd) in Lq(Rd) (1≤q≤p＜∞). The weak asymptotic behavior is established for the corresponding quantities.
Average widths of anisotropic Besov-Wiener classes
Institute of Scientific and Technical Information of China (English)
蒋艳杰
2000-01-01
This paper concems the problem of average σ-K width and average σ-L width of some anisotropic Besov-wiener classes Spqθr(Rd) and Spqθr(Rd) in Lq(Rd) (1≤≤q≤p<∞). The weak asymptotic behavior is established for the corresponding quantities.
Change of Scale Formulas for Wiener Integrals Related to Fourier-Feynman Transform and Convolution
Directory of Open Access Journals (Sweden)
Bong Jin Kim
2014-01-01
Full Text Available Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in Banach algebra S on classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel class F(B and in a generalized Fresnel class FA1,A2 on abstract Wiener space. We express Fourier-Feynman transform and convolution product of functionals in S as limits of Wiener integrals. Moreover we obtain change of scale formulas for Wiener integrals related to Fourier-Feynman transform and convolution product of these functionals.
Energy Technology Data Exchange (ETDEWEB)
Maldacena, Juan [School of Natural Sciences, Institute for Advanced Study,1 Einstein Drive, Princeton, NJ (United States); Shenker, Stephen H. [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University,382 Via Pueblo Mall, Stanford, CA (United States); Stanford, Douglas [School of Natural Sciences, Institute for Advanced Study,1 Einstein Drive, Princeton, NJ (United States)
2016-08-17
We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ{sub L}≤2πk{sub B}T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.
Uncertainty Relation for Chaos
Yahalom, A; Levitan, J; Elgressy, G; Horwitz, L P; Ben-Zion, Y
2011-01-01
A necessary condition for the emergence of chaos is given. It is well known that the emergence of chaos requires a positive exponent which entails diverging trajectories. Here we show that this is not enough. An additional necessary condition for the emergence of chaos in the region where the trajectory of the system goes through, is that the product of the maximal positive exponent times the duration in which the system configuration point stays in the unstable region should exceed unity. We give a theoretical analysis justifying this result and a few examples.
Chaos applications in telecommunications
Stavroulakis, Peter
2005-01-01
IntroductionPeter StavroulakisChaotic Signal Generation and Transmission Antonio Cândido Faleiros,Waldecir João Perrella,TâniaNunes Rabello,Adalberto Sampaio Santos, andNeiYoshihiro SomaChaotic Transceiver Design Arthur Fleming-DahlChaos-Based Modulation and DemodulationTechniques Francis C.M. Lau and Chi K. TseA Chaos Approach to Asynchronous DS-CDMASystems S. Callegari, G. Mazzini, R. Rovatti, and G. SettiChannel Equalization in Chaotic CommunicationSystems Mahmut CiftciOptical Communications using ChaoticTechniques Gregory D. VanWiggerenAPPENDIX AFundamental Concepts of the Theory ofChaos a
Maldacena, Juan; Stanford, Douglas
2015-01-01
We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent $\\lambda_L \\le 2 \\pi k_B T/\\hbar$. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.
Directory of Open Access Journals (Sweden)
David Murphy
2011-11-01
Full Text Available About 20 years ago, while lost in the midst of my PhD research, I mused over proposed titles for my thesis. I was pretty pleased with myself when I came up with Chaos Rules (the implied double meaning was deliberate, or more completely, Chaos Rules: An Exploration of the Work of Instructional Designers in Distance Education. I used the then-emerging theories of chaos and complexity to underpin my analysis. So it was with more than a little excitement that I read the call for contributions to this special issue of IRRODL. What follows is a walk-through of my thesis with an emphasis on the contribution of chaos and complexity theory.
Exploiting chaos for applications
Energy Technology Data Exchange (ETDEWEB)
Ditto, William L., E-mail: wditto@hawaii.edu [Department of Physics and Astronomy, University of Hawaii at Mānoa, Honolulu, Hawaii 96822 (United States); Sinha, Sudeshna, E-mail: sudeshna@iisermohali.ac.in [Indian Institute of Science Education and Research (IISER), Mohali, Knowledge City, Sector 81, SAS Nagar, PO Manauli 140306, Punjab (India)
2015-09-15
We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.
Description of Wiener bounds of multicomponent composites by barycentric coordinates
Peiponen, Kai-Erik; Gornov, Evgeny
2006-07-01
Wiener bounds for effective complex permittivity of multicomponent composites are treated by use of barycentric coordinates, a convex hull, and conformal mapping in a complex plane. Depending on the complexity of the multiphase system, the bounds provide singly or multiply connected regions that can be used in estimating the limits of the effective permittivity of the composite. The present modeling is important, e.g., in estimating spectral properties of nanocomposites in engineering and nanomedicine and in terahertz-based security imaging.
Towards a theory of BV functions in abstract Wiener spaces
Ambrosio, Luigi; Miranda, Michele; Maniglia, Stefania; Pallara, Diego
2010-08-01
Functions of bounded variation in an abstract Wiener space, i.e., an infinite dimensional Banach space endowed with a Gaussian measure and a related differentiable structure, have been introduced by M. Fukushima and M. Hino using Dirichlet forms, and their properties have been studied with tools from stochastics. In this paper we reformulate, with purely analytical tools, the definition and the main properties of BV functions, and start investigating further properties.
On the error estimate for cubature on Wiener space
Cass, Thomas
2011-01-01
It was pointed out in Crisan, Ghazali [2] that the error estimate for the cubature on Wiener space algorithm developed in Lyons, Victoir [11] requires an additional assumption on the drift. In this note we demonstrate that it is straightforward to adopt the analysis of Kusuoka [7] to obtain a general estimate without an additional assumptions on the drift. In the process we slightly sharpen the bounds derived in [7].
A Field-Theoretic Approach to the Wiener Sausage
Nekovar, S.; Pruessner, G.
2016-05-01
The Wiener Sausage, the volume traced out by a sphere attached to a Brownian particle, is a classical problem in statistics and mathematical physics. Initially motivated by a range of field-theoretic, technical questions, we present a single loop renormalised perturbation theory of a stochastic process closely related to the Wiener Sausage, which, however, proves to be exact for the exponents and some amplitudes. The field-theoretic approach is particularly elegant and very enjoyable to see at work on such a classic problem. While we recover a number of known, classical results, the field-theoretic techniques deployed provide a particularly versatile framework, which allows easy calculation with different boundary conditions even of higher momenta and more complicated correlation functions. At the same time, we provide a highly instructive, non-trivial example for some of the technical particularities of the field-theoretic description of stochastic processes, such as excluded volume, lack of translational invariance and immobile particles. The aim of the present work is not to improve upon the well-established results for the Wiener Sausage, but to provide a field-theoretic approach to it, in order to gain a better understanding of the field-theoretic obstacles to overcome.
Fractal Patterns and Chaos Games
Devaney, Robert L.
2004-01-01
Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.
Enlightenment philosophers’ ideas about chaos
Directory of Open Access Journals (Sweden)
A. V. Kulik
2014-07-01
It is grounded that the philosopher and enlightener Johann Gottfried von Herder advanced an idea of objectivity of process of transformation chaos into order. It is shown that idea of «The law of nature» existing as for ordering chaos opened farreaching prospects for researches of interaction with chaos.
Introducing chaos a graphic guide
Sardar, Ziauddin; Abrams, Iwona
2014-01-01
Explains how chaos makes its presence felt in many varieties of event, from the fluctuation of animal populations to the ups and downs of the stock market. This book also examines the roots of chaos in modern mathematics and physics, and explores the relationship between chaos and complexity.
A Rotation of Admixable Operators on Abstract Wiener Space with Applications
Directory of Open Access Journals (Sweden)
Jae Gil Choi
2013-01-01
Full Text Available We investigate certain rotation properties of the abstract Wiener measure. To determine our rotation property for the Wiener measure, we introduce the concept of an admixable operator via an algebraic structure on abstract Wiener space. As for applications, we define the analytic Fourier-Feynman transform and the convolution product associated with the admixable operators and proceed to establish the relationships between this transform and the corresponding convolution product.
The hyper edge-Wiener index of corona product of graphs
Directory of Open Access Journals (Sweden)
Abolghasem Soltani
2015-09-01
Full Text Available Let G be a simple connected graph. The edge-Wiener index W e (G is the sum of all distances between edges in G , whereas the hyper edge-Wiener index WW e (G is defined as {\\footnotesize WW e (G=12 W e (G+12 W 2 e (G }, where {footnotesize W 2 e (G=sumlimits leftf,grightsubseteqE(G d 2 e (f,g }. In this paper, we present explicit formula for the hyper edge-Wiener index of corona product of two graphs. Also, we use it to determine the hyper edge-Wiener index of some chemical graphs.
Shigehara, T; Mishima, T; Cheon, T; Shigehara, Takaomi; Mizoguchi, Hiroshi; Mishima, Taketoshi; Cheon, Taksu
1998-01-01
In this paper, we show that two-dimensional billiards with point interactions inside exhibit a chaotic nature in the microscopic world, although their classical counterpart is non-chaotic. After deriving the transition matrix of the system by using the self-adjoint extension theory of functional analysis, we deduce the general condition for the appearance of chaos. The prediction is confirmed by numerically examining the statistical properties of energy spectrum of rectangular billiards with multiple point interactions inside. The dependence of the level statistics on the strength as well as the number of the scatterers is displayed. KEYWORDS: wave chaos, quantum mechanics, pseudointegrable billiard, point interaction, functional analysis
Dissipative structures and chaos
Mori, Hazime
1998-01-01
This monograph consists of two parts and gives an approach to the physics of open nonequilibrium systems. Part I derives the phenomena of dissipative structures on the basis of reduced evolution equations and includes Bénard convection and Belousov-Zhabotinskii chemical reactions. Part II discusses the physics and structures of chaos. While presenting a construction of the statistical physics of chaos, the authors unify the geometrical and statistical descriptions of dynamical systems. The shape of chaotic attractors is characterized, as are the mixing and diffusion of chaotic orbits and the fluctuation of energy dissipation exhibited by chaotic systems.
On the relation between Zenkevich and Wiener indices of alkanes
Directory of Open Access Journals (Sweden)
ZARKO BOSKOVIC
2004-04-01
Full Text Available A relatively complicated relation was found to exist between the quantity U, recently introduced by Zenkevich (providing a measure of internal molecular energy, and the Wiener index W (measuring molecular surface area and intermolecular forces. We now report a detailed analysis of this relation and show that, in the case of alkanes, its main features are reproduced by the formula U = aW + b + gn1; where n1 is the number of methyl groups, and a, b and g are constants, depending only on the number of carbon atoms. Thus, for isomeric alkanes with the same number of methyl groups, U and W are linearly correlated.
Improved Multistage Wiener Filters in Nonhomogeneous Clutter Environments
Institute of Scientific and Technical Information of China (English)
Bin Tang; Xue-Gang Wang; Ke-Song Chen
2008-01-01
A new method combining space-time preprocessing with multistage Wiener filters (STPMWF) is proposed to improve the performance of space-time adaptive processing (STAP) in nonhomogeneous clutter scenario. The new scheme only requires the data from the primary range bin, thus it can suppress discrete interferers efficiently, without calculating the inverse of covariance matrix. Comparing to the original MWF approach, the proposed scheme can be regarded as practical solutions for robust and effective STAP of nonhomogeneous radar data. The theoretical analysis shows that our STPMWF is simple in implementation and fast in convergence. The numeric results by using simulated data exhibit a good agreement with the proposed theory.
A Description of Quantum Chaos
Inoue, K; Ohya, M; Inoue, Kei; Kossakowski, Andrzej; Ohya, Masanori
2004-01-01
A measure describing the chaos of a dynamics was introduced by two complexities in information dynamics, and it is called the chaos degree. In particular, the entropic chaos degree has been used to characterized several dynamical maps such that logistis, Baker's, Tinckerbel's in classical or quantum systems. In this paper, we give a new treatment of quantum chaos by defining the entropic chaos degree for quantum transition dynamics, and we prove that every non-chaotic quantum dynamics, e.g., dissipative dynamics, has zero chaos degree. A quantum spin 1/2 system is studied by our chaos degree, and it is shown that this degree well describes the chaotic behavior of the spin system.
Akhmet, Marat
2012-01-01
Morphogenesis, as it is understood in a wide sense by Ren\\'e Thom, is considered for various types of chaos. That is, those, obtained by period-doubling cascade, Devaney's and Li-Yorke chaos. Moreover, in discussion form we consider inheritance of intermittency, the double-scroll Chua's attractor and quasiperiodical motions as a possible skeleton of a chaotic attractor. To make our introduction of the paper more clear, we have to say that one may consider other various accompanying concepts of chaos such that a structure of the chaotic attractor, its fractal dimension, form of the bifurcation diagram, the spectra of Lyapunov exponents, etc. We make comparison of the main concept of our paper with Turing's morphogenesis and John von Neumann automata, considering that this may be not only formal one, but will give ideas for the chaos development in the morphogenesis of Turing and for self-replicating machines. To provide rigorous study of the subject, we introduce new definitions such as chaotic sets of functio...
Directory of Open Access Journals (Sweden)
Kratochvíl C.
2007-10-01
Full Text Available The purpose of this article is to provide an elementary introduction to the subject of chaos in the electromechanical drive systems. In this article, we explore chaotic solutions of maps and continuous time systems. These solutions are also bounded like equilibrium, periodic and quasiperiodic solutions.
Inverse anticipating chaos synchronization.
Shahverdiev, E M; Sivaprakasam, S; Shore, K A
2002-07-01
We derive conditions for achieving inverse anticipating synchronization where a driven time-delay chaotic system synchronizes to the inverse future state of the driver. The significance of inverse anticipating chaos in delineating synchronization regimes in time-delay systems is elucidated. The concept is extended to cascaded time-delay systems.
DEFF Research Database (Denmark)
Lindberg, Erik
1996-01-01
order limit cycle is found. If the the forward Early voltage parameter is added chaos is observed again. An examination of the eigenvalues of the oscillator with the simple memoryless Ebers-Moll BJT injection model is presented. By adding bulk resistors to the model stable limit cycles of orders 1, 2, 3...
DEFF Research Database (Denmark)
Lindberg, Erik
1996-01-01
Can we believe in the results of our circuit simulators ? Is it possible to distinguish between results due to numerical chaos and resultsdue to the eventual chaotic nature of our modelsof physical systems ?. Three experiments with SPICE are presented: (1) A "stable" active RCcircuit with poles i...
Pure E and B polarization maps via Wiener filtering
Bunn, Emory F
2016-01-01
In order to draw scientific conclusions from observations of cosmic microwave background (CMB) polarization, it is necessary to separate the contributions of the E and B components of the data. For data with incomplete sky coverage, there are ambiguous modes, which can be sourced by either E or B signals. Techniques exist for producing "pure" E and B maps, which are guaranteed to be free of cross-contamination, although the standard method, which involves constructing an eigenbasis, has a high computational cost. We show that such pure maps can be thought of as resulting from the application of a Wiener filter to the data. This perspective leads to far more efficient methods of producing pure maps. Moreover, by expressing the idea of purification in the general framework of Wiener filtering (i.e., maximization of a posterior probability), it leads to a variety of generalizations of the notion of pure E and B maps, e.g., accounting for noise or other contaminants in the data as well as correlations with temper...
Wiener filter reloaded: fast signal reconstruction without preconditioning
Kodi Ramanah, Doogesh; Lavaux, Guilhem; Wandelt, Benjamin D.
2017-06-01
We present a high-performance solution to the Wiener filtering problem via a formulation that is dual to the recently developed messenger technique. This new dual messenger algorithm, like its predecessor, efficiently calculates the Wiener filter solution of large and complex data sets without preconditioning and can account for inhomogeneous noise distributions and arbitrary mask geometries. We demonstrate the capabilities of this scheme in signal reconstruction by applying it on a simulated cosmic microwave background temperature data set. The performance of this new method is compared to that of the standard messenger algorithm and the preconditioned conjugate gradient (PCG) approach, using a series of well-known convergence diagnostics and their processing times, for the particular problem under consideration. This variant of the messenger algorithm matches the performance of the PCG method in terms of the effectiveness of reconstruction of the input angular power spectrum and converges smoothly to the final solution. The dual messenger algorithm outperforms the standard messenger and PCG methods in terms of execution time, as it runs to completion around two and three to four times faster than the respective methods, for the specific problem considered.
Pure E and B polarization maps via Wiener filtering
Bunn, Emory F.; Wandelt, Benjamin
2017-08-01
In order to draw scientific conclusions from observations of cosmic microwave background (CMB) polarization, it is necessary to separate the contributions of the E and B components of the data. For data with incomplete sky coverage, there are ambiguous modes, which can be sourced by either E or B signals. Techniques exist for producing "pure" E and B maps, which are guaranteed to be free of cross-contamination, although the standard method, which involves constructing an eigenbasis, has a high computational cost. We show that such pure maps can be thought of as resulting from the application of a Wiener filter to the data. This perspective leads to far more efficient methods of producing pure maps. Moreover, by expressing the idea of purification in the general framework of Wiener filtering (i.e., maximization of a posterior probability), it leads to a variety of generalizations of the notion of pure E and B maps, e.g., accounting for noise or other contaminants in the data as well as correlations with temperature anisotropy.
Wiener index and Diameter of a Planar Graph in Subquadratic Time
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
2009-01-01
Consider the problem of computing the sum of distances between each pair of vertices of an unweighted graph. This sum is also known as the Wiener index of the graph, a generalization of a definition given by H. Wiener in 1947. A molecular topological index is a value obtained from the graph...
Asymptotic independence of multiple Wiener-It\\^o integrals and the resulting limit laws
Nourdin, Ivan
2011-01-01
We characterize the asymptotic independence of multiple Wiener-It\\^o integrals. As a consequence of this characterization, we derive the celebrated fourth moment theorem of Nualart and Peccati and other related results on the multivariate convergence of multiple Wiener-It\\^o integrals, that involve Gaussian and non Gaussian limits.
BV-regularity for the Malliavin derivative of the maximum of the Wiener process
2013-01-01
We show that, on the classical Wiener space, the random variable $M = \\sup_{0\\le t \\le T} W_t$ admits a measure as second Malliavin derivative, whose total variation measure is finite and singular w.r.t. the Wiener measure.
Converting transient chaos into sustained chaos by feedback control
Lai, Ying-Cheng; Grebogi, Celso
1994-02-01
A boundary crisis is a catastrophic event in which a chaotic attractor is suddenly destroyed, leaving a nonattracting chaotic saddle in its place in the phase space. Based on the controlling-chaos idea [E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990)], we present a method for stabilizing chaotic trajectories on the chaotic saddle by applying only small parameter perturbations. This strategy enables us to convert transient chaos into sustained chaos, thereby restoring attracting chaotic motion.
Chaotic System Identification Based on a Fuzzy Wiener Model with Particle Swarm Optimization
Institute of Scientific and Technical Information of China (English)
LI Yong; TANG Ying-Gan
2010-01-01
@@ A fuzzy Wiener model is proposed to identify chaotic systems.The proposed fuzzy Wiener model consists of two parts,one is a linear dynamic subsystem and the other is a static nonlinear part,which is represented by the Takagi-Sugeno fuzzy model Identification of chaotic systems is converted to find optimal parameters of the fuzzy Wiener model by minimizing the state error between the original chaotic system and the fuzzy Wiener model.Particle swarm optimization algorithm,a global optimizer,is used to search the optimal parameter of the fuzzy Wiener model.The proposed method can identify the parameters of the linear part and nonlinear part simultaneously.Numerical simulations for Henón and Lozi chaotic system identification show the effectiveness of the proposed method.
DWT and DCT embedded watermarking using chaos theory
McLauchlan, Lifford; Mehrübeoglu, Mehrübe
2010-08-01
In this research, a new combination discrete cosine transform (DCT) and discrete wavelet transform (DWT) based watermarking system is studied. The first embedded watermark is encrypted using a chaos function, specifically the Lorenz function, based key to further conceal the data. A chaos based embedded watermark method in the DCT domain with blind watermark identification is developed and tested. Next the system is modified to utilize a second watermark embedding and identification/detection process. The second uses a pseudo random number generated (PRNG) watermark that is developed with a function of a Lorenz attractor data point as the seed state for the PRNG watermark in the detection process in the DWT domain. The efficacy of the DCT based technique, DWT based method as well as the combined DCT and DWT method is then compared to a previous techniques such as a NN based DWT based watermark embedding and identification. The three studied methods are subjected to a subset of the Checkmark attacks. Results for projection, shearing, warping, linear distortions, and Wiener filtering attacks are shown for the DWT embedded case.
Energy Technology Data Exchange (ETDEWEB)
Tél, Tamás [Institute for Theoretical Physics, Eötvös University, and MTA-ELTE Theoretical Physics Research Group, Pázmány P. s. 1/A, Budapest H-1117 (Hungary)
2015-09-15
We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.
Chaos control of cardiac arrhythmias.
Garfinkel, A; Weiss, J N; Ditto, W L; Spano, M L
1995-01-01
Chaos theory has shown that many disordered and erratic phenomena are in fact deterministic, and can be understood causally and controlled. The prospect that cardiac arrhythmias might be instances of deterministic chaos is therefore intriguing. We used a recently developed method of chaos control to stabilize a ouabain-induced arrhythmia in rabbit ventricular tissue in vitro. Extension of these results to clinically significant arrhythmias such as fibrillation will require overcoming the additional obstacles of spatiotemporal complexity.
Chaos detection and predictability
Gottwald, Georg; Laskar, Jacques
2016-01-01
Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data. In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists. The book cover...
Wireless communication with chaos.
Ren, Hai-Peng; Baptista, Murilo S; Grebogi, Celso
2013-05-03
The modern world fully relies on wireless communication. Because of intrinsic physical constraints of the wireless physical media (multipath, damping, and filtering), signals carrying information are strongly modified, preventing information from being transmitted with a high bit rate. We show that, though a chaotic signal is strongly modified by the wireless physical media, its Lyapunov exponents remain unaltered, suggesting that the information transmitted is not modified by the channel. For some particular chaotic signals, we have indeed proved that the dynamic description of both the transmitted and the received signals is identical and shown that the capacity of the chaos-based wireless channel is unaffected by the multipath propagation of the physical media. These physical properties of chaotic signals warrant an effective chaos-based wireless communication system.
Hosur, Pavan; Roberts, Daniel A; Yoshida, Beni
2015-01-01
We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.
Schuster, H G
2008-01-01
This long-awaited revised second edition of the standard reference on the subject has been considerably expanded to include such recent developments as novel control schemes, control of chaotic space-time patterns, control of noisy nonlinear systems, and communication with chaos, as well as promising new directions in research. The contributions from leading international scientists active in the field provide a comprehensive overview of our current level of knowledge on chaos control and its applications in physics, chemistry, biology, medicine, and engineering. In addition, they show the overlap with the traditional field of control theory in the engineering community.An interdisciplinary approach of interest to scientists and engineers working in a number of areas
Marklof, J
2005-01-01
The central objective in the study of quantum chaos is to characterize universal properties of quantum systems that reflect the regular or chaotic features of the underlying classical dynamics. Most developments of the past 25 years have been influenced by the pioneering models on statistical properties of eigenstates (Berry 1977) and energy levels (Berry and Tabor 1977; Bohigas, Giannoni and Schmit 1984). Arithmetic quantum chaos (AQC) refers to the investigation of quantum system with additional arithmetic structures that allow a significantly more extensive analysis than is generally possible. On the other hand, the special number-theoretic features also render these systems non-generic, and thus some of the expected universal phenomena fail to emerge. Important examples of such systems include the modular surface and linear automorphisms of tori (`cat maps') which will be described below.
Energy Technology Data Exchange (ETDEWEB)
Hosur, Pavan; Qi, Xiao-Liang [Department of Physics, Stanford University,476 Lomita Mall, Stanford, California 94305 (United States); Roberts, Daniel A. [Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technology,77 Massachusetts Ave, Cambridge, Massachusetts 02139 (United States); Yoshida, Beni [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Walter Burke Institute for Theoretical Physics, California Institute of Technology,1200 E California Blvd, Pasadena CA 91125 (United States)
2016-02-01
We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.
Energy Technology Data Exchange (ETDEWEB)
Bick, Christian [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Bernstein Center for Computational Neuroscience (BCCN), 37077 Göttingen (Germany); Institute for Mathematics, Georg–August–Universität Göttingen, 37073 Göttingen (Germany); Kolodziejski, Christoph [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); III. Physical Institute—Biophysics, Georg–August–Universität Göttingen, 37077 Göttingen (Germany); Timme, Marc [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Institute for Nonlinear Dynamics, Georg–August–Universität Göttingen, 37077 Göttingen (Germany)
2014-09-01
Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.
Noise tolerant spatiotemporal chaos computing
Energy Technology Data Exchange (ETDEWEB)
Kia, Behnam; Kia, Sarvenaz; Ditto, William L. [Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822 (United States); Lindner, John F. [Physics Department, The College of Wooster, Wooster, Ohio 44691 (United States); Sinha, Sudeshna [Indian Institute of Science Education and Research (IISER), Mohali, Punjab 140306 (India)
2014-12-01
We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.
Noise tolerant spatiotemporal chaos computing.
Kia, Behnam; Kia, Sarvenaz; Lindner, John F; Sinha, Sudeshna; Ditto, William L
2014-12-01
We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.
Tailoring wavelets for chaos control.
Wei, G W; Zhan, Meng; Lai, C-H
2002-12-31
Chaos is a class of ubiquitous phenomena and controlling chaos is of great interest and importance. In this Letter, we introduce wavelet controlled dynamics as a new paradigm of dynamical control. We find that by modifying a tiny fraction of the wavelet subspaces of a coupling matrix, we could dramatically enhance the transverse stability of the synchronous manifold of a chaotic system. Wavelet controlled Hopf bifurcation from chaos is observed. Our approach provides a robust strategy for controlling chaos and other dynamical systems in nature.
Voglis, Nikos
2003-01-01
Galaxies and Chaos examines the application of tools developed for Nonlinear Dynamical Systems to Galactic Dynamics and Galaxy Formation, as well as to related issues in Celestial Mechanics. The contributions collected in this volume have emerged from selected presentations at a workshop on this topic and key chapters have been suitably expanded in order to be accessible to nonspecialist researchers and postgraduate students wishing to enter this exciting field of research.
DEFF Research Database (Denmark)
Lindberg, Erik
1996-01-01
Can we believe in the results of our circuit simulators ? Is it possible to distinguish between results due to numerical chaos and resultsdue to the eventual chaotic nature of our modelsof physical systems ?. Three experiments with SPICE are presented: (1) A "stable" active RCcircuit with poles i...... in the models of the circuits to be analyzed. If trimmed properly SPICE normally gives the correct result....
Earnshow, R; Jones, H
1991-01-01
This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot i...
Ruette, Sylvie
2017-01-01
The aim of this book is to survey the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. The papers on this topic are numerous and widely scattered in the literature; some of them are little known, difficult to find, or originally published in Russian, Ukrainian, or Chinese. Dynamical systems given by the iteration of a continuous map on an interval have been broadly studied because they are simple but nevertheless exhibit complex behaviors. They also allow numerical simulations, which enabled the discovery of some chaotic phenomena. Moreover, the "most interesting" part of some higher-dimensional systems can be of lower dimension, which allows, in some cases, boiling it down to systems in dimension one. Some of the more recent developments such as distributional chaos, the relation between entropy and Li-Yorke chaos, sequence entropy, and maps with infinitely many branches are presented in book form for the first time. The author gi...
van De Water W; de Weger J
2000-11-01
We study the control of chaos in an experiment on a parametrically excited pendulum whose excitation mechanism is not perfect. This imperfection leads to a weakly excited degree of freedom with an associated small eigenvalue. Although the state of the pendulum could be characterized well and although the perturbation is weak, we fail to control chaos. From a numerical model we learn that the small eigenvalue cannot be ignored when attempting control. However, the estimate of this eigenvalue from an (experimental) time series is elusive. The reason is that points in an experimental time series are distributed according to the natural measure. It is this extremely uneven distribution of points that thwarts attempts to measure eigenvalues that are very different. Another consequence of the phase-space distribution of points for control is the occurrence of logarithmic-oscillations in the waiting time before control can be attempted. We come to the conclusion that chaos needs to be destroyed before the information needed for its control can be obtained.
Wiener-Hammerstein system identification - an evolutionary approach
Naitali, Abdessamad; Giri, Fouad
2016-01-01
The problem of identifying parametric Wiener-Hammerstein (WH) systems is addressed within the evolutionary optimisation context. Specifically, a hybrid culture identification method is developed that involves model structure adaptation using genetic recombination and model parameter learning using particle swarm optimisation. The method enjoys three interesting features: (1) the risk of premature convergence of model parameter estimates to local optima is significantly reduced, due to the constantly maintained diversity of model candidates; (2) no prior knowledge is needed except for upper bounds on the system structure indices; (3) the method is fully autonomous as no interaction is needed with the user during the optimum search process. The performances of the proposed method will be illustrated and compared to alternative methods using a well-established WH benchmark.
GIRSANOV＇S THEOREM ON ABSTRACT WIENER SPACES
Institute of Scientific and Technical Information of China (English)
ZHANGYINNAN
1997-01-01
Let (E, H,u) be an abstract Wiener space in the sense of L. Gross. It is proved that if u is a measurable map from E to H such that u ∈ W2.1(H,u) and there esists a constant a1 0 < a < 1, such that either ∑n || Dnu(w)||2H < a2 or ||u(w+ h)- u(w)||H < a||h||H a. s. for every h ∈ H and E(exp(108/(1-a)2(∑||Dnu||H))))＜∞,then the measure uoT-1 is equivalent to u, where T(w) = w + u(w) for w ∈ E. And the explicit expreesion of the Padon-Nikodym derivative (cf. Theorem 2.1) is given.
An Extension of SIC Predictions to the Wiener Coactive Model.
Houpt, Joseph W; Townsend, James T
2011-06-01
The survivor interaction contrasts (SIC) is a powerful measure for distinguishing among candidate models of human information processing. One class of models to which SIC analysis can apply are the coactive, or channel summation, models of human information processing. In general, parametric forms of coactive models assume that responses are made based on the first passage time across a fixed threshold of a sum of stochastic processes. Previous work has shown that that the SIC for a coactive model based on the sum of Poisson processes has a distinctive down-up-down form, with an early negative region that is smaller than the later positive region. In this note, we demonstrate that a coactive process based on the sum of two Wiener processes has the same SIC form.
MINLIP for the Identification of Monotone Wiener Systems
Pelckmans, Kristiaan
2010-01-01
This paper studies the MINLIP estimator for the identification of Wiener systems consisting of a sequence of a linear FIR dynamical model, and a monotonically increasing (or decreasing) static function. Given $T$ observations, this algorithm boils down to solving a convex quadratic program with $O(T)$ variables and inequality constraints, implementing an inference technique which is based entirely on model complexity control. The resulting estimates of the linear submodel are found to be almost consistent when no noise is present in the data, under a condition of smoothness of the true nonlinearity and local Persistency of Excitation (local PE) of the data. This result is novel as it does not rely on classical tools as a 'linearization' using a Taylor decomposition, nor exploits stochastic properties of the data. It is indicated how to extend the method to cope with noisy data, and empirical evidence contrasts performance of the estimator against other recently proposed techniques.
Institute of Scientific and Technical Information of China (English)
M.Kalpana; P.Balasubramaniam
2013-01-01
We investigate the stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks (MJFCNNs) with discrete,unbounded distributed delays,and the Wiener process based on sampled-data control using the linear matrix inequality (LMI) approach.The Lyapunov-Krasovskii functional combined with the input delay approach as well as the free-weighting matrix approach is employed to derive several sufficient criteria in terms of LMIs to ensure that the delayed MJFCNNs with the Wiener process is stochastic asymptotical synchronous.Restrictions (e.g.,time derivative is smaller than one) are removed to obtain a proposed sampled-data controller.Finally,a numerical example is provided to demonstrate the reliability of the derived results.
Noise and speckle reduction in synthetic aperture radar imagery by nonparametric Wiener filtering.
Caprari, R S; Goh, A S; Moffatt, E K
2000-12-10
We present a Wiener filter that is especially suitable for speckle and noise reduction in multilook synthetic aperture radar (SAR) imagery. The proposed filter is nonparametric, not being based on parametrized analytical models of signal statistics. Instead, the Wiener-Hopf equation is expressed entirely in terms of observed signal statistics, with no reference to the possibly unobservable pure signal and noise. This Wiener filter is simple in concept and implementation, exactly minimum mean-square error, and directly applicable to signal-dependent and multiplicative noise. We demonstrate the filtering of a genuine two-look SAR image and show how a nonnegatively constrained version of the filter substantially reduces ringing.
System identification of Wiener systems with B-spline functions using De Boor recursion
Hong, X.; Mitchell, R. J.; Chen, S.
2013-09-01
In this article a simple and effective algorithm is introduced for the system identification of the Wiener system using observational input/output data. The nonlinear static function in the Wiener system is modelled using a B-spline neural network. The Gauss-Newton algorithm is combined with De Boor algorithm (both curve and the first order derivatives) for the parameter estimation of the Wiener model, together with the use of a parameter initialisation scheme. Numerical examples are utilised to demonstrate the efficacy of the proposed approach.
Chaos Theory and Post Modernism
Snell, Joel
2009-01-01
Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a…
Kaszás, Bálint; Feudel, Ulrike; Tél, Tamás
2016-12-01
We investigate the death and revival of chaos under the impact of a monotonous time-dependent forcing that changes its strength with a non-negligible rate. Starting on a chaotic attractor it is found that the complexity of the dynamics remains very pronounced even when the driving amplitude has decayed to rather small values. When after the death of chaos the strength of the forcing is increased again with the same rate of change, chaos is found to revive but with a different history. This leads to the appearance of a hysteresis in the complexity of the dynamics. To characterize these dynamics, the concept of snapshot attractors is used, and the corresponding ensemble approach proves to be superior to a single trajectory description, that turns out to be nonrepresentative. The death (revival) of chaos is manifested in a drop (jump) of the standard deviation of one of the phase-space coordinates of the ensemble; the details of this chaos-nonchaos transition depend on the ratio of the characteristic times of the amplitude change and of the internal dynamics. It is demonstrated that chaos cannot die out as long as underlying transient chaos is present in the parameter space. As a condition for a "quasistatically slow" switch-off, we derive an inequality which cannot be fulfilled in practice over extended parameter ranges where transient chaos is present. These observations need to be taken into account when discussing the implications of "climate change scenarios" in any nonlinear dynamical system.
Chaos Theory and Post Modernism
Snell, Joel
2009-01-01
Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a…
Institute of Scientific and Technical Information of China (English)
方锦清; 罗晓曙; 陈关荣; 翁甲强
2001-01-01
Beam halo-chaos is essentially a complex spatiotemporal chaotic motion in a periodic-focusing channel of a highpower linear proton accelerator. The controllability condition for beam halo-chaos is analysed qualitatively. A special nonlinear control method, i.e. the wavelet-based function feedback, is proposed for controlling beam halochaos. Particle-in-cell simulations are used to explore the nature of halo-chaos formation, which has shown that the beam hMo-chaos is suppressed effectively after using nonlinear control for the proton beam with an initial full Gaussian distribution. The halo intensity factor Hav is reduced from 14%o to zero, and the other statistical physical quantities of beam halo-chaos are more than doubly reduced. The potential applications of such nonlinear control in experiments are briefly pointed out.
Chaos Criminology: A critical analysis
McCarthy, Adrienne L.
There has been a push since the early 1980's for a paradigm shift in criminology from a Newtonian-based ontology to one of quantum physics. Primarily this effort has taken the form of integrating Chaos Theory into Criminology into what this thesis calls 'Chaos Criminology'. However, with the melding of any two fields, terms and concepts need to be translated properly, which has yet to be done. In addition to proving a translation between fields, this thesis also uses a set of criteria to evaluate the effectiveness of the current use of Chaos Theory in Criminology. While the results of the theory evaluation reveal that the current Chaos Criminology work is severely lacking and in need of development, there is some promise in the development of Marx's dialectical materialism with Chaos Theory.
Linear and Nonlinear Dynamical Chaos
Chirikov, B V
1997-01-01
Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal results of the studies into chaos in classical mechanics are presented in some detail, including the strong local instability and robustness of the motion, continuity of both the phase space as well as the motion spectrum, and time reversibility but nonrecurrency of statistical evolution, within the general picture of chaos as a specific case of dynamical behavior. Analysis of the apparently very deep and challenging contradictions of this picture with the quantum principles is given. The quantum view of dynamical chaos, as an attempt to resolve these contradictions guided by the correspondence principle and based upon the characteristic time scales of quantum evolution, is explained. The picture of the quantum chaos as a new generic dynamical phenomenon is outlined together wit...
A fast image super-resolution algorithm using an adaptive Wiener filter.
Hardie, Russell
2007-12-01
A computationally simple super-resolution algorithm using a type of adaptive Wiener filter is proposed. The algorithm produces an improved resolution image from a sequence of low-resolution (LR) video frames with overlapping field of view. The algorithm uses subpixel registration to position each LR pixel value on a common spatial grid that is referenced to the average position of the input frames. The positions of the LR pixels are not quantized to a finite grid as with some previous techniques. The output high-resolution (HR) pixels are obtained using a weighted sum of LR pixels in a local moving window. Using a statistical model, the weights for each HR pixel are designed to minimize the mean squared error and they depend on the relative positions of the surrounding LR pixels. Thus, these weights adapt spatially and temporally to changing distributions of LR pixels due to varying motion. Both a global and spatially varying statistical model are considered here. Since the weights adapt with distribution of LR pixels, it is quite robust and will not become unstable when an unfavorable distribution of LR pixels is observed. For translational motion, the algorithm has a low computational complexity and may be readily suitable for real-time and/or near real-time processing applications. With other motion models, the computational complexity goes up significantly. However, regardless of the motion model, the algorithm lends itself to parallel implementation. The efficacy of the proposed algorithm is demonstrated here in a number of experimental results using simulated and real video sequences. A computational analysis is also presented.
DEFF Research Database (Denmark)
Lykke, Marianne; Lund, Haakon; Skov, Mette
2016-01-01
CHAOS (Cultural Heritage Archive Open System) provides streaming access to more than 500.000 broad-casts by the Danish Broadcast Corporation from 1931 and onwards. The archive is part of the LARM project with the purpose of enabling researchers to search, annotate, and interact with recordings....... To optimally sup-port the researchers a user-centred approach was taken to develop the platform and related metadata scheme. Based on the requirements a three level metadata scheme was developed: (1) core archival metadata, (2) LARM metadata, and (3) project-specific metadata. The paper analyses how.......fm’s strength in providing streaming access to a large, shared corpus of broadcasts....
DEFF Research Database (Denmark)
Lykke, Marianne; Skov, Mette; Lund, Haakon
CHAOS (Cultural Heritage Archive Open System) provides streaming access to more than 500.000 broad-casts by the Danish Broadcast Corporation from 1931 and onwards. The archive is part of the LARM project with the purpose of enabling researchers to search, annotate, and interact with recordings....... To optimally sup-port the researchers a user-centred approach was taken to develop the platform and related metadata scheme. Based on the requirements a three level metadata scheme was developed: (1) core archival metadata, (2) LARM metadata, and (3) project-specific metadata. The paper analyses how.......fm’s strength in providing streaming access to a large, shared corpus of broadcasts....
Nonhyperbolic homoclinic chaos
Cicogna, G
1999-01-01
Homoclinic chaos is usually examined with the hypothesis of hyperbolicity of the critical point. We consider here, following a (suitably adjusted) classical analytic method, the case of non-hyperbolic points and show that, under a Melnikov-type condition plus an additional assumption, the negatively and positively asymptotic sets persist under periodic perturbations, together with their infinitely many intersections on the Poincaré section. We also examine, by means of essentially the same procedure, the case of (heteroclinic) orbits tending to the infinity; this case includes in particular the classical Sitnikov 3--body problem.
Brun, T A
1993-01-01
Using the decoherence formalism of Gell-Mann and Hartle, a quantum system is found which is the equivalent of the classical chaotic Duffing oscillator. The similarities and the differences from the classical oscillator are examined; in particular, a new concept of quantum maps is introduced, and alterations in the classical strange attractor due to the presence of scale- dependent quantum effects are studied. Classical quantities such as the Lyapunov exponents and fractal dimension are examined, and quantum analogs are suggested. These results are generalized into a framework for quantum dissipative chaos, and there is a brief discussion of other work in this area.
Baran, V; Baran, Virgil; Bonasera, Aldo
1998-01-01
The asymptotic distance between trajectories $d_{\\infty}$, is studied in detail to characterize the occurrence of chaos. We show that this quantity is quite distinct and complementary to the Lyapunov exponents, and it allows for a quantitave estimate for the folding mechanism which keeps the motion bounded in phase space. We study the behaviour of $d_{\\infty}$ in simple unidimensional maps. Near a critical point $d_{\\infty}$ has a power law dependence on the control parameter. Furthermore, at variance with the Lyapunov exponents, it shows jumps when there are sudden changes on the available phase-space.
Dembiński, S. T.; Makowski, A. J.; Pepłowski, P.
1993-02-01
We report for the first time quantum calculations for the so-called bouncer model, the classical analog of which is well known to manifest a chaotic behavior. Three versions of our model are fully tractable quantum mechanically and are potentially a rich source of data for establishing properties of a quantum system of which the classical mechanics can be chaotic. Among the results presented here, consequences of the varying bandwidth of infinite-dimensional transition matrices on the use of the correspondence between classical chaos and non-Poissonian quasienergy statistics are discussed.
2004-01-01
15 May 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows the results of a small landslide off of a hillslope in the Aureum Chaos region of Mars. Mass movement occurred from right (the slope) to left (the lobate feature pointed left). Small dark dots in the landslide area are large boulders. This feature is located near 2.6oS, 24.5oW. This picture covers an area approximately 3 km (1.9 mi) across and is illuminated by sunlight from the left/upper left.
2004-01-01
15 May 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows the results of a small landslide off of a hillslope in the Aureum Chaos region of Mars. Mass movement occurred from right (the slope) to left (the lobate feature pointed left). Small dark dots in the landslide area are large boulders. This feature is located near 2.6oS, 24.5oW. This picture covers an area approximately 3 km (1.9 mi) across and is illuminated by sunlight from the left/upper left.
Stochastic Volterra Equation Driven by Wiener Process and Fractional Brownian Motion
Directory of Open Access Journals (Sweden)
Zhi Wang
2013-01-01
Full Text Available For a mixed stochastic Volterra equation driven by Wiener process and fractional Brownian motion with Hurst parameter H>1/2, we prove an existence and uniqueness result for this equation under suitable assumptions.
Laplace asymptotic expansions of conditional Wiener integrals and generalized Mehler kernel formulas
Davies, Ian; Truman, Aubrey
1982-11-01
Imitating Schilder's results for Wiener integrals rigorous Laplace asymptotic expansions are proven for conditional Wiener integrals. Applications are given for deriving generalized Mehler kernel formulas, up to arbitrarily high orders in powers of ℏ, for exp{-TH(ℏ)/ℏ}(x, y), T>0 where H(ℏ)=[(-ℏ2/2)Δ1+V], Δ1 being the one-dimensional Laplacian, V being a real-valued potential V∈C∞(R), bounded below, together with its second derivative.
Directory of Open Access Journals (Sweden)
Lincheng Zhou
2015-08-01
Full Text Available This paper focuses on the parameter identification problem for Wiener nonlinear dynamic systems with moving average noises. In order to improve the convergence rate, the gradient-based iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates, and to compute iteratively the noise estimates based on the obtained parameter estimates. The simulation results show that the proposed algorithm can effectively estimate the parameters of Wiener systems with moving average noises.
Diagonal Kernel Point Estimation of th-Order Discrete Volterra-Wiener Systems
Directory of Open Access Journals (Sweden)
Pirani Massimiliano
2004-01-01
Full Text Available The estimation of diagonal elements of a Wiener model kernel is a well-known problem. The new operators and notations proposed here aim at the implementation of efficient and accurate nonparametric algorithms for the identification of diagonal points. The formulas presented here allow a direct implementation of Wiener kernel identification up to the th order. Their efficiency is demonstrated by simulations conducted on discrete Volterra systems up to fifth order.
Laws of the Iterated Logarithm for High-Dimensional Wiener Sausage
Institute of Scientific and Technical Information of China (English)
Yan Qing WANG; Fu Qing GAO
2011-01-01
Let {β(s),s≥0} be the standard Brownian motion in Rd with d≥4 and let |Wr(t)| be the volume of the Wiener sausage associated with {β(s),s≥0} observed until time t.From the central limit theorem of Wiener sausage,we know that when d≥4 the limit distribution is normal.In this paper,we study the laws of the iterated logarithm for |Wr(t)|-E|Wr(t)| in this case.
Wiener Reconstruction of Galaxy Surveys in Spherical Harmonics
Lahav, O; Hoffman, Y; Schärf, C A; Zaroubi, S
1993-01-01
The analysis of whole-sky galaxy surveys commonly suffers from the problems of shot-noise and incomplete sky coverage (e.g. at the Zone of Avoidance). The orthogonal set of spherical harmonics is utilized here to expand the observed galaxy distribution. We show that in the framework of Bayesian statistics and Gaussian random fields the $4 \\pi$ harmonics can be recovered and the shot-noise can be removed, giving the most probable picture of the underlying density field. The correction factor from observed to reconstructed harmonics turns out to be the well-known Wiener filter (the ratio of signal to signal+noise), which is also derived by requiring minimum variance. We apply the method to the projected 1.2 Jy IRAS survey. The reconstruction confirms the connectivity of the Supergalactic Plane across the Galactic Plane (at Galactic longitude $l \\sim 135^o$ and $l \\sim 315^o$) and the Puppis cluster behind the Galactic Plane ($ l \\sim 240^o$). The method can be extended to 3-D in both real and redshift space, an...
ZUR ENTWICKLUNG DES WIENER STADTRECHTS IM 13. JAHRHUNDERT
Institute of Scientific and Technical Information of China (English)
1994-01-01
Die Stadt Wien erlangte im Hochmittelalter als eine wichtige mitteleuropǎische Zwischenhandelsstadt groBe Bedeutung. lhre Entwicklung verdankt der Wiener Raum dem Handelsverkehr an Donau. Der frühmittelalterliche Femhandel benutzte in erster Linie den von der Natur vorgezeichneten Weg und die von ihr geschaffene VerkehrsstraBe. Die WasserstraBe ist vor allem benutzbar, weil sie offenkundig schneller und billiger ist. Wien liegt am Kreuzungspunkt zweier damalig wichtiger StraBen: der DonaustraBe, die die Mittel Europas durchquert; der LandstraBe, die von ltalien über den Semmering nach Mǎhren und Polen ist. Die DonaustraBe ist eine bedeutende West-Ost-FluBverbindung Europas, bzw. die ǎlteste und wichtigste FernhandelsstraBe. Sie verband die westlichen Nachbaren sterreichs, vornehmlich Bayern und Schwaben, mit den wirtschaftlich noch unterentwickelten Lǎndern im Osten, z.B. Ungarn, einerseits; anderseits eine Reihe schiffbarer Nebenflüsse, durch die das Innere der Alpen miteinander verbunden und der
On Wiener filtering and the physics behind statistical modeling.
Marbach, Ralf
2002-01-01
The closed-form solution of the so-called statistical multivariate calibration model is given in terms of the pure component spectral signal, the spectral noise, and the signal and noise of the reference method. The "statistical" calibration model is shown to be as much grounded on the physics of the pure component spectra as any of the "physical" models. There are no fundamental differences between the two approaches since both are merely different attempts to realize the same basic idea, viz., the spectrometric Wiener filter. The concept of the application-specific signal-to-noise ratio (SNR) is introduced, which is a combination of the two SNRs from the reference and the spectral data. Both are defined and the central importance of the latter for the assessment and development of spectroscopic instruments and methods is explained. Other statistics like the correlation coefficient, prediction error, slope deficiency, etc., are functions of the SNR. Spurious correlations and other practically important issues are discussed in quantitative terms. Most important, it is shown how to use a priori information about the pure component spectra and the spectral noise in an optimal way, thereby making the distinction between statistical and physical calibrations obsolete and combining the best of both worlds. Companies and research groups can use this article to realize significant savings in cost and time for development efforts.
An interview with Murray Jackson by Jan Wiener.
Jackson, Murray
2011-04-01
Murray Jackson was among the early trainees at the Society of Analytical Psychology (SAP) drawn to Jungian ideas during the 1950s when the training was still relatively informal. He was born in Australia where he became a doctor and came to London to study psychiatry with a particular interest in psychosis. He was influenced by Michael Fordham with whom he had an analysis and his four papers, published in the Journal of Analytical Psychology in the early 1960s, contributed significantly to the growing interest in clinical technique, particularly transference, that developed in the Society at that time. Later, he retrained at the British Institute of Psychoanalysis in the Kleinian tradition and was the first consultant at the Maudsley Hospital to run a 10-bed unit for severely mentally ill patients applying psychoanalytic principles. In April 2010, Jan Wiener interviewed Murray Jackson in France, where he now lives in retirement, about his interest and subsequent disappointment in Jungian ideas as well as his involvement with the Society of Analytical Psychology at a particular point in its history. After a brief introduction, the interview is reproduced in full.
Peccati, Giovanni
2016-01-01
Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolvi...
Chaos a very short introduction
Smith, Leonard
2007-01-01
Chaos: A Very Short Introduction shows that we all have an intuitive understanding of chaotic systems. It uses accessible maths and physics (replacing complex equations with simple examples like pendulums, railway lines, and tossing coins) to explain the theory, and points to numerous examples in philosophy and literature (Edgar Allen Poe, Chang-Tzu, and Arthur Conan Doyle) that illuminate the problems. The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction.
Quantum chaos in nuclear physics
Energy Technology Data Exchange (ETDEWEB)
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu [St. Petersburg State University (Russian Federation)
2016-07-15
A definition of classical and quantum chaos on the basis of the Liouville–Arnold theorem is proposed. According to this definition, a chaotic quantum system that has N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) that are determined by the symmetry of the Hamiltonian for the system being considered. Quantitative measures of quantum chaos are established. In the classical limit, they go over to the Lyapunov exponent or the classical stability parameter. The use of quantum-chaos parameters in nuclear physics is demonstrated.
Stalling chaos control accelerates convergence
Bick, Christian; Kolodziejski, Christoph; Timme, Marc
2013-06-01
Since chaos control has found its way into many applications, the development of fast, easy-to-implement and universally applicable chaos control methods is of crucial importance. Predictive feedback control has been widely applied but suffers from a speed limit imposed by highly unstable periodic orbits. We show that this limit can be overcome by stalling the control, thereby taking advantage of the stable directions of the uncontrolled chaotic map. This analytical finding is confirmed by numerical simulations, giving a chaos-control method that is capable of successfully stabilizing periodic orbits of high period.
Schmidt, Britney E.
2013-10-01
A critical question for the habitability of Europa remains: how does the ice shell work? The detection of shallow subsurface lenses below Europa’s chaos implies that the ice shell is recycled rapidly and that Europa may be currently active. While this is not the first time liquid water has been implicated for Europa, the location of these features combined with new perspective on their dynamics frames the question in a new way. Melt lenses are intriguing potential habitats. Moreover, their formation requires the existence of impurities within the upper ice shell that may be sources of energy for microorganisms. Geomorphic evidence also exists for hydraulic redistribution of fluids both vertically and horizontally through pores and fractures. This process, observed in terrestrial ice shelves, may preserve liquid water within the ice matrix over many kilometers from the source. Horizontal transport of material may produce interconnectivity between distinct regions of Europa, thus preserving habitable conditions within the ice over a longer duration. At a surface age of 40-90 Myr, with 25-50% covered by chaos terrain, Europa's resurfacing rate is very high and water likely plays a significant role. Because of the vigor of overturn implied by this new work, it is likely that surface and subsurface materials are well-mixed within the largest and deepest lenses, providing a mechanism for bringing oxidants and other surface contaminants to the deeper ice shell where it can reach the ocean by convective or compositional effects. The timescales over which large lenses refreeze are large compared to the timescales for vertical transport, while the timescales for smaller lenses are comparable to or shorter than convective timescales. Moreover, marine ice accretion at the bottom of the ice shell may be contributing to a compositional buoyancy engine that would change the makeup of the ice shell. From this point of view, we evaluate the habitability of Europa’s ice and
Tristán-Vega, Antonio; Brion, Véronique; Vegas-Sánchez-Ferrero, Gonzalo; Aja-Fernández, Santiago
2013-01-01
We present a new method for denoising of Diffusion Weighted Images (DWI) that shares several desirable features of state-of-the-art proposals: 1) it works with the squared-magnitude signal, allowing for a closed-form formulation as a Linear Minimum Mean Squared Error (LMMSE) estimator, a.k.a. Wiener filter; 2) it jointly accounts for the DWI channels altogether, being able to unveil anatomical structures that remain hidden in each separated channel; 3) it uses a Non-Local Means (NLM)-like scheme to discriminate voxels corresponding to different fiber bundles, being able to enhance the anatomical structures of the DWI. We report extensive experiments evidencing the new approach outperforms several related methods for all the range of input signal-to-noise ratios (SNR). An open-source C++ implementation of the algorithm is also provided for the sake of reproducibility.
Chaos and complexity by design
Roberts, Daniel A.; Yoshida, Beni
2017-04-01
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the "frame poten-tial," which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We show that the norm squared of a generalization of out-of-time-order 2 k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. Additionally, we prove that these 2 k-point correlators for Pauli operators completely determine the k-fold channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.
Chaos and complexity by design
Roberts, Daniel A
2016-01-01
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the "frame potential," which is minimized by unitary $k$-designs and measures the $2$-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We show that the norm squared of a generalization of out-of-time-order $2k$-point correlators is proportional to the $k$th frame potential, providing a quantitative connection between chaos and pseudorandomness. Additionally, we prove that these $2k$-point correlators for Pauli operators completely determine the $k$-fold channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.
DEFF Research Database (Denmark)
Lykke, Marianne; Lund, Haakon; Skov, Mette
2016-01-01
CHAOS (Cultural Heritage Archive Open System) provides streaming access to more than 500,000 broadcasts by the Danish Broadcast Corporation from 1931 and onwards. The archive is part of the LARM project with the purpose of enabling researchers to search, annotate, and interact with recordings....... To support the researchers the optimal way, a usercentred approach was taken to develop the platform and related metadata scheme. Based on the requirements, a three level metadata scheme was developed: 1) core archival metadata, 2) LARM metadata, and 3) project-specific metadata. The paper analyses how...... metadata are project-specific, they have been applied to serve as invaluable access points for fellow researchers due to their factual and neutral nature. The researchers particularly stress LARM.fm’s strength in providing streaming access to a large, shared corpus of broadcasts....
Directory of Open Access Journals (Sweden)
Akio Matsumoto
1997-01-01
Full Text Available This study augments the traditional linear cobweb model with lower and upper bounds for variations of output. Its purpose is to detect the relationship between the output constraints and the dynamics of the modified model. Due to the upper and lower bounds, a transitional function takes on a tilted z-profile having three piecewise segments with two turning points. It prevents the price (or quantity dynamics from explosive oscillations. This study demonstrates, by presenting numerical examples, that the modified cobweb model can generate various dynamics ranging from stable periodic cycles to ergodic chaos if a product of the marginal propensity to consume and the marginal product is greater than unity.
Mitchener, W Garrett; Nowak, Martin A
2004-04-01
Human language is a complex communication system with unlimited expressibility. Children spontaneously develop a native language by exposure to linguistic data from their speech community. Over historical time, languages change dramatically and unpredictably by accumulation of small changes and by interaction with other languages. We have previously developed a mathematical model for the acquisition and evolution of language in heterogeneous populations of speakers. This model is based on game dynamical equations with learning. Here, we show that simple examples of such equations can display complex limit cycles and chaos. Hence, language dynamical equations mimic complicated and unpredictable changes of languages over time. In terms of evolutionary game theory, we note that imperfect learning can induce chaotic switching among strict Nash equilibria.
Ruelle, David
1991-01-01
Comment expliquer le hasard ? Peut-on rendre raison de l'irraisonnable ? Ce livre, où il est question des jeux de dés, des loteries, des billards, des attracteurs étranges, de l'astrologie et des oracles, du temps qu'il fera, du libre arbitre, de la mécanique quantique, de l'écoulement des fluides, du théorème de Gödel et des limites de l'entendement humain, expose les fondements et les conséquences de la théorie du chaos. David Ruelle est membre de l'Académie des sciences et professeur de physique théorique à l'Institut des hautes études scientifiques de Bures-sur-Yvette.
Ercsey-Ravasz, Maria
2012-01-01
The mathematical structure of the widely popular Sudoku puzzles is akin to typical hard constraint satisfaction problems that lie at the heart of many applications, including protein folding and the general problem of finding the ground state of a glassy spin system. Via an exact mapping of Sudoku into a deterministic, continuous-time dynamical system, here we show that the difficulty of Sudoku translates into transient chaotic behavior exhibited by the dynamical system. In particular, we show that the escape rate $\\kappa$, an invariant characteristic of transient chaos, provides a single scalar measure of the puzzle's hardness, which correlates well with human difficulty level ratings. Accordingly, $\\eta = -\\log_{10}{\\kappa}$ can be used to define a "Richter"-type scale for puzzle hardness, with easy puzzles falling in the range $0 3$. To our best knowledge, there are no known puzzles with $\\eta > 4$.
Wernecke, Hendrik; Gros, Claudius
2016-01-01
For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation is split into an initial decrease characterized by the maximal Lyapunov exponent and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. The time scales of both processes can be either of the same or of very different orders of magnitude. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall size of the attractor) for exceedingly long times and therefore remain partially predictable. We introduce a 0-1 indicator for chaos capable of describing this scenario, arguing, in addition, that the chaotic closed braids found close to a period-doubling transition are generically partially predictable.
Stochastic Estimation via Polynomial Chaos
2015-10-01
TΨ is a vector with P+1 elements. With these dimensions, (29) is solvable by standard numerical linear algebra techniques. The specific matrix...initial conditions for partial differential equations. Here, the elementary theory of the polynomial chaos is presented followed by the details of a...the elementary theory of the polynomial chaos is presented followed by the details of a number of example calculations where the statistical mean and
Boundary condition may change chaos
Energy Technology Data Exchange (ETDEWEB)
Itoh, Sanae-I.; Yagi, Masatoshi [Kyushu Univ., RIAM, Kasuga, Fukuoka (Japan); Kawai, Yoshinobu [Kyushu Univ., Interdisciplinary Graduate School of Engineering Sciences, Kasuga, Fukuoka (Japan)
2001-07-01
Role of boundary condition for the appearance of chaos is examined. Imposition of the boundary condition is interpreted as the reduction of the system size L. For a demonstration, Rayleigh-Benard instability is considered and the shell model analysis is applied. It is shown that the reduction of L reduces the number of positive Lyapunov exponent of the system, hence opens the route from the turbulence, to the chaos and to the limit cycle/fixed point. (author)
Institute of Scientific and Technical Information of China (English)
王艳清
2007-01-01
In this paper, we study one-dimensional Wiener sausage. Using the property of Brownian motion and the contraction principle , we get moderate deviations and law of the iterated logarithm for the length of intersection of p one-dimensional Wiener sausages.%本文研究一维Wiener sausage.利用布朗运动的相关性质和收缩原理,得到p个Wiener sausage相交部分长度的中偏差和重对数律.
Remaining useful life prediction based on the Wiener process for an aviation axial piston pump
Institute of Scientific and Technical Information of China (English)
Wang Xingjian; Lin Siru; Wang Shaoping; He Zhaomin; Zhang Chao
2016-01-01
An aviation hydraulic axial piston pump’s degradation from comprehensive wear is a typical gradual failure model. Accurate wear prediction is difficult as random and uncertain char-acteristics must be factored into the estimation. The internal wear status of the axial piston pump is characterized by the return oil flow based on fault mechanism analysis of the main frictional pairs in the pump. The performance degradation model is described by the Wiener process to predict the remaining useful life (RUL) of the pump. Maximum likelihood estimation (MLE) is performed by utilizing the expectation maximization (EM) algorithm to estimate the initial parameters of the Wiener process while recursive estimation is conducted utilizing the Kalman filter method to estimate the drift coefficient of the Wiener process. The RUL of the pump is then calculated accord-ing to the performance degradation model based on the Wiener process. Experimental results indi-cate that the return oil flow is a suitable characteristic for reflecting the internal wear status of the axial piston pump, and thus the Wiener process-based method may effectively predicate the RUL of the pump.
2012 Symposium on Chaos, Complexity and Leadership
Erçetin, Şefika
2014-01-01
These proceedings from the 2012 symposium on "Chaos, complexity and leadership" reflect current research results from all branches of Chaos, Complex Systems and their applications in Management. Included are the diverse results in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of Chaos and Complex Systems. Also highlighted are Leadership and Management applications of Chaos and Complexity Theory.
Directory of Open Access Journals (Sweden)
Anass Benjebbour
2008-02-01
Full Text Available In the future, there will be a growing need for more flexible but efficient utilization of radio resources. Increased flexibility in radio transmission, however, yields a higher likelihood of interference owing to limited coordination among users. In this paper, we address the problem of flexible spectrum sharing where a wideband single carrier modulated signal is spectrally overlapped by unknown narrowband interference (NBI and where a cyclic Wiener filter is utilized for nonparametric NBI suppression at the receiver. The pulse shape design for the wideband signal is investigated to improve the NBI suppression capability of cyclic Wiener filtering. Specifically, two pulse shaping schemes, which outperform existing raised cosine pulse shaping schemes even for the same amount of excess bandwidth, are proposed. Based on computer simulation, the interference suppression capability of cyclic Wiener filtering is evaluated for both the proposed and existing pulse shaping schemes under several interference conditions and over both AWGN and Rayleigh fading channels.
Directory of Open Access Journals (Sweden)
Benjebbour Anass
2008-01-01
Full Text Available Abstract In the future, there will be a growing need for more flexible but efficient utilization of radio resources. Increased flexibility in radio transmission, however, yields a higher likelihood of interference owing to limited coordination among users. In this paper, we address the problem of flexible spectrum sharing where a wideband single carrier modulated signal is spectrally overlapped by unknown narrowband interference (NBI and where a cyclic Wiener filter is utilized for nonparametric NBI suppression at the receiver. The pulse shape design for the wideband signal is investigated to improve the NBI suppression capability of cyclic Wiener filtering. Specifically, two pulse shaping schemes, which outperform existing raised cosine pulse shaping schemes even for the same amount of excess bandwidth, are proposed. Based on computer simulation, the interference suppression capability of cyclic Wiener filtering is evaluated for both the proposed and existing pulse shaping schemes under several interference conditions and over both AWGN and Rayleigh fading channels.
Soft Sensor Model Derived from Wiener Model Structure:Modeling and Identification
Institute of Scientific and Technical Information of China (English)
曹鹏飞; 罗雄麟
2014-01-01
The processes of building dynamic and static relationships between secondary and primary variables are usually integrated in most of nonlinear dynamic soft sensor models. However, such integration limits the estimation accuracy of soft sensor models. Wiener model effectively describes dynamic and static characteristics of a system with the structure of dynamic and static submodels in cascade. We propose a soft sensor model derived from Wiener model structure, which is an extension of Wiener model. Dynamic and static relationships between secondary and primary variables are built respectively to describe the dynamic and static characteristics of system. The feasibility of this model is verified. Then the expression of discrete model is derived for soft sensor system. Conjugate gradi-ent algorithm is applied to identify the dynamic and static model parameters alternately. Corresponding update method for soft sensor system is also given. Case studies confirm the effectiveness of the proposed model, alternate identification algorithm, and update method.
Modeling Distortion Signals of Power Grid Based on Wiener-G Functionals
Institute of Scientific and Technical Information of China (English)
XiaoBing Zhang; YunHui Li; GuoZhi Fang
2014-01-01
The uniform mathematical model of distortion signals in power grid has been setup with the theory of Wiener-G Functional. Firstly, the Matlab simulation models were established. Secondly, the Wiener kernel of power load was found based on the Gaussian white noise as input. And then the uniform mathematical model of the power grid signal was established according to the homogeneous of the same order of Wiener functional series. Finally, taking three typical distortion sources which are semiconductor rectifier, electric locomotive and electric arc furnace in power grid as examples, we have validated the model through the Matlab simulation and analyzed the simulation errors. The results show that the uniform mathematical model of distortion signals in power grid can approximation the actual model by growing the items of the series under the condition of the enough storage space and computing speed.
Security analysis of chaotic communication systems based on Volterra-Wiener-Korenberg model
Energy Technology Data Exchange (ETDEWEB)
Lei Min [State Key Lab of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)] e-mail: leimin@sjtu.edu.cn; Meng Guang [State Key Lab of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China); Feng Zhengjin [Institute of Mechatronic Control System, Shanghai Jiao Tong University, Shanghai 200030 (China)
2006-04-01
Pseudo-randomicity is an important cryptological characteristic for proof of encryption algorithms. This paper proposes a nonlinear detecting method based on Volterra-Wiener-Korenberg model and suggests an autocorrelation function to analyze the pseudo-randomicity of chaotic secure systems under different sampling interval. The results show that: (1) the increase of the order of the chaotic transmitter will not necessarily result in a high degree of security; (2) chaotic secure systems have higher and stronger pseudo-randomicity at sparse sampling interval due to the similarity of chaotic time series to the noise; (3) Volterra-Wiener-Korenberg method can also give a further appropriate sparse sampling interval for improving the security of chaotic secure communication systems. For unmasking chaotic communication systems, the Volterra-Wiener-Korenberg technique can be applied to analyze the chaotic time series with surrogate data.
Barrow, John D; Barrow, John D.; Dabrowski, Mariusz P.
1998-01-01
We investigate Bianchi type IX ''Mixmaster'' universes within the framework of the low-energy tree-level effective action for string theory, which (when the ''stringy'' 2-form axion potential vanishes) is formally the same as the Brans-Dicke action with $\\omega =-1$. We show that, unlike the case of general relativity in vacuum, there is no Mixmaster chaos in these string cosmologies. In the Einstein frame an infinite sequence of chaotic oscillations of the scale factors on approach to the initial singularity is impossible, as it was in general relativistic Mixmaster universes in the presence of stiff -fluid matter (or a massless scalar field). A finite sequence of oscillations of the scale factors approximated by Kasner metrics is possible, but it always ceases when all expansion rates become positive. In the string frame the evolution through Kasner epochs changes to a new form which reflects the duality symmetry of the theory. Again, we show that chaotic oscillations must end after a finite time. The need ...
Contopoulos, George
2008-01-01
We distinguish two types of stickiness in systems of two degrees of freedom (a) stickiness around an island of stability and (b) stickiness in chaos, along the unstable asymptotic curves of unstable periodic orbits. We studied these effects in the standard map with a rather large nonlinearity K=5, and we emphasized the role of the asymptotic curves U, S from the central orbit O and the asymptotic curves U+U-S+S- from the simplest unstable orbit around the island O1. We calculated the escape times (initial stickiness times) for many initial points outside but close to the island O1. The lines that separate the regions of the fast from the slow escape time follow the shape of the asymptotic curves S+,S-. We explained this phenomenon by noting that lines close to S+ on its inner side (closer to O1) approach a point of the orbit 4/9, say P1, and then follow the oscillations of the asymptotic curve U+, and escape after a rather long time, while the curves outside S+ after their approach to P1 follow the shape of t...
Hashimoto, Koji; Yoshida, Kentaroh
2016-01-01
Assigning a chaos index for vacua of generic quantum field theories is a challenging problem. We find chaotic behavior of chiral condensates of a quantum gauge theory at strong coupling limit, by using the AdS/CFT correspondence. We evaluate the time evolution of homogeneous quark condensates and in an N=2 supersymmetric QCD with the SU(N_c) gauge group at large N_c and at large 't Hooft coupling lambda. At an equivalent classical gravity picture, a Lyapunov exponent is readily defined. We show that the condensates exhibit chaotic behavior for energy density E > (6x10^2) (N_c/lambda^2) (m_q)^4 where m_q is the quark mass. The energy region of the chaotic vacua of the N=2 supersymmetric QCD increases for smaller N_c or larger lambda. The Lyapunov exponent is calculated as a function of the theory (N_c,lambda,E), showing that the N=2 supersymmetric QCD is more chaotic for smaller N_c.
Energy Technology Data Exchange (ETDEWEB)
Kot, M.
1990-07-01
A recurrent theme of much recent research is that seemingly random fluctuations often occur as the result of simple deterministic mechanisms. Hence, much of the recent work in nonlinear dynamics has centered on new techniques for identifying order in seemingly chaotic systems. To determine the robustness of these techniques, chaos must, to some extent, be brought into the laboratory. Preliminary investigations of the forced double-Monod equations, a model for a predator and a prey in a chemostat with periodic variation in inflowing substrate concentration, suggest that simple microbial systems may provide the perfect framework for determining the efficacy and relevance of the new nonlinear dynamics in dealing with complex population dynamics. This research has two main goals, that is the mathematical analysis and computer simulation of the periodically forced double-Monod equations and of related models; and experimental (chemostat) population studies that evaluate the accuracy and generality of the models, and that judge the usefulness of various new techniques of nonlinear dynamics to the study of populations.
A thought to illustrate the uncertainty principle on the base of Otto-Wiener's experiment
Das, Tapas
2014-01-01
In this short paper a new thought experiment has been introduced to illustrate the famous Heisenberg's uncertainty principle based on Otto-Wiener's experiment (1890) associated with standing light waves. This illustration is quite easy as well as far more realizing than all other thought experiments generally found in textbooks. In this work seeding of quantum nature of light has been done with the Otto-Wiener's experiment. May be this new thought experiment will help the students to understand the Heisenberg's principle in a better way and also enhance their interest of learning quantum mechanics from the beginning of their course.
Some sufficient conditions for Hamiltonian property in terms of Wiener-type invariants
Indian Academy of Sciences (India)
Meijun Kuang; Guihua Huang; Hanyuan Deng
2016-02-01
The Wiener-type invariants of a simple connected graph = (,) can be expressed in terms of the quantities $W_{f} = \\sum_{\\{u,v\\}\\subseteq V} f (d_{G}(u, v))$ for various choices of the function (), where (, ) is the distance between vertices and in . In this paper, we give some sufficient conditions for a connected graph to be Hamiltonian, a connected graph to be traceable, and a connected bipartite graph to be Hamiltonian in terms of the Wiener-type invariants.
Directory of Open Access Journals (Sweden)
Houda Salhi
2016-01-01
Full Text Available This paper deals with the parameter estimation problem for multivariable nonlinear systems described by MIMO state-space Wiener models. Recursive parameters and state estimation algorithms are presented using the least squares technique, the adjustable model, and the Kalman filter theory. The basic idea is to estimate jointly the parameters, the state vector, and the internal variables of MIMO Wiener models based on a specific decomposition technique to extract the internal vector and avoid problems related to invertibility assumption. The effectiveness of the proposed algorithms is shown by an illustrative simulation example.
Angius, S.; Bisegni, C.; Ciuffetti, P.; Di Pirro, G.; Foggetta, L. G.; Galletti, F.; Gargana, R.; Gioscio, E.; Maselli, D.; Mazzitelli, G.; Michelotti, A.; Orrù, R.; Pistoni, M.; Spagnoli, F.; Spigone, D.; Stecchi, A.; Tonto, T.; Tota, M. A.; Catani, L.; Di Giulio, C.; Salina, G.; Buzzi, P.; Checcucci, B.; Lubrano, P.; Piccini, M.; Fattibene, E.; Michelotto, M.; Cavallaro, S. R.; Diana, B. F.; Enrico, F.; Pulvirenti, S.
2016-01-01
The paper is aimed to present the !CHAOS open source project aimed to develop a prototype of a national private Cloud Computing infrastructure, devoted to accelerator control systems and large experiments of High Energy Physics (HEP). The !CHAOS project has been financed by MIUR (Italian Ministry of Research and Education) and aims to develop a new concept of control system and data acquisition framework by providing, with a high level of aaabstraction, all the services needed for controlling and managing a large scientific, or non-scientific, infrastructure. A beta version of the !CHAOS infrastructure will be released at the end of December 2015 and will run on private Cloud infrastructures based on OpenStack.
Turiaci, Gustavo J.; Verlinde, Herman
2016-12-01
We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov behavior and a spectrum of Ruelle resonances. We use this insight to identify a lattice model for quantum chaos, built from parafermionic spin variables with an equation of motion given by a Y-system. Finally we point to a relation between the spectrum of Ruelle resonances of a CFT and the analytic properties of OPE coefficients between light and heavy operators. In our model, this spectrum agrees with the quasi-normal modes of the BTZ black hole.
Turiaci, Gustavo
2016-01-01
We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov behavior and a spectrum of Ruelle resonances. We use this insight to identify a lattice model for quantum chaos, built from parafermionic spin variables with an equation of motion given by a Y-system. Finally we point to a relation between the spectrum of Ruelle resonances of a CFT and the analytic properties of OPE coefficients between light and heavy operators. In our model, this spectrum agrees with the quasi-normal modes of the BTZ black hole.
La factorización de una transformada de Fourier en el método de Wiener-Hopf
Directory of Open Access Journals (Sweden)
José Rosales-Ortega
2009-02-01
Full Text Available Using the Wiener-Hopf method, we factorize the Fourier Transform of the kernel of a singular integral equation as the product of two functions: one holomorphic in the upper semiplan and the other holomophic in the lower semiplan. Keywords: function product, Fourier transform, Wiener-Hopf method.
Non-uniform Sampling Sets in Wiener-amalgam Space%Wiener-amalgam空间的非均匀采样集
Institute of Scientific and Technical Information of China (English)
李松华
2008-01-01
研究了由Wiener-amalgam空间中的函数φ生成的整平移不变子空间V2(φ)的采样集X问题,并运用生成子φ的连续模(oscillation)刻画了构成V2(加φ)的采样集X的一个充分条件.
The information geometry of chaos
Cafaro, Carlo
2008-10-01
In this Thesis, we propose a new theoretical information-geometric framework (IGAC, Information Geometrodynamical Approach to Chaos) suitable to characterize chaotic dynamical behavior of arbitrary complex systems. First, the problem being investigated is defined; its motivation and relevance are discussed. The basic tools of information physics and the relevant mathematical tools employed in this work are introduced. The basic aspects of Entropic Dynamics (ED) are reviewed. ED is an information-constrained dynamics developed by Ariel Caticha to investigate the possibility that laws of physics---either classical or quantum---may emerge as macroscopic manifestations of underlying microscopic statistical structures. ED is of primary importance in our IGAC. The notion of chaos in classical and quantum physics is introduced. Special focus is devoted to the conventional Riemannian geometrodynamical approach to chaos (Jacobi geometrodynamics) and to the Zurek-Paz quantum chaos criterion of linear entropy growth. After presenting this background material, we show that the ED formalism is not purely an abstract mathematical framework, but is indeed a general theoretical scheme from which conventional Newtonian dynamics is obtained as a special limiting case. The major elements of our IGAC and the novel notion of information geometrodynamical entropy (IGE) are introduced by studying two "toy models". To illustrate the potential power of our IGAC, one application is presented. An information-geometric analogue of the Zurek-Paz quantum chaos criterion of linear entropy growth is suggested. Finally, concluding remarks emphasizing strengths and weak points of our approach are presented and possible further research directions are addressed. At this stage of its development, IGAC remains an ambitious unifying information-geometric theoretical construct for the study of chaotic dynamics with several unsolved problems. However, based on our recent findings, we believe it already
1989-01-01
Le mouvement brownien ; la mémoire des atomes ; le chaos ; déterminisme et prédictabilité ; déterminisme et chaos ; les phénomènes de physique et les échelles de longueur ; un ordre caché dans la matière désordonnée ; les verres de spin et l'étude des milieux désordonnés ; la convection ; la croissance fractale ; la physique de la matière hétérogène ; la matière ultradivisée.
ergodicity and chaos in geomorphology
Aadel, S.; Gaiumi, M.
2009-04-01
The past three dicades can be considered as a period in which the fundamentals of scientific epistemology have been subjected to drastic revision.The dissemination of the general theory of systems in 1972 , one year after the death of ludwing von Berthalanfi , the proposition of fuzzy logic by Zade, and the foemulation of chaos theory in 1986 by Harison and Biswas allserved to explode the myth that scientific thought was invulnerable. This paper , which has resulted from the theoretical investigation of project based on the paraglicial sediment and glacial evidence on the Zagros-pishkoh to explain the elements of chaos theory and their compatibility with ergodic geomorphology
Sprott, J C
2013-04-01
This paper demonstrates that an artificial neural network training on time-series data from the logistic map at the onset of chaos trains more effectively when it is weakly chaotic. This suggests that a modest amount of chaos in the brain in addition to the ever present random noise might be beneficial for learning. In such a case, human subjects might exhibit an increased Lyapunov exponent in their EEG recordings during the performance of creative tasks, suggesting a possible line of future research.
Enhancing chaoticity of spatiotemporal chaos.
Li, Xiaowen; Zhang, Heqiao; Xue, Yu; Hu, Gang
2005-01-01
In some practical situations strong chaos is needed. This introduces the task of chaos control with enhancing chaoticity rather than suppressing chaoticity. In this paper a simple method of linear amplifications incorporating modulo operations is suggested to make spatiotemporal systems, which may be originally chaotic or nonchaotic, strongly chaotic. Specifically, this control can eliminate periodic windows, increase the values and the number of positive Lyapunov exponents, make the probability distributions of the output chaotic sequences more homogeneous, and reduce the correlations of chaotic outputs for different times and different space units. The applicability of the method to practical tasks, in particular to random number generators and secure communications, is briefly discussed.
Chaos and transient chaos in an experimental nonlinear pendulum
de Paula, Aline Souza; Savi, Marcelo Amorim; Pereira-Pinto, Francisco Heitor Iunes
2006-06-01
Pendulum is a mechanical device that instigates either technological or scientific studies, being associated with the measure of time, stabilization devices as well as ballistic applications. Nonlinear characteristic of the pendulum attracts a lot of attention being used to describe different phenomena related to oscillations, bifurcation and chaos. The main purpose of this contribution is the analysis of chaos in an experimental nonlinear pendulum. The pendulum consists of a disc with a lumped mass that is connected to a rotary motion sensor. This assembly is driven by a string-spring device that is attached to an electric motor and also provides torsional stiffness to the system. A magnetic device provides an adjustable dissipation of energy. This experimental apparatus is modeled and numerical simulations are carried out. Free and forced vibrations are analyzed showing that numerical results are in close agreement with those obtained from experimental data. This analysis shows that the experimental pendulum has a rich response, presenting periodic response, chaos and transient chaos.
Deterministic polarization chaos from a laser diode
Virte, Martin; Thienpont, Hugo; Sciamanna, Marc
2014-01-01
Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect - i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence no chaos can be generated unless with additional forcing or parameter modulation. Here we report the first counter-example of a free-running laser diode generating chaos. The underlying physics is a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time-series and show theoretically the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles at first sight a noise-driven mode hopping but shows opposite statistical properties. Our findings open up new research areas that combine the high speed performances of microcavity lasers with controllable and integrated sources of optical chaos.
Generalized Local Time of the Indefinite Wiener Integral:White Noise Approach
Institute of Scientific and Technical Information of China (English)
Jingjun GUO
2012-01-01
In this paper,the generalized local time of the indefinite Wiener integral Xt is discussed through white noise approach,which means to regard the local time as a Hida distribution.Moreover,similar result is also obtained in case of two independent Brownian motions by using the similar approach.
Noise degradation system using Wiener filter and CORDIC based FFT/IFFT processor
Institute of Scientific and Technical Information of China (English)
Yasodai A; Ramprasad A V
2015-01-01
On augmentation of past work, an effective Wiener filter and its application for noise suppression combined with a formed CORDIC based FFT/IFFT processor with improved speed were executed. The pipelined methodology was embraced for expanding the execution of the system. The proposed Wiener filter was planned in such an approach to evacuate the iteration issues in ordinary Wiener filter. The division process was supplanted by a productive inverse and multiplication process in the proposed design. An enhanced design for matrix inverse with reduced computation complexity was executed. The wide-ranging framework processing was focused around IEEE-754 standard single precision floating point numbers. The Wiener filter and the entire system design was integrated and actualized on VIRTEX 5 FPGA stage and re-enacted to approve the results in Xilinx ISE 13.4. The results show that a productive decrease in power and area is developed by adjusting the proposed technique for speech signal noise degradation with latency ofn/2 clock cycles and substantial throughput result per every 12 clock cycles forn-bit precision. The execution of proposed design is exposed to be 31.35% more effective than that of prevailing strategies.
Optimization of the reconstruction and anti-aliasing filter in a Wiener filter system
Wesselink, J.M.; Berkhoff, A.P.
2006-01-01
This paper discusses the influence of the reconstruction and anti-aliasing filters on the performance of a digital implementation of a Wiener filter for active noise control. The overall impact will be studied in combination with a multi-rate system approach. A reconstruction and anti-aliasing filte
WIENER KERNEL ANALYSIS OF INNER-EAR FUNCTION IN THE AMERICAN BULLFROG
VANDIJK, P; WIT, HP; SEGENHOUT, JM; TUBIS, A
1994-01-01
The response of 17 primary auditory nerve fibers in the American bullfrog (Rana catesbeiana) to acoustic noise stimulation of the tympanic membrane was recorded. For each fiber, the first- and second-order Wiener kernels, k(1)(tau(1)) and k(2)(tau(1),tau(2)), were computed by cross correlation of th
BL_Wiener Denoising Method for Removal of Speckle Noise in Ultrasound Image
Directory of Open Access Journals (Sweden)
Suhaila Sari
2015-02-01
Full Text Available Medical imaging techniques are extremely important tools in medical diagnosis. One of these important imaging techniques is ultrasound imaging. However, during ultrasound image acquisition process, the quality of image can be degraded due to corruption by speckle noise. The enhancement of ultrasound images quality from the 2D ultrasound imaging machines is expected to provide medical practitioners more reliable medical images in their patients’ diagnosis. However, developing a denoising technique which could remove noise effectively without eliminating the image’s edges and details is still an ongoing issue. The objective of this paper is to develop a new method that is capable to remove speckle noise from the ultrasound image effectively. Therefore, in this paper we proposed the utilization of Bilateral Filter and Adaptive Wiener Filter (BL_Wiener denoising method for images corrupted by speckle noise. Bilateral Filter is a non-linear filter effective in removing noise, while Adaptive Wiener Filter balances the tradeoff between inverse filtering and noise smoothing by removing additive noise while inverting blurring. From our simulation results, it is found that the BL_Wiener method has improved between 0.89 [dB] to 3.35 [dB] in terms of PSNR for test images in different noise levels in comparison to conventional methods.
Functions of Bounded Variation on the Classical Wiener Space and an Extended Ocone-Karatzas Formula
Pratelli, Maurizio
2011-01-01
We prove an extension of the Ocone-Karatzas integral representation, valid for all $BV$ functions on the classical Wiener space. We establish also an elementary chain rule formula and use it to compute explicit integral representations for some classes of $BV$ composite random variables.
Wiener-kernel analysis of responses to noise of chinchilla auditory-nerve fibers
Recio-Spinoso, A; Temchin, AN; van Dijk, P; Fan, YH; Ruggero, MA
2005-01-01
Responses to broadband Gaussian white noise were recorded in auditory-nerve fibers of deeply anesthetized chinchillas and analyzed by computation of zeroth-, first-, and second-order Wiener kernels. The first- order kernels ( similar to reverse correlations or "revcors") of fibers with characteristi
Optimization of the reconstruction and anti-aliasing filter in a wiener filter system
Wesselink, J.M.; Berkhoff, A.P.
2006-01-01
This paper discusses the influence of the reconstruction and anti-aliasing filters on the performance of a digital implementation of a Wiener filter for active noise control. The overall impact will be studied in combination with a multi-rate system approach. A reconstruction and anti-aliasing filte
Degradation data analysis based on a generalized Wiener process subject to measurement error
Li, Junxing; Wang, Zhihua; Zhang, Yongbo; Fu, Huimin; Liu, Chengrui; Krishnaswamy, Sridhar
2017-09-01
Wiener processes have received considerable attention in degradation modeling over the last two decades. In this paper, we propose a generalized Wiener process degradation model that takes unit-to-unit variation, time-correlated structure and measurement error into considerations simultaneously. The constructed methodology subsumes a series of models studied in the literature as limiting cases. A simple method is given to determine the transformed time scale forms of the Wiener process degradation model. Then model parameters can be estimated based on a maximum likelihood estimation (MLE) method. The cumulative distribution function (CDF) and the probability distribution function (PDF) of the Wiener process with measurement errors are given based on the concept of the first hitting time (FHT). The percentiles of performance degradation (PD) and failure time distribution (FTD) are also obtained. Finally, a comprehensive simulation study is accomplished to demonstrate the necessity of incorporating measurement errors in the degradation model and the efficiency of the proposed model. Two illustrative real applications involving the degradation of carbon-film resistors and the wear of sliding metal are given. The comparative results show that the constructed approach can derive a reasonable result and an enhanced inference precision.
Interdisciplinarity in Norbert Wiener, a mathematician-philosopher of our time.
Montagnini, Leone
2017-10-01
The paper focuses on interdisciplinarity in Norbert Wiener looking at his scientific work from a unitary point of view. It begins with a bird's-eye view of the history of the term "interdisciplinarity", pointing out how the word was the result of a movement of ideas that took place in US science along the whole Twentieth century. This way, the Wiener's conceptions and practices concerning interdisciplinarity are compared with their historical context, showing analogies and peculiarities. For Wiener, interdisciplinary research by very small groups whose members have a very broad interdisciplinary basis is an essential prerequisite for new fundamental ideas for invention and discoveries. On the contrary, in his opinion, mass attacks by large well financed interdisciplinary research groups with a big number of overspecialized member is useful only in a second phase in which invention and discoveries need to be implemented by designers and developers. Finally, through a conceptual matching between Wiener's ideas and the ones of José Ortega y Gasset, it appears how the Wienerian small interdisciplinary group would fit better with the Kuhnian revolutionary phase in science, while the big interdisciplinary group would fit better to the Kuhnian normal science. Copyright © 2017 Elsevier B.V. All rights reserved.
WIENER-HOPF SOLVER WITH SMOOTH PROBABILITY DISTRIBUTIONS OF ITS COMPONENTS
Directory of Open Access Journals (Sweden)
Mr. Vladimir A. Smagin
2016-12-01
Full Text Available The Wiener – Hopf solver with smooth probability distributions of its component is presented. The method is based on hyper delta approximations of initial distributions. The use of Fourier series transformation and characteristic function allows working with the random variable method concentrated in transversal axis of absc.
Average Widths of Sobolev-Wiener Classes with Mixed Smoothness in Lq(rd)
Institute of Scientific and Technical Information of China (English)
He Ping WANG
2001-01-01
In this paper, the average σ-K width of Sobolev-Wiener classes Srpq W with mixed smooth ness in Lq(Rd) is studied for 1 ＜ q ≤ p ＜∞ and the weak asymptotical behavior of these quantities is obtained.
Lecar, M; Holman, M; Murray, N
2002-01-01
The physical basis of chaos in the solar system is now better understood: in all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its Kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new ``short-period'' comet is discovered each year. They are believed to come from the ``Kuiper Belt'' (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury, in 10^{12} years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 10^9 times the age of the solar ...
On the Mechanisms Behind Chaos
DEFF Research Database (Denmark)
Lindberg, Erik
2006-01-01
behind the chaotic behavior, e.g. one group is based on the sudden interrupt of inductive currents, another group is based on the sudden parallel coupling of capacitors with different voltages, and a third group may be based on multiplication of signals. An example of chaos based on disturbance...
Distributed chaos in turbulent wakes
Bershadskii, A
2016-01-01
Soft and hard spontaneous breaking of space translational symmetry (homogeneity) have been studied in turbulent wakes by means of distributed chaos. In the case of the soft translational symmetry breaking the vorticity correlation integral $\\int_{V} \\langle {\\boldsymbol \\omega} ({\\bf x},t) \\cdot {\\boldsymbol \\omega} ({\\bf x} + {\\bf r},t) \\rangle_{V} d{\\bf r}$ dominates the distributed chaos and the chaotic spectra $\\exp-(k/k_{\\beta})^{\\beta }$ have $\\beta =1/2$. In the case of the hard translational symmetry breaking, control on the distributed chaos is switched from one type of fundamental symmetry to another (in this case to Lagrangian relabeling symmetry). Due to the Noether's theorem the relabeling symmetry results in the inviscid helicity conservation and helicity correlation integral $I=\\int \\langle h({\\bf x},t)~h({\\bf x}+{\\bf r}, t)\\rangle d{\\bf r}$ (Levich-Tsinober invariant) dominates the distributed chaos with $\\beta =1/3$. Good agreement with the experimatal data has been established for turbulent ...
Wang, Frank Y
2009-01-01
The general public has been made aware of the research field of "chaos" by the book of that title by James Gleick. This paper will focus on the achievements of Sonya Kovalevskaya, Mary Cartwright, and Mary Tsingou, whose pioneer works were not mentioned in Gleick's book.
Chaos Behaviour of Molecular Orbit
Institute of Scientific and Technical Information of China (English)
LIU Shu-Tang; SUN Fu-Yan; SHEN Shu-Lan
2007-01-01
Based on H(u)ckel's molecular orbit theory,the chaos and;bifurcation behaviour of a molecular orbit modelled by a nonlinear dynamic system is studied.The relationship between molecular orbit and its energy level in the nonlinear dynamic system is obtained.
MHD turbulence and distributed chaos
Bershadskii, A
2016-01-01
It is shown, using results of recent direct numerical simulations, that spectral properties of distributed chaos in MHD turbulence with zero mean magnetic field are similar to those of hydrodynamic turbulence. An exception is MHD spontaneous breaking of space translational symmetry, when the stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$ has $\\beta=4/7$.
ON THE WEIGHTED VARIABLE EXPONENT AMALGAM SPACE W (Lp(x), Lqm)
Institute of Scientific and Technical Information of China (English)
A.Turan GURKANLI; Ismail AYDIN
2014-01-01
In [4] , a new family W (Lp(x), Lqm) of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space Lp(x) (R) and the global component is a weighted Lebesgue space Lqm (R). This present paper is a sequel to our work [4]. In Section 2, we discuss necessary and sufficient conditions for the equality W Lp(x), Lqm=Lq (R) . Later we give some characterization of Wiener amalgam space WLp(x), Lqm. In Section 3 we define the Wiener amalgam space W FLp(x),Lq m and investigate some properties of this space, where F Lp(x) is the image of Lp(x) under the Fourier transform. In Section 4, we discuss boundedness of the Hardy-Littlewood maximal operator between some Wiener amalgam spaces.
Does chaos assist localization or delocalization?
Energy Technology Data Exchange (ETDEWEB)
Tan, Jintao; Luo, Yunrong; Hai, Wenhua, E-mail: whhai2005@aliyun.com [Department of Physics and Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha 410081 (China); Lu, Gengbiao [Department of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410004 (China)
2014-12-01
We aim at a long-standing contradiction between chaos-assisted tunneling and chaos-related localization study quantum transport of a single particle held in an amplitude-modulated and tilted optical lattice. We find some near-resonant regions crossing chaotic and regular regions in the parameter space, and demonstrate that chaos can heighten velocity of delocalization in the chaos-resonance overlapping regions, while chaos may aid localization in the other chaotic regions. The degree of localization enhances with increasing the distance between parameter points and near-resonant regions. The results could be useful for experimentally manipulating chaos-assisted transport of single particles in optical or solid-state lattices.
Advances in chaos theory and intelligent control
Vaidyanathan, Sundarapandian
2016-01-01
The book reports on the latest advances in and applications of chaos theory and intelligent control. Written by eminent scientists and active researchers and using a clear, matter-of-fact style, it covers advanced theories, methods, and applications in a variety of research areas, and explains key concepts in modeling, analysis, and control of chaotic and hyperchaotic systems. Topics include fractional chaotic systems, chaos control, chaos synchronization, memristors, jerk circuits, chaotic systems with hidden attractors, mechanical and biological chaos, and circuit realization of chaotic systems. The book further covers fuzzy logic controllers, evolutionary algorithms, swarm intelligence, and petri nets among other topics. Not only does it provide the readers with chaos fundamentals and intelligent control-based algorithms; it also discusses key applications of chaos as well as multidisciplinary solutions developed via intelligent control. The book is a timely and comprehensive reference guide for graduate s...
Controlling neuronal noise using chaos control
Christini, D J; Christini, David J; Collins, James J
1995-01-01
Chaos control techniques have been applied to a wide variety of experimental systems, including magneto-elastic ribbons, lasers, chemical reactions, arrhythmic cardiac tissue, and spontaneously bursting neuronal networks. An underlying assumption in all of these studies is that the system being controlled is chaotic. However, the identification of chaos in experimental systems, particularly physiological systems, is a difficult and often misleading task. Here we demonstrate that the chaos criteria used in a recent study can falsely classify a noise-driven, non-chaotic neuronal model as being chaotic. We apply chaos control, periodic pacing, and anticontrol to the non-chaotic model and obtain results which are similar to those reported for apparently chaotic, {\\em in vitro} neuronal networks. We also obtain similar results when we apply chaos control to a simple stochastic system. These novel findings challenge the claim that the aforementioned neuronal networks were chaotic and suggest that chaos control tech...
How Can We Observe and Describe Chaos?
Kossakowski, A; Togawa, Y; Kossakowski, Andrzej; Ohya, Masanori; Togawa, Yosio
2003-01-01
We propose a new approach to define chaos in dynamical systems from the point of view of Information Dynamics. Observation of chaos in reality depends upon how to observe it, for instance, how to take the scale in space and time. Therefore it is natural to abandon taking several mathematical limiting procedures. We take account of them, and chaos degree previously introduced is redefined in this paper.
Systems Fragility: The Sociology of Chaos
2015-03-01
THE SOCIOLOGY OF CHAOS by Lori R. Hodges March 2015 Thesis Advisor: Robert Josefek Second Reader: Wayne Porter THIS PAGE INTENTIONALLY...SUBTITLE 5. FUNDING NUMBER S SYSTEMS FRAGILITY: THE SOCIOLOGY OF CHAOS 6. AUTHOR(S) Lori R. Hodges 7. PERFORMING OR GANIZATION NA:iVIE(S) AND...INTENTIONALLY LEFT BLANK ii Approved for public release; distribution is unlimited SYSTEMS FRAGILITY: THE SOCIOLOGY OF CHAOS Lori R. Hodges
Robust chaos in smooth unimodal maps
Andrecut, M.; Ali, M. K.
2001-08-01
Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhood of the parameter space. It has been conjectured that robust chaos cannot occur in smooth systems [E. Barreto, B. Hunt, and C. Grebogi, Phys. Rev. Lett. 78, 4561 (1997); 80, 3049 (1998)]. Contrary to this conjecture, we describe a general procedure for generating robust chaos in smooth unimodal maps.
Chaos suppression in gas-solid fluidization.
Pence, Deborah V.; Beasley, Donald E.
1998-06-01
Fluidization in granular materials occurs primarily as a result of a dynamic balance between gravitational forces and forces resulting from the flow of a fluid through a bed of discrete particles. For systems where the fluidizing medium and the particles have significantly different densities, density wave instabilities create local pockets of very high void fraction termed bubbles. The fluidization regime is termed the bubbling regime. Such a system is appropriately termed a self-excited nonlinear system. The present study examines chaos suppression resulting from an opposing oscillatory flow in gas-solid fluidization. Time series data representing local, instantaneous pressure were acquired at the surface of a horizontal cylinder submerged in a bubbling fluidized bed. The particles had a weight mean diameter of 345 &mgr;m and a narrow size distribution. The state of fluidization corresponded to the bubbling regime and total air flow rates employed in the present study ranged from 10% to 40% greater than that required for minimum fluidization. The behavior of time-varying local pressure in fluidized beds in the absence of a secondary flow is consistent with deterministic chaos. Kolmogorov entropy estimates from local, instantaneous pressure suggest that the degree of chaotic behavior can be substantially suppressed by the presence of an opposing, oscillatory secondary flow. Pressure signals clearly show a "phase-locking" phenomenon coincident with the imposed frequency. In the present study, the greatest degree of suppression occurred for operating conditions with low primary and secondary flow rates, and a secondary flow oscillation frequency of 15 Hz. (c) 1998 American Institute of Physics.
Fitzpatrick, A Liam
2016-01-01
We use results on Virasoro conformal blocks to study chaotic dynamics in CFT$_2$ at large central charge c. The Lyapunov exponent $\\lambda_L$, which is a diagnostic for the early onset of chaos, receives $1/c$ corrections that may be interpreted as $\\lambda_L = \\frac{2 \\pi}{\\beta} \\left( 1 + \\frac{12}{c} \\right)$. However, out of time order correlators receive other equally important $1/c$ suppressed contributions that do not have such a simple interpretation. We revisit the proof of a bound on $\\lambda_L$ that emerges at large $c$, focusing on CFT$_2$ and explaining why our results do not conflict with the analysis leading to the bound. We also comment on relationships between chaos, scattering, causality, and bulk locality.
Energy Technology Data Exchange (ETDEWEB)
Fitzpatrick, A. Liam [Department of Physics, Boston University,590 Commonwealth Avenue, Boston, MA 02215 (United States); Kaplan, Jared [Department of Physics and Astronomy, Johns Hopkins University,3400 N. Charles St, Baltimore, MD 21218 (United States)
2016-05-12
We use results on Virasoro conformal blocks to study chaotic dynamics in CFT{sub 2} at large central charge c. The Lyapunov exponent λ{sub L}, which is a diagnostic for the early onset of chaos, receives 1/c corrections that may be interpreted as λ{sub L}=((2π)/β)(1+(12/c)). However, out of time order correlators receive other equally important 1/c suppressed contributions that do not have such a simple interpretation. We revisit the proof of a bound on λ{sub L} that emerges at large c, focusing on CFT{sub 2} and explaining why our results do not conflict with the analysis leading to the bound. We also comment on relationships between chaos, scattering, causality, and bulk locality.
Olsen, L F; Degn, H
1977-05-12
Dynamic systems are usually thought to have either monotonic or periodic behaviour. Although the possibility of other types of behaviour has been recognised for many years, the existence of non-monotonic, non-periodic behaviour in dynamic systems has been firmly established only recently. It is termed chaotic behaviour. A review on the rapidly expanding literature on chaos in discrete model systems described by difference equations has been published by May. Rössler, on the other hand, has discussed a few published works on systems of differential equations with chaotic solutions, and he has proposed a three-component chemical model system which he argues has chaotic solutions [figure see text]. The argument is based on a theorem by Li and Yorke. Here we report the finding of chaotic behaviour as an experimental result in an enzyme system (peroxidase). Like Rössler we base our identification of chaos on the theorem by Li and Yorke.
The chaos cookbook a practical programming guide
Pritchard, Joe
2014-01-01
The Chaos Cookbook: A Practical Programming Guide discusses the use of chaos in computer programming. The book is comprised of 11 chapters that tackle various topics relevant to chaos and programming. Chapter 1 reviews the concept of chaos, and Chapter 2 discusses the iterative functions. Chapters 3 and 4 cover differential and Lorenz equations. Chapter 5 talks about strange attractors, while Chapter 6 deals with the fractal link. The book also discusses the Mandelbrot set, and then covers the Julia sets. The other fractal systems and the cellular automata are also explained. The last chapter
Analysis of FBC deterministic chaos
Energy Technology Data Exchange (ETDEWEB)
Daw, C.S.
1996-06-01
It has recently been discovered that the performance of a number of fossil energy conversion devices such as fluidized beds, pulsed combustors, steady combustors, and internal combustion engines are affected by deterministic chaos. It is now recognized that understanding and controlling the chaotic elements of these devices can lead to significantly improved energy efficiency and reduced emissions. Application of these techniques to key fossil energy processes are expected to provide important competitive advantages for U.S. industry.
Random Behaviour in Quantum Chaos
Garbaczewski, P
2001-01-01
We demonstrate that a family of radial Ornstein-Uhlenbeck stochastic processes displays an ergodic behaviour appropriate for known quantum chaos universality classes of nearest neighbour spacing distributions. A common feature of those parametric processes is an asymptotic balance between the radial (Bessel-type) repulsion and the harmonic attraction, as manifested in the general form of forward drifts $b(x) = {{N-1}\\over {2x}} - x$, ($N = 2,3,5$ correspond respectively to the familiar GOE, GUE and GSE cases).
Polynomial-Chaos-based Kriging
Schöbi, R; Sudret, B.; Wiart, J.
2015-01-01
International audience; Computer simulation has become the standard tool in many engineering fields for designing and optimizing systems, as well as for assessing their reliability. Optimization and uncertainty quantification problems typically require a large number of runs of the computational model at hand, which may not be feasible with high-fidelity models directly. Thus surrogate models (a.k.a metamodels) have been increasingly investigated in the last decade. Polynomial Chaos Expansion...
Temperature chaos and quenched heterogeneities
Barucca, Paolo; Parisi, Giorgio; Rizzo, Tommaso
2014-03-01
We present a treatable generalization of the Sherrington-Kirkpatrick (SK) model which introduces correlations in the elements of the coupling matrix through multiplicative disorder on the single variables and investigate the consequences on the phase diagram. We define a generalized qEA parameter and test the structural stability of the SK results in this correlated case evaluating the de Almeida-Thouless line of the model. As a main result we demonstrate the increase of temperature chaos effects due to heterogeneities.
Chaos Control in Mechanical Systems
Directory of Open Access Journals (Sweden)
Marcelo A. Savi
2006-01-01
Full Text Available Chaos has an intrinsically richness related to its structure and, because of that, there are benefits for a natural system of adopting chaotic regimes with their wide range of potential behaviors. Under this condition, the system may quickly react to some new situation, changing conditions and their response. Therefore, chaos and many regulatory mechanisms control the dynamics of living systems, conferring a great flexibility to the system. Inspired by nature, the idea that chaotic behavior may be controlled by small perturbations of some physical parameter is making this kind of behavior to be desirable in different applications. Mechanical systems constitute a class of system where it is possible to exploit these ideas. Chaos control usually involves two steps. In the first, unstable periodic orbits (UPOs that are embedded in the chaotic set are identified. After that, a control technique is employed in order to stabilize a desirable orbit. This contribution employs the close-return method to identify UPOs and a semi-continuous control method, which is built up on the OGY method, to stabilize some desirable UPO. As an application to a mechanical system, a nonlinear pendulum is considered and, based on parameters obtained from an experimental setup, analyses are carried out. Signals are generated by numerical integration of the mathematical model and two different situations are treated. Firstly, it is assumed that all state variables are available. After that, the analysis is done from scalar time series and therefore, it is important to evaluate the effect of state space reconstruction. Delay coordinates method and extended state observers are employed with this aim. Results show situations where these techniques may be used to control chaos in mechanical systems.
Hamiltonian chaos and fractional dynamics
Zaslavsky, George M
2008-01-01
The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image ...
Kasimov, Aslan R.
2013-03-08
We propose the following model equation, ut+1/2(u2−uus)x=f(x,us) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x=0 for any t≥0. Here, us(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equation retains the essential physics needed to reproduce many properties of detonations in gaseous reactive mixtures: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.
Oodaira, Hiroshi
1989-01-01
A large deviations result is obtained for a class of self-similar processes represented by multiple Wiener integrals, which includes the limit processes appearing in functional "non-central" limit theorems.
An iterative denoising system based on Wiener filtering with application to biomedical images
Lahmiri, Salim
2017-05-01
Biomedical image denoising systems are important for accurate clinical diagnosis. The purpose of this study is to present a simple and effective iterative multistep image denoising system based on Wiener filtering (WF) where the denoised image from one stage is the input to the next stage. The denoising process stops when a particular condition measured by image energy is adaptively achieved. The proposed iterative system is tested on real clinical images and performance is measured by the well-known peak-signal-to-noise-ratio (PSNR) statistic. Experimental results showed that the proposed iterative system outperforms conventional image denoising algorithms; including wavelet packet (WP), fourth order partial differential equation (FOPDE), nonlocal Euclidean means (NLEM), first order local statistics (FOLS), and single Wiener filter used as baseline model. The experimental results demonstrate that the proposed approach can remove noise automatically and effectively while edges and texture characteristics are preserved.
Model Predictive Control Based on Kalman Filter for Constrained Hammerstein-Wiener Systems
Directory of Open Access Journals (Sweden)
Man Hong
2013-01-01
Full Text Available To precisely track the reactor temperature in the entire working condition, the constrained Hammerstein-Wiener model describing nonlinear chemical processes such as in the continuous stirred tank reactor (CSTR is proposed. A predictive control algorithm based on the Kalman filter for constrained Hammerstein-Wiener systems is designed. An output feedback control law regarding the linear subsystem is derived by state observation. The size of reaction heat produced and its influence on the output are evaluated by the Kalman filter. The observation and evaluation results are calculated by the multistep predictive approach. Actual control variables are computed while considering the constraints of the optimal control problem in a finite horizon through the receding horizon. The simulation example of the CSTR tester shows the effectiveness and feasibility of the proposed algorithm.
Liang, Xiao; Wang, Linshan; Wang, Yangfan; Wang, Ruili
2016-09-01
In this paper, we focus on the long time behavior of the mild solution to delayed reaction-diffusion Hopfield neural networks (DRDHNNs) driven by infinite dimensional Wiener processes. We analyze the existence, uniqueness, and stability of this system under the local Lipschitz function by constructing an appropriate Lyapunov-Krasovskii function and utilizing the semigroup theory. Some easy-to-test criteria affecting the well-posedness and stability of the networks, such as infinite dimensional noise and diffusion effect, are obtained. The criteria can be used as theoretic guidance to stabilize DRDHNNs in practical applications when infinite dimensional noise is taken into consideration. Meanwhile, considering the fact that the standard Brownian motion is a special case of infinite dimensional Wiener process, we undertake an analysis of the local Lipschitz condition, which has a wider range than the global Lipschitz condition. Two samples are given to examine the availability of the results in this paper. Simulations are also given using the MATLAB.
A Bayesian Framework for Reliability Assessment via Wiener Process and MCMC
Directory of Open Access Journals (Sweden)
Huibing Hao
2014-01-01
Full Text Available The population and individual reliability assessment are discussed, and a Bayesian framework is proposed to integrate the population degradation information and individual degradation data. Different from fixed effect Wiener process modeling, the population degradation path is characterized by a random effect Wiener process, and the model can capture sources of uncertainty including unit to unit variation and time correlated structure. Considering that the model is so complicated and analytically intractable, Markov Chain Monte Carlo (MCMC method is used to estimate the unknown parameters in the population model. To achieve individual reliability assessment, we exploit a Bayesian updating method, by which the unknown parameters are updated iteratively. Based on updated results, the residual use life and reliability evaluation are obtained. A lasers data example is given to demonstrate the usefulness and validity of the proposed model and method.
Kazemi, Mahdi; Arefi, Mohammad Mehdi
2016-12-15
In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used.
Solution of Stochastic Nonlinear PDEs Using Automated Wiener-Hermite Expansion
Al-Juhani, Amnah
2014-01-06
The solution of the stochastic differential equations (SDEs) using Wiener-Hermite expansion (WHE) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In WHE approach, there is no randomness directly involved in the computations. One does not have to rely on pseudo random number generators, and there is no need to solve the SDEs repeatedly for many realizations. Instead, the deterministic system is solved only once. For previous research efforts see [2, 4].
DEFF Research Database (Denmark)
Blurton, Steven Paul; Kesselmeier, M.; Gondan, Matthias
2012-01-01
related work on the density of first-passage times [Navarro, D.J., Fuss, I.G. (2009). Fast and accurate calculations for first-passage times in Wiener diffusion models. Journal of Mathematical Psychology, 53, 222-230]. Two representations exist for the distribution, both including infinite series. We......We propose an improved method for calculating the cumulative first-passage time distribution in Wiener diffusion models with two absorbing barriers. This distribution function is frequently used to describe responses and error probabilities in choice reaction time tasks. The present work extends...... derive upper bounds for the approximation error resulting from finite truncation of the series, and we determine the number of iterations required to limit the error below a pre-specified tolerance. For a given set of parameters, the representation can then be chosen which requires the least...
三维Wiener Sausage体积的中偏差%Moderate Deviations for the Volume of Three-Dimensional Wiener Sausage
Institute of Scientific and Technical Information of China (English)
王艳清
2011-01-01
Let ｛β(s), s ≥ 0｝ be the standard Brownian motion in R3 and let ｜Wr(t)｜ be the volume of the Wiener sausage associated with｛β(s), s ≥ 0｝ observed until time t. From the central limit theorem, we know that (｜Wr(t)｜ - E｜Wr(t)｜)(√tlogt) weakly converges to a normal distribution. In this paper, we study the corresponding moderate deviation.%令{β(s),s≥0}表示R3空间中的标准Brown运动,|Wτ(t)|表示由{β(s),s≥0}产生的观察至时间t且以r为半径的Wiener sausage的体积.由中心极限定理可知,(|Wr(t)|-E|Wr(t)|)/√tlogt弱收敛至正态分布.本文研究这种情况下的中偏差.
Song, Jae Hee; Kim, Choye; Yoo, Yangmo
2015-03-01
Effective vein visualization is clinically important for various point-of-care applications, such as needle insertion. It can be achieved by utilizing ultrasound imaging or by applying infrared laser excitation and monitoring its absorption. However, while these approaches can be used for vein visualization, they are not suitable for point-of-care applications because of their cost, time, and accessibility. In this paper, a new vein visualization method based on multispectral Wiener estimation is proposed and its real-time implementation on a smart phone is presented. In the proposed method, a conventional RGB camera on a commercial smart phone (i.e., Galaxy Note 2, Samsung Electronics Inc., Suwon, Korea) is used to acquire reflectance information from veins. Wiener estimation is then applied to extract the multispectral information from the veins. To evaluate the performance of the proposed method, an experiment was conducted using a color calibration chart (ColorChecker Classic, X-rite, Grand Rapids, MI, USA) and an average root-mean-square error of 12.0% was obtained. In addition, an in vivo subcutaneous vein imaging experiment was performed to explore the clinical performance of the smart phone-based Wiener estimation. From the in vivo experiment, the veins at various sites were successfully localized using the reconstructed multispectral images and these results were confirmed by ultrasound B-mode and color Doppler images. These results indicate that the presented multispectral Wiener estimation method can be used for visualizing veins using a commercial smart phone for point-of-care applications (e.g., vein puncture guidance).
Blanco Massani, M; Molina, V; Sanchez, M; Renaud, V; Eisenberg, P; Vignolo, G
2014-05-16
Bacteriocins from lactic acid bacteria have potential as natural food preservatives. In this study two active (synthetic and gluten) films were obtained by the incorporation of lactocin 705 and lactocin AL705, bacteriocins produced by Lactobacillus curvatus CRL705 with antimicrobial activity against spoilage lactic acid bacteria and Listeria. Antimicrobial film effectiveness was determined in Wieners inoculated with Lactobacillus plantarum CRL691 and Listeria innocua 7 (10(4)CFU/g) stored at 5°C during 45days. Active and control (absence of bacteriocins) packages were prepared and bacterial counts in selective media were carried out. Visual inspection and pH measurement of Wieners were also performed. Typical growth of both inoculated microorganisms was observed in control packages which reached 10(6)-10(7)CFU/g at the end of storage period. In the active packages, L. innocua 7 was effectively inhibited (2.5 log cycles reduction at day 45), while L. plantarum CRL691 was only slightly inhibited (0.5 log cycles) up to the second week of storage, then counts around 10(6)-10(7)CFU/g were reached. Changes in pH values from 6.3 to 5.8 were produced and gas formation was observed in active and control packages. The low inhibitory effectiveness against lactic acid bacteria is in correlation with the low activity observed for lactocin 705 in the presence of fat; Wieners fat content (20-30%) may adversely affect antimicrobial activity. This study supports the feasibility of using polymers activated with L. curvatus CRL705 bacteriocins to control Listeria on the surface of Wieners and highlights the importance of evaluating antimicrobial packaging systems for each particular food application.
A sharp lower bound for the Wiener index of a graph
Balakrishnan, R; Iyer, K V
2010-01-01
Given a simple connected undirected graph G, the Wiener index W(G) of G is defined as half the sum of the distances over all pairs of vertices of G. In practice, G corresponds to what is known as the molecular graph of an organic compound. We obtain a sharp lower bound for W(G) of an arbitrary graph in terms of the order, size and diameter of G.
Color Image Denoising Using Stationary Wavelet Transform and Adaptive Wiener Filter
Directory of Open Access Journals (Sweden)
Iman M.G. Alwan
2012-01-01
Full Text Available The denoising of a natural image corrupted by Gaussian noise is a problem in signal or image processing. Much work has been done in the field of wavelet thresholding but most of it was focused on statistical modeling of wavelet coefficients and the optimal choice of thresholds. This paper describes a new method for the suppression of noise in image by fusing the stationary wavelet denoising technique with adaptive wiener filter. The wiener filter is applied to the reconstructed image for the approximation coefficients only, while the thresholding technique is applied to the details coefficients of the transform, then get the final denoised image is obtained by combining the two results. The proposed method was applied by using MATLAB R2010a with color images contaminated by white Gaussian noise. Compared with stationary wavelet and wiener filter algorithms, the experimental results show that the proposed method provides better subjective and objective quality, and obtain up to 3.5 dB PSNR improvement.
Stochastic Chaos with Its Control and Synchronization
Institute of Scientific and Technical Information of China (English)
Zhang Ying; Xu Wei; Zhang Tianshu; Yang Xiaoli; Wu Cunli; Fang Tong
2008-01-01
The discovery of chaos in the sixties of last century was a breakthrough in concept,revealing the truth that some disorder behavior, called chaos, could happen even in a deterministic nonlinear system under barely deterministic disturbance. After a series of serious studies, people begin to acknowledge that chaos is a specific type of steady state motion other than the conventional periodic and quasi-periodic ones, featuring a sensitive dependence on initial conditions, resulting from the intrinsic randomness of a nonlinear system itself. In fact, chaos is a collective phenomenon consisting of massive individual chaotic responses, corresponding to different initial conditions in phase space. Any two adjacent individual chaotic responses repel each other, thus causing not only the sensitive dependence on initial conditions but also the existence of at least one positive top Lyapunov exponent (TLE) for chaos. Meanwhile, all the sample responses share one common invariant set on the Poincaré map, called chaotic attractor,which every sample response visits from time to time ergodically. So far, the existence of at least one positive TLE is a commonly acknowledged remarkable feature of chaos. We know that there are various forms of uncertainties in the real world. In theoretical studies, people often use stochastic models to describe these uncertainties, such as random variables or random processes.Systems with random variables as their parameters or with random processes as their excitations are often called stochastic systems. No doubt, chaotic phenomena also exist in stochastic systems, which we call stochastic chaos to distinguish it from deterministic chaos in the deterministic system. Stochastic chaos reflects not only the intrinsic randomness of the nonlinear system but also the external random effects of the random parameter or the random excitation.Hence, stochastic chaos is also a collective massive phenomenon, corresponding not only to different initial
Lambda and the edge of chaos in recurrent neural networks.
Seifter, Jared; Reggia, James A
2015-01-01
The idea that there is an edge of chaos, a region in the space of dynamical systems having special meaning for complex living entities, has a long history in artificial life. The significance of this region was first emphasized in cellular automata models when a single simple measure, λCA, identified it as a transitional region between order and chaos. Here we introduce a parameter λNN that is inspired by λCA but is defined for recurrent neural networks. We show through a series of systematic computational experiments that λNN generally orders the dynamical behaviors of randomly connected/weighted recurrent neural networks in the same way that λCA does for cellular automata. By extending this ordering to larger values of λNN than has typically been done with λCA and cellular automata, we find that a second edge-of-chaos region exists on the opposite side of the chaotic region. These basic results are found to hold under different assumptions about network connectivity, but vary substantially in their details. The results show that the basic concept underlying the lambda parameter can usefully be extended to other types of complex dynamical systems than just cellular automata.
Discretization chaos - Feedback control and transition to chaos
Grantham, Walter J.; Athalye, Amit M.
1990-01-01
Problems in the design of feedback controllers for chaotic dynamical systems are considered theoretically, focusing on two cases where chaos arises only when a nonchaotic continuous-time system is discretized into a simpler discrete-time systems (exponential discretization and pseudo-Euler integration applied to Lotka-Volterra competition and prey-predator systems). Numerical simulation results are presented in extensive graphs and discussed in detail. It is concluded that care must be taken in applying standard dynamical-systems methods to control systems that may be discontinuous or nondifferentiable.
Chaos in nonlinear oscillations controlling and synchronization
Lakshamanan, M
1996-01-01
This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.
Radio lighting based on dynamic chaos generators
Dmitriev, Alexander; Gerasimov, Mark; Itskov, Vadim
2016-01-01
A problem of lighting objects and surfaces with artificial sources of noncoherent microwave radiation with the aim to observe them using radiometric equipment is considered. Transmitters based on dynamic chaos generators are used as sources of noncoherent wideband microwave radiation. An experimental sample of such a device, i.e., a radio lighting lamp based on a chaos microgenerator and its performance are presented.
The CHAOS-4 geomagnetic field model
DEFF Research Database (Denmark)
Olsen, Nils; Lühr, H.; Finlay, Chris;
2014-01-01
We present CHAOS-4, a new version in the CHAOS model series, which aims to describe the Earth's magnetic field with high spatial and temporal resolution. Terms up to spherical degree of at least n = 85 for the lithospheric field, and up to n = 16 for the time-varying core field are robustly deter...
"Chaos" Theory: Implications for Educational Research.
Lindsay, Jean S.
"Chaos" theory is a revolutionary new paradigm developed by scientists to study the behavior of natural systems. "Chaos" refers to the tendency of dynamic non-linear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Major tenets of the theory are presented. The precedent for use of models developed in the natural…
The CHAOS-4 Geomagnetic Field Model
DEFF Research Database (Denmark)
Olsen, Nils; Finlay, Chris; Lühr, H.
We present CHAOS-4, a new version in the CHAOS model series, which aims at describing the Earth's magnetic field with high spatial resolution (terms up to spherical degree n=90 for the crustal field, and up to n=16 for the time-varying core field are robustly determined) and high temporal resolut...
Weak chaos in the asymmetric heavy top
Barrientos, M; Ranada, A F
1995-01-01
We consider the dynamics of the slightly asymmetric heavy top, a non-integrable system obtained from the Lagrange top by breaking the symmetry of its inertia tensor. It shows signs of weak chaos, which we study numerically. We argue that it is a good example for introducing students to non-integrability and chaos. (author)
PHASE CHAOS IN THE DISCRETE KURAMOTO MODEL
DEFF Research Database (Denmark)
Maistrenko, V.; Vasylenko, A.; Maistrenko, Y.;
2010-01-01
The paper describes the appearance of a novel, high-dimensional chaotic regime, called phase chaos, in a time-discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It arises from the nonlinear inter...
SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos
Ahlfeld, R.; Belkouchi, B.; Montomoli, F.
2016-09-01
A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10
4th international interdisciplinary chaos symposium
Banerjee, Santo; Caglar, Suleyman; Ozer, Mehmet; Chaos and complex systems
2013-01-01
Complexity Science and Chaos Theory are fascinating areas of scientific research with wide-ranging applications. The interdisciplinary nature and ubiquity of complexity and chaos are features that provides scientists with a motivation to pursue general theoretical tools and frameworks. Complex systems give rise to emergent behaviors, which in turn produce novel and interesting phenomena in science, engineering, as well as in the socio-economic sciences. The aim of all Symposia on Chaos and Complex Systems (CCS) is to bring together scientists, engineers, economists and social scientists, and to discuss the latest insights and results obtained in the area of corresponding nonlinear-system complex (chaotic) behavior. Especially for the “4th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems,” which took place April 29th to May 2nd, 2012 in Antalya, Turkey, the scope of the symposium had been further enlarged so as to encompass the presentation of work from circuits to econophysic...
Chaos the science of predictable random motion
Kautz, Richard
2011-01-01
Based on only elementary mathematics, this engaging account of chaos theory bridges the gap between introductions for the layman and college-level texts. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle, the mathematical monster at the heart of chaos. The presentation is enhanced by many figures, animations of chaotic motion (available on a companion CD), and biographical sketches of the pioneers of dynamics and chaos theory. To ensure accessibility to motivated high school students, care has been taken to explain advanced mathematical concepts simply, including exponentials and logarithms, probability, correlation, frequency analysis, fractals, and transfinite numbers. These tools help to resolve the intriguing paradox of motion that is predictable and yet random, while the final chapter explores the various ways chaos theory has been put to practical use.
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2013-01-01
This third edition of “Semiconductor Lasers, Stability, Instability and Chaos” was significantly extended. In the previous edition, the dynamics and characteristics of chaos in semiconductor lasers after the introduction of the fundamental theory of laser chaos and chaotic dynamics induced by self-optical feedback and optical injection was discussed. Semiconductor lasers with new device structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are interesting devices from the viewpoint of chaotic dynamics since they essentially involve chaotic dynamics even in their free-running oscillations. These topics are also treated with respect to the new developments in the current edition. Also the control of such instabilities and chaos control are critical issues for applications. Another interesting and important issue of semiconductor laser chaos in this third edition is chaos synchronization between two lasers and the application to optical secure communication. One o...
0-1 Test for Chaos in a Fractional Order Financial System with Investment Incentive
Directory of Open Access Journals (Sweden)
Baogui Xin
2013-01-01
weighted integral thought, the fractional order derivative's economics meaning is given. The 0-1 test algorithm and the improved Adams-Bashforth-Moulton predictor-corrector scheme are employed to detect numerically the chaos in the proposed fractional order financial system.
Prediction based chaos control via a new neural network
Energy Technology Data Exchange (ETDEWEB)
Shen Liqun [School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001 (China)], E-mail: liqunshen@gmail.com; Wang Mao [Space Control and Inertia Technology Research Center, Harbin Institute of Technology, Harbin 150001 (China); Liu Wanyu [School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001 (China); Sun Guanghui [Space Control and Inertia Technology Research Center, Harbin Institute of Technology, Harbin 150001 (China)
2008-11-17
In this Letter, a new chaos control scheme based on chaos prediction is proposed. To perform chaos prediction, a new neural network architecture for complex nonlinear approximation is proposed. And the difficulty in building and training the neural network is also reduced. Simulation results of Logistic map and Lorenz system show the effectiveness of the proposed chaos control scheme and the proposed neural network.
Critical states of transient chaos
Kaufmann, Z; Szépfalusy, P
1999-01-01
One-dimensional maps exhibiting transient chaos and defined on two preimages of the unit interval [0,1] are investigated. It is shown that such maps have continuously many conditionally invariant measures $\\mu_{\\sigma}$ scaling at the fixed point at $x=0$ as $x^{\\sigma}$, but smooth elsewhere. Here $\\sigma$ should be smaller than a critical value $\\sigma_{c}$ that is related to the spectral properties of the Frobenius-Perron operator. The corresponding natural measures are proven to be entirely concentrated on the fixed point.
A. Fitzpatrick; Kaplan, Jared
2016-01-01
We use results on Virasoro conformal blocks to study chaotic dynamics in CFT 2 at large central charge c . The Lyapunov exponent λ L , which is a diagnostic for the early onset of chaos, receives 1 /c corrections that may be interpreted as λ L = 2 π β 1 + 12 c $$ {\\lambda}_L=\\frac{2\\pi }{\\beta}\\left(1+\\frac{12}{c}\\right) $$ . However, out of time order correlators receive other equally important 1 /c suppressed contributions that do not have such a simple interpretation. We revisit the proof ...
Energy Technology Data Exchange (ETDEWEB)
Bunimovich, Leonid A., E-mail: bunimovh@math.gatech.edu [ABC Program, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Vela-Arevalo, Luz V., E-mail: luzvela@math.gatech.edu [School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)
2015-09-15
A brief review is presented of some recent findings in the theory of chaotic dynamics. We also prove a statement that could be naturally considered as a dual one to the Poincaré theorem on recurrences. Numerical results demonstrate that some parts of the phase space of chaotic systems are more likely to be visited earlier than other parts. A new class of chaotic focusing billiards is discussed that clearly violates the main condition considered to be necessary for chaos in focusing billiards.
Chaos control in duffing system
Energy Technology Data Exchange (ETDEWEB)
Wang Ruiqi [Department of Electrical Engineering and Electronics, Osaka Sangyo University, Nakagaito 3-1-1, Daito, Osaka 574-8530 (Japan); Deng Jin [Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080 (China); Graduate School of the Chinese Academy of Sciences, Beijing 100039 (China); Jing Zhujun [Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080 (China); Department of Mathematics, Hunan Normal University, Hunan, Changsha 410081 (China); E-mail: jingzj@math.ac.cn
2006-01-01
Analytical and numerical results concerning the inhibition of chaos in Duffing's equation with two weak forcing excitations are presented. We theoretically give parameter-space regions by using Melnikov's function, where chaotic states can be suppressed. The intervals of initial phase difference between the two excitations for which chaotic dynamics can be eliminated are given. Meanwhile, the influence of the phase difference on Lyapunov exponents for different frequencies is investigated. Numerical simulation results show the consistence with the theoretical analysis and the chaotic motions can be controlled to period-motions by adjusting parameter of suppressing excitation.
Institute of Scientific and Technical Information of China (English)
2001-01-01
In this work, we proposed the wavelet-based feedback controller is as follows: G = -g{fab(rrms)-fab(am)} (1)where the master wavelet function is in a simplified form(2)where a and b are scaling and translation constants, respectively. C is a selected constant. The main reason of using wavelet function for controller design is that it has strong nonlinearity and excellent localization property. It turns out that for halo-chaos control purpose, the translation b can be very small, so for simplicity one may let b = 0 . Our goal of control is rms→am, in this
The Effect of Bands and Ridges on Chaos Formation on Europa
Everett Hedgepeth, Joshua; Schmidt, Britney E.
2016-10-01
Europa presents a dynamic and varied surface, but the most enticing component is arguably its chaos structures. With it, the surface and subsurface can interact, but in order to fully understand if this is occurring we have to properly parameterize the surface structural integrity. We consider the Schmidt et al. (2011) method of classifying icebergs by feature type to study what features remained intact in the chaos matrix. In this work we expand on this idea. We hypothesize that ridges and bands exhibit higher structural strengths than plains. Subsequently, less of the stronger band or ridge material is destroyed during chaos formation than plains material, leaving behind large blocks of ice (i.e. icebergs) comprised mainly of ridges and bands, with matrix formed predominantly from plains materials. We begin by mapping the surface at and near Murias chaos including surrounding chaos regions. Maps are used to infer what paleo-topographic features existed before each chaos formed. We perform a multivariate regression to correlate the amount of icebergs present to the amount of surface that was covered by either bands, plains, or ridges. We find ridges play the biggest role in the production of icebergs with a weighted value of 40%. Bands may play a smaller role (13%), but plains show little to no correlation (5%). Further mapping will better reveal if this trend holds true in other regions. This statistical analysis supports our hypothesis, and further work will better quantify what is occurring. We will address the energy expended in the chaos regions via movement and rotation of icebergs during the formation event and through ice-melt.
An Experimental Investigation of Secure Communication With Chaos Masking
Dhar, Sourav
2007-01-01
The most exciting recent development in nonlinear dynamics is realization that chaos can be useful. One application involves "Secure Communication". Two piecewise linear systems with switching nonlinearities have been taken as chaos generators. In the present work the phenomenon of secure communication with chaos masking has been investigated experimentally. In this investigation chaos which is generated from two chaos generators is masked with the massage signal to be transmitted, thus makes communication is more secure.
Markov transitions and the propagation of chaos
Energy Technology Data Exchange (ETDEWEB)
Gottlieb, Alexander David [Univ. of California, Berkeley, CA (United States)
1998-12-01
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also s how that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution.
Simulation of stochastic systems via polynomial chaos expansions and convex optimization
Fagiano, Lorenzo
2012-01-01
Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model, or the computation of large numbers of simulation runs, rendering the approach too time consuming and impracticable for applications with more than a handful of random variables. We introduce a novel computationally tractable technique for computing the coefficients of polynomial chaos expansions. The approach exploits a regularization technique with a particular choice of weighting matrices, which allow to take into account the specific features of Polynomial Chaos expansions. The method, completely based on convex optimization, can be applied to problems with a large number of random variables and uses a modest number of Monte Carlo simulations, while avoiding model manipulations. Additional information on the stochastic process, when available, can be also incorporated i...
Towards CHAOS-5 - How can Swarm contribute?
DEFF Research Database (Denmark)
Finlay, Chris; Olsen, Nils; Tøffner-Clausen, Lars
2014-01-01
The launch of ESA's satellite trio Swarm in November 2013 opens an exciting new chapter in the observation and monitoring of Earth's magnetic field from space. We report preliminary results from an extension of the CHAOS series of geomagnetic field models to include both scalar and vector field...... observations from the three Swarm satellites, along with the most recent quasi-definitive ground observatory data. The fit of this new update CHAOS field model to the Swarm observations will be presented in detail providing useful insight the initial Swarm data. Enhancements of the CHAOS modelling scheme...
Chaos from simple models to complex systems
Cencini, Massimo; Vulpiani, Angelo
2010-01-01
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theor
Physics and Applications of Laser Diode Chaos
Sciamanna, Marc
2015-01-01
An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.
Chaos dynamic characteristics during mine fires
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Mine fires break out and continue in confmed scopes, studying mine fire dynamics characteristics is very usefulto prevent and control fire. The judgement index of fire chaos characteristics was introduced, chaos analysis of mine Fireprocess was described, and the reconstruction of phase space was also presented. An example of mine fire was calculated.The computations show that it is feasible to analyze mine fire dynamic characteristics with chaos theory, and indicate thatfire preoeas is a catastrophe, that is to say, the fire system changes from one state to another during mine fire
Chua's circuit a paradigm for chaos
1993-01-01
For uninitiated researchers, engineers, and scientists interested in a quick entry into the subject of chaos, this book offers a timely collection of 55 carefully selected papers covering almost every aspect of this subject. Because Chua's circuit is endowed with virtually every bifurcation phenomena reported in the extensive literature on chaos, and because it is the only chaotic system which can be easily built by a novice, simulated in a personal computer, and tractable mathematically, it has become a paradigm for chaos, and a vehicle for illustrating this ubiquitous phenomenon. Its supreme
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2008-01-01
This monograph describes fascinating recent progress in the field of chaos, stability and instability of semiconductor lasers. Applications and future prospects are discussed in detail. The book emphasizes the various dynamics induced in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Recent results of both theoretical and experimental investigations are presented. Demonstrating applications of semiconductor laser chaos, control and noise, Semiconductor Lasers describes suppression and chaotic secure communications. For those who are interested in optics but not familiar with nonlinear systems, a brief introduction to chaos analysis is presented.
Design of RLS Wiener Fixed-Lag Smoother in Linear Discrete-Time Stochastic Systems
2015-01-01
This paper newly presents the recursive least-squares (RLS) fixed-lag smoother using the covariance information and then the RLS Wiener fixed-lag smoother in linear discrete-time wide-sense stationary stochastic systems. Here, the additional disturbance in the measurement of the signal is white noise. The signal is uncorrelated with observed noise. It is assumed that the signal process is fitted to the autoregressive (AR) model of order NN. For this AR model of order NN, in the proposed fixed...
ℋ∞ constant gain state feedback stabilization of stochastic hybrid systems with Wiener process
Directory of Open Access Journals (Sweden)
E. K. Boukas
2004-01-01
Full Text Available This paper considers the stabilization problem of the class of continuous-time linear stochastic hybrid systems with Wiener process. The ℋ∞ state feedback stabilization problem is treated. A state feedback controller with constant gain that does not require access to the system mode is designed. LMI-based conditions are developed to design the state feedback controller with constant gain that stochastically stabilizes the studied class of systems and, at the same time, achieve the disturbance rejection of a desired level. The minimum disturbance rejection is also determined. Numerical examples are given to show the usefulness of the proposed results.
Las huellas del plan para Bogotá de le Corbusier, Sert y Wiener
2010-01-01
This essay is the basis for a thesis, according to which an urban transcendent planning tool belonging to the functional ideology of the Modern Movement may be acknowledged as being of prime importance. The theme is the Plan for Bogotá, elaborated in several phases by Le Corbusier and Josep Lluís Sert & Paul Lester Wiener between 1949 and 1963, This is a work which has been very sparsely mentioned in international historiography of architecture and/or urban planning, and has ge...
THE RECOVERY OF FUNCTIONS OF PALEY-WIENER CLASS FROM IRREGULAR SAMPLINGS
Institute of Scientific and Technical Information of China (English)
房艮孙; 陈雪冬
2002-01-01
It is shown that a function f which is in the classical Paley-Wiener class,and its k-th derivative f(k) can be recovered in the metric Lq(R),2＜ q ≤∞, from its values on irregularly distributed discrete sampling set {ti}j ∈zas limits of polynomial spline interpolation when the order of the splines goes to infinity, where {ti}j∈z is a real sequence such that {eitj∈}j∈z constitutes a Riesz basis for L2([-π, π]).
Novel application of Wiener vis-à-vis Szeged indices: Antitubercular activities of quinolones
Indian Academy of Sciences (India)
Vijay K Agarwal; Shahnaz Bano; Keshav C Mathur; Padmakar V Khadikar
2000-04-01
The paper gives a brief account of the recently introduced Szeged index (Sz). Using this index antitubercular activities of N-2,4-difluorophenyl quinolones are subjected to quantitative structure-activity relationship analysis. The potential of Sz related to the Wiener index (W) is critically discussed. In addition, Huckel molecular orbital energies: HOMO, LUMO and total were also used for comparing and modelling antitubercular activities of the quinolones. The results, based on univariate as well as multivariate regressions, have shown that W, Sz and total give better results and that the correlations improve in multivariate regression analyses.
NAČRTOVANJE KARIERNIH POTI V ZAVAROVALNICI WIENER STADTISCHE D.D.
Arko, Anja
2012-01-01
Diplomska naloga obravnava pomen razvoja posameznikove kariere v sklopu organizacije, ki je v našem primeru zavarovalnica Wiener Stadtische. Načrtovanje kariere zaposlenih ter trenutno stanje organizacije je predstavljeno z vidika izobraževanja, komuniciranja med zaposlenimi in nadrejenimi, z vidika stopnje motiviranosti, ki jo imajo zavarovalni zastopniki za boljše in produktivnejše opravljanje svojega dela. Poleg vsega naštetega pa so pomembni tudi različni načini planiranja, saj lahko z nj...
Approximation methods for a class of discrete Wiener-Hopf equations
Directory of Open Access Journals (Sweden)
Michał A. Nowak
2009-01-01
Full Text Available In this paper, we consider approximation methods for operator equations of the form \\[Au + Bu = f,\\] where \\(A\\ is a discrete Wiener-Hopf operator on \\(l_p\\ (\\(1 \\leq p \\lt \\infty\\ which symbol has roots on the unit circle with arbitrary multiplicities (not necessary integers. Conditions on perturbation \\(B\\ and \\(f\\ are given in order to guarantee the applicability of projection-iterative methods. Effective error estimates, and simultaneously, decaying properties for solutions are obtained in terms of some smooth spaces.
Monaural separation of dependent audio sources based on a generalized Wiener filter
DEFF Research Database (Denmark)
Ma, Guilin; Agerkvist, Finn T.; Luther, J.B.
2007-01-01
) coefficients of the dependent sources is modeled by complex Gaussian mixture models in the frequency domain from samples of individual sources to capture the properties of the sources and their correlation. During the second stage, the mixture is separated through a generalized Wiener filter, which takes......This paper presents a two-stage approach for single- channel separation of dependent audio sources. The proposed algorithm is developed in the Bayesian framework and designed for general audio signals. In the first stage of the algorithm, the joint distribution of discrete Fourier transform (DFT...
IMAGE DE-BLURRING USING WIENER DE-CONVOLUTION AND WAVELET FOR DIFFERENT BLURRING KERNEL
M.Tech Research Scholar Shuchi Singh*, Asst Professor Vipul Awasthi, Asst Professor NitinSahu
2016-01-01
Image de-convolution is an active research area of recovering a sharp image after blurring by a convolution. One of the problems in image de-convolution is how to preserve the texture structures while removing blur in presence of noise. Various methods have been used for such as gradient based methods, sparsity based methods, and nonlocal self-similarity methods. In this thesis, we have used the conventional non-blind method of Wiener de-convolution. Further Wavelet denoising has been used to...
Capacity of Discrete-Time Wiener Phase Noise Channels to Within a Constant Gap
Barletta, Luca; Rini, Stefano
2017-01-01
The capacity of the discrete-time channel affected by both additive Gaussian noise and Wiener phase noise is studied. Novel inner and outer bounds are presented, which differ of at most $6.65$ bits per channel use for all channel parameters. The capacity of this model can be subdivided in three regimes: (i) for large values of the frequency noise variance, the channel behaves similarly to a channel with circularly uniform iid phase noise; (ii) when the frequency noise variance is small, the e...
On the asymptotic internal path length and the asymptotic Wiener index of random split trees
Munsonius, G O
2011-01-01
The random split tree introduced by Devroye (1999) is considered. We derive a second order expansion for the mean of its internal path length and furthermore obtain a limit law by the contraction method. As an assumption we need the splitter having a Lebesgue density and mass in every neighborhood of 1. We use properly stopped homogeneous Markov chains, for which limit results in total variation distance as well as renewal theory are used. Furthermore, we extend this method to obtain the corresponding results for the Wiener index.
Chaos concepts, control and constructive use
Bolotin, Yurii; Yanovsky, Vladimir
2017-01-01
This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interf...
Semiconductor lasers stability, instability and chaos
Ohtsubo, Junji
2017-01-01
This book describes the fascinating recent advances made concerning the chaos, stability and instability of semiconductor lasers, and discusses their applications and future prospects in detail. It emphasizes the dynamics in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Applications of semiconductor laser chaos, control and noise, and semiconductor lasers are also demonstrated. Semiconductor lasers with new structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are intriguing and promising devices. Current topics include fast physical number generation using chaotic semiconductor lasers for secure communication, development of chaos, quantum-dot semiconductor lasers and quantum-cascade semiconductor lasers, and vertical-cavity surface-emitting lasers. This fourth edition has been significantly expanded to reflect the latest developments. The fundamental theory of laser chaos and the chaotic dynamics in se...
Superfluid (quantum) turbulence and distributed chaos
Bershadskii, A
2016-01-01
Properties of distributed chaos in superfluid (quantum) turbulence have been studied using the data of recent direct numerical simulations (HVBK two-fluid model for He II, and a moving grid in the frames of Gross-Pitaevskii model of the Bose-Einstein condensates at low temperatures). It is found that for the viscous (normal) component of the velocity field in He II the viscosity dominates the distributed chaos with the stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$ and $\\beta = 2/3$. For the superfluid component the distributed chaos is dominated by the vorticity correlation integral with $\\beta =1/2$ (the soft spontaneous breaking of the space translational symmetry - homogeneity). For very low temperature the distributed chaos is tuned to the large-scale coherent motions: the viscous (normal) component is tuned to the fundamental mode, whereas the superfluid component is subharmonically tuned. For the Gross-Pitaevskii superfluid turbulence incompressible part of the energy spectrum (containing ...
The danger of wishing for chaos.
McSharry, Patrick
2005-10-01
With the discovery of chaos came the hope of finding simple models that would be capable of explaining complex phenomena. Numerous papers claimed to find low-dimensional chaos in a number of areas ranging from the weather to the stock market. Years later, many of these claims have been disproved and the fantastic hopes pinned on chaos have been toned down as research with more realistic objectives follows. The difficulty in calculating reliable estimates of the correlation dimension and the maximal Lyapunov exponent, two of the hallmarks of chaos, are explored. Given that nonlinear dynamics is a relatively new and growing field of science, the need for statistical testing is greater than ever. Surrogate data provides one possible approach but great care is needed in generating relevant surrogates and in interpreting the results. Examples of misleading applications and challenges for the future of research in nonlinear dynamics are discussed.
Optimized chaos control with simple limiters.
Wagner, C; Stoop, R
2001-01-01
We present an elementary derivation of chaos control with simple limiters using the logistic map and the Henon map as examples. This derivation provides conditions for optimal stabilization of unstable periodic orbits of a chaotic attractor.
A simple method of chaos control
Shahverdiev, E M
1998-01-01
A simple method to perform chaos control without the need of complex numerical and analytical calculations is proposed. The method works for dynamical systems with bounded solutions and in the trivial case of constant Jacobians.
Relation of Origins of Primitive Chaos
Ogasawara, Yoshihito
2014-01-01
A new concept, primitive chaos, was proposed, as a concept closely related to the fundamental problems of sciences themselves such as determinism, causality, free will, predictability, and time asymmetry [{\\em J. Phys. Soc. Jpn.} {\\bf 2014}, {\\em 83}, 1401]. This concept is literally a primitive chaos in such a sense that it leads to the characteristic properties of the conventional chaos under natural conditions. Then, two contrast concepts, nondegenerate Peano continuum and Cantor set, are known as the origins of the primitive chaos. In this study, the relation of these origins is investigated with the aid of a mathematical method, topology. Then, we can see the emergence of interesting concepts such as the relation of whole and part, and coarse graining, which imply the essence of our intrinsic recognition for phenomena.
Sándor, Bulcsú; Tél, Tamás; Néda, Zoltán
2013-01-01
The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by spring to an external static point, and due to the dragging effect of the belt the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can only be achieved by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic dynamics and phase transition-like behavior. Noise induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks, around five.
Chaos, Fractals and Their Applications
Thompson, J. Michael T.
2016-12-01
This paper gives an up-to-date account of chaos and fractals, in a popular pictorial style for the general scientific reader. A brief historical account covers the development of the subject from Newton’s laws of motion to the astronomy of Poincaré and the weather forecasting of Lorenz. Emphasis is given to the important underlying concepts, embracing the fractal properties of coastlines and the logistics of population dynamics. A wide variety of applications include: NASA’s discovery and use of zero-fuel chaotic “superhighways” between the planets; erratic chaotic solutions generated by Euler’s method in mathematics; atomic force microscopy; spontaneous pattern formation in chemical and biological systems; impact mechanics in offshore engineering and the chatter of cutting tools; controlling chaotic heartbeats. Reference is made to a number of interactive simulations and movies accessible on the web.
Detecting chaos from time series
Xiaofeng, Gong; Lai, C. H.
2000-02-01
In this paper, an entirely data-based method to detect chaos from the time series is developed by introducing icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> p -neighbour points (the p -steps icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> -neighbour points). We demonstrate that for deterministic chaotic systems, there exists a linear relationship between the logarithm of the average number of icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> p -neighbour points, lnn p ,icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> , and the time step, p . The coefficient can be related to the KS entropy of the system. The effects of the embedding dimension and noise are also discussed.
Compressive Sensing with Optical Chaos
Rontani, D.; Choi, D.; Chang, C.-Y.; Locquet, A.; Citrin, D. S.
2016-12-01
Compressive sensing (CS) is a technique to sample a sparse signal below the Nyquist-Shannon limit, yet still enabling its reconstruction. As such, CS permits an extremely parsimonious way to store and transmit large and important classes of signals and images that would be far more data intensive should they be sampled following the prescription of the Nyquist-Shannon theorem. CS has found applications as diverse as seismology and biomedical imaging. In this work, we use actual optical signals generated from temporal intensity chaos from external-cavity semiconductor lasers (ECSL) to construct the sensing matrix that is employed to compress a sparse signal. The chaotic time series produced having their relevant dynamics on the 100 ps timescale, our results open the way to ultrahigh-speed compression of sparse signals.
Ergodic theory, randomness, and "chaos".
Ornstein, D S
1989-01-13
Ergodic theory is the theory of the long-term statistical behavior of dynamical systems. The baker's transformation is an object of ergodic theory that provides a paradigm for the possibility of deterministic chaos. It can now be shown that this connection is more than an analogy and that at some level of abstraction a large number of systems governed by Newton's laws are the same as the baker's transformation. Going to this level of abstraction helps to organize the possible kinds of random behavior. The theory also gives new concrete results. For example, one can show that the same process could be produced by a mechanism governed by Newton's laws or by a mechanism governed by coin tossing. It also gives a statistical analog of structural stability.
Control of collective network chaos
Energy Technology Data Exchange (ETDEWEB)
Wagemakers, Alexandre, E-mail: alexandre.wagemakers@urjc.es; Sanjuán, Miguel A. F., E-mail: miguel.sanjuan@urjc.es [Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid (Spain); Barreto, Ernest, E-mail: ebarreto@gmu.edu; So, Paul, E-mail: paso@gmu.edu [School of Physics, Astronomy, and Computational Sciences and The Krasnow Institute for Advanced Study, George Mason University, Fairfax, Virginia 22030 (United States)
2014-06-01
Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of “reduced” ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity.
Control of collective network chaos
Wagemakers, Alexandre; Barreto, Ernest; Sanjuán, Miguel A. F.; So, Paul
2014-06-01
Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of "reduced" ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity.
Mano, Omer; Clark, Damon A
2017-01-01
Sensory neuroscience seeks to understand and predict how sensory neurons respond to stimuli. Nonlinear components of neural responses are frequently characterized by the second-order Wiener kernel and the closely-related spike-triggered covariance (STC). Recent advances in data acquisition have made it increasingly common and computationally intensive to compute second-order Wiener kernels/STC matrices. In order to speed up this sort of analysis, we developed a graphics processing unit (GPU)-accelerated module that computes the second-order Wiener kernel of a system's response to a stimulus. The generated kernel can be easily transformed for use in standard STC analyses. Our code speeds up such analyses by factors of over 100 relative to current methods that utilize central processing units (CPUs). It works on any modern GPU and may be integrated into many data analysis workflows. This module accelerates data analysis so that more time can be spent exploring parameter space and interpreting data.
A watermarking algorithm satisfying topological chaos properties
Bahi, Jacques M
2008-01-01
A new watermarking algorithm is given, it is based on the so-called chaotic iterations and on the choice of some coefficients which are deduced from the description of the carrier medium. After defining these coefficients, chaotic discrete iterations are used to encrypt the watermark and to embed it in the carrier medium. This procedure generates a topological chaos and ensures that the required properties of a watermarking algorithm are satisfied. Key-words: Watermarking, Encryption, Chaotic iterations, Topological chaos, Information hiding
Detecting nonlinearity and chaos in epidemic data
Energy Technology Data Exchange (ETDEWEB)
Ellner, S.; Gallant, A.R. [North Carolina State Univ., Raleigh, NC (United States). Dept. of Statistics; Theiler, J. [Santa Fe Inst., NM (United States)]|[Los Alamos National Lab., NM (United States)
1993-08-01
Historical data on recurrent epidemics have been central to the debate about the prevalence of chaos in biological population dynamics. Schaffer and Kot who first recognized that the abundance and accuracy of disease incidence data opened the door to applying a range of methods for detecting chaos that had been devised in the early 1980`s. Using attractor reconstruction, estimates of dynamical invariants, and comparisons between data and simulation of SEIR models, the ``case for chaos in childhood epidemics`` was made through a series of influential papers beginning in the mid 1980`s. The proposition that the precise timing and magnitude of epidemic outbreaks are deterministic but chaotic is appealing, since it raises the hope of finding determinism and simplicity beneath the apparently stochastic and complicated surface of the data. The initial enthusiasm for methods of detecting chaos in data has been followed by critical re-evaluations of their limitations. Early hopes of a ``one size fits all`` algorithm to diagnose chaos vs. noise in any data set have given way to a recognition that a variety of methods must be used, and interpretation of results must take into account the limitations of each method and the imperfections of the data. Our goals here are to outline some newer methods for detecting nonlinearity and chaos that have a solid statistical basis and are suited to epidemic data, and to begin a re-evaluation of the claims for nonlinear dynamics and chaos in epidemics using these newer methods. We also identify features of epidemic data that create problems for the older, better known methods of detecting chaos. When we ask ``are epidemics nonlinear?``, we are not questioning the existence of global nonlinearities in epidemic dynamics, such as nonlinear transmission rates. Our question is whether the data`s deviations from an annual cyclic trend (which would reflect global nonlinearities) are described by a linear, noise-driven stochastic process.
Thiel, Marco; Kurths, Jürgen; Romano, M. Carmen; Moura, Alessandro; Károlyi, György
In the celebratory dinner honouring Celso Grebogi's 60th birthday, a number of scientists in the area of chaos were asked by James Yorke to tell the tale about how they got involved in the field. Since all the participants have played crucial roles in the development of the subject, their stories give unique insights into the historical development of dynamical systems and chaos. We have transcribed their tales here.
Topologically Induced Chaos in the Open Universe
Tomaschitz, R
1994-01-01
An elementary account on chaos, its origins, and its physical impact in an infinite and multiply connected space-time is given. The anisotropy of the microwave background and the violation of the space-reflection symmetry (parity) by topological self-interference are reviewed in this context. Keywords: Robertson-Walker cosmology, relativistic chaos, chaotic nucleus, center of the Universe, CP violation, self-interference, background radiation, anisotropy, particle creation, hyperbolic manifold, deformation space, topology change, Kleinian group, limit set, mixing, shadowing.
Terminal chaos for information processing in neurodynamics.
Zak, M
1991-01-01
New nonlinear phenomenon-terminal chaos caused by failure of the Lipschitz condition at equilibrium points of dynamical systems is introduced. It is shown that terminal chaos has a well organized probabilistic structure which can be predicted and controlled. This gives an opportunity to exploit this phenomenon for information processing. It appears that chaotic states of neurons activity are associated with higher level of cognitive processes such as generalization and abstraction.
Chaos control using sliding-mode theory
Energy Technology Data Exchange (ETDEWEB)
Nazzal, Jamal M. [Faculty of Engineering, Al-Ahliyya Amman University, Post Code 19328 Amman (Jordan)]. E-mail: jnazzal@ammanu.edu.jo; Natsheh, Ammar N. [Faculty of Engineering, Al-Ahliyya Amman University, Post Code 19328 Amman (Jordan)
2007-07-15
Chaos control means to design a controller that is able to mitigating or eliminating the chaos behavior of nonlinear systems that experiencing such phenomenon. In this paper, a nonlinear Sliding-Mode Controller (SMC) is presented. Two nonlinear chaotic systems are chosen to be our case study in this paper, the well known Chua's circuit and Lorenz system. The study shows the effectiveness of the designed nonlinear Sliding-Mode Controller.
Chaos control in traffic flow models
Shahverdiev, E M; Shahverdiev, Elman Mohammed; Tadaki, Shin-ichi
1998-01-01
Chaos control in some of the one- and two-dimensional traffic flow dynamical models in the mean field theory is studied.One dimensional model is investigated taking into account the effect of random delay. Two dimensional model takes into account the effects of overpasses, symmetric distribution of cars and blockages of cars moving in the same direction. Chaos synchronization is performed within both replica and nonreplica approaches, and using parameter perturbation method.
The average errors for Hermite-Fejr interpolation on the Wiener space
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
For 1≤ p < ∞, firstly we prove that for an arbitrary set of distinct nodes in [-1, 1], it is impossible that the errors of the Hermite-Fejr interpolation approximation in L p -norm are weakly equivalent to the corresponding errors of the best polynomial approximation for all continuous functions on [-1, 1]. Secondly, on the ground of probability theory, we discuss the p-average errors of Hermite-Fejr interpolation sequence based on the extended Chebyshev nodes of the second kind on the Wiener space. By our results we know that for 1≤ p < ∞ and 2≤ q < ∞, the p-average errors of Hermite-Fejr interpolation approximation sequence based on the extended Chebyshev nodes of the second kind are weakly equivalent to the p-average errors of the corresponding best polynomial approximation sequence for L q -norm approximation. In comparison with these results, we discuss the p-average errors of Hermite-Fejr interpolation approximation sequence based on the Chebyshev nodes of the second kind and the p-average errors of the well-known Bernstein polynomial approximation sequence on the Wiener space.
Kudryavtsev, Oleg
2013-01-01
In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation. The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps. The method is applicable for pricing barrier and American options. The pricing problem is reduced to the sequence of linear algebraic systems with a dense Toeplitz matrix; then the Wiener-Hopf factorization method is applied. We give an important probabilistic interpretation based on the infinitely divisible distributions theory to the Laurent operators in the correspondent factorization identity. Notice that our algorithm has the same complexity as the ones which use the explicit-implicit scheme, with a tridiagonal matrix. However, our method is more accurate. We support the advantage of the new method in terms of accuracy and convergence by using numerical experiments.
Curvelet Domain Empirical Wiener Filter%曲波域经验Wiener滤波
Institute of Scientific and Technical Information of China (English)
李伟; 杨航
2013-01-01
利用全变差(TV)估计,设计一种曲波域Wiener滤波,提出一种新的基于曲波的图像去噪算法.该算法结合了曲波的优点和TV模型对图像边界的保持能力:TV模型用来设计经验Wiener滤波,在曲波域实现应用.数值实验表明,该方法比曲波收缩和基于TV模型的方法效果更好.%The purpose of this letter is to develop a new curvelet denoising algorithm for denoising images corrupted with additive white Gaussian noise (AWGN). We used a total variation (TV) estimate as means to design a curvelet-domain Wiener filter. The TV estimate indirectly yields the estimate of the image that is leveraged into the design of the filter. A peculiar aspect of this method is its use of TV and curvelet base, i. e. , the TV for the design of the empirical Wiener filter and curvlet base for its application. Numerical examples demonstrate that our method can perform better than curvelet shrinkage and TV-based method. Curvelets have been mathematically proven to represent distributed discontinuities such as edges better than traditional wavelets.
Improvement for Speech Signal based on Post Wiener Filter and Adjustable Beam-Former
Directory of Open Access Journals (Sweden)
Xiaorong Tong
2013-06-01
Full Text Available In this study, a two-stage filter structure is introduced for speech enhancement. The first stage is an adjustable filter and sum beam-former with four-microphone array. The control of beam-forming filter is realized by adjusting only a single control variable. Different from the adaptive beam-forming filter, the proposed filter structure does not bring to any adaptive error noise, thus, it also does not bring the trouble to the second stage of the speech signal processing. The second stage of the proposed filter is a Wiener filter. The estimation of signal’s power spectrum for Wiener filter is realized by cross-correlation between primary outputs of two adjacent directional beams. This estimation is based on the assumption that the noise outputs of the two adjacent directional beams come from two independent noise source but the speech outputs come from the same speech source. The simulation results shown that the proposed algorithm can improve the Signal-Noise-Ratio (SNR about 6 dB.
Stochastic system identification of skin properties: linear and wiener static nonlinear methods.
Chen, Yi; Hunter, Ian W
2012-10-01
Wiener static nonlinear system identification was used to study the linear dynamics and static nonlinearities in the response of skin and underlying tissue under indentation in vivo. A device capable of measuring the dynamic mechanical properties of bulk skin tissue was developed and it incorporates a custom-built Lorentz force actuator that measures the dynamic compliance between the input force (system identification technique produced a variance accounted for (VAF) of 75-81% and Wiener static nonlinear techniques increased the VAF by 5%. Localized linear techniques increased the VAF to 85-95% with longer tests. Indentation experiments were conducted on 16 test subjects to determine device sensitivity and repeatability. Using the device, the coefficient of variation of test metrics was found to be as low as 2% for a single test location. The measured tissue stiffness was 300 N/m near the surface and 4.5 kN/m for high compression. The damping ranged from 5 to 23 N s/m. The bulk skin properties were also shown to vary significantly with gender and body mass index. The device and techniques used in this research can be applied to consumer product analysis, medical diagnosis and tissue research.
Medical image denoising using dual tree complex thresholding wavelet transform and Wiener filter
Directory of Open Access Journals (Sweden)
Hilal Naimi
2015-01-01
Full Text Available Image denoising is the process to remove the noise from the image naturally corrupted by the noise. The wavelet method is one among various methods for recovering infinite dimensional objects like curves, densities, images, etc. The wavelet techniques are very effective to remove the noise because of their ability to capture the energy of a signal in few energy transform values. The wavelet methods are based on shrinking the wavelet coefficients in the wavelet domain. We propose in this paper, a denoising approach basing on dual tree complex wavelet and shrinkage with the Wiener filter technique (where either hard or soft thresholding operators of dual tree complex wavelet transform for the denoising of medical images are used. The results proved that the denoised images using DTCWT (Dual Tree Complex Wavelet Transform with Wiener filter have a better balance between smoothness and accuracy than the DWT and are less redundant than SWT (StationaryWavelet Transform. We used the SSIM (Structural Similarity Index Measure along with PSNR (Peak Signal to Noise Ratio and SSIM map to assess the quality of denoised images.
Energy Technology Data Exchange (ETDEWEB)
NONE
2004-07-01
These two volumes contain the proceedings of the 25th Vienna Engine Symposium of 29/30 April 2004. Traditionally, international attendants are invited to this symposium to identify and discuss new trends in internal combustion engines. The following subjects were discussed this year: New gasoline and diesel engines; Special marine and motorcycle engines; Diesel engines of the future; Acoustic effects of mixing and combustion; Introduction to synthetic fuels; New findings in charge cycles, charging, design, calculation, simulation, gears, components, and exhaust purification; Future perspectives. The proceedings volumes were published by Professor Dr. H.P. Lenz, managing director of Oesterreichischer Verein fuer Kraftfahrzeugtechnik (OeVK).(orig.) [German] In diesem zweibaendingen Werk werden die Vortraege des 25. Internationalen Wiener Motorensymposiums vom 29./30 April 2004 wiedergegeben und damit einer breiten Oeffentlichkeit zugaenglich gemacht. Aufgabe der Wiener Motorensymposien ist es, Entwicklungsrichtungen im Bereich der Verbrennungsmotoren unter internationaler Beteiligung aufzuzeigen und zu diskutieren. Dieses Werk befasst sich unter anderem mit folgenden neuen Entwicklungen: Motoren: Neue Otto- und Diesel-Motoren; Sondermotoren fuer Boot und Motorrad; Dieselmotor in der Zukunft? Kraftstoffe: Einfluss von Gemischbildung und Verbrennung auf die Akustik; Einstieg in synthetische Kunststoffe; neue Erkenntnisse auf den Gebieten: Ladungswechsel, Aufladung; Konstruktion; Berechnung; Simulation; Getriebe; Komponenten; Abgasreinigung; Zukunftsperspektiven. Herausgeber: Univ.-Prof. Dr. H.P. Lenz; Vorsitzender der Oesterreichischen Vereins fuer Kraftfahrzeugtechnik (OeVK). (orig.)
Energy Technology Data Exchange (ETDEWEB)
NONE
2004-07-01
These two volumes contain the proceedings of the 25th Vienna Engine Symposium of 29/30 April 2004. Traditionally, international attendants are invited to this symposium to identify and discuss new trends in internal combustion engines. The following subjects were discussed this year: New gasoline and diesel engines; Special marine and motorcycle engines; Diesel engines of the future; Acoustic effects of mixing and combustion; Introduction to synthetic fuels; New findings in charge cycles, charging, design, calculation, simulation, gears, components, and exhaust purification; Future perspectives. The proceedings volumes were published by Professor Dr. H.P. Lenz, managing director of Oesterreichischer Verein fuer Kraftfahrzeugtechnik (OeVK). (orig.) [German] In diesem zweibaendingen Werk werden die Vortraege des 25. Internationalen Wiener Motorensymposiums vom 29./30 April 2004 wiedergegeben und damit einer breiten Oeffentlichkeit zugaenglich gemacht. Aufgabe der Wiener Motorensymposien ist es, Entwicklungsrichtungen im Bereich der Verbrennungsmotoren unter internationaler Beteiligung aufzuzeigen und zu diskutieren. Dieses Werk befasst sich unter anderem mit folgenden neuen Entwicklungen: Motoren: Neue Otto- und Diesel-Motoren; Sondermotoren fuer Boot und Motorrad; Dieselmotor in der Zukunft? Kraftstoffe: Einfluss von Gemischbildung und Verbrennung auf die Akustik; Einstieg in synthetische Kunststoffe; neue Erkenntnisse auf den Gebieten: Ladungswechsel, Aufladung; Konstruktion; Berechnung; Simulation; Getriebe; Komponenten; Abgasreinigung; Zukunftsperspektiven. Herausgeber: Univ.-Prof. Dr. H.P. Lenz; Vorsitzender der Oesterreichischen Vereins fuer Kraftfahrzeugtechnik (OeVK). (orig.)
Wiener filtering with a seismic underground array at the Sanford Underground Research Facility
Coughlin, Michael; Christensen, Nelson; Dergachev, Vladimir; DeSalvo, Riccardo; Kandhasamy, Shivaraj; Mandic, Vuk
2014-01-01
A seismic array has been deployed at the Sanford Underground Research Facility in the former Homestake mine, South Dakota, to study the underground seismic environment. This includes exploring the advantages of constructing a third-generation gravitational-wave detector underground. A major noise source would be Newtonian noise, which is induced by fluctuations in the local gravitational field. The hope is that a combination of a low-noise seismic environment and coherent noise subtraction using seismometers in the vicinity of the detector could suppress the Newtonian noise to required levels. In this paper, we use Wiener filtering techniques to subtract coherent noise in a seismic array in the form of oceanic microseisms. We achieve more than an order of magnitude noise cancellation between about 0.05-0.5 Hz. We examine the variation in the Wiener filter coefficients over the course of the day, showing how local activities impact the filter. We also study the variation in coefficients over the course of a mo...
Cellular Signaling Networks Function as Generalized Wiener-Kolmogorov Filters to Suppress Noise
Hinczewski, Michael; Thirumalai, D.
2014-10-01
Cellular signaling involves the transmission of environmental information through cascades of stochastic biochemical reactions, inevitably introducing noise that compromises signal fidelity. Each stage of the cascade often takes the form of a kinase-phosphatase push-pull network, a basic unit of signaling pathways whose malfunction is linked with a host of cancers. We show that this ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov optimal noise filter. Using concepts from umbral calculus, we generalize the linear Wiener-Kolmogorov theory, originally introduced in the context of communication and control engineering, to take nonlinear signal transduction and discrete molecule populations into account. This allows us to derive rigorous constraints for efficient noise reduction in this biochemical system. Our mathematical formalism yields bounds on filter performance in cases important to cellular function—such as ultrasensitive response to stimuli. We highlight features of the system relevant for optimizing filter efficiency, encoded in a single, measurable, dimensionless parameter. Our theory, which describes noise control in a large class of signal transduction networks, is also useful both for the design of synthetic biochemical signaling pathways and the manipulation of pathways through experimental probes such as oscillatory input.
Cellular Signaling Networks Function as Generalized Wiener-Kolmogorov Filters to Suppress Noise
Directory of Open Access Journals (Sweden)
Michael Hinczewski
2014-10-01
Full Text Available Cellular signaling involves the transmission of environmental information through cascades of stochastic biochemical reactions, inevitably introducing noise that compromises signal fidelity. Each stage of the cascade often takes the form of a kinase-phosphatase push-pull network, a basic unit of signaling pathways whose malfunction is linked with a host of cancers. We show that this ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov optimal noise filter. Using concepts from umbral calculus, we generalize the linear Wiener-Kolmogorov theory, originally introduced in the context of communication and control engineering, to take nonlinear signal transduction and discrete molecule populations into account. This allows us to derive rigorous constraints for efficient noise reduction in this biochemical system. Our mathematical formalism yields bounds on filter performance in cases important to cellular function—such as ultrasensitive response to stimuli. We highlight features of the system relevant for optimizing filter efficiency, encoded in a single, measurable, dimensionless parameter. Our theory, which describes noise control in a large class of signal transduction networks, is also useful both for the design of synthetic biochemical signaling pathways and the manipulation of pathways through experimental probes such as oscillatory input.
New RLS Wiener Smoother for Colored Observation Noise in Linear Discrete-time Stochastic Systems
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Seiichi Nakamori
2013-12-01
Full Text Available In the estimation problems, rather than the white observation noise, there are cases where the observation noise is modeled by the colored noise process. In the observation equation, the observed value y(k is given as a sum of the signal z(k=Hx(k and the colored observation noise v_c(k. In this paper, the observation equation is converted to the new observation equation for the white observation noise. In accordance with the observation equation for the white observation noise, this paper proposes new RLS Wiener estimation algorithms for the fixed-point smoothing and filtering estimates in linear discrete-time wide-sense stationary stochastic systems. The RLS Wiener estimators require the following information: (a the system matrix for the state vector x(k; (b the observation matrix H; (c the variance of the state vector x(k; (d the system matrix for the colored observation noise v_c(k; (e the variance of the colored observation noise.
Chaos in World Politics: A Reflection
Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.
Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.
Energy Technology Data Exchange (ETDEWEB)
Kwok, Sau Fa, E-mail: kwok@dfi.uem.br
2012-08-15
A Langevin equation with multiplicative white noise and its corresponding Fokker-Planck equation are considered in this work. From the Fokker-Planck equation a transformation into the Wiener process is provided for different orders of prescription in discretization rule for the stochastic integrals. A few applications are also discussed. - Highlights: Black-Right-Pointing-Pointer Fokker-Planck equation corresponding to the Langevin equation with mul- tiplicative white noise is presented. Black-Right-Pointing-Pointer Transformation of diffusion processes into the Wiener process in different prescriptions is provided. Black-Right-Pointing-Pointer The prescription parameter is associated with the growth rate for a Gompertz-type model.
Genome chaos: survival strategy during crisis.
Liu, Guo; Stevens, Joshua B; Horne, Steven D; Abdallah, Batoul Y; Ye, Karen J; Bremer, Steven W; Ye, Christine J; Chen, David J; Heng, Henry H
2014-01-01
Genome chaos, a process of complex, rapid genome re-organization, results in the formation of chaotic genomes, which is followed by the potential to establish stable genomes. It was initially detected through cytogenetic analyses, and recently confirmed by whole-genome sequencing efforts which identified multiple subtypes including "chromothripsis", "chromoplexy", "chromoanasynthesis", and "chromoanagenesis". Although genome chaos occurs commonly in tumors, both the mechanism and detailed aspects of the process are unknown due to the inability of observing its evolution over time in clinical samples. Here, an experimental system to monitor the evolutionary process of genome chaos was developed to elucidate its mechanisms. Genome chaos occurs following exposure to chemotherapeutics with different mechanisms, which act collectively as stressors. Characterization of the karyotype and its dynamic changes prior to, during, and after induction of genome chaos demonstrates that chromosome fragmentation (C-Frag) occurs just prior to chaotic genome formation. Chaotic genomes seem to form by random rejoining of chromosomal fragments, in part through non-homologous end joining (NHEJ). Stress induced genome chaos results in increased karyotypic heterogeneity. Such increased evolutionary potential is demonstrated by the identification of increased transcriptome dynamics associated with high levels of karyotypic variance. In contrast to impacting on a limited number of cancer genes, re-organized genomes lead to new system dynamics essential for cancer evolution. Genome chaos acts as a mechanism of rapid, adaptive, genome-based evolution that plays an essential role in promoting rapid macroevolution of new genome-defined systems during crisis, which may explain some unwanted consequences of cancer treatment.
Chaos in Black holes Surrounded by Electromagnetic Fields
Santoprete, Manuele; Cicogna, Giampaolo
2001-01-01
In this paper we prove the occurence of chaos for charged particles moving around a Schwarzshild black hole, perturbed by uniform electric and magnetic fields. The appearance of chaos is studied resorting to the Poincare'-Melnikov method.
Montagnini, Leone; Tabacchi, Marco Elio; Termini, Settimo
2016-01-01
Is Biophysics an interdisciplinary science? In order to answer this rhetorical question, it can be useful to look back at history of disciplines, as well as that of the scientific institutions helping their development. In this contribution some aspects of the unusual hodgepodge of concepts involving Biophysics, the legacy of Cybernetics, cognitive science and the central figure of Norbert Wiener are presented and discussed.
Directory of Open Access Journals (Sweden)
A. Azócar
2010-01-01
Full Text Available We show that the one-sided regularizations of the generator of any uniformly continuous and convex compact valued composition operator, acting in the spaces of functions of bounded variation in the sense of Wiener, is an affine function.
vanDijk, P; Wit, HP; Segenhout, JM
1997-01-01
Wiener kernel analysis was used to characterize the auditory pathway from tympanic membrane to single primary auditory nerve fibers in the European edible frog, Rana esculenta. Nerve fiber signals were recorded in response to white Gaussian noise. By cross-correlating the noise stimulus and the nerv
2nd International Symposium on Chaos, Complexity and Leadership
Banerjee, Santo
2015-01-01
These proceedings from the 2013 symposium on "Chaos, complexity and leadership" reflect current research results from all branches of Chaos, Complex Systems and their applications in Management. Included are the diverse results in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of Chaos and Complex Systems. Also highlighted are Leadership and Management applications of Chaos and Complexity Theory.
Controlling Beam Halo-chaos Using a Special Nonlinear Method
Institute of Scientific and Technical Information of China (English)
2002-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry,medicine, and national defense. Some general engineering methods for chaos control have been developedin recent years, but they generally are unsuccessful for beam halo-chaos suppression due to manytechnical constraints. Beam halo-chaos is essentially a spatotemporal chaotic motion within a high power
Regularly timed events amid chaos
Blakely, Jonathan N.; Cooper, Roy M.; Corron, Ned J.
2015-11-01
We show rigorously that the solutions of a class of chaotic oscillators are characterized by regularly timed events in which the derivative of the solution is instantaneously zero. The perfect regularity of these events is in stark contrast with the well-known unpredictability of chaos. We explore some consequences of these regularly timed events through experiments using chaotic electronic circuits. First, we show that a feedback loop can be implemented to phase lock the regularly timed events to a periodic external signal. In this arrangement the external signal regulates the timing of the chaotic signal but does not strictly lock its phase. That is, phase slips of the chaotic oscillation persist without disturbing timing of the regular events. Second, we couple the regularly timed events of one chaotic oscillator to those of another. A state of synchronization is observed where the oscillators exhibit synchronized regular events while their chaotic amplitudes and phases evolve independently. Finally, we add additional coupling to synchronize the amplitudes, as well, however in the opposite direction illustrating the independence of the amplitudes from the regularly timed events.
Energy Technology Data Exchange (ETDEWEB)
Dattani, Justine [Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY (United Kingdom); Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA (United Kingdom); Blake, Jack C.H. [Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY (United Kingdom); Hilker, Frank M., E-mail: f.hilker@bath.ac.uk [Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY (United Kingdom)
2011-10-31
Designing intervention methods to control chaotic behavior in dynamical systems remains a challenging problem, in particular for systems that are difficult to access or to measure. We propose a simple, intuitive technique that modifies the values of the state variables directly toward a certain target. The intervention takes into account the difference to the target value, and is a combination of traditional proportional feedback and constant feedback methods. It proves particularly useful when the target corresponds to the equilibrium of the uncontrolled system, and is available or can be estimated from expert knowledge (e.g. in biology and economy). -- Highlights: → We propose a chaos control method that forces the system to a certain target. → The intervention takes into account the difference to the target value. → It can be seen as a combination of proportional and constant feedback methods. → The method is very robust and highly efficient in the long-term. → It is particularly applicable when suitable target values are known or available.
The Capabilities of Chaos and Complexity
Directory of Open Access Journals (Sweden)
David L. Abel
2009-01-01
Full Text Available To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization must all be carefully defined and distinguished. In addition their cause-and-effect relationships and mechanisms of action must be delineated. Are there any formal (non physical, abstract, conceptual, algorithmic components to chaos, complexity, self-ordering and organization, or are they entirely physicodynamic (physical, mass/energy interaction alone? Chaos and complexity can produce some fascinating self-ordered phenomena. But can spontaneous chaos and complexity steer events and processes toward pragmatic benefit, select function over non function, optimize algorithms, integrate circuits, produce computational halting, organize processes into formal systems, control and regulate existing systems toward greater efficiency? The question is pursued of whether there might be some yet-to-be discovered new law of biology that will elucidate the derivation of prescriptive information and control. Ã¢Â€ÂœSystemÃ¢Â€Â will be rigorously defined. Can a low-informational rapid succession of PrigogineÃ¢Â€Â™s dissipative structures self-order into bona fide organization?
Generic superweak chaos induced by Hall effect.
Ben-Harush, Moti; Dana, Itzhack
2016-05-01
We introduce and study the "kicked Hall system" (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic (B) and electric (E) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of B and E and in the weak-chaos regime of sufficiently small nonintegrability parameter κ (the kicking strength), there exists a generic family of periodic kicking potentials for which the Hall effect from B and E significantly suppresses the weak chaos, replacing it by "superweak" chaos (SWC). This means that the system behaves as if the kicking strength were κ^{2} rather than κ. For E=0, SWC is known to be a classical fingerprint of quantum antiresonance, but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic web" in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small κ. In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems.
Cybernetics and Social Order. Models and Images of Society in Norbert Wiener and Karl Deutsch
Directory of Open Access Journals (Sweden)
Roberto Carradore
2013-07-01
Full Text Available The present contribution aims at defining the relation between cybernetics and social theory from the perspective of society as order. After an historical framework of the cybernetic movement, a careful reading of the works of Norbert Wiener, in which he introduced the concept of feed-back and the idea of information society, has revealed a keen awareness about the social effects of technological innovation. Among the social scientists who had made use of cybernetic concepts, it has been considered the work of Karl Deutsch, which was one of the first completely cybernetic perspective for the study of political and social phenomena. The main conclusion is that cybernetics, as a meeting point between different disciplines, has produced an image of self-regulated society in line with the image of society as order.
Wiener's Loop Filter for PLL-Based Carrier Recovery of OQPSK and MSK-Type Modulations
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Arnaldo Spalvieri
2008-01-01
Full Text Available This letter considers carrier recovery for offset quadrature phase shift keying (OQPSK and minimum shift keying-type (MSK-type modulations based on phase-lock loop (PLL. The concern of the letter is the optimization of the loop filter of the PLL. The optimization is worked out in the light of Wiener's theory taking into account the phase noise affecting the incoming carrier, the additive white Gaussian noise that is present on the channel, and the self-noise produced by the phase detector. Delay in the loop, which may affect the numerical implementation of the PLL, is also considered. Closed-form expressions for the loop filter and for the mean-square error are given for the case where the phase noise is characterized as a first-order process.
High order recombination and an application to cubature on Wiener space
Litterer, Christian
2010-01-01
Particle methods are widely used because they can provide accurate descriptions of evolving measures. Recently it has become clear that by stepping outside the Monte-Carlo paradigm these methods can be of higher order with effective and transparent error bounds. A weakness of particle methods(particularly in the higher order case) is the tendency for the number of particles to explode if the process is iterated and accuracy preserved. In this paper we identify a new approach that allows dynamic recombination in such methods and retains the high order accuracy by simplifying the support of the intermediate measures used in the iteration. We describe an algorithm that can be used to simplify the support of a discrete measure and give an application to the cubature on Wiener space method developed by Lyons, Victoir [12].
Identification of Wiener systems with nonlinearity being piecewise-linear function
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Identification of the Wiener system with the nonlinear block being a piecewise-linear function is considered in the paper, generalizing the results given by H. E. Chen to the case of noisy observation. Recursive algorithms are given for estimating all unknown parameters contained in the system, and their strong consistency is proved. The estimation method is similar to that used by H. E. Chen for Hammerstein systems with the same nonlinearity. However, the assumption imposed by H. E. Chen on the availability of an upper bound for the nonsmooth points of the piecewise-linear function has been removed in this paper with the help of designing an additional algorithm for estimating the upper bound.
Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders
El Beltagy, Mohamed
2016-01-06
In this work, the Wiener-Hermite Expansion (WHE) is used to solve stochastic nonlinear PDEs excited with noise. The generation of the equivalent set of deterministic integro-differential equations is automated and hence allows for high order terms of WHE. The automation difficulties are discussed, solved and implemented to output the final system to be solved. A numerical Pikard-like algorithm is suggested to solve the resulting deterministic system. The automated WHE is applied to the 1D diffusion equation and to the heat equation. The results are compared with previous solutions obtained with WHEP (WHE with perturbation) technique. The solution obtained using the suggested WHE technique is shown to be the limit of the WHEP solutions with infinite number of corrections. The automation is extended easily to account for white-noise of higher dimension and for general nonlinear PDEs.
Directory of Open Access Journals (Sweden)
Ignacio Santamaría
2008-04-01
Full Text Available This paper treats the identification of nonlinear systems that consist of a cascade of a linear channel and a nonlinearity, such as the well-known Wiener and Hammerstein systems. In particular, we follow a supervised identification approach that simultaneously identifies both parts of the nonlinear system. Given the correct restrictions on the identification problem, we show how kernel canonical correlation analysis (KCCA emerges as the logical solution to this problem. We then extend the proposed identification algorithm to an adaptive version allowing to deal with time-varying systems. In order to avoid overfitting problems, we discuss and compare three possible regularization techniques for both the batch and the adaptive versions of the proposed algorithm. Simulations are included to demonstrate the effectiveness of the presented algorithm.
Institute of Scientific and Technical Information of China (English)
唐圣金; 郭晓松; 于传强; 周志杰; 周召发; 张邦成
2014-01-01
Real time remaining useful life (RUL) prediction based on condition monitoring is an essential part in condition based maintenance (CBM). In the current methods about the real time RUL prediction of the nonlinear degradation process, the measurement error is not considered and forecasting uncertainty is large. Therefore, an approximate analytical RUL distribution in a closed-form of a nonlinear Wiener based degradation process with measurement errors was proposed. The maximum likelihood estimation approach was used to estimate the unknown fixed parameters in the proposed model. When the newly observed data are available, the random parameter is updated by the Bayesian method to make the estimation adapt to the item’s individual characteristic and reduce the uncertainty of the estimation. The simulation results show that considering measurement errors in the degradation process can significantly improve the accuracy of real time RUL prediction.
Blind Identification of SIMO Wiener Systems Based on Kernel Canonical Correlation Analysis
Van Vaerenbergh, Steven; Via, Javier; Santamaria, Ignacio
2013-05-01
We consider the problem of blind identification and equalization of single-input multiple-output (SIMO) nonlinear channels. Specifically, the nonlinear model consists of multiple single-channel Wiener systems that are excited by a common input signal. The proposed approach is based on a well-known blind identification technique for linear SIMO systems. By transforming the output signals into a reproducing kernel Hilbert space (RKHS), a linear identification problem is obtained, which we propose to solve through an iterative procedure that alternates between canonical correlation analysis (CCA) to estimate the linear parts, and kernel canonical correlation (KCCA) to estimate the memoryless nonlinearities. The proposed algorithm is able to operate on systems with as few as two output channels, on relatively small data sets and on colored signals. Simulations are included to demonstrate the effectiveness of the proposed technique.
The rate of decay of the Wiener sausage in local Dirichlet space
Gibson, Lee R
2010-01-01
In the context of a heat kernel diffusion which admits a Gaussian type estimate with parameter beta on a local Dirichlet space, we consider the log asymptotic behavior of the negative exponential moments of the Wiener sausage. We show that the log asymptotic behavior up to time t^{beta}V(x,t) is V(x,t), which is analogous to the Euclidean result. Here V(x,t) represents the mass of the ball of radius t about a point x of the local Dirichlet space. The proof uses a known coarse graining technique to obtain the upper asymptotic, but must be adapted to for use without translation invariance in this setting. This result provides the first such asymptotics for several other contexts, including diffusions on complete Riemannian manifolds with non-negative Ricci curvature.
Adaptive multiple subtraction with wavelet-based complex unary Wiener filters
Ventosa, Sergi; Huard, Irène; Pica, Antonio; Rabeson, Hérald; Ricarte, Patrice; Duval, Laurent
2011-01-01
Multiple attenuation is a crucial task in seismic data processing because multiples usually cover primaries from fundamental reflectors. Predictive multiple suppression methods remove these multiples by building an adapted model, aiming at being subtracted from the original signal. However, before the subtraction is applied, a matching filter is required to minimize amplitude differences and misalignments between actual multiples and their prediction, and thus to minimize multiples in the input dataset after the subtraction. In this work we focus on the subtraction element. We propose an adaptive multiple removal technique in a 1-D complex wavelet frame combined with a non-stationary adaptation performed via single-sample (unary) Wiener filters, consistently estimated on overlapping windows in the transformed domain. This approach greatly simplifies the matching filter estimation and, despite its simplicity, compares promisingly with standard adaptive 2-D methods, both in terms of results and retained speed a...
Remaining useful life prediction for an adaptive skew-Wiener process model
Huang, Zeyi; Xu, Zhengguo; Ke, Xiaojie; Wang, Wenhai; Sun, Youxian
2017-03-01
Predicting the remaining useful life for operational devices plays a critical role in prognostics and health management. As the models based on the stochastic processes are widely used for characterizing the degradation trajectory, an adaptive skew-Wiener model, which is much more flexible than traditional stochastic process models, is proposed to model the degradation drift of industrial devices. To make full use of the prior knowledge and the historical information, an on-line filtering algorithm is proposed for state estimation, a two-stage algorithm is adopted to estimate unknown parameters as well. For remaining useful life prediction, a novel result is presented with an explicit form based on the closed skew normal distribution. Finally, sufficient Monte Carlo simulations and an application for ball bearings in rotating electrical machines are used to validate our approach.
Chaos Theory as a Model for Managing Issues and Crises.
Murphy, Priscilla
1996-01-01
Uses chaos theory to model public relations situations in which the salient feature is volatility of public perceptions. Discusses the premises of chaos theory and applies them to issues management, the evolution of interest groups, crises, and rumors. Concludes that chaos theory is useful as an analogy to structure image problems and to raise…
Chaos control and synchronization in a fractional neuron network system
Energy Technology Data Exchange (ETDEWEB)
Zhou Shangbo [Computer Department of Chongqing University, Chongqing 400044 (China); Li Hua [Department of Mathematics and Computer Science, University of Lethbridge, T1K 3M4 (Canada)], E-mail: hua.li@uleth.ca; Zhu Zhengzhou [Computer Department of Chongqing University, Chongqing 400044 (China)
2008-05-15
In this paper, an algorithm of numerical solution for fractional differential equations is presented. Chaos in a neuron network system is also illustrated. Moreover, chaos feedback control and synchronization systems are constructed. The study and experiment indicate that the chaos in fractional order neuron networks could be controlled and synchronized.
Parker, Matthew D; Jones, Lynette A; Hunter, Ian W; Taberner, A J; Nash, M P; Nielsen, P M F
2017-01-01
A triaxial force-sensitive microrobot was developed to dynamically perturb skin in multiple deformation modes, in vivo. Wiener static nonlinear identification was used to extract the linear dynamics and static nonlinearity of the force-displacement behavior of skin. Stochastic input forces were applied to the volar forearm and thenar eminence of the hand, producing probe tip perturbations in indentation and tangential extension. Wiener static nonlinear approaches reproduced the resulting displacements with variances accounted for (VAF) ranging 94-97%, indicating a good fit to the data. These approaches provided VAF improvements of 0.1-3.4% over linear models. Thenar eminence stiffness measures were approximately twice those measured on the forearm. Damping was shown to be significantly higher on the palm, whereas the perturbed mass typically was lower. Coefficients of variation (CVs) for nonlinear parameters were assessed within and across individuals. Individual CVs ranged from 2% to 11% for indentation and from 2% to 19% for extension. Stochastic perturbations with incrementally increasing mean amplitudes were applied to the same test areas. Differences between full-scale and incremental reduced-scale perturbations were investigated. Different incremental preloading schemes were investigated. However, no significant difference in parameters was found between different incremental preloading schemes. Incremental schemes provided depth-dependent estimates of stiffness and damping, ranging from 300 N/m and 2 Ns/m, respectively, at the surface to 5 kN/m and 50 Ns/m at greater depths. The device and techniques used in this research have potential applications in areas, such as evaluating skincare products, assessing skin hydration, or analyzing wound healing.
Experimental modeling of Wiener filters estimated on an operating diesel engine
Drouet, Julie; Leclère, Quentin; Parizet, Etienne
2015-01-01
Sound source separation in diesel engines can be implemented using a Wiener filter, or spectrofilter, that can extract the combustion contribution in the overall noise. In this study this filter characterizes the transfer function between a cylinder pressure and a measurement point. An engine is characterized by several filters (one for each cylinder) which are estimated for many operating conditions (engine speed and load). The purpose of this work is to obtain an averaged spectrofilter allowing the synthesis of combustion noise in all operating conditions. This synthesis should be accurate enough to be used in perceptive studies. In order to refine the spectrofilter estimation in the medium frequency band, this paper consists in taking advantage of the multitude of information given by the estimations from different operating conditions. To do this, an experimental model is adopted so modal parameters are extracted from a great number of measured filters. Different procedures such as the ESPRIT method or the LSCE method (modal analysis) are used to decompose the impulse responses on a complex exponential basis. The spectrofilters estimated from different operating conditions are analyzed and compared in this reduced basis, in order to identify the underlying structural parameters. These parameters are compared to the results of an experimental characterization of the stopped engine. The accuracy of the synthesis (number of components of the filter) is an important issue because these filters will be used in perceptive applications, extracting combustion noises. This paper is an extended version of the work initially presented at the conference Surveillance 6 in November 2011 in Compiègne, France [1] (J. Drouet, Quentin Leclere, Etienne Parizet. Experimental modeling of Wiener filters estimated on an operating diesel engine, in: Proceedings of the Surveillance, vol. 6, Compi'egne, France, 2011.).
Cannistraci, Carlo Vittorio
2015-01-26
Denoising multidimensional NMR-spectra is a fundamental step in NMR protein structure determination. The state-of-the-art method uses wavelet-denoising, which may suffer when applied to non-stationary signals affected by Gaussian-white-noise mixed with strong impulsive artifacts, like those in multi-dimensional NMR-spectra. Regrettably, Wavelet\\'s performance depends on a combinatorial search of wavelet shapes and parameters; and multi-dimensional extension of wavelet-denoising is highly non-trivial, which hampers its application to multidimensional NMR-spectra. Here, we endorse a diverse philosophy of denoising NMR-spectra: less is more! We consider spatial filters that have only one parameter to tune: the window-size. We propose, for the first time, the 3D extension of the median-modified-Wiener-filter (MMWF), an adaptive variant of the median-filter, and also its novel variation named MMWF*. We test the proposed filters and the Wiener-filter, an adaptive variant of the mean-filter, on a benchmark set that contains 16 two-dimensional and three-dimensional NMR-spectra extracted from eight proteins. Our results demonstrate that the adaptive spatial filters significantly outperform their non-adaptive versions. The performance of the new MMWF* on 2D/3D-spectra is even better than wavelet-denoising. Noticeably, MMWF* produces stable high performance almost invariant for diverse window-size settings: this signifies a consistent advantage in the implementation of automatic pipelines for protein NMR-spectra analysis.
Nonlinear Physics Integrability, Chaos and Beyond
Lakshmanan, M
1997-01-01
Integrability and chaos are two of the main concepts associated with nonlinear physical systems which have revolutionized our understanding of them. Highly stable exponentially localized solitons are often associated with many of the important integrable nonlinear systems while motions which are sensitively dependent on initial conditions are associated with chaotic systems. Besides dramatically raising our perception of many natural phenomena, these concepts are opening up new vistas of applications and unfolding technologies: Optical soliton based information technology, magnetoelectronics, controlling and synchronization of chaos and secure communications, to name a few. These developments have raised further new interesting questions and potentialities. We present a particular view of some of the challenging problems and payoffs ahead in the next few decades by tracing the early historical events, summarizing the revolutionary era of 1950-70 when many important new ideas including solitons and chaos were ...
Nonlinear Dynamics and Chaos: Advances and Perspectives
Thiel, Marco; Romano, M. Carmen; Károlyi, György; Moura, Alessandro
2010-01-01
This book is a collection of contributions on various aspects of active frontier research in the field of dynamical systems and chaos. Each chapter examines a specific research topic and, in addition to reviewing recent results, also discusses future perspectives. The result is an invaluable snapshot of the state of the field by some of its most important researchers. The first contribution in this book, "How did you get into Chaos?", is actually a collection of personal accounts by a number of distinguished scientists on how they entered the field of chaos and dynamical systems, featuring comments and recollections by James Yorke, Harry Swinney, Floris Takens, Peter Grassberger, Edward Ott, Lou Pecora, Itamar Procaccia, Michael Berry, Giulio Casati, Valentin Afraimovich, Robert MacKay, and last but not least, Celso Grebogi, to whom this volume is dedicated.
Nonlinear dynamics and quantum chaos an introduction
Wimberger, Sandro
2014-01-01
The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.
Avoiding Quantum Chaos in Quantum Computation
Berman, G P; Izrailev, F M; Tsifrinovich, V I
2001-01-01
We study a one-dimensional chain of nuclear $1/2-$spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. According to the standard viewpoint, the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a magnetic field gradient helps to avoid quantum chaos which turns out to disappear with an increase of the number of qubits. We give analytical estimates which explain this effect, together with numerical data supporting
About the Concept of Quantum Chaos
Directory of Open Access Journals (Sweden)
Ignacio S. Gomez
2017-05-01
Full Text Available The research on quantum chaos finds its roots in the study of the spectrum of complex nuclei in the 1950s and the pioneering experiments in microwave billiards in the 1970s. Since then, a large number of new results was produced. Nevertheless, the work on the subject is, even at present, a superposition of several approaches expressed in different mathematical formalisms and weakly linked to each other. The purpose of this paper is to supply a unified framework for describing quantum chaos using the quantum ergodic hierarchy. Using the factorization property of this framework, we characterize the dynamical aspects of quantum chaos by obtaining the Ehrenfest time. We also outline a generalization of the quantum mixing level of the kicked rotator in the context of the impulsive differential equations.
Hyperbolic Chaos A Physicist’s View
Kuznetsov, Sergey P
2012-01-01
"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.
Chaos Concepts, Control and Constructive Use
Bolotin, Yurii; Yanovsky, Vladimir
2009-01-01
The study of chaotic behaviour in nonlinear, dynamical systems is now a well established research domain with ramifications into all fields of sciences, spanning a vast range of applications, from celestial mechanics, via climate change, to the functioning of brownian motors in cells. A more recent discovery is that chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter itself for the system under investigation, stochastic resonance being a prime example. The present work is putting emphasis on the latter aspects, and after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing relevant algorithms for both Hamiltonian and dissipative systems amongst others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance and a survey of ratchet models. This short and concise pr...
Harnessing quantum transport by transient chaos.
Yang, Rui; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso; Pecora, Louis M
2013-03-01
Chaos has long been recognized to be generally advantageous from the perspective of control. In particular, the infinite number of unstable periodic orbits embedded in a chaotic set and the intrinsically sensitive dependence on initial conditions imply that a chaotic system can be controlled to a desirable state by using small perturbations. Investigation of chaos control, however, was largely limited to nonlinear dynamical systems in the classical realm. In this paper, we show that chaos may be used to modulate or harness quantum mechanical systems. To be concrete, we focus on quantum transport through nanostructures, a problem of considerable interest in nanoscience, where a key feature is conductance fluctuations. We articulate and demonstrate that chaos, more specifically transient chaos, can be effective in modulating the conductance-fluctuation patterns. Experimentally, this can be achieved by applying an external gate voltage in a device of suitable geometry to generate classically inaccessible potential barriers. Adjusting the gate voltage allows the characteristics of the dynamical invariant set responsible for transient chaos to be varied in a desirable manner which, in turn, can induce continuous changes in the statistical characteristics of the quantum conductance-fluctuation pattern. To understand the physical mechanism of our scheme, we develop a theory based on analyzing the spectrum of the generalized non-Hermitian Hamiltonian that includes the effect of leads, or electronic waveguides, as self-energy terms. As the escape rate of the underlying non-attracting chaotic set is increased, the imaginary part of the complex eigenenergy becomes increasingly large so that pointer states are more difficult to form, making smoother the conductance-fluctuation pattern.
Ventilatory chaos is impaired in carotid atherosclerosis.
Directory of Open Access Journals (Sweden)
Laurence Mangin
Full Text Available Ventilatory chaos is strongly linked to the activity of central pattern generators, alone or influenced by respiratory or cardiovascular afferents. We hypothesized that carotid atherosclerosis should alter ventilatory chaos through baroreflex and autonomic nervous system dysfunctions. Chaotic dynamics of inspiratory flow was prospectively evaluated in 75 subjects undergoing carotid ultrasonography: 27 with severe carotid stenosis (>70%, 23 with moderate stenosis (<70%, and 25 controls. Chaos was characterized by the noise titration method, the correlation dimension and the largest Lyapunov exponent. Baroreflex sensitivity was estimated in the frequency domain. In the control group, 92% of the time series exhibit nonlinear deterministic chaos with positive noise limit, whereas only 68% had a positive noise limit value in the stenoses groups. Ventilatory chaos was impaired in the groups with carotid stenoses, with significant parallel decrease in the noise limit value, correlation dimension and largest Lyapunov exponent, as compared to controls. In multiple regression models, the percentage of carotid stenosis was the best in predicting the correlation dimension (p<0.001, adjusted R(2: 0.35 and largest Lyapunov exponent (p<0.001, adjusted R(2: 0.6. Baroreflex sensitivity also predicted the correlation dimension values (p = 0.05, and the LLE (p = 0.08. Plaque removal after carotid surgery reversed the loss of ventilatory complexity. To conclude, ventilatory chaos is impaired in carotid atherosclerosis. These findings depend on the severity of the stenosis, its localization, plaque surface and morphology features, and is independently associated with baroreflex sensitivity reduction. These findings should help to understand the determinants of ventilatory complexity and breathing control in pathological conditions.
Institute of Scientific and Technical Information of China (English)
李军海; 文汉江; 刘焕玲; 朱广彬
2012-01-01
本文利用UTCSR 2003年1月到2008年8月间的GRACE Level-2 RL04重力场模型估计了南极冰盖质量变化.计算过程中分别采用高斯和Wiener滤波两种平滑方法,分别采用22、43和65个月重力场模型计算Wiener滤波信号与噪声函数,得出以下结论:在实际的计算过程中需要具体计算Wiener滤波平滑因子值,65个月GRACE重力场模型计算得到的Wiener滤波权值非常接近于平滑半径为540km高斯滤波权值；采用两种不同的滤波方法在相同区域质量变化率基本相同.%Gravity solutions from GRACE level-2 RL04 released by UTCSR for the period January 2003 to August 2008 were used to estimate the rates of Antarctic ice mass change. The Gaussian and Wiener filtering smoothing method were used respectively during the process. The signal and noise function of Wiener filtering were calculated respectively by 22, 43 and 65 months time gravity model, and the result was that the model signal and noise functions relate to the selected time period. Therefore smoothing factor values of Wiener filter need to be calculated during the process. The weights of Gaussian filter and Wiener filter computed by 65 GRACE gravity solutions were computed and it was very close to the Gaussian smoothing radius of 540km. The ice mass rates in the west Antartic Amundsen and the east Antartic Enderby land were computed and the mass rates at the same area were almost the same using the two different filtering methods.
Quantum chaos on a critical Fermi surface
Patel, Aavishkar A
2016-01-01
We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of $N$ species of fermions at non-zero density coupled to a $U(1)$ gauge field in two spatial dimensions, and determine the Lyapunov rate and the butterfly velocity in an extended RPA approximation. The thermal diffusivity is found to be universally related to these chaos parameters, i.e. the relationship is independent of $N$, the gauge coupling constant, the Fermi velocity, the Fermi surface curvature, and high energy details.
Atoms in static fields Chaos or Diffraction?
Dando, P A
1998-01-01
A brief review of the manifestations of classical chaos observed in atomic systems is presented. Particular attention is paid to the analysis of atomic spectra by periodic orbit-type theories. For diamagnetic non-hydrogenic Rydberg atoms, the dynamical explanation for observed spectral features has been disputed. By building on our previous work on the photoabsorption spectrum, we show how, by the addition of diffractive terms, the spectral fluctuations in the energy level spectrum of general Rydberg atoms can be obtained with remarkable precision from the Gutzwiller trace formula. This provides further evidence that non-hydrogenic systems are most naturally described in terms of diffraction rather than classical chaos.
SENSITIVE ERROR ANALYSIS OF CHAOS SYNCHRONIZATION
Institute of Scientific and Technical Information of China (English)
HUANG XIAN-GAO; XU JIAN-XUE; HUANG WEI; L(U) ZE-JUN
2001-01-01
We study the synchronizing sensitive errors of chaotic systems for adding other signals to the synchronizing signal.Based on the model of the Henon map masking, we examine the cause of the sensitive errors of chaos synchronization.The modulation ratio and the mean square error are defined to measure the synchronizing sensitive errors by quality.Numerical simulation results of the synchronizing sensitive errors are given for masking direct current, sinusoidal and speech signals, separately. Finally, we give the mean square error curves of chaos synchronizing sensitivity and threedimensional phase plots of the drive system and the response system for masking the three kinds of signals.
Chaos in an imperfectly premixed model combustor
Energy Technology Data Exchange (ETDEWEB)
Kabiraj, Lipika, E-mail: lipika.kabiraj@tu-berlin.de; Saurabh, Aditya; Paschereit, Christian O. [Hermann Föttinger Institut, Technische Universität Berlin (Germany); Karimi, Nader [School of Engineering, University of Glasgow (United Kingdom); Sailor, Anna [University of Wisconsin-Madison, Madison 53706 (United States); Mastorakos, Epaminondas; Dowling, Ann P. [Department of Engineering, University of Cambridge (United Kingdom)
2015-02-15
This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration.
Distributed chaos and inertial ranges in turbulence
Bershadskii, A
2016-01-01
It is shown that appearance of inertial range of scales, adjacent to distributed chaos range, results in adiabatic invariance of an energy correlation integral for isotropic homogeneous turbulence and for buoyancy driven turbulence (with stable or unstable stratification, including Rayleigh-Taylor mixing zone). Power spectrum of velocity field for distributed chaos dominated by this adiabatic invariant has a stretched exponential form $\\propto \\exp(-k/k_{\\beta})^{3/5}$. Results of recent direct numerical simulations have been used in order to support these conclusions.
USING OPTIMAL FEEDBACK CONTROL FOR CHAOS TARGETING
Institute of Scientific and Technical Information of China (English)
PENG ZHAO-WANG; ZHONG TING-XIU
2000-01-01
Since the conventional open-loop optimal targeting of chaos is very sensitive to noise, a close-loop optimal targeting method is proposed to improve the targeting performance under noise. The present optimal targeting model takes into consideration both precision and speed of the targeting procedure. The parameters, rather than the output, of the targeting controller, are directly optimized to obtain optimal chaos targeting. Analysis regarding the mechanism is given from physics aspect and numerical experiment on the Hénon map is carried out to compare the targeting performance under noise between the close-loop and the open-loop methods.
Experimental realization of chaos control by thresholding.
Murali, K; Sinha, Sudeshna
2003-07-01
We report the experimental verification of thresholding as a versatile tool for efficient and flexible chaos control. The strategy here simply involves monitoring a single state variable and resetting it when it exceeds a threshold. We demonstrate the success of the technique in rapidly controlling different chaotic electrical circuits, including a hyperchaotic circuit, onto stable fixed points and limit cycles of different periods, by thresholding just one variable. The simplicity of this controller entailing no run-time computation, and the ease and rapidity of switching between different targets it offers, suggests a potent tool for chaos based applications.
Investigation on evolutionary optimization of chaos control
Energy Technology Data Exchange (ETDEWEB)
Zelinka, Ivan [Faculty of Applied Informatics, Tomas Bata University in Zli' n, Nad Stranemi 4511, 762 72 Zli' n (Czech Republic)], E-mail: zelinka@fai.utb.cz; Senkerik, Roman [Faculty of Applied Informatics, Tomas Bata University in Zli' n, Nad Stranemi 4511, 762 72 Zli' n (Czech Republic)], E-mail: senkerik@fai.utb.cz; Navratil, Eduard [Faculty of Applied Informatics, Tomas Bata University in Zli' n, Nad Stranemi 4511, 762 72 Zli' n (Czech Republic)], E-mail: enavratil@fai.utb.cz
2009-04-15
This work deals with an investigation on optimization of the feedback control of chaos based on the use of evolutionary algorithms. The main objective is to show that evolutionary algorithms are capable of optimization of chaos control. As models of deterministic chaotic systems, one-dimensional Logistic equation and two-dimensional Henon map were used. The optimizations were realized in several ways, each one for another set of parameters of evolution algorithms or separate cost functions. The evolutionary algorithm SOMA (self-organizing migrating algorithm) was used in four versions. For each version simulations were repeated several times to show and check for robustness of the applied method.
DEFF Research Database (Denmark)
Rennison, Betina Wolfgang
of management differently. In this chaos of codes the managerial challenge is to take a second order position in order to strategically manage the communication that manages management itself. Key words: Management; personnel management; human-relations; pay-system; communication; system-theory; discursive...
Chaos and fractals an elementary introduction
Feldman, David P
2012-01-01
For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.
Controlling chaos to solutions with complex eigenvalues.
Kwon, Oh-Jong; Lee, Hoyun
2003-02-01
We derive formulas for parameter and variable perturbations to control chaos using linearized dynamics. They are available irrespective of the dimension of the system, the number of perturbed parameters or variables, and the kinds of eigenvalues of the linearized dynamics. We illustrate this using the two coupled Duffing oscillators and the two coupled standard maps.
Chaos in the Belousov-Zhabotinsky reaction
Field, Richard J.
The dynamics of reacting chemical systems is governed by typically polynomial differential equations that may contain nonlinear terms and/or embedded feedback loops. Thus the dynamics of such systems may exhibit features associated with nonlinear dynamical systems, including (among others): temporal oscillations, excitability, multistability, reaction-diffusion-driven formation of spatial patterns, and deterministic chaos. These behaviors are exhibited in the concentrations of intermediate chemical species. Bifurcations occur between particular dynamic behaviors as system parameters are varied. The governing differential equations of reacting chemical systems have as variables the concentrations of all chemical species involved, as well as controllable parameters, including temperature, the initial concentrations of all chemical species, and fixed reaction-rate constants. A discussion is presented of the kinetics of chemical reactions as well as some thermodynamic considerations important to the appearance of temporal oscillations and other nonlinear dynamic behaviors, e.g., deterministic chaos. The behavior, chemical details, and mechanism of the oscillatory Belousov-Zhabotinsky Reaction (BZR) are described. Furthermore, experimental and mathematical evidence is presented that the BZR does indeed exhibit deterministic chaos when run in a flow reactor. The origin of this chaos seems to be in toroidal dynamics in which flow-driven oscillations in the control species bromomalonic acid couple with the BZR limit cycle...
A Framework for Chaos Theory Career Counselling
Pryor, Robert G. L.
2010-01-01
Theory in career development counselling provides a map that counsellors can use to understand and structure the career counselling process. It also provides a means to communicate this understanding and structuring to their clients as part of the counselling intervention. The chaos theory of careers draws attention to the complexity,…
Chaos in a Bose-Einstein condensate
Institute of Scientific and Technical Information of China (English)
Wang Zhi-Xia; Ni Zheng-Guo; Cong Fu-Zhong; Liu Xue-Shen; Chen Lei
2010-01-01
It is demonstrated that Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose-Einstein condensate driven by time-periodic harmonic or inverted-harmonic potential.A formally exact solution of the timedependent Gross-Pitaevskii equation is constructed,which describes the matter shock waves with chaotic or periodic amplitudes and phases.
Dynamic system uncertainty propagation using polynomial chaos
Directory of Open Access Journals (Sweden)
Xiong Fenfen
2014-10-01
Full Text Available The classic polynomial chaos method (PCM, characterized as an intrusive methodology, has been applied to uncertainty propagation (UP in many dynamic systems. However, the intrusive polynomial chaos method (IPCM requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method (NIPCM that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.
Spatio-temporal chaos : A solvable model
Diks, C; Takens, F; DeGoede, J
1997-01-01
A solvable coupled map lattice model exhibiting spatio-temporal chaos is studied. Exact expressions are obtained for the spectra of Lyapunov exponents as a function of the model parameters. Although the model has spatio-temporal structure, the time series measured at a single lattice site are shown
Quantum dynamical entropies in discrete classical chaos
Energy Technology Data Exchange (ETDEWEB)
Benatti, Fabio [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Cappellini, Valerio [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Zertuche, Federico [Instituto de Matematicas, UNAM, Unidad Cuernavaca, AP 273-3, Admon. 3, 62251 Cuernavaca, Morelos (Mexico)
2004-01-09
We discuss certain analogies between quantization and discretization of classical systems on manifolds. In particular, we will apply the quantum dynamical entropy of Alicki and Fannes to numerically study the footprints of chaos in discretized versions of hyperbolic maps on the torus.
Teaching Chaos to Art College Students
Blum, Ben
2001-03-01
This is a report of the author's teaching the basic concepts of chaos to students at Massachusetts College of Art. In order to bypass the students' aversion to mathematics stemming from earlier difficult experiences with mathematics, the course started with some symbolism which was totally unfamiliar to them: a Boolean system based on Brown's Laws of Form. This was then used to develop the mathematical ideas of duality and self-reference. After that was a general survey of the various areas of mathematics using Guillen's Bridges to Infinity. Chaos was then introduced using Gleick's Chaos, which provides a very engaging narrative, along with an introduction to the basic ideas. Two different strategies were used to introduce the mathematical ideas. First, making use of the students' visual orientation, sensitive dependence on initial conditions, fractional dimension, fractals, the Koch snowflake, self-similiarity, and statistical self-similiarity were covered pictorially. Second, so that the students could get a real feeling for the mathematics of chaos, they individually worked out a recurrence equation with varying seeds, using a hand-held calculator.
Chaos in Practice: Techniques for Career Counsellors
Pryor, Robert G. L.; Bright, Jim
2005-01-01
The chaos theory of careers emphasises continual change, the centrality and importance of chance events, the potential of minor events to have disproportionately large impacts on subsequent events, and the capacity for dramatic phase shifts in career behaviour. This approach challenges traditional approaches to career counselling, assumptions…
Dynamic system uncertainty propagation using polynomial chaos
Institute of Scientific and Technical Information of China (English)
Xiong Fenfen; Chen Shishi; Xiong Ying
2014-01-01
The classic polynomial chaos method (PCM), characterized as an intrusive methodology, has been applied to uncertainty propagation (UP) in many dynamic systems. However, the intrusive polynomial chaos method (IPCM) requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method (NIPCM) that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.
Many-body chaos at weak coupling
Stanford, Douglas
2016-10-01
The strength of chaos in large N quantum systems can be quantified using λ L , the rate of growth of certain out-of-time-order four point functions. We calculate λ L to leading order in a weakly coupled matrix Φ4 theory by numerically diagonalizing a ladder kernel. The computation reduces to an essentially classical problem.
Chaos control applied to heart rhythm dynamics
Energy Technology Data Exchange (ETDEWEB)
Borem Ferreira, Bianca, E-mail: biaborem@gmail.com [Universidade Federal do Rio de Janeiro, COPPE, Department of Mechanical Engineering, P.O. Box 68.503, 21.941.972 Rio de Janeiro, RJ (Brazil); Souza de Paula, Aline, E-mail: alinedepaula@unb.br [Universidade de Brasi' lia, Department of Mechanical Engineering, 70.910.900 Brasilia, DF (Brazil); Amorim Savi, Marcelo, E-mail: savi@mecanica.ufrj.br [Universidade Federal do Rio de Janeiro, COPPE, Department of Mechanical Engineering, P.O. Box 68.503, 21.941.972 Rio de Janeiro, RJ (Brazil)
2011-08-15
Highlights: > A natural cardiac pacemaker is modeled by a modified Van der Pol oscillator. > Responses related to normal and chaotic, pathological functioning of the heart are investigated. > Chaos control methods are applied to avoid pathological behaviors of heart dynamics. > Different approaches are treated: stabilization of unstable periodic orbits and chaos suppression. - Abstract: The dynamics of cardiovascular rhythms have been widely studied due to the key aspects of the heart in the physiology of living beings. Cardiac rhythms can be either periodic or chaotic, being respectively related to normal and pathological physiological functioning. In this regard, chaos control methods may be useful to promote the stabilization of unstable periodic orbits using small perturbations. In this article, the extended time-delayed feedback control method is applied to a natural cardiac pacemaker described by a mathematical model. The model consists of a modified Van der Pol equation that reproduces the behavior of this pacemaker. Results show the ability of the chaos control strategy to control the system response performing either the stabilization of unstable periodic orbits or the suppression of chaotic response, avoiding behaviors associated with critical cardiac pathologies.
Control and synchronization of spatiotemporal chaos.
Ahlborn, Alexander; Parlitz, Ulrich
2008-01-01
Chaos control methods for the Ginzburg-Landau equation are presented using homogeneously, inhomogeneously, and locally applied multiple delayed feedback signals. In particular, it is shown that a small number of control cells is sufficient for stabilizing plane waves or for trapping spiral waves, and that successful control is closely connected to synchronization of the dynamics in regions close to the control cells.
Chaos: A Very Short Introduction
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Klages, R [School of Mathematical Sciences, Mile End Road, London, E1 4NS (United Kingdom)
2007-07-20
This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is 'no more complicated than X=2. Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and 'phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes 'real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this
CHAOS-BASED ADVANCED ENCRYPTION STANDARD
Abdulwahed, Naif B.
2013-05-01
This thesis introduces a new chaos-based Advanced Encryption Standard (AES). The AES is a well-known encryption algorithm that was standardized by U.S National Institute of Standard and Technology (NIST) in 2001. The thesis investigates and explores the behavior of the AES algorithm by replacing two of its original modules, namely the S-Box and the Key Schedule, with two other chaos- based modules. Three chaos systems are considered in designing the new modules which are Lorenz system with multiplication nonlinearity, Chen system with sign modules nonlinearity, and 1D multiscroll system with stair case nonlinearity. The three systems are evaluated on their sensitivity to initial conditions and as Pseudo Random Number Generators (PRNG) after applying a post-processing technique to their output then performing NIST SP. 800-22 statistical tests. The thesis presents a hardware implementation of dynamic S-Boxes for AES that are populated using the three chaos systems. Moreover, a full MATLAB package to analyze the chaos generated S-Boxes based on graphical analysis, Walsh-Hadamard spectrum analysis, and image encryption analysis is developed. Although these S-Boxes are dynamic, meaning they are regenerated whenever the encryption key is changed, the analysis results show that such S-Boxes exhibit good properties like the Strict Avalanche Criterion (SAC) and the nonlinearity and in the application of image encryption. Furthermore, the thesis presents a new Lorenz-chaos-based key expansion for the AES. Many researchers have pointed out that there are some defects in the original key expansion of AES and thus have motivated such chaos-based key expansion proposal. The new proposed key schedule is analyzed and assessed in terms of confusion and diffusion by performing the frequency and SAC test respectively. The obtained results show that the new proposed design is more secure than the original AES key schedule and other proposed designs in the literature. The proposed
Improving visibility of X-ray phase-contrast imaging with Wiener filtering.
Gong, Shaorun; Gao, Feng; Zhou, Zhongxing
2010-01-01
To investigate the degrading effects of the physical parameters on the in-line X-ray phase-contrast imaging (XPCi), a simulation tool based on the Fresnel/Kirchhoff diffraction integral was firstly developed with comprehensively considering effects of the source-to-sample (S-S) and sample-to-detector (S-D) distances, the practical characteristics of a polychromatic and finite size source, the point spread function (PSF) of the fluorescent screen and the spatial resolution of the detector on the theoretical phase-contrast pattern. By a comparison between the simulative profile and the experimental one under the commonly-used parameters, an acceptable consistency has been demonstrated in despite of the deviation between the theoretically-predicted contrast (0.188) and the original experimental one (0.12). From the simulations, it is apparently observed that the fine interference pattern has been severely degraded by the finite spatial resolution, and will inevitably be further deteriorated by the system noise in practice. Since the image quality of the X-ray phase-contrast imaging is strongly dependent on the physical parameters of the system, a model-based deblurring procedure to upgrade the image visibility is preferably desired. As a simple restoration way, a Wiener filter was then introduced to offer an optimal tradeoff between the contrast preservation and the noise suppression. Finally, to minimize the deviation resulting from the finite spatial resolution, one-dimensional interpolation was performed by positioning the set square at a tiny angle to the vertical direction. The result after the Wiener-filtering-based deblurring has shown a considerably improved profile visibility: the processed experimental contrast (0.156) increased by 30% as compared to the original one (0.12) in company with the increase in the signal-to-noise ratio (SNR) by 0.9dB. With the trend of the post-filtered experimental contrast to the theoretical one, it could be motivated that
Institute of Scientific and Technical Information of China (English)
Wen Sheng WANG
2002-01-01
Let {W(t); t ≥ 0} be a standard Wiener process and S be the Strassen set of functions.We investigate the exact rates of convergence to zero (as T →∞) of the variables suP0≤t≤T-aT inff∈ssuP0≤x≤1 |Yt,T(x) - f(x)| and inf0≤t≤T-aT suP0≤x≤1 |Yt,T(x) - f(x)| for any given f ∈ S, whereYt,T(x) = (W(t + xaT) - W(t))(2aT(logTa-1T1 + loglog T))-1/2.We establish a relation between how small the increments are and the functional limit resultsof Csorgo-Revesz increments for a Wiener process. Similar results for partial sums of i.i.d. randomvariables are also given.
Controlling halo-chaos via wavelet-based feedback
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Jin-Qing Fang
2002-01-01
Full Text Available Halo-chaos in high-current accelerator has become one of the key issues because it can cause excessive radioactivity from the accelerators and significantly limits the applications of the new accelerators in industrial and other fields. Some general engineering methods for chaos control have been developed, but they generally are unsuccessful for halo-chaos suppression due to many technical constraints. In this article, controllability condition for beam halo-chaos is analyzed qualitatively. Then Particles-in-Cell (PIC simulations explore the nature of beam halo-chaos formation. A nonlinear control method and wavelet function feedback controller are proposed for controlling beam halo-chaos. After control of beam halo-chaos for initial proton beam with water bag distributions, the beam halo strength factor H is reduced to zero, and other statistical physical quantities of beam halo-chaos are doubly reduced. The results show that the developed methods in this paper are very effective for proton beam halo-chaos suppression. Potential application of the halo-chaos control method is finally pointed out.
Local times and excursion theory for Brownian motion a tale of Wiener and Itô measures
Yen, Ju-Yi
2013-01-01
This monograph discusses the existence and regularity properties of local times associated to a continuous semimartingale, as well as excursion theory for Brownian paths. Realizations of Brownian excursion processes may be translated in terms of the realizations of a Wiener process under certain conditions. With this aim in mind, the monograph presents applications to topics which are not usually treated with the same tools, e.g.: arc sine law, laws of functionals of Brownian motion, and the Feynman-Kac formula.
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Basharov, A. M., E-mail: basharov@gmail.com [National Research Centre ' Kurchatov Institute,' (Russian Federation)
2012-09-15
It is shown that the effective Hamiltonian representation, as it is formulated in author's papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are 'locked' inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.
Basharov, A. M.
2012-09-01
It is shown that the effective Hamiltonian representation, as it is formulated in author's papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are "locked" inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.
Mano, Omer
2017-01-01
Sensory neuroscience seeks to understand and predict how sensory neurons respond to stimuli. Nonlinear components of neural responses are frequently characterized by the second-order Wiener kernel and the closely-related spike-triggered covariance (STC). Recent advances in data acquisition have made it increasingly common and computationally intensive to compute second-order Wiener kernels/STC matrices. In order to speed up this sort of analysis, we developed a graphics processing unit (GPU)-accelerated module that computes the second-order Wiener kernel of a system’s response to a stimulus. The generated kernel can be easily transformed for use in standard STC analyses. Our code speeds up such analyses by factors of over 100 relative to current methods that utilize central processing units (CPUs). It works on any modern GPU and may be integrated into many data analysis workflows. This module accelerates data analysis so that more time can be spent exploring parameter space and interpreting data. PMID:28068420
Peña, M.
2016-10-01
Achieving acceptable signal-to-noise ratio (SNR) can be difficult when working in sparsely populated waters and/or when species have low scattering such as fluid filled animals. The increasing use of higher frequencies and the study of deeper depths in fisheries acoustics, as well as the use of commercial vessels, is raising the need to employ good denoising algorithms. The use of a lower Sv threshold to remove noise or unwanted targets is not suitable in many cases and increases the relative background noise component in the echogram, demanding more effectiveness from denoising algorithms. The Adaptive Wiener Filter (AWF) denoising algorithm is presented in this study. The technique is based on the AWF commonly used in digital photography and video enhancement. The algorithm firstly increments the quality of the data with a variance-dependent smoothing, before estimating the noise level as the envelope of the Sv minima. The AWF denoising algorithm outperforms existing algorithms in the presence of gaussian, speckle and salt & pepper noise, although impulse noise needs to be previously removed. Cleaned echograms present homogenous echotraces with outlined edges.
Wiener Reconstruction of All-Sky Galaxy Surveys in Spherical Harmonics
Lahav, O.; Fisher, K. B.; Hoffman, Y.; Scharf, C. A.; Zaroubi, S.
1994-03-01
The analysis of whole-sky galaxy surveys commonly suffers from the problems of shot-noise and incomplete sky coverage (e.g., at the Zone of Avoidance). The orthogonal set of spherical harmonics is utilized here to expand the observed galaxy distribution. We show that in the framework of Bayesian statistics and Gaussian random fields the 4π harmonics can be recovered and the shot-noise can be removed, giving the optimal picture of the underlying density field. The correction factor from observed to reconstructed harmonics turns out to be the well-known Wiener filter (the ratio of signal to signal + noise), which is also derived by requiring minimum variance. We apply the method to the projected 1.2 Jy IRAS survey. The reconstruction confirms the connectivity of the supergalactic plane across the Galactic plane (at Galactic longitude l~135^deg^ and l~315^deg^) and the Puppis cluster behind the Galactic plane (l~240^deg^). The method can be extended to three dimensions in both real and redshift space, and applied to other cosmic phenomena such as the COBE microwave background maps.
Directory of Open Access Journals (Sweden)
Zhen Chen
2016-01-01
Full Text Available Accelerated degradation test (ADT has been widely used to assess highly reliable products’ lifetime. To conduct an ADT, an appropriate degradation model and test plan should be determined in advance. Although many historical studies have proposed quite a few models, there is still room for improvement. Hence we propose a Nonlinear Generalized Wiener Process (NGWP model with consideration of the effects of stress level, product-to-product variability, and measurement errors for a higher estimation accuracy and a wider range of use. Then under the constraints of sample size, test duration, and test cost, the plans of constant-stress ADT (CSADT with multiple stress levels based on the NGWP are designed by minimizing the asymptotic variance of the reliability estimation of the products under normal operation conditions. An optimization algorithm is developed to determine the optimal stress levels, the number of units allocated to each level, inspection frequency, and measurement times simultaneously. In addition, a comparison based on degradation data of LEDs is made to show better goodness-of-fit of the NGWP than that of other models. Finally, optimal two-level and three-level CSADT plans under various constraints and a detailed sensitivity analysis are demonstrated through examples in this paper.
Harmonies of disorder Norbert Wiener : a mathematician-philosopher of our time
Montagnini, Leone
2017-01-01
This book presents the entire body of thought of Norbert Wiener (1894–1964), knowledge of which is essential if one wishes to understand and correctly interpret the age in which we live. The focus is in particular on the philosophical and sociological aspects of Wiener’s thought, but these aspects are carefully framed within the context of his scientific journey. Important biographical events, including some that were previously unknown, are also highlighted, but while the book has a biographical structure, it is not only a biography. The book is divided into four chronological sections, the first two of which explore Wiener’s development as a philosopher and logician and his brilliant interwar career as a mathematician, supported by his philosophical background. The third section considers his research during World War II, which drew upon his previous scientific work and reflections and led to the birth of cybernetics. Finally, the radical post-war shift in Wiener’s intellectual path is considered, e...
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Masakiyo Miyazawa
2012-01-01
Full Text Available We extend the framework of Neuts' matrix analytic approach to a reflected process generated by a discrete time multidimensional Markov additive process. This Markov additive process has a general background state space and a real vector valued additive component, and generates a multidimensional reflected process. Our major interest is to derive a closed form formula for the stationary distribution of this reflected process. To this end, we introduce a real valued level, and derive new versions of the Wiener-Hopf factorization for the Markov additive process with the multidimensional additive component. In particular, itis represented by moment generating functions, and we consider the domain for it to be valid.Our framework is general enough to include multi-server queues and/or queueing networks as well as non-linear time series which are currently popular in financial and actuarial mathematics. Our results yield structural results for such models. As an illustration, we apply our results to extend existing results on the tail behavior of reflected processes.A major theme of this work is to connect recent work on matrix analytic methods to classical probabilistic studies on Markov additive processes. Indeed, using purely probabilistic methods such as censoring, duality, level crossing and time-reversal (which are known in the matrix analytic methods community but date back to Arjas & Speed [2] and Pitman [29], we extend and unify existing results in both areas.
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Li Sun
2016-01-01
Full Text Available It is assumed that the drift parameter is dependent on the acceleration variables and the diffusion coefficient remains the same across the whole accelerated degradation test (ADT in most of the literature based on Wiener process. However, the diffusion coefficient variation would also become obvious in some applications with the stress increasing. Aiming at the phenomenon, the paper concludes that both the drift parameter and the diffusion parameter depend on stress variables based on the invariance principle of failure mechanism and Nelson assumption. Accordingly, constant stress accelerated degradation process (CSADP and step stress accelerated degradation process (SSADP with random effects are modeled. The unknown parameters in the established model are estimated based on the property of degradation and degradation increment, separately for CASDT and SSADT, by the maximum likelihood estimation approach with measurement error. In addition, the simulation steps of accelerated degradation data are provided and simulated step stress accelerated degradation data is designed to validate the proposed model compared to other models. Finally, a case study of CSADT is conducted to demonstrate the benefits of our model in the practical engineering.
Nonlinear modeling of activated sludge process using the Hammerstein-Wiener structure
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Frącz Paweł
2016-01-01
Full Text Available The paper regards to physical model of the Activated Sludge Process, which is a part of the wastewater treatment. The aim of the study was to describe nitrogen transformation process and the demand of chemical fractions, involved in the ASP process. Moreover, the non-linear relationship between the flow of wastewater and the consumed electrical energy, used by the blowers, was determined. Such analyses are important from the economical and environmental point of view. Assuming that the total power does not change the blower is charging during a year an energy amount of approx. 613 MW. This illustrates in particular the scale of the demand for energy consumption in the biological aeration unit. The aim is to minimize the energy consumption through first building a model of ASP and then through optimization of the overall process by modifying chosen parameter in numerical simulations. In this paper example measurement and analysis results of nitrite and ammonium nitrogen concentrations in the aeration reactor and the active power consumed by blowers for the aeration process were presented. Further the ASP modeling procedure, which uses the Hammerstein-Wiener structure and example verification results were presented. Based on the achieved results it was stated that the developed set of methodologies may be used to improve and expand the overriding control system for system for wastewater treatment plant.
Optomechanically induced stochastic resonance and chaos transfer between optical fields
Monifi, Faraz; Zhang, Jing; Özdemir, Şahin Kaya; Peng, Bo; Liu, Yu-Xi; Bo, Fang; Nori, Franco; Yang, Lan
2016-06-01
Chaotic dynamics has been reported in many physical systems and has affected almost every field of science. Chaos involves hypersensitivity to the initial conditions of a system and introduces unpredictability into its output. Thus, it is often unwanted. Interestingly, the very same features make chaos a powerful tool to suppress decoherence, achieve secure communication and replace background noise in stochastic resonance—a counterintuitive concept that a system's ability to transfer information can be coherently amplified by adding noise. Here, we report the first demonstration of chaos-induced stochastic resonance in an optomechanical system, as well as the optomechanically mediated chaos transfer between two optical fields such that they follow the same route to chaos. These results will contribute to the understanding of nonlinear phenomena and chaos in optomechanical systems, and may find applications in the chaotic transfer of information and for improving the detection of otherwise undetectable signals in optomechanical systems.
Chaos and dynamics of spinning particles in Kerr spacetime
Han, Wen-Biao
2010-01-01
We study chaos dynamics of spinning particles in Kerr spacetime of rotating black holes use the Papapetrou equations by numerical integration. Because of spin, this system exists many chaos solutions, and exhibits some exceptional dynamic character. We investigate the relations between the orbits chaos and the spin magnitude S, pericenter, polar angle and Kerr rotation parameter a by means of a kind of brand new Fast Lyapulov Indicator (FLI) which is defined in general relativity. The classical definition of Lyapulov exponent (LE) perhaps fails in curve spacetime. And we emphasize that the Poincar\\'e sections cannot be used to detect chaos for this case. Via calculations, some new interesting conclusions are found: though chaos is easier to emerge with bigger S, but not always depends on S monotonically; the Kerr parameter a has a contrary action on the chaos occurrence. Furthermore, the spin of particles can destroy the symmetry of the orbits about the equatorial plane. And for some special initial condition...
Chaos in electric drive systems analysis control and application
Chau, K T
2011-01-01
In Chaos in Electric Drive Systems: Analysis, Control and Application authors Chau and Wang systematically introduce an emerging technology of electrical engineering that bridges abstract chaos theory and practical electric drives. The authors consolidate all important information in this interdisciplinary technology, including the fundamental concepts, mathematical modeling, theoretical analysis, computer simulation, and hardware implementation. The book provides comprehensive coverage of chaos in electric drive systems with three main parts: analysis, control and application. Corresponding drive systems range from the simplest to the latest types: DC, induction, synchronous reluctance, switched reluctance, and permanent magnet brushless drives.The first book to comprehensively treat chaos in electric drive systemsReviews chaos in various electrical engineering technologies and drive systemsPresents innovative approaches to stabilize and stimulate chaos in typical drivesDiscusses practical application of cha...
Control of Beam Halo-Chaos by Soliton
Institute of Scientific and Technical Information of China (English)
BAI Long; WENG Jia-Qiang; FANG Jin-Qing
2005-01-01
@@ The Kapchinsky-Vladimirsky beam through an alternating-gradient quadrupole magnetic field is studied using the particle-core model. The beam halo-chaos is found, and the soliton controller is proposed based on the mechanism of halo formation and strategy of controlling halo-chaos. We perform a multiparticle simulation to control the halo by soliton controller, and find that the halo-chaos and its regeneration can be eliminated. It is shown that our control method is effective.
Chaotic and Chaos-Like Behavior in Continued Fractions
Shuji, OBATA; Shigeru, OHKURO; Toshiaki, MAEDA; Physics Laboratory, Faculty of Science and Engineering, Tokyo Denki University; Laboratory of Information aud System Engineering, Hachinohe Institute of Technology; DEPARTMENT OF MATHEMATICAL SCIENCES, TOKYO DENKI UNIVERSITY
1999-01-01
Chaotic and chaos-like behavior in continued fractions is studied with respect to several types of maps, including a logistic map. Various numerical phenomena in the continued fractions are investigated, where the fractions correspond to fractal structures. Cyclic terms in the Cauchy distribution areas are introduced, including the chaos-like behavior. It is indicated that such mixed states of distributions and cycles are common in the chaotic and chaos-like behavior.
Testing for deterministic monetary chaos: Metric and topological diagnostics
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Barkoulas, John T. [Department of Finance and Quantitative Analysis, Georgia Southern University, Statesboro, GA 30460 (United States)], E-mail: jbarkoul@georgiasouthern.edu
2008-11-15
The evidence of deterministic chaos in monetary aggregates tends to be contradictory in the literature. We revisit the issue of monetary chaos by applying tools based on both the metric (correlation dimension and Lyapunov exponents) and topological (recurrence plots) approaches to chaos. For simple-sum and divisia monetary aggregates over an expanded sample period, the empirical evidence from both approaches is negative for monetary chaotic dynamics.
Quantum Chaos in Physical Systems: from Super Conductors to Quarks
Bittner, Elmar; Markum, Harald; Pullirsch, Rainer
2001-01-01
This article is the written version of a talk delivered at the Bexbach Colloquium of Science 2000 and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. Several examples of physical systems exhibiting quantum chaos ranging from nuclear to solid state physics are presented. The presentation concludes with recent research work on quantum chromodynamics and the qua...
Chaos theory perspective for industry clusters development
Yu, Haiying; Jiang, Minghui; Li, Chengzhang
2016-03-01
Industry clusters have outperformed in economic development in most developing countries. The contributions of industrial clusters have been recognized as promotion of regional business and the alleviation of economic and social costs. It is no doubt globalization is rendering clusters in accelerating the competitiveness of economic activities. In accordance, many ideas and concepts involve in illustrating evolution tendency, stimulating the clusters development, meanwhile, avoiding industrial clusters recession. The term chaos theory is introduced to explain inherent relationship of features within industry clusters. A preferred life cycle approach is proposed for industrial cluster recessive theory analysis. Lyapunov exponents and Wolf model are presented for chaotic identification and examination. A case study of Tianjin, China has verified the model effectiveness. The investigations indicate that the approaches outperform in explaining chaos properties in industrial clusters, which demonstrates industrial clusters evolution, solves empirical issues and generates corresponding strategies.
Experimental chaos detection in the Duffing oscillator
Eyebe Fouda, J. S. Armand; Bodo, Bertrand; Djeufa, Guy M. D.; Sabat, Samrat L.
2016-04-01
This paper presents a comparative study of four algorithms namely the maximal Lyapunov exponent (MLE), 0-1 test, conditional entropy of ordinal patterns (CPE) and recently developed permutation largest slope entropy (PLSE) algorithm for experimental chaos detection in the Duffing oscillator. We consider an electrical model of the Duffing oscillator and its equivalent electronic circuit for generating the data to validate the effectiveness of the algorithms. The performance of the PLSE is compared with the 0-1 test and the CPE algorithms on the data set obtained from the simulated circuit; and with the MLE for the data collected from the experimental circuit. The experimental data are acquired using a digital oscilloscope with 1 MHz sampling frequency. From the comparison of the experimental spectra of the four methods with the analog phase portraits of the real system, it appears that the PLSE is the more reliable algorithm for chaos detection from experimental data.
Measurement induced chaos with entangled states
Kiss, T; Tóth, L D; Gábris, A; Jex, I; Alber, G
2011-01-01
Quantum control, in a broad sense, may include measurement of quantum systems and, as a feed back operation, selection from an ensemble conditioned on the measurements. The resulting dynamics can be nonlinear and, if applied iteratively, can lead to true chaos in a quantum system. We consider the dynamics of an ensemble of two qubit systems subjected to measurement and conditional selection. We prove that the iterative dynamics leads to true chaos in the entanglement of the qubits. A class of special initial states exhibits high sensitivity to the initial conditions. In the parameter space of the special initial states we identify two types of islands: one converging to a separable state, while the other being asymptotically completely entangled. The islands form a fractal like structure. Adding noise to the initial state introduces a further stable asymptotic cycle.
Migraine--new perspectives from chaos theory.
Kernick, D
2005-08-01
Converging from a number of disciplines, non-linear systems theory and in particular chaos theory offer new descriptive and prescriptive insights into physiological systems. This paper briefly reviews an approach to physiological systems from these perspectives and outlines how these concepts can be applied to the study of migraine. It suggests a wide range of potential applications including new approaches to classification, treatment and pathophysiological mechanisms. A hypothesis is developed that suggests that dysfunctional consequences can result from a mismatch between the complexity of the environment and the system that is seeking to regulate it and that the migraine phenomenon is caused by an incongruity between the complexity of mid brain sensory integration and cortical control networks. Chaos theory offers a new approach to the study of migraine that complements existing frameworks but may more accurately reflect underlying physiological mechanisms.
Tuning quantum measurements to control chaos
Eastman, Jessica K.; Hope, Joseph J.; Carvalho, André R. R.
2017-01-01
Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the quantum-to-classical transition of chaotic systems. In this work we focus on the effect of varying monitoring strategies, i.e. for a given decoherence model and a fixed environmental coupling, there is still freedom on how to monitor a quantum system. We show here that there is a region between the deep quantum regime and the classical limit where the choice of the monitoring parameter allows one to control the complex behaviour of the system, leading to either the emergence or suppression of chaos. Our work shows that this is a result from the interplay between quantum interference effects induced by the nonlinear dynamics and the effectiveness of the decoherence for different measurement schemes. PMID:28317933
Poincaré chaos and unpredictable functions
Akhmet, Marat; Fen, Mehmet Onur
2017-07-01
The results of this study are continuation of the research of Poincaré chaos initiated in the papers (M. Akhmet and M.O. Fen, Commun Nonlinear Sci Numer Simulat 40 (2016) 1-5; M. Akhmet and M.O. Fen, Turk J Math, doi:10.3906/mat-1603-51, in press). We focus on the construction of an unpredictable function, continuous on the real axis. As auxiliary results, unpredictable orbits for the symbolic dynamics and the logistic map are obtained. By shaping the unpredictable function as well as Poisson function we have performed the first step in the development of the theory of unpredictable solutions for differential and discrete equations. The results are preliminary ones for deep analysis of chaos existence in differential and hybrid systems. Illustrative examples concerning unpredictable solutions of differential equations are provided.
Polynomial chaos representation of databases on manifolds
Energy Technology Data Exchange (ETDEWEB)
Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)
2017-04-15
Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.
Quantum chaos in QCD and hadrons
Markum, H; Pullirsch, R; Sengl, B; Wagenbrunn, R F; Markum, Harald; Plessas, Willibald; Pullirsch, Rainer; Sengl, Bianka; Wagenbrunn, Robert F.
2005-01-01
This article is the written version of a talk delivered at the Workshop on Nonlinear Dynamics and Fundamental Interactions in Tashkent and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. In accordance to the title, the presentation is twofold and begins with research results on quantum chromodynamics and the quark-gluon plasma. We conclude with recent research work on the spectroscopy of baryons. Within the framework of a relativistic constituent quark model we investigate the excitation spectra of the nucleon and the delta with regard to a possible chaotic behavior for the cases when a hyperfine interaction of either Goldstone-boson-exchange or one-gluon-exchange type is added to the confinement interaction. Agreement with predictions from the experimental hadron spectrum is established.
An exploration of dynamical systems and chaos
Argyris, John H; Haase, Maria; Friedrich, Rudolf
2015-01-01
This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlar...
Chaos in effective classical and quantum dynamics
Casetti, L; Modugno, M; Casetti, Lapo; Gatto, Raoul; Modugno, Michele
1998-01-01
We investigate the dynamics of classical and quantum N-component phi^4 oscillators in presence of an external field. In the large N limit the effective dynamics is described by two-degree-of-freedom classical Hamiltonian systems. In the classical model we observe chaotic orbits for any value of the external field, while in the quantum case chaos is strongly suppressed. A simple explanation of this behaviour is found in the change in the structure of the orbits induced by quantum corrections. Consistently with Heisenberg's principle, quantum fluctuations are forced away from zero, removing in the effective quantum dynamics a hyperbolic fixed point that is a major source of chaos in the classical model.
Kac-Moody Algebras and Controlled Chaos
Wesley, D H
2007-01-01
Compactification can control chaotic Mixmaster behavior in gravitational systems with p-form matter: we consider this in light of the connection between supergravity models and Kac-Moody algebras. We show that different compactifications define "mutations" of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems determined by hyperbolic (but not strictly hyperbolic) algebras. Cosmological models with a smooth pre-big bang phase require that chaos is absent: we show that compactification alone cannot eliminate chaos in the simplest compactifications of the heterotic string on a Calabi-Yau, or M theory on a manifold of G_2 holonomy.
Buoyancy driven turbulence and distributed chaos
Bershadskii, A
2016-01-01
It is shown, using results of recent direct numerical simulations, laboratory experiments and atmospheric measurements, that buoyancy driven turbulence exhibits a broad diversity of the types of distributed chaos with its stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$. The distributed chaos with $\\beta = 1/3$ (determined by the helicity correlation integral) is the most common feature of the stably stratified turbulence (due to the strong helical waves presence). These waves mostly dominate spectral properties of the vertical component of velocity field, while the horizontal component is dominated by the diffusive processes both for the weak and strong stable stratification ($\\beta =2/3$). For the last case influence of the low boundary can overcome the wave effects and result in $\\beta =1/2$ for the vertical component of the velocity field (the spontaneous breaking of the space translational symmetry - homogeneity). For the unstably stratified turbulence in the Rayleigh-Taylor mixing zone the di...
Chaos A Program Collection for the PC
Korsch, Hans Jürgen; Hartmann, Timo
2008-01-01
This new edition strives yet again to provide readers with a working knowledge of chaos theory and dynamical systems through parallel introductory explanations in the book and interaction with carefully-selected programs supplied on the accompanying diskette. The programs enable readers, especially advanced-undergraduate students in physics, engineering, and math, to tackle relevant physical systems quickly on their PCs, without distraction from algorithmic details. For the third edition of Chaos: A Program Collection for the PC, each of the previous twelve programs is polished and rewritten in C++ (both Windows and Linux versions are included). A new program treats kicked systems, an important class of two-dimensional problems, which is introduced in Chapter 13. Each chapter follows the structure: theoretical background; numerical techniques; interaction with the program; computer experiments; real experiments and empirical evidence; reference. Interacting with the many numerical experiments have proven to h...
Chaos in hydrodynamic BL Herculis models
Smolec, R
2014-01-01
We present non-linear, convective, BL Her-type hydrodynamic models that show complex variability characteristic for deterministic chaos. The bifurcation diagram reveals a rich structure, with many phenomena detected for the first time in hydrodynamic models of pulsating stars. The phenomena include not only period doubling cascades en route to chaos (detected in earlier studies) but also periodic windows within chaotic band, type-I and type-III intermittent behaviour, interior crisis bifurcation and others. Such phenomena are known in many textbook chaotic systems, from the simplest discrete logistic map, to more complex systems like Lorenz equations. We discuss the physical relevance of our models. Although except of period doubling such phenomena were not detected in any BL Her star, chaotic variability was claimed in several higher luminosity siblings of BL Her stars - RV Tau variables, and also in longer-period, luminous irregular pulsators. Our models may help to understand these poorly studied stars. Pa...
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
Frozen spatial chaos induced by boundaries
Eguiluz, V M; Piro, O; Balle, S; Eguiluz, Victor M.; Hernandez-Garcia, Emilio; Piro, Oreste; Balle, Salvador
1999-01-01
We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.
Chaos control of parametric driven Duffing oscillators
Energy Technology Data Exchange (ETDEWEB)
Jin, Leisheng; Mei, Jie; Li, Lijie, E-mail: L.Li@swansea.ac.uk [College of Engineering, Swansea University, Swansea SA2 8PP (United Kingdom)
2014-03-31
Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.
Chaos in a topologically transitive system
Institute of Scientific and Technical Information of China (English)
XIONG; Jincheng
2005-01-01
The chaotic phenomena have been studied in a topologically transitive system and it has been shown that the erratic time dependence of orbits in such a topologically transitive system is more complicated than what described by the well-known technology "Li-Yorke chaos". The concept "sensitive dependency on initial conditions" has been generalized, and the chaotic phenomena has been discussed for transitive systems with the generalized sensitive dependency property.
Complex motions and chaos in nonlinear systems
Machado, José; Zhang, Jiazhong
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.
Computer Auxiliary Analysis for Stochasticity of Chaos
Institute of Scientific and Technical Information of China (English)
ZHAOGeng; FANGJin-qing
2003-01-01
In this work, we propose a mathematics-physical statistic analytical method for stochastic process of chaos, based on stochastic test via combination measurement of Monobit and Runs. Computer auxiliary analysis shows that it is of stochasticity for stochastic number produced from the chaotic circuit. Our software is written by VB and C++, the later can be tested by the former, and at the same time it is verified by stochastic number produced by the computer. So the data treatment results are reliable.
Reducing or enhancing chaos using periodic orbits.
Bachelard, R; Chandre, C; Leoncini, X
2006-06-01
A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local bifurcations). Depending on the values of the residues, reflecting their linear stability properties, a set of invariant tori is destroyed or created in the neighborhood of the chosen periodic orbits. An application on a paradigmatic system, a forced pendulum, illustrates the method.
Chaos in free electron laser oscillators
Energy Technology Data Exchange (ETDEWEB)
Bruni, C. [Univ Paris 11, LAL, UMR 8607, F-91898 Orsay, (France); Bachelard, R.; Couprie, M.E. [Synchrotron SOLEIL, F-91192 Gif Sur Yvette, (France); Garzella, D. [CEA DSM DRECAM SPAM, F-91191 Gif Sur Yvette, (France); Orlandi, G.L. [CR Frascati FIM FISACC, ENEA, I-00044 Frascati, (Italy)
2009-07-01
The chaotic nature of a storage-ring free electron laser (FEL) is investigated. The derivation of a low embedding dimension for the dynamics allows the low-dimensionality of this complex system to be observed, whereas its unpredictability is demonstrated, in some ranges of parameters, by a positive Lyapounov exponent. The route to chaos is then explored by tuning a single control parameter, and a period-doubling cascade is evidenced, as well as intermittence. (authors)
Chaos: Understanding and Controlling Laser Instability
Blass, William E.
1997-01-01
In order to characterize the behavior of tunable diode lasers (TDL), the first step in the project involved the redesign of the TDL system here at the University of Tennessee Molecular Systems Laboratory (UTMSL). Having made these changes it was next necessary to optimize the new optical system. This involved the fine adjustments to the optical components, particularly in the monochromator, to minimize the aberrations of coma and astigmatism and to assure that the energy from the beam is focused properly on the detector element. The next step involved the taking of preliminary data. We were then ready for the analysis of the preliminary data. This required the development of computer programs that use mathematical techniques to look for signatures of chaos. Commercial programs were also employed. We discovered some indication of high dimensional chaos, but were hampered by the low sample rate of 200 KSPS (kilosamples/sec) and even more by our sample size of 1024 (1K) data points. These limitations were expected and we added a high speed data acquisition board. We incorporated into the system a computer with a 40 MSPS (million samples/sec) data acquisition board. This board can also capture 64K of data points so that were then able to perform the more accurate tests for chaos. The results were dramatic and compelling, we had demonstrated that the lead salt diode laser had a chaotic frequency output. Having identified the chaotic character in our TDL data, we proceeded to stage two as outlined in our original proposal. This required the use of an Occasional Proportional Feedback (OPF) controller to facilitate the control and stabilization of the TDL system output. The controller was designed and fabricated at GSFC and debugged in our laboratories. After some trial and error efforts, we achieved chaos control of the frequency emissions of the laser. The two publications appended to this introduction detail the entire project and its results.
Optimal chaos control through reinforcement learning.
Gadaleta, Sabino; Dangelmayr, Gerhard
1999-09-01
A general purpose chaos control algorithm based on reinforcement learning is introduced and applied to the stabilization of unstable periodic orbits in various chaotic systems and to the targeting problem. The algorithm does not require any information about the dynamical system nor about the location of periodic orbits. Numerical tests demonstrate good and fast performance under noisy and nonstationary conditions. (c) 1999 American Institute of Physics.
Chaos control of parametric driven Duffing oscillators
Jin, Leisheng; Mei, Jie; Li, Lijie
2014-03-01
Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.
Murakami, A; Ohtsubo, J
2001-06-01
Chaos synchronization using a continuous chaos control method was studied in two identical chaotic laser systems consisting of semiconductor lasers and optical feedback from an external mirror. Numerical calculations for rate equations indicate that the stability of chaos synchronization depends significantly on the external mirror position. We performed a linear stability analysis for the rate equations. Our results show that the stability of the synchronization is much influenced by the mode interaction between the relaxation oscillation frequency of the semiconductor laser and the external cavity frequency. Due to this interaction, an intensive mode competition between the two frequencies destroys the synchronization, but stable synchronization can be achieved when the mode competition is very weak.
Bifurcations and Chaos in Duffing Equation
Institute of Scientific and Technical Information of China (English)
2007-01-01
The Duffing equation with even-odd asymmetrical nonlinear-restoring force and one external forcing is investigated. The conditions of existence of primary resonance, second-order, third-order subharmonics, m-order subharmonics and chaos are given by using the second-averaging method, the Melnikov method and bifurcation theory. Numerical simulations including bifurcation diagram, bifurcation surfaces and phase portraits show the consistence with the theoretical analysis. The numerical results also exhibit new dynamical behaviors including onset of chaos, chaos suddenly disappearing to periodic orbit, cascades of inverse period-doubling bifurcations, period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, symmetry-breaking of periodic orbits, interleaving occurrence of chaotic behaviors and period-one orbit, a great abundance of periodic windows in transient chaotic regions with interior crises and boundary crisis and varied chaotic attractors. Our results show that many dynamical behaviors are strictly departure from the behaviors of the Duffing equation with odd-nonlinear restoring force.
Chaos in Chiral Condensates in Gauge Theories
Hashimoto, Koji; Murata, Keiju; Yoshida, Kentaroh
2016-12-01
Assigning a chaos index for dynamics of generic quantum field theories is a challenging problem because the notion of a Lyapunov exponent, which is useful for singling out chaotic behavior, works only in classical systems. We address the issue by using the AdS /CFT correspondence, as the large Nc limit provides a classicalization (other than the standard ℏ→0 ) while keeping nontrivial quantum condensation. We demonstrate the chaos in the dynamics of quantum gauge theories: The time evolution of homogeneous quark condensates ⟨q ¯q ⟩ and ⟨q ¯γ5q ⟩ in an N =2 supersymmetric QCD with the S U (Nc) gauge group at large Nc and at a large 't Hooft coupling λ ≡NcgYM2 exhibits a positive Lyapunov exponent. The chaos dominates the phase space for energy density E ≳(6 ×1 02)×mq4(Nc/λ2), where mq is the quark mass. We evaluate the largest Lyapunov exponent as a function of (Nc,λ ,E ) and find that the N =2 supersymmetric QCD is more chaotic for smaller Nc.
Towards an optimal sampling of peculiar velocity surveys for Wiener Filter reconstructions
Sorce, Jenny G.; Hoffman, Yehuda; Gottlöber, Stefan
2017-06-01
The Wiener Filter (WF) technique enables the reconstruction of density and velocity fields from observed radial peculiar velocities. This paper aims at identifying the optimal design of peculiar velocity surveys within the WF framework. The prime goal is to test the dependence of the reconstruction quality on the distribution and nature of data points. Mock data sets, extending to 250 h-1 Mpc, are drawn from a constrained simulation that mimics the local Universe to produce realistic mock catalogues. Reconstructed fields obtained with these mocks are compared to the reference simulation. Comparisons, including residual distributions, cell-to-cell and bulk velocities, imply that the presence of field data points is essential to properly measure the flows. The fields reconstructed from mocks that consist only of galaxy cluster data points exhibit poor-quality bulk velocities. In addition, the reconstruction quality depends strongly on the grouping of individual data points into single points to suppress virial motions in high-density regions. Conversely, the presence of a Zone of Avoidance hardly affects the reconstruction. For a given number of data points, a uniform sample does not score any better than a sample with decreasing number of data points with the distance. The best reconstructions are obtained with a grouped survey containing field galaxies: assuming no error, they differ from the simulated field by less than 100 km s-1 up to the extreme edge of the catalogues or up to a distance of three times the mean distance of data points for non-uniform catalogues. The overall conclusions hold when errors are added.
The chaos and order in nuclear molecular dynamics; Chaos i porzadek w jadrowej dynamice molekularnej
Energy Technology Data Exchange (ETDEWEB)
Srokowski, T. [Institute of Nuclear Physics, Cracow (Poland)
1995-12-31
The subject of the presented report is role of chaos in scattering processes in the frame of molecular dynamics. In this model, it is assumed that scattering particles (nuclei) consist of not-interacted components as alpha particles or {sup 12}C, {sup 16}O and {sup 20}Ne clusters. The results show such effects as dynamical in stabilities and fractal structure as well as compound nuclei decay and heavy-ion fusion. The goal of the report is to make the reader more familiar with the chaos model and its application to nuclear phenomena. 157 refs, 40 figs.
Application of Chaos Theory to Psychological Models
Blackerby, Rae Fortunato
This dissertation shows that an alternative theoretical approach from physics--chaos theory--offers a viable basis for improved understanding of human beings and their behavior. Chaos theory provides achievable frameworks for potential identification, assessment, and adjustment of human behavior patterns. Most current psychological models fail to address the metaphysical conditions inherent in the human system, thus bringing deep errors to psychological practice and empirical research. Freudian, Jungian and behavioristic perspectives are inadequate psychological models because they assume, either implicitly or explicitly, that the human psychological system is a closed, linear system. On the other hand, Adlerian models that require open systems are likely to be empirically tenable. Logically, models will hold only if the model's assumptions hold. The innovative application of chaotic dynamics to psychological behavior is a promising theoretical development because the application asserts that human systems are open, nonlinear and self-organizing. Chaotic dynamics use nonlinear mathematical relationships among factors that influence human systems. This dissertation explores these mathematical relationships in the context of a sample model of moral behavior using simulated data. Mathematical equations with nonlinear feedback loops describe chaotic systems. Feedback loops govern the equations' value in subsequent calculation iterations. For example, changes in moral behavior are affected by an individual's own self-centeredness, family and community influences, and previous moral behavior choices that feed back to influence future choices. When applying these factors to the chaos equations, the model behaves like other chaotic systems. For example, changes in moral behavior fluctuate in regular patterns, as determined by the values of the individual, family and community factors. In some cases, these fluctuations converge to one value; in other cases, they diverge in
Chaos: A Topic for Interdisciplinary Education in Physics
Bae, Saebyok
2009-01-01
Since society and science need interdisciplinary works, the interesting topic of chaos is chosen for interdisciplinary education in physics. The educational programme contains various university-level activities such as computer simulations, chaos experiment and team projects besides ordinary teaching. According to the participants, the programme…
Master Teachers: Making a Difference on the Edge of Chaos
Chapin, Dexter
2008-01-01
The No Child Left Behind legislation, by legitimizing a stark, one-size-fits-all, industrial model of education, has denied the inherent complexity and richness of what teachers do. Discussing teaching in terms of Chaos Theory, Chapin explains that while excellent teaching may occur at the edge of chaos, it is not chaotic. There are patterns…
Major open problems in chaos theory and nonlinear dynamics
Li, Y Charles
2013-01-01
Nowadays, chaos theory and nonlinear dynamics lack research focuses. Here we mention a few major open problems: 1. an effective description of chaos and turbulence, 2. rough dependence on initial data, 3. arrow of time, 4. the paradox of enrichment, 5. the paradox of pesticides, 6. the paradox of plankton.
Controlling Beam Halo-Chaos via Time-Delayed Feedback
Institute of Scientific and Technical Information of China (English)
FANG Jin-Qing; WENG Jia-Qiang; ZHU Lun-Wu; LUO Xiao-Shu
2004-01-01
The study of controlling high-current proton beam halo-chaos has become a key concerned issue for many important applications. In this paper, time-delayed feedback control method is proposed for beam halo-chaos. Particle in cell simulation results show that the method is very effective and has some advantages for high-current beam experiments and engineering.
Using a quantum computer to investigate quantum chaos
Schack, Ruediger
1997-01-01
We show that the quantum baker's map, a prototypical map invented for theoretical studies of quantum chaos, has a very simple realization in terms of quantum gates. Chaos in the quantum baker's map could be investigated experimentally on a quantum computer based on only 3 qubits.
Universal properties of dynamically complex systems - The organization of chaos
Procaccia, Itamar
1988-06-01
The complex dynamic behavior of natural systems far from equilibrium is discussed. Progress that has been made in understanding universal aspects of the paths to such behavior, of the trajectories at the borderline of chaos, and of the nature of the complexity in the chaotic regime, is reviewed. The emerging grammar of chaos is examined.
The "Chaos" Pattern in Piaget's Theory of Cognitive Development.
Lindsay, Jean S.
Piaget's theory of the cognitive development of the child is related to the recently developed non-linear "chaos" model. The term "chaos" refers to the tendency of dynamical, non-linear systems toward irregular, sometimes unpredictable, deterministic behavior. Piaget identified this same pattern in his model of cognitive development in children.…
Chaos: A Topic for Interdisciplinary Education in Physics
Bae, Saebyok
2009-01-01
Since society and science need interdisciplinary works, the interesting topic of chaos is chosen for interdisciplinary education in physics. The educational programme contains various university-level activities such as computer simulations, chaos experiment and team projects besides ordinary teaching. According to the participants, the programme…
Experimental Control of Instabilities and Chaos in Fast Dynamical Systems
1997-06-01
is short (- 10 cm) [153]-[155]; these studies have more recently been considered from the chaos control viewpoint [42]. The apparatus required to...13] Christini, David J., and James A. Collins. Controlling Nonchaotic Neuronal Noise Using Chaos Control Techniques. Phys. Rev. Lett. 75:2782-2785
Multi-channel Wiener Filter for Speech Dereverberation in Hearing Aids - Sensitivity to DoA Errors
DEFF Research Database (Denmark)
Kuklasinski, Adam; Doclo, Simon; Jensen, Søren Holdt
2016-01-01
In this paper we study the robustness of a recently proposed Multi-channel Wiener Filter-based speech dereverberation algorithm to errors in the assumed direction of arrival (DoA) of the target speech. Different subsets of microphones of a pair of behind-the-ear hearing aids are used to construct...... various monaural and binaural configurations of the algorithm. Via a simulation experiment with frontally positioned target it is shown, that when correct DoA is assumed binaural configurations of the algorithm almost double the improvement of PESQ measure over monaural configurations. However...
Erbium - doped fiber laser systems: Routes to chaos
Directory of Open Access Journals (Sweden)
Rubežić Vesna
2014-01-01
Full Text Available Erbium-doped fiber laser systems exhibit a large variety of complex dynamical behaviors, bifurcations and attractors. In this paper, the chaotic behavior which can be achieved under certain conditions in a laser system with erbium-doped fiber, is discussed. The chaos in this system occurs through several standard scenarios. In this paper, the simulation sequence of quasiperiodic, intermittent and period-doubling scenario transitions to chaos is shown. Quasiperiodic and intermittent transitions to chaos are shown on the example system with a single ring. The electro-optical modulator was applied to the system for modulating the loss in the cavity. We used the sinusoidal and rectangular signals for modulation. Generation of chaos is achieved by changing the parameters of signal for modulation. Period-doubling transition to chaos is illustrated in a system with two rings. Simulation results are shown in the time domain and phase space.
Replication of chaos in neural networks, economics and physics
Akhmet, Marat
2016-01-01
This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.
$\\mathcal{PT}$-Symmetry-Breaking Chaos in Optomechanics
Lü, Xin-You; Ma, Jin-Yong; Wu, Ying
2015-01-01
We demonstrate a $\\mathcal{PT}$-symmetry-breaking chaos in optomechanical system (OMS), which features an ultralow driving threshold. In principle, this chaos will emerge once a driving laser is applied to the cavity mode and lasts for a period of time. The driving strength is inversely proportional to the starting time of chaos. This originally comes from the dynamical enhancement of nonlinearity by field localization in $\\mathcal{PT}$-symmetry-breaking phase ($\\mathcal{PT}$BP). Moreover, this chaos is switchable by tuning the system parameters so that a $\\mathcal{PT}$-symmetry phase transition occurs. This work may fundamentally broaden the regimes of cavity optomechanics and nonlinear optics. It offers the prospect of exploring ultralow-power-laser triggered chaos and its potential applications in secret communication.
Dynamical chaos in chip-scale optomechanical oscillators
Wu, Jiagui; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Xia, Guangqiong; Wong, Chee Wei
2016-01-01
Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here we report the first generation of dynamical chaos in silicon optomechanical oscillators, enabled by the strong and coupled nonlinearities of Drude electron-hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the complexity of chaos. The correlation dimension D2 is determined at ~ 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate about 2.94*the fundamental optomechanical oscillation. The corresponding nonlinear dynamical maps demonstrate the plethora of subharmonics, bifurcations, and stable regimes, along with distinct transitional routes into chaotic states. The chaos generation in our mesoscopic...
Population Floors and the Persistence of Chaos in Ecological Models.
Ruxton; Rohani
1998-06-01
Chaotic dynamics have been observed in a wide range of population models. Here we describe the effects of perturbing several of these models so as to introduce a non-zero minimum population size. This perturbation generally reduces the likelihood of observing chaos, in both discrete and continuous time models. The extent of this effect depends on whether chaos is generated through period-doubling, quasiperiodicity, or intermittence. Chaos reached via the quasiperiodic route is more robust against the perturbation than period-doubling chaos, whilst the inclusion of a population floor in a model exhibiting intermittent chaos may increase the frequency of population bursts although these become non-chaotic. Copyright 1998 Academic Press.
Directory of Open Access Journals (Sweden)
Glawar B
2002-01-01
Full Text Available Die Inzidenz isolierter epileptischer Anfälle nach Schlaganfällen wird in der Literatur zwischen 4 und 15 % angegeben. Die Wahrscheinlichkeit, eine Epilepsie nach einem zerebrovaskulären Ereignis zu entwickeln, liegt nach bisherigen Erkenntnissen zwischen 4 und 9 %. In einer prospektiven, multizentrischen Datenerhebung im Rahmen der Wiener Schlaganfalldatenbank werden seit Oktober 1998 Patienten mit der Diagnose Schlaganfall (nach der WHO-Definition und TIA, die innerhalb von 72 Stunden nach dem Ereignis zur Aufnahme an eine neurologische Abteilung kommen, erfaßt. Unter anderem werden auch Auftreten und Art von epileptischen Anfällen nach dem Ereignis beziehungsweise die Entwicklung einer vaskulären Epilepsie erfaßt. Für die vorliegende Fragestellung wurden die Daten von 1969 Patienten inklusive einer Dreimonatskontrolle ausgewertet. 82 dieser 1969 Patienten (= 4,2 % erlitten einen oder mehrere epileptische Anfälle nach dem Ereignis. Bei 55 Patienten (= 67 % trat der erste Anfall innerhalb von 24 Stunden, entsprechend einem Immediatanfall, auf. 22 Patienten (= 27 % hatten den ersten Anfall innerhalb der ersten 14 Tage, und bei 5 Personen (= 6 % wurde der erste Anfall erst zu einem späteren Zeitpunkt dokumentiert. Bei 67 % (n = 55 traten fokale Anfälle mit/ohne sekundäre Generalisierung auf, und bei ca. 33 % (n = 27 kam es zu phänomenologisch primär generalisierten Anfällen. In einer multivariaten Analyse zeigt sich, daß vor allem Patienten mit initial schwerer Behinderung nach dem NIH-Stroke Score ein höheres Risiko haben, epileptische Anfälle zu entwickeln. Bei 12 Patienten trat mehr als ein epileptischer Anfall auf, dies entspricht einer Inzidenz von 0,6 % für die Entwicklung einer vaskulären Epilepsie. In einem Beobachtungszeitraum von 3 Monaten sind noch nicht alle Patienten, die epileptische Anfälle entwickeln, erfaßt. Längere Beobachtungszeiträume und Kontrollen nach einem und nach zwei Jahren werden ausf
ORDER IN THE CHAOS IN SPORTS ORGANIZATIONS
Directory of Open Access Journals (Sweden)
Mehran Azarian
2014-07-01
Full Text Available Purpose: Nowadays, scientists consider the world as a combination of some systems that work in a self -organizing way and the result of such a way is unpredictable and accidential states. Compulsory Natural rules are affective in such circumstances. Also it is known that systems work in a circular form in which order ends in disorder and vice versa. The idea of world as something simple has already replaced by a complicated and contradictory world. The study aim is to survey chaordic organizations characters of sport organizations. Materials and methods : For this purpose we used a standard questionnaire with appropriate reliability and validity. The statistical population of the study are whole staff of sport and youth head-quarter of west Azarbaijan province that are 89 (sample number is equal to the population's. We used Kolmogrov- Smirnov test to study data normal distribution, and in respect of normal distribution of data to test hypothesis we used sample t test and also descriptive statistical methods like mean and standard deviation, through SPSS 18. Questionnaires were filled out by whole staff of sport and youth head-quarters of west Azarbaijan province. Results: Results of this study, which have got through a single-sample t-test, show that sport organizations have six characteristics of welcoming to innovation, coherence, uncertainty, non-linearity, unpredictability, and ugly structure. It’s just the grade of the characteristic of recruiting competent staffs that is low in sport organizations; in fact they don’t enjoy it. But, within assessing the main hypothesis of the research that was around the feature of chaos-order, it was resulted that sport organizations have characteristics of a chaos-order organization and they can be considered as a chaos-order organization. Conclusions: According to the results of this study and t-table we can deduce that sport organizations are chaordic organization.
Conduction at the onset of chaos
Baldovin, Fulvio
2017-02-01
After a general discussion of the thermodynamics of conductive processes, we introduce specific observables enabling the connection of the diffusive transport properties with the microscopic dynamics. We solve the case of Brownian particles, both analytically and numerically, and address then whether aspects of the classic Onsager's picture generalize to the non-local non-reversible dynamics described by logistic map iterates. While in the chaotic case numerical evidence of a monotonic relaxation is found, at the onset of chaos complex relaxation patterns emerge.
Intramolecular quantum chaos in doped helium nanodroplets
Polyakova, E.; Stolyarov, D.; Zhang, X.; Kresin, V. V.; Wittig, C.
2003-07-01
A mass spectrometric depletion spectrum (17 700-18 300 cm -1) is reported for NO 2 in superfluid (0.37 K) helium nanodroplets. Gas phase NO 2 is believed to be vibronically chaotic at these energies. Transitions are broadened and blue-shifted relative to their gas phase counterparts. The spectrum is fitted reasonably well by setting all of the widths and shifts equal to 7 cm -1. Modest dispersions (i.e., 90% lie within 2 cm -1 of the central values) are consistent with quantum chaos in NO 2. Relaxation is dominated by interactions of NO 2 with its non-superfluid helium nearest neighbors.
Wave Dynamical Chaos in Superconducting Microwave Cavities
Rehfeld, H; Dembowski, C; Gräf, H D; Hofferbert, R; Richter, A; Lengeler, Herbert
1997-01-01
During the last few years we have studied the chaotic behavior of special Euclidian geometries, so-called billiards, from the quantum or in more general sense "wave dynamical" point of view. Due to the equivalence between the stationary Schroedinger equation and the classical Helmholtz equation in the two-dimensional case (plain billiards), it is possible to simulate "quantum chaos" with the help of macroscopic, superconducting microwave cavities. Using this technique we investigated spectra of three billiards from the family of Pascal's Snails (Robnik-Billiards) with a different chaoticity in each case in order to test predictions of standard stochastical models for classical chaotic systems.
A new optimization algorithm based on chaos
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this article, some methods are proposed for enhancing the converging velocity of the COA (chaos optimization algorithm) based on using carrier wave two times, which can greatly increase the speed and efficiency of the first carrier wave's search for the optimal point in implementing the sophisticated searching during the second carrier wave is faster and more accurate.In addition, the concept of using the carrier wave three times is proposed and put into practice to tackle the multi-variables optimization problems, where the searching for the optimal point of the last several variables is frequently worse than the first several ones.
Delayed self-synchronization in homoclinic chaos
Arecchi, F. T.; Meucci, R.; Allaria, E.; di Garbo, A.; Tsimring, L. S.
2002-04-01
The chaotic spike train of a homoclinic dynamical system is self-synchronized by applying a time-delayed correction proportional to the laser output intensity. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long-periodic orbits is possible. On these orbits, the dynamics appears chaotic over a finite time, but then it repeats with a recurrence time that is slightly longer than the delay time. The effect, called delayed self-synchronization, displays analogies with neurodynamic events that occur in the buildup of long-term memories.
Quantum chaos and the black hole horizon
CERN. Geneva
2016-01-01
Thanks to AdS/CFT, the analogy between black holes and thermal systems has become a practical tool, shedding light on thermalization, transport, and entanglement dynamics. Continuing in this vein, recent work has shown how chaos in the boundary CFT can be analyzed in terms of high energy scattering right on the horizon of the dual black hole. The analysis revolves around certain out-of-time-order correlation functions, which are simple diagnostics of the butterfly effect. We will review this work, along with a general bound on these functions that implies black holes are the most chaotic systems in quantum mechanics. (NB Room Change to Main Auditorium)
Geometry in the large and hyperbolic chaos
Energy Technology Data Exchange (ETDEWEB)
Hasslacher, B.; Mainieri, R.
1998-11-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The authors calculated observables in strongly chaotic systems. This is difficult to do because of a lack of a workable orbit classification for such systems. This is due to global geometrical information from the original dynamical system being entangled in an unknown way throughout the orbit sequence. They used geometrical methods from modern mathematics and recent connections between global geometry and modern quantum field theory to study the natural geometrical objects belonging to hard chaos-hyperbolic manifolds.
Chaos Synchronization in Two Coupled Duffing Oscillators
Institute of Scientific and Technical Information of China (English)
方见树; 荣曼生; 方焯; 刘小娟
2001-01-01
We have obtained two general unstable periodic solutions near the homoclinic orbits of two coupled Duffing oscillators with weak periodic perturbations by using the direct perturbation technique. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors. The corresponding numerical results show that the phase portraits in the (x, u) and (y, v) planes are identical and are synchronized when the parameters of the two coupled oscillators are identical, but they are different and asynchronized when there is any difference between these parameters. It has been shown that the system parameters play a very important role in chaos control and synchronization.
Time reversibility, computer simulation, and chaos
Hoover, William Graham
1999-01-01
A small army of physicists, chemists, mathematicians, and engineers has joined forces to attack a classic problem, the "reversibility paradox", with modern tools. This book describes their work from the perspective of computer simulation, emphasizing the author's approach to the problem of understanding the compatibility, and even inevitability, of the irreversible second law of thermodynamics with an underlying time-reversible mechanics. Computer simulation has made it possible to probe reversibility from a variety of directions and "chaos theory" or "nonlinear dynamics" has supplied a useful
Cryptography with chaos at the physical level
Energy Technology Data Exchange (ETDEWEB)
Machado, Romuel F. E-mail: romuelm@iceb.ufop.br; Baptista, Murilo S.; Grebogi, C
2004-09-01
In this work, we devise a chaos-based secret key cryptography scheme for digital communication where the encryption is realized at the physical level, that is, the encrypting transformations are applied to the wave signal instead to the symbolic sequence. The encryption process consists of transformations applied to a two-dimensional signal composed of the message carrying signal and an encrypting signal that has to be a chaotic one. The secret key, in this case, is related to the number of times the transformations are applied. Furthermore, we show that due to its chaotic nature, the encrypting signal is able to hide the statistics of the original signal.
Quasiperiodic graphs at the onset of chaos
Luque, B.; Cordero-Gracia, M.; Gómez, M.; Robledo, A.
2013-12-01
We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers.
Chaos in classical D0-brane mechanics
Energy Technology Data Exchange (ETDEWEB)
Gur-Ari, Guy [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Hanada, Masanori [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Yukawa Institute for Theoretical Physics, Kyoto University,Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502 (Japan); The Hakubi Center for Advanced Research, Kyoto University,Yoshida Ushinomiyacho, Sakyo-ku, Kyoto 606-8501 (Japan); Shenker, Stephen H. [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States)
2016-02-15
We study chaos in the classical limit of the matrix quantum mechanical system describing D0-brane dynamics. We determine a precise value of the largest Lyapunov exponent, and, with less precision, calculate the entire spectrum of Lyapunov exponents. We verify that these approach a smooth limit as N→∞. We show that a classical analog of scrambling occurs with fast scrambling scaling, t{sub ∗}∼log S. These results confirm the k-locality property of matrix mechanics discussed by Sekino and Susskind.
Bose-Hubbard Hamiltonian: Quantum chaos approach
Kolovsky, Andrey R.
2016-03-01
We discuss applications of the theory of quantum chaos to one of the paradigm models of many-body quantum physics — the Bose-Hubbard (BH) model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the BH model and the governing semiclassical equations of motion. We analyze these equations for the problem of Bloch oscillations (BOs) of cold atoms where a number of experimental results are available. The paper is written for nonexperts and can be viewed as an introduction to the field.
Feigenbaum graphs at the onset of chaos
Energy Technology Data Exchange (ETDEWEB)
Luque, Bartolo; Lacasa, Lucas [Dept. Matemática Aplicada y Estadística, ETSI Aeronáuticos, Universidad Politécnica de Madrid (Spain); Robledo, Alberto, E-mail: robledo@fisica.unam.mx [Instituto de Física y Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México (Mexico)
2012-11-01
We analyze the properties of networks obtained from the trajectories of unimodal maps at the transition to chaos via the horizontal visibility (HV) algorithm. We find that the network degrees fluctuate at all scales with amplitude that increases as the size of the network grows, and can be described by a spectrum of graph-theoretical generalized Lyapunov exponents. We further define an entropy growth rate that describes the amount of information created along paths in network space, and find that such entropy growth rate coincides with the spectrum of generalized graph-theoretical exponents, constituting a set of Pesin-like identities for the network.
Effect of Chaos on Relativistic Quantum Tunneling
2012-06-01
andAkis R., Phys. Rev. Lett., 103 (2009) 054101;Huang L., Lai Y.-C. and Grebogi C., Chaos, 21 (2011) 013102. [3] Novoselov K. S., Geim A. K., Morozov S. V...Feng R., Dai Z., Marchenkov A. N., Conrad E. H., First P. N. and de Heer W. A., J. Phys. Chem. B, 108 (2004) 19912; Novoselov K. S., Geim A. K., Morozov...P., Nature, 438 (2005) 201; Castro Neto A. H., Guinea F., Peres N. M. R., Novoselov K. S. and Geim A. K., Rev. Mod. Phys., 81 (2009) 109; Das Sarma S
Energy Technology Data Exchange (ETDEWEB)
Asano, Yuhma; Kawai, Daisuke; Yoshida, Kentaroh [Department of Physics, Kyoto University,Kyoto 606-8502 (Japan)
2015-06-29
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ansätze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincaré sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.
Polarization chaos in an optically pumped laser.
Serrat, C; Kul'minskii, A; Vilaseca, R; Corbalán, R
1995-06-15
We study the steady-state and dynamic behavior of an optically pumped J = 0 ? J = 1 ? J = 0 laser operating with an isotropic ring cavity and an axial magnetic field. The gain anisotropy induced by a linearly polarized pump-laser f ield leads, in the steady state, to locking of the two circularly polarized components of the laser field, which acquires a linear polarization parallel to that of the pump field. In the presence of laser intensity instabilities, however, locking does not occur, and polarization instabilities appear. For the f irst time to our knowledge, polarization chaos has been found in a laser system.
River of kings [Mae Nam Chao Phraya
Energy Technology Data Exchange (ETDEWEB)
Mogg, R.
1997-10-01
Low rainfall and a growing demand for water have had profound effects on water supplies in Thailand`s Mae Nam Chao Phraya river basin. In particular, low water levels are causing problems at the Bhumibol and Sirikit dams, as rice farms are threatened. The work of a Government sponsored think-tank set up to coordinate water management in the region is describe. Strategies may include use of groundwater at peak demand, recycling waste water and improve technical efficiency to reduce distribution losses. Any such policy changes will inevitably have widespread political, economic and social consequences. (UK)
Self-organized chaos through polyhomeostatic optimization.
Markovic, D; Gros, Claudius
2010-08-06
The goal of polyhomeostatic control is to achieve a certain target distribution of behaviors, in contrast to homeostatic regulation, which aims at stabilizing a steady-state dynamical state. We consider polyhomeostasis for individual and networks of firing-rate neurons, adapting to achieve target distributions of firing rates maximizing information entropy. We show that any finite polyhomeostatic adaption rate destroys all attractors in Hopfield-like network setups, leading to intermittently bursting behavior and self-organized chaos. The importance of polyhomeostasis to adapting behavior in general is discussed.
Importance of packing in spiral defect chaos
Indian Academy of Sciences (India)
Kapilanjan Krishna
2008-04-01
We develop two measures to characterize the geometry of patterns exhibited by the state of spiral defect chaos, a weakly turbulent regime of Rayleigh-Bénard convection. These describe the packing of contiguous stripes within the pattern by quantifying their length and nearest-neighbor distributions. The distributions evolve towards unique distribution with increasing Rayleigh number that suggests power-law scaling for the dynamics in the limit of infinite system size. The techniques are generally applicable to patterns that are reducible to a binary representation.
Using chaos to improve measurement precision
Institute of Scientific and Technical Information of China (English)
何斌; 杨灿军; 周银生; 陈鹰
2002-01-01
If the measuring signals wore input to the chaotic dynamic system as initial parameters, the system outputs might be in steady state, periodic state or chaos state. If the chaotic dynamic system outputs controlled in the periodic states, the periodic numbers would be changed most with the signals. Our novel method is to add chaotic dynamic vibration to the measurement or sensor system. The sensor sensitivity and precision of a measurement system would be improved with this method. Chaotic dynamics measurement algorithms are given and their sensitivity to parameters are analyzed in this paper. The effects of noises on the system are discussed,
Using chaos to improve measurement precision
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
If the measuring signals were input to the chaotic dynamic system as initial parameters, the system outputs might be in steady state, periodic state or chaos state. If the chaotic dynamic system outputs controlled in the periodic states, the periodic numbers would be changed most with the signals. Our novel method is to add chaotic dynamic vibration to the measurement or sensor system.The sensor sensitivity and precision of a measurement system would be improved with this method. Chaotic dynamics measurement algorithms are given and their sensitivity to parameters are analyzed in this paper. The effects of noises on the system are discussed.
Asano, Yuhma; Kawai, Daisuke; Yoshida, Kentaroh
2015-06-01
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ansätze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincaré sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.
Asano, Yuhma; Yoshida, Kentaroh
2015-01-01
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ans\\"atze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincar\\'e sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.
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Experimental Chaos - Proceedings of the 3rd Conference
Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep
1996-10-01
The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio
Energy Technology Data Exchange (ETDEWEB)
Warnock, R.L.
1996-02-01
Ordinary quantum theory is a statistical theory without an underlying probability space. The Wiener-Siegel theory provides a probability space, defined in terms of the usual wave function and its ``stochastic coordinates``; i.e., projections of its components onto differentials of complex Wiener processes. The usual probabilities of quantum theory emerge as measures of subspaces defined by inequalities on stochastic coordinates. Since each point {alpha} of the probability space is assigned values (or arbitrarily small intervals) of all observables, the theory gives a pseudo-classical or ``hidden-variable`` view in which normally forbidden concepts are allowed. Joint probabilities for values of noncommuting variables are well-defined. This paper gives a brief description of the theory, including a new generalization to incorporate spin, and reports the first concrete calculation of a joint probability for noncommuting components of spin of a single particle. Bohm`s form of the Einstein-Podolsky-Rosen Gedankenexperiment is discussed along the lines of Carlen`s paper at this Congress. It would seem that the ``EPR Paradox`` is avoided, since to each {alpha} the theory assigns opposite values for spin components of two particles in a singlet state, along any axis. In accordance with Bell`s ideas, the price to pay for this attempt at greater theoretical detail is a disagreement with usual quantum predictions. The disagreement is computed and found to be large.
Energy Technology Data Exchange (ETDEWEB)
Lenz, H.P. (comp.)
2003-07-01
This two-volume publication contains the papers of the 24th International Vienna Engine Symposium of 15/16 May 2003. Among the subjects discussed are: New gasoline engines, DI gasoline engines and diesel engines, new high-performance engines, future engines and transmission systems; Diesel soot, structure and health hazards, diesel exhaust treatment, gasoline DI ignition, hydrogen, fuel injection and variable valve control; future co-operations, creativity and trademarks. [German] In diesem zweibaendigen Werk werden die Vortraege des 24. Internationalen Wiener Motorensymposiums vom 15./16. Mai 2003 wiedergegeben und damit einer breiten Oeffentlichkeit zugaenglich gemacht. Aufgabe der Wiener Motorensymposien ist es, kurzfristig und komprimiert Themen von besonderer Aktualitaet auf dem Gebiet des Verbrennungsmotors zu behandeln. Dieses Werk befasst sich u.a. mit folgenden neuen Entwicklungen: Motoren und Getriebe: neue Otto-, Otto-Direkteinspritzungs- und Diesel-Motoren; neue Hoechstleistungsmotoren; zukuenftige Motoren und Getriebe; neue Erkenntnisse auf den Gebieten: Dieselruss: Struktur und Gesundheitsgefaehrdung, Diesel-Abgasnachbehandlung, Otto-Direkteinspritzungs-Zuendung, Wasserstoff, Einspritzung und variable Ventilsteuerung; Zukunftsperspektiven: Allianzen, Kreativitaet und Marken. - Herausgeber: Univ.-Prof. Dr. techn. Dipl.-Ing. H.P. Lenz, Vorsitzender des Oesterreichischen Vereins fuer Kraftfahrzeugtechnik (OeVK), Wien. (orig.)
Directory of Open Access Journals (Sweden)
Yoshinobu Tamura
2015-06-01
Full Text Available At present, many cloud services are managed by using open source software, such as OpenStack and Eucalyptus, because of the unification management of data, cost reduction, quick delivery and work savings. The operation phase of cloud computing has a unique feature, such as the provisioning processes, the network-based operation and the diversity of data, because the operation phase of cloud computing changes depending on many external factors. We propose a jump diffusion model with two-dimensional Wiener processes in order to consider the interesting aspects of the network traffic and big data on cloud computing. In particular, we assess the stability of cloud software by using the sample paths obtained from the jump diffusion model with two-dimensional Wiener processes. Moreover, we discuss the optimal maintenance problem based on the proposed jump diffusion model. Furthermore, we analyze actual data to show numerical examples of dependability optimization based on the software maintenance cost considering big data on cloud computing.
Domes, pits, and small chaos on Europa produced by water sills
Michaut, Chloé; Manga, Michael
2014-03-01
Pits, domes, and small chaos on Europa's surface are quasi-circular features a few to a few tens of kilometers in diameter. We examine if injection of water sills into Europa's ice shell and their subsequent evolution can induce successive surface deformations similar to the morphologies of these features. We study the dynamics of water spreading within the elastic part of the ice shell and show that the mechanical properties of ice exert a strong control on the lateral extent of the sill. At shallow depths, water makes room for itself by lifting the overlying ice layer and water weight promotes lateral spreading of the sill. In contrast, a deep sill bends the underlying elastic layer and its weight does not affect its spreading. In that case, the sill lateral extent is limited by the fracture toughness of ice and the sill can thicken substantially. After emplacement, cooling of the sill warms the surrounding ice and thins the overlying elastic ice layer. As a result, preexisting stresses in the elastic part of the ice shell increase locally to the point that they may disrupt the ice above the sill (small chaos). Disruption of the surface also allows for partial isostatic compensation of water weight, leading to a topographic depression at the surface (pit), of the order of ~102 m. Complete water solidification finally causes expansion of the initial sill volume and results in an uplifted topography (dome) of ~102m.
Equilibrium behavior of coarse-grained chaos
Egolf, David A.; Ballard, Christopher C.; Esty, C. Clark
2015-03-01
A wide variety of systems exhibiting spatiotemporal chaos have been shown to be extensive, in that their fractal dimensions grow linearly with volume. Ruelle argued that this extensivity is evidence that these systems can be viewed as a gas of weakly-interacting regions. We have tested this idea by performing large-scale computational studies of spatiotemporal chaos in the 1D complex Ginzburg-Landau equation, and we have found that aspects of the coarse-grained system are well-described not only as a gas, but as an equilibrium gas -- in particular, a Tonks gas (and variants) in the grand canonical ensemble. Furthermore, for small system sizes, the average number of particles in the corresponding Tonks gas exhibits oscillatory, decaying deviations from extensivity in agreement with deviations in the fractal dimension found by Fishman and Egolf. This result not only supports Ruelle's picture but also suggests that the coarse-grained behavior of this far-from-equilibrium system might be understood using equilibrium statistical mechanics.
Order and chaos in soft condensed matter
Indian Academy of Sciences (India)
A K Sood; Rajesh Ganapathy
2006-07-01
Soft matter, like colloidal suspensions and surfactant gels, exhibit strong response to modest external perturbations. This paper reviews our recent experiments on the nonlinear flow behaviour of surfactant worm-like micellar gels. A rich dynamic behaviour exhibiting regular, quasi-periodic, intermittency and chaos is observed. In particular, we have shown experimentally that the route to chaos is via Type-II intermittency in shear thinning worm-like micellar solution of cetyltrimethylammonium tosylate where the strength of flow-concentration coupling is tuned by the addition of sodium chloride. A Poincaré first return map of the time series and the probability distribution of laminar length between burst events show that our data are consistent with Type-II intermittency. The existence of a `Butterfly' intensity pattern in small angle light scattering (SALS) measurements performed simultaneously with the rheological measurements confirms the coupling of flow to concentration fluctuations in the system under study. The scattered depolarised intensity in SALS, sensitive to orientational order fluctuations, shows the same time-dependence (like intermittency) as that of shear stress.
Chaos induced by coupling between Josephson junctions
Shukrinov, Yu. M.; Azemtsa-Donfack, H.; Botha, A. E.
2015-02-01
It is found that, in a stack of intrinsic Josephson junctions in layered high temperature superconductors under external electromagnetic radiation, the chaotic features are triggered by interjunction coupling, i.e., the coupling between different junctions in the stack. While the radiation is well known to produce chaotic effects in the single junction, the effect of interjunction coupling is fundamentally different and it can lead to the onset of chaos via a different route to that of the single junction. A precise numerical study of the phase dynamics of intrinsic Josephson junctions, as described by the CCJJ+DC model, is performed. We demonstrate the charging of superconducting layers, in a bias current interval corresponding to a Shapiro step subharmonic, due to the creation of a longitudinal plasma wave along the stack of junctions. With increase in radiation amplitude chaotic behavior sets in. The chaotic features of the coupled Josephson junctions are analyzed by calculations of the Lyapunov exponents. We compare results for a stack of junctions to the case of a single junction and prove that the observed chaos is induced by the coupling between the junctions. The use of Shapiro step subharmonics may allow longitudinal plasma waves to be excited at low radiation power.
Rapid dynamical chaos in an exoplanetary system
Deck, Katherine M; Agol, Eric; Carter, Joshua A; Lissauer, Jack J; Ragozzine, Darin; Winn, Joshua N
2012-01-01
We report on the long-term dynamical evolution of the two-planet Kepler-36 system, which we studied through numerical integrations of initial conditions that are consistent with observations of the system. The orbits are chaotic with a Lyapunov time of only ~10 years. The chaos is a consequence of a particular set of orbital resonances, with the inner planet orbiting 34 times for every 29 orbits of the outer planet. The rapidity of the chaos is due to the interaction of the 29:34 resonance with the nearby first order 6:7 resonance, in contrast to the usual case in which secular terms in the Hamiltonian play a dominant role. Only one contiguous region of phase space, accounting for ~4.5% of the sample of initial conditions studied, corresponds to planetary orbits that do not show large scale orbital instabilities on the timescale of our integrations (~200 million years). The long-lived subset of the allowed initial conditions are those that satisfy the Hill stability criterion by the largest margin. Any succes...
Quantum chaos and holographic tensor models
Krishnan, Chethan; Sanyal, Sambuddha; Subramanian, P. N. Bala
2017-03-01
A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large- N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.
Chaos and structure of level densities
Energy Technology Data Exchange (ETDEWEB)
Moller, Peter [Los Alamos National Laboratory; Aberg, Sven [LUND SWEDEN; Uhrenholt, Henrik [LUND SWEDEN; Ickhikawa, Takatoshi [RIKEN
2008-01-01
The energy region of the first few MeV above the ground state shows interesting features of the nucleus. Beyond an ordered energy region just above the ground-state the dynamics changes, and chaotic features are observed in the neutron resonance region. The statistical properties of energies and wave-functions are common to all chaotic nuclei. However, if instead a global property, like the local level-density function is studied, strong structure effects emerge. In this contribution we discuss these two different facets of warm nuclei. In section 2 the onset of chaos with increasing excitation energy is discussed, with both experimental observations and proposed theoretical mechanisms as starting points. The structure of level densities in the same excitation energy region based on the two different starting points, is treated in section 3, where we give a short presentation of a newly developed combinatorial level-density modell. Some results from the model are presented and discussed. Two coexisting facets of warm nuclei, quantum chaos and structure of the level density, are considered. A newly developed combinatorial level-density model is presented, and the role of collective enhancements discussed. An example of extreme parity enhancement is shown.
Decrease of cardiac chaos in congestive heart failure
Poon, Chi-Sang; Merrill, Christopher K.
1997-10-01
The electrical properties of the mammalian heart undergo many complex transitions in normal and diseased states. It has been proposed that the normal heartbeat may display complex nonlinear dynamics, including deterministic chaos,, and that such cardiac chaos may be a useful physiological marker for the diagnosis and management, of certain heart trouble. However, it is not clear whether the heartbeat series of healthy and diseased hearts are chaotic or stochastic, or whether cardiac chaos represents normal or abnormal behaviour. Here we have used a highly sensitive technique, which is robust to random noise, to detect chaos. We analysed the electrocardiograms from a group of healthy subjects and those with severe congestive heart failure (CHF), a clinical condition associated with a high risk of sudden death. The short-term variations of beat-to-beat interval exhibited strongly and consistently chaotic behaviour in all healthy subjects, but were frequently interrupted by periods of seemingly non-chaotic fluctuations in patients with CHF. Chaotic dynamics in the CHF data, even when discernible, exhibited a high degree of random variability over time, suggesting a weaker form of chaos. These findings suggest that cardiac chaos is prevalent in healthy heart, and a decrease in such chaos may be indicative of CHF.
Spirals, chaos, and new mechanisms of wave propagation.
Chen, P S; Garfinkel, A; Weiss, J N; Karagueuzian, H S
1997-02-01
The chaos theory is based on the idea that phenomena that appear disordered and random may actually be produced by relatively simple deterministic mechanisms. The disordered (aperiodic) activation that characterizes a chaotic motion is reached through one of a few well-defined paths that are characteristic of nonlinear dynamical systems. Our group has been studying VF using computerized mapping techniques. We found that in electrically induced VF, reentrant wavefronts (spiral waves) are present both in the initial tachysystolic stage (resembling VT) and the later tremulous incoordination stage (true VF). The electrophysiological characteristics associated with the transition from VT to VF is compatible with the quasiperiodic route to chaos as described in the Ruelle-Takens theorem. We propose that specific restitution of action potential duration (APD) and conduction velocity properties can cause a spiral wave (the primary oscillator) to develop additional oscillatory modes that lead to spiral meander and breakup. When spiral waves begin to meander and are modulated by other oscillatory processes, the periodic activity is replaced by unstable quasiperiodic oscillation, which then undergoes transition to chaos, signaling the onset of VF. We conclude that VF is a form of deterministic chaos. The development of VF is compatible with quasiperiodic transition to chaos. These results indicate that both the prediction and the control of fibrillation are possible based on the chaos theory and with the advent of chaos control algorithms.
From chaos to order methodologies, perspectives and applications
Chen Guan Rong
1998-01-01
Chaos control has become a fast-developing interdisciplinary research field in recent years. This book is for engineers and applied scientists who want to have a broad understanding of the emerging field of chaos control. It describes fundamental concepts, outlines representative techniques, provides case studies, and highlights recent developments, putting the reader at the forefront of current research.Important topics presented in the book include: Fundamentals of nonlinear dynamical systems, essential for understanding and developing chaos control methods.; Parametric variation and paramet
Manifestation of resonance-related chaos in coupled Josephson junctions
Energy Technology Data Exchange (ETDEWEB)
Shukrinov, Yu.M. [BLTP, JINR, Dubna, Moscow Region, 141980 (Russian Federation); Hamdipour, M. [BLTP, JINR, Dubna, Moscow Region, 141980 (Russian Federation); Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan (Iran, Islamic Republic of); Kolahchi, M.R. [Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan (Iran, Islamic Republic of); Botha, A.E., E-mail: bothaae@unisa.ac.za [Department of Physics, University of South Africa, P.O. Box 392, Pretoria 0003 (South Africa); Suzuki, M. [Photonics and Electronics Science and Engineering Center and Department of Electronic Science and Engineering, Kyoto University, Kyoto 615-8510 (Japan)
2012-11-01
Manifestation of chaos in the temporal dependence of the electric charge is demonstrated through the calculation of the maximal Lyapunov exponent, phase–charge and charge–charge Lissajous diagrams and correlation functions. It is found that the number of junctions in the stack strongly influences the fine structure in the current–voltage characteristics and a strong proximity effect results from the nonperiodic boundary conditions. The observed resonance-related chaos exhibits intermittency. The criteria for a breakpoint region with no chaos are obtained. Such criteria could clarify recent experimental observations of variations in the power output from intrinsic Josephson junctions in high temperature superconductors.
Manifestation of resonance-related chaos in coupled Josephson junctions
Shukrinov, Yu. M.; Hamdipour, M.; Kolahchi, M. R.; Botha, A. E.; Suzuki, M.
2012-11-01
Manifestation of chaos in the temporal dependence of the electric charge is demonstrated through the calculation of the maximal Lyapunov exponent, phase-charge and charge-charge Lissajous diagrams and correlation functions. It is found that the number of junctions in the stack strongly influences the fine structure in the current-voltage characteristics and a strong proximity effect results from the nonperiodic boundary conditions. The observed resonance-related chaos exhibits intermittency. The criteria for a breakpoint region with no chaos are obtained. Such criteria could clarify recent experimental observations of variations in the power output from intrinsic Josephson junctions in high temperature superconductors.
Controlling beam halo-chaos via backstepping design
Institute of Scientific and Technical Information of China (English)
Gao Yuan; Kong Feng
2008-01-01
A backstepping control method is proposed for controlling beam halo-chaos in the periodic focusing channels PFCs) of high-current ion accelerator. The analysis and numerical results show that the method, via adjusting an exterior magnetic field, is effective to control beam halo chaos with five types of initial distribution ion beams, all statistical quantities of the beam halo-chaos are largely reduced, and the uniformity of ion beam is improved. This control method has an important value of application, for the exterior magnetic field can be easily adjusted in the periodical magnetic focusing channels in experiment.
Chaos Theory: A Contribution to the Formation of Strategies
Directory of Open Access Journals (Sweden)
Marcio Luiz Marietto
2011-12-01
Full Text Available It is our intention, through this work, to contribute to the understanding of the influence of chaos theory on the formation of organizational strategies in the dynamic and complex environment in which organizations are embedded. In this sense, we present a theoretical review, leveraged by a dialectical epistemology, in which we propose to show some attributes of chaos theory and theoretical assumptions to be considered in the context of different areas of organizational strategy, with the goal of trying to elucidate and approximate the analytical characteristics of both theories and make evident how chaos theory can contribute to and/or influence the formation of business strategies.
Evidence of low-dimensional chaos in magnetized plasma turbulence
Zivkovic, Tatjana
2008-01-01
We analyze probe data obtained from a toroidal magnetized plasma configuration suitable for studies of low-frequency gradient-driven instabilities. These instabilities give rise to field-aligned convection rolls analogous to Rayleigh-Benard cells in neutral fluids, and may theoretically develop similar routes to chaos. When using mean-field dimension analysis, we observe low dimensionality, but this could originate from either low-dimensional chaos, periodicity or quasi-periodicity. Therefore, we apply recurrence plot analysis as well as estimation of the largest Lyapunov exponent. These analyses provide evidence of low-dimensional chaos, in agreement with theoretical predictions.
Contributions of plasma physics to chaos and nonlinear dynamics
Escande, D. F.
2016-11-01
This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact. [15 April 2016
Chaos-based hash function (CBHF) for cryptographic applications
Energy Technology Data Exchange (ETDEWEB)
Amin, Mohamed [Dept. of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom 32511 (Egypt)], E-mail: mamin04@yahoo.com; Faragallah, Osama S. [Dept. of Computer Science and Engineering, Faculty of Electronic Engineering, Menoufia University, Menouf 32952 (Egypt)], E-mail: osam_sal@yahoo.com; Abd El-Latif, Ahmed A. [Dept. of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom 32511 (Egypt)], E-mail: ahmed_rahiem@yahoo.com
2009-10-30
As the core of cryptography, hash is the basic technique for information security. Many of the hash functions generate the message digest through a randomizing process of the original message. Subsequently, a chaos system also generates a random behavior, but at the same time a chaos system is completely deterministic. In this paper, an algorithm for one-way hash function construction based on chaos theory is introduced. Theoretical analysis and computer simulation indicate that the algorithm can satisfy all performance requirements of hash function in an efficient and flexible manner and secure against birthday attacks or meet-in-the-middle attacks, which is good choice for data integrity or authentication.
Quantum Chaos in Physical Systems from Super Conductors to Quarks
Bittner, E; Pullirsch, R; Bittner, Elmar; Markum, Harald; Pullirsch, Rainer
2001-01-01
This article is the written version of a talk delivered at the Bexbach Colloquium of Science 2000 and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. Several examples of physical systems exhibiting quantum chaos ranging from nuclear to solid state physics are presented. The presentation concludes with recent research work on quantum chromodynamics and the quark-gluon plasma. In the case of a chemical potential the eigenvalue spectrum becomes complex and one has to deal with non-Hermitian random-matrix theory.