WorldWideScience

Sample records for weighted wiener chaos

  1. Wiener Index, Diameter, and Stretch Factor of a Weighted Planar Graph in Subquadratic Time

    DEFF Research Database (Denmark)

    Wulff-Nilsen, Christian

    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......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...

  2. Computation of conditional Wiener integrals by the composite approximation formulae with weight

    International Nuclear Information System (INIS)

    Lobanov, Yu.Yu.; 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

  3. 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.

  4. Norbert Wiener

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education. Norbert Wiener. Articles written in Resonance – Journal of Science Education. Volume 4 Issue 1 January 1999 pp 80-88 Reflections. Some Moral and Technical Consequences of Automation · Norbert Wiener · More Details Fulltext PDF ...

  5. PC analysis of stochastic differential equations driven by Wiener noise

    KAUST Repository

    Le Maitre, Olivier; Knio, Omar

    2015-01-01

    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

  6. 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...

  7. The influence of noise on nonlinear time series detection based on Volterra-Wiener-Korenberg model

    Energy Technology Data Exchange (ETDEWEB)

    Lei Min [State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)], E-mail: leimin@sjtu.edu.cn; Meng Guang [State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)

    2008-04-15

    This paper studies the influence of noises on Volterra-Wiener-Korenberg (VWK) nonlinear test model. Our numerical results reveal that different types of noises lead to different behavior of VWK model detection. For dynamic noise, it is difficult to distinguish chaos from nonchaotic but nonlinear determinism. For time series, measure noise has no impact on chaos determinism detection. This paper also discusses various behavior of VWK model detection with surrogate data for different noises.

  8. Weight of fitness deviation governs strict physical chaos in replicator dynamics

    Science.gov (United States)

    Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar

    2018-03-01

    Replicator equation—a paradigm equation in evolutionary game dynamics—mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions—fixed points, periodic orbits, and chaotic trajectories—are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.

  9. Weight of fitness deviation governs strict physical chaos in replicator dynamics.

    Science.gov (United States)

    Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar

    2018-03-01

    Replicator equation-a paradigm equation in evolutionary game dynamics-mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions-fixed points, periodic orbits, and chaotic trajectories-are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.

  10. Nonlinear Dynamic Surface Control of Chaos in Permanent Magnet Synchronous Motor Based on the Minimum Weights of RBF Neural Network

    Directory of Open Access Journals (Sweden)

    Shaohua Luo

    2014-01-01

    Full Text Available This paper is concerned with the problem of the nonlinear dynamic surface control (DSC of chaos based on the minimum weights of RBF neural network for the permanent magnet synchronous motor system (PMSM wherein the unknown parameters, disturbances, and chaos are presented. RBF neural network is used to approximate the nonlinearities and an adaptive law is employed to estimate unknown parameters. Then, a simple and effective controller is designed by introducing dynamic surface control technique on the basis of first-order filters. Asymptotically tracking stability in the sense of uniformly ultimate boundedness is achieved in a short time. Finally, the performance of the proposed controller is testified through simulation results.

  11. PC analysis of stochastic differential equations driven by Wiener noise

    KAUST Repository

    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.

  12. Beurling Algebra Analogues of the Classical Theorems of Wiener ...

    Indian Academy of Sciences (India)

    absolutely convergent for some weight on the set of integers Z . If is nowhere vanishing on , then there exists a weight on Z such that 1/ had -absolutely convergent Fourier series. This includes Wiener's classical theorem. As a corollary ...

  13. Spectral image reconstruction using an edge preserving spatio-spectral Wiener estimation.

    Science.gov (United States)

    Urban, Philipp; Rosen, Mitchell R; Berns, Roy S

    2009-08-01

    Reconstruction of spectral images from camera responses is investigated using an edge preserving spatio-spectral Wiener estimation. A Wiener denoising filter and a spectral reconstruction Wiener filter are combined into a single spatio-spectral filter using local propagation of the noise covariance matrix. To preserve edges the local mean and covariance matrix of camera responses is estimated by bilateral weighting of neighboring pixels. We derive the edge-preserving spatio-spectral Wiener estimation by means of Bayesian inference and show that it fades into the standard Wiener reflectance estimation shifted by a constant reflectance in case of vanishing noise. Simulation experiments conducted on a six-channel camera system and on multispectral test images show the performance of the filter, especially for edge regions. A test implementation of the method is provided as a MATLAB script at the first author's website.

  14. Chaos control of the brushless direct current motor using adaptive dynamic surface control based on neural network with the minimum weights

    International Nuclear Information System (INIS)

    Luo, Shaohua; Wu, Songli; Gao, Ruizhen

    2015-01-01

    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

  15. Chaos control of the brushless direct current motor using adaptive dynamic surface control based on neural network with the minimum weights.

    Science.gov (United States)

    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.

  16. A light weight secure image encryption scheme based on chaos & DNA computing

    Directory of Open Access Journals (Sweden)

    Bhaskar Mondal

    2017-10-01

    Full Text Available This paper proposed a new light weight secure cryptographic scheme for secure image communication. In this scheme the plain image is permuted first using a sequence of pseudo random number (PRN and encrypted by DeoxyriboNucleic Acid (DNA computation. Two PRN sequences are generated by a Pseudo Random Number Generator (PRNG based on cross coupled chaotic logistic map using two sets of keys. The first PRN sequence is used for permuting the plain image whereas the second PRN sequence is used for generating random DNA sequence. The number of rounds of permutation and encryption may be variable to increase security. The scheme is proposed for gray label images but the scheme may be extended for color images and text data. Simulation results exhibit that the proposed scheme can defy any kind of attack.

  17. Wiener filter applied to a neutrongraphic system

    International Nuclear Information System (INIS)

    Crispim, V.R.; Lopes, R.T.; Borges, J.C.

    1986-01-01

    The randon characteristics of the image formation process influence the spatial image obtained in a neutrongraphy. Several methods can be used to optimize this image, though estimation of the noise added to the original signal. This work deals with the optimal filtering technique, using Wiener's filter. A simulation is made, where the signal (spatial resolution function) has a Lorentz's form, and ten kinds of random noise with increasing R.M.S. are generated and individually added to the original signal. Wiener's filter is applied to different noise amplitudes and the behaviour of the spatial resolution function for our system is also analysed. (Author) [pt

  18. Cubature on Wiener Space: Pathwise Convergence

    International Nuclear Information System (INIS)

    Bayer, Christian; Friz, Peter K.

    2013-01-01

    Cubature on Wiener space (Lyons and Victoir in Proc. R. Soc. Lond. A 460(2041):169–198, 2004) provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models.We give a random walk interpretation of cubature and similar (e.g. the Ninomiya–Victoir) weak approximation schemes. By using rough path analysis, we are able to establish weak convergence for general path-dependent option prices.

  19. Quantum chaos

    International Nuclear Information System (INIS)

    Steiner, F.

    1994-01-01

    A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace formular is discussed as a sound mathematical basis for the semiclassical quantization of chaos. Two conjectures are presented on the basis of which it is argued that there are unique fluctuation properties in quantum mechanics which are universal and, in a well defined sense, maximally random if the corresponding classical system is strongly chaotic. These properties constitute the quantum mechanical analogue of the phenomenon of chaos in classical mechanics. Thus quantum chaos has been found. (orig.)

  20. Colored chaos

    International Nuclear Information System (INIS)

    Mueller, B.

    1997-01-01

    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

  1. Colored chaos

    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.

  2. Oracle Wiener filtering of a Gaussian signal

    NARCIS (Netherlands)

    Babenko, A.; Belitser, E.

    2011-01-01

    We study the problem of filtering a Gaussian process whose trajectories, in some sense, have an unknown smoothness ß0 from the white noise of small intensity e. If we knew the parameter ß0, we would use the Wiener filter which has the meaning of oracle. Our goal is now to mimic the oracle, i.e.,

  3. Oracle Wiener filtering of a Gaussian signal

    NARCIS (Netherlands)

    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.,

  4. Evaluation of multichannel Wiener filters applied to fine resolution passive microwave images of first-year sea ice

    Science.gov (United States)

    Full, William E.; Eppler, Duane T.

    1993-01-01

    The effectivity of multichannel Wiener filters to improve images obtained with passive microwave systems was investigated by applying Wiener filters to passive microwave images of first-year sea ice. Four major parameters which define the filter were varied: the lag or pixel offset between the original and the desired scenes, filter length, the number of lines in the filter, and the weight applied to the empirical correlation functions. The effect of each variable on the image quality was assessed by visually comparing the results. It was found that the application of multichannel Wiener theory to passive microwave images of first-year sea ice resulted in visually sharper images with enhanced textural features and less high-frequency noise. However, Wiener filters induced a slight blocky grain to the image and could produce a type of ringing along scan lines traversing sharp intensity contrasts.

  5. Defining chaos.

    Science.gov (United States)

    Hunt, Brian R; Ott, Edward

    2015-09-01

    In this paper, we propose, discuss, and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers, and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call "expansion entropy," and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.

  6. A phenomenological calculus of Wiener description space.

    Science.gov (United States)

    Richardson, I W; Louie, A H

    2007-10-01

    The phenomenological calculus is a categorical example of Robert Rosen's modeling relation. This paper is an alligation of the phenomenological calculus and generalized harmonic analysis, another categorical example. Our epistemological exploration continues into the realm of Wiener description space, in which constitutive parameters are extended from vectors to vector-valued functions of a real variable. Inherent in the phenomenology are fundamental representations of time and nearness to equilibrium.

  7. Quantum chaos

    International Nuclear Information System (INIS)

    Cejnar, P.

    2007-01-01

    Chaos is a name given in physics to a branch which, within classical mechanics, studies the consequences of sensitive dependences of the behavior of physical systems on the starting conditions, i.e., the 'butterfly wing effect'. However, how to describe chaotic behavior in the world of quantum particles? It appears that quantum mechanics does not admit the sensitive dependence on the starting conditions, and moreover, predicts a substantial suppression of chaos also at the macroscopic level. Still, the quantum properties of systems that are chaotic in terms of classical mechanics differ basically from the properties of classically arranged systems. This topic is studied by a field of physics referred to as quantum chaos. (author)

  8. Digital, realizable Wiener filtering in two-dimensions

    International Nuclear Information System (INIS)

    Ekstrom, M.P.

    1979-01-01

    The extension of Wiener's classical mean-square filtering theory to the estimation of two-dimensional (2-D), discrete random fields is discussed. In analogy with the 1-D case, the optimal realizable filter is derived by solution of a 2-D discrete Wiener--Hopf equation using a spectral factorization procedure. Computational algorithms for performing the required calculations are discussed. 3 figures

  9. Iani Chaos

    Science.gov (United States)

    2005-01-01

    [figure removed for brevity, see original site] Context image for PIA03200 Iani Chaos This VIS image of Iani Chaos shows the layered deposit that occurs on the floor. It appears that the layers were deposited after the chaos was formed. Image information: VIS instrument. Latitude 2.3S, Longitude 342.3E. 17 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.

  10. Modeling of memristor-based chaotic systems using nonlinear Wiener adaptive filters based on backslash operator

    International Nuclear Information System (INIS)

    Zhao, Yibo; Jiang, Yi; Feng, Jiuchao; Wu, Lifu

    2016-01-01

    Highlights: • A novel nonlinear Wiener adaptive filters based on the backslash operator are proposed. • The identification approach to the memristor-based chaotic systems using the proposed adaptive filters. • The weight update algorithm and convergence characteristics for the proposed adaptive filters are derived. - Abstract: Memristor-based chaotic systems have complex dynamical behaviors, which are characterized as nonlinear and hysteresis characteristics. Modeling and identification of their nonlinear model is an important premise for analyzing the dynamical behavior of the memristor-based chaotic systems. This paper presents a novel nonlinear Wiener adaptive filtering identification approach to the memristor-based chaotic systems. The linear part of Wiener model consists of the linear transversal adaptive filters, the nonlinear part consists of nonlinear adaptive filters based on the backslash operator for the hysteresis characteristics of the memristor. The weight update algorithms for the linear and nonlinear adaptive filters are derived. Final computer simulation results show the effectiveness as well as fast convergence characteristics. Comparing with the adaptive nonlinear polynomial filters, the proposed nonlinear adaptive filters have less identification error.

  11. A novel definition of the overall hyper-wiener index for unsaturated hydrocarbons.

    Science.gov (United States)

    Li, Xinhua; Hu, Maolin; Xiao, Hongping

    2004-01-01

    By replacing the distances between pairs of vertices with the relative distances, we define a novel overall hyper-Wiener index (NOR); the novel overall hyper-Wiener index extends the usefulness of the hyper-Wiener index and the overall hyper-Wiener index to unsaturated hydrocarbons.

  12. Quantum Chaos

    Energy Technology Data Exchange (ETDEWEB)

    Bohigas, Oriol [Laboratoire de Physique Theorique et Modeles Statistiques, Orsay (France)

    2005-04-18

    Are there quantum signatures, for instance in the spectral properties, of the underlying regular or chaotic nature of the corresponding classical motion? Are there universality classes? Within this framework the merging of two at first sight seemingly disconnected fields, namely random matrix theories (RMT) and quantum chaos (QC), is briefly described. Periodic orbit theory (POT) plays a prominent role. Emphasis is given to compound nucleus resonances and binding energies, whose shell effects are examined from this perspective. Several aspects are illustrated with Riemann's {zeta}-function, which has become a testing ground for RMT, QC, POT, and their relationship.

  13. Quantum Chaos

    International Nuclear Information System (INIS)

    Bohigas, Oriol

    2005-01-01

    Are there quantum signatures, for instance in the spectral properties, of the underlying regular or chaotic nature of the corresponding classical motion? Are there universality classes? Within this framework the merging of two at first sight seemingly disconnected fields, namely random matrix theories (RMT) and quantum chaos (QC), is briefly described. Periodic orbit theory (POT) plays a prominent role. Emphasis is given to compound nucleus resonances and binding energies, whose shell effects are examined from this perspective. Several aspects are illustrated with Riemann's ζ-function, which has become a testing ground for RMT, QC, POT, and their relationship

  14. On the Wiener Polarity Index of Lattice Networks.

    Science.gov (United States)

    Chen, Lin; Li, Tao; Liu, Jinfeng; Shi, Yongtang; Wang, Hua

    2016-01-01

    Network structures are everywhere, including but not limited to applications in biological, physical and social sciences, information technology, and optimization. Network robustness is of crucial importance in all such applications. Research on this topic relies on finding a suitable measure and use this measure to quantify network robustness. A number of distance-based graph invariants, also known as topological indices, have recently been incorporated as descriptors of complex networks. Among them the Wiener type indices are the most well known and commonly used such descriptors. As one of the fundamental variants of the original Wiener index, the Wiener polarity index has been introduced for a long time and known to be related to the cluster coefficient of networks. In this paper, we consider the value of the Wiener polarity index of lattice networks, a common network structure known for its simplicity and symmetric structure. We first present a simple general formula for computing the Wiener polarity index of any graph. Using this formula, together with the symmetric and recursive topology of lattice networks, we provide explicit formulas of the Wiener polarity index of the square lattices, the hexagonal lattices, the triangular lattices, and the 33 ⋅ 42 lattices. We also comment on potential future research topics.

  15. Remaining useful life prediction based on variation coefficient consistency test of a Wiener process

    Directory of Open Access Journals (Sweden)

    Juan LI

    2018-01-01

    Full Text Available High-cost equipment is often reused after maintenance, and whether the information before the maintenance can be used for the Remaining Useful Life (RUL prediction after the maintenance is directly determined by the consistency of the degradation pattern before and after the maintenance. Aiming at this problem, an RUL prediction method based on the consistency test of a Wiener process is proposed. Firstly, the parameters of the Wiener process estimated by Maximum Likelihood Estimation (MLE are proved to be biased, and a modified unbiased estimation method is proposed and verified by derivation and simulations. Then, the h statistic is constructed according to the reciprocal of the variation coefficient of the Wiener process, and the sampling distribution is derived. Meanwhile, a universal method for the consistency test is proposed based on the sampling distribution theorem, which is verified by simulation data and classical crack degradation data. Finally, based on the consistency test of the degradation model, a weighted fusion RUL prediction method is presented for the fuel pump of an airplane, and the validity of the presented method is verified by accurate computation results of real data, which provides a theoretical and practical guidance for engineers to predict the RUL of equipment after maintenance.

  16. Aureum Chaos

    Science.gov (United States)

    2003-01-01

    [figure removed for brevity, see original site] Released 11 November 2003Aureum Chaos is a large crater that was filled with sediment after its formation. After the infilling of sediment, something occurred that caused the sediment to be broken up into large, slumped blocks and smaller knobs. Currently, it is believed that the blocks and knobs form when material is removed from the subsurface, creating void space. Subsurface ice was probably heated, and the water burst out to the surface, maybe forming a temporary lake. Other areas of chaos terrain have large outflow channels that emanate from them, indicating that a tremendous amount of water was released.Image information: VIS instrument. Latitude -3.2, Longitude 331 East (29 West). 19 meter/pixel resolution.Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.

  17. Arsinoes Chaos

    Science.gov (United States)

    2003-01-01

    [figure removed for brevity, see original site] At the easternmost end of Valles Marineris, a rugged, jumbled terrain known as chaos displays a stratigraphy that could be described as precarious. Perched on top of the jumbled blocks is another layer of sedimentary material that is in the process of being eroded off the top. This material is etched by the wind into yardangs before it ultimately is stripped off to reveal the existing chaos.Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.Image information: VIS instrument. Latitude -7.8, Longitude 19.1 East (340.9 West). 19 meter/pixel resolution.

  18. 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.

  19. Quantum signatures of chaos or quantum chaos?

    International Nuclear Information System (INIS)

    Bunakov, V. E.

    2016-01-01

    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.

  20. Preconditioner-free Wiener filtering with a dense noise matrix

    Science.gov (United States)

    Huffenberger, Kevin M.

    2018-05-01

    This work extends the Elsner & Wandelt (2013) iterative method for efficient, preconditioner-free Wiener filtering to cases in which the noise covariance matrix is dense, but can be decomposed into a sum whose parts are sparse in convenient bases. The new method, which uses multiple messenger fields, reproduces Wiener-filter solutions for test problems, and we apply it to a case beyond the reach of the Elsner & Wandelt (2013) method. We compute the Wiener-filter solution for a simulated Cosmic Microwave Background (CMB) map that contains spatially varying, uncorrelated noise, isotropic 1/f noise, and large-scale horizontal stripes (like those caused by atmospheric noise). We discuss simple extensions that can filter contaminated modes or inverse-noise-filter the data. These techniques help to address complications in the noise properties of maps from current and future generations of ground-based Microwave Background experiments, like Advanced ACTPol, Simons Observatory, and CMB-S4.

  1. Hydaspis Chaos

    Science.gov (United States)

    2002-01-01

    [figure removed for brevity, see original site] Collapsed terrain in Hydapsis Chaos.This is the source terrain for several outflow channels. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.VIS Instrument. Latitude 3.2, Longitude 333.2 East. 19 meter/pixel resolution.

  2. Embrace the Chaos

    Science.gov (United States)

    Huwe, Terence K.

    2009-01-01

    "Embracing the chaos" is an ongoing challenge for librarians. Embracing the chaos means librarians must have a plan for responding to the flood of new products, widgets, web tools, and gizmos that students use daily. In this article, the author argues that library instruction and access services have been grappling with that chaos with…

  3. Soil transfer function obtention by Wiener's optimum filter

    International Nuclear Information System (INIS)

    Flores Ruiz, J.H.

    1987-01-01

    Transfer function in nuclear power plant Laguna Verde, Veracruz, using Wiener filter. This paper deal with identification of complex structural and soil-interaction systems often are modeling in nuclear industry. Nonparametric identification techniques are used to analyse the response of a class nonlinear vibrations. Efficient computational algorithms and experimental techniques based input-output system methods such as the Wiener-Kernel approach and least-square regression techniques are applied to get the transfer function in nuclear power plant Laguna Verde, Veracruz (Mexico) (Author)

  4. Quaternion Wiener Deconvolution for Noise Robust Color Image Registration

    Czech Academy of Sciences Publication Activity Database

    Pedone, M.; Bayro-Corrochano, E.; Flusser, Jan; Heikkilä, J.

    2015-01-01

    Roč. 22, č. 9 (2015), s. 1278-1282 ISSN 1070-9908 R&D Projects: GA ČR GA13-29225S Keywords : Clifford algebra * multivector derivative * phase correlation * quaternion * Wiener filter Subject RIV: JD - Computer Applications, Robotics Impact factor: 1.661, year: 2015 http://library.utia.cas.cz/separaty/2015/ZOI/flusser-0441249.pdf

  5. Colored Chaos

    Science.gov (United States)

    2004-01-01

    [figure removed for brevity, see original site] Released 7 May 2004 This daytime visible color image was collected on May 30, 2002 during the Southern Fall season in Atlantis Chaos. The THEMIS VIS camera is capable of capturing color images of the martian surface using its five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from the use of multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation. Image information: VIS instrument. Latitude -34.5, Longitude 183.6 East (176.4 West). 38 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D

  6. Auream Chaos

    Science.gov (United States)

    2005-01-01

    [figure removed for brevity, see original site] The THEMIS VIS camera is capable of capturing color images of the Martian surface using five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from using multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation. This false color image was collected during Southern Fall and shows part of the Aureum Chaos. Image information: VIS instrument. Latitude -3.6, Longitude 332.9 East (27.1 West). 35 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS

  7. Chaos theory in politics

    CERN Document Server

    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.

  8. The Chaos of Katrina

    National Research Council Canada - National Science Library

    Morris, Jr, Gerald W

    2007-01-01

    .... The study investigates whether chaos theory, part of complexity science, can extract information from Katrina contracting data to help managers make better logistics decisions during disaster relief operations...

  9. A General Accelerated Degradation Model Based on the Wiener Process.

    Science.gov (United States)

    Liu, Le; Li, Xiaoyang; Sun, Fuqiang; Wang, Ning

    2016-12-06

    Accelerated degradation testing (ADT) is an efficient tool to conduct material service reliability and safety evaluations by analyzing performance degradation data. Traditional stochastic process models are mainly for linear or linearization degradation paths. However, those methods are not applicable for the situations where the degradation processes cannot be linearized. Hence, in this paper, a general ADT model based on the Wiener process is proposed to solve the problem for accelerated degradation data analysis. The general model can consider the unit-to-unit variation and temporal variation of the degradation process, and is suitable for both linear and nonlinear ADT analyses with single or multiple acceleration variables. The statistical inference is given to estimate the unknown parameters in both constant stress and step stress ADT. The simulation example and two real applications demonstrate that the proposed method can yield reliable lifetime evaluation results compared with the existing linear and time-scale transformation Wiener processes in both linear and nonlinear ADT analyses.

  10. The Lie Bracket of Adapted Vector Fields on Wiener Spaces

    International Nuclear Information System (INIS)

    Driver, B. K.

    1999-01-01

    Let W(M) be the based (at o element of M) path space of a compact Riemannian manifold M equipped with Wiener measure ν . This paper is devoted to considering vector fields on W(M) of the form X s h (σ )=P s (σ)h s (σ ) where P s (σ ) denotes stochastic parallel translation up to time s along a Wiener path σ element of W(M) and {h s } i sanelementof [0,1] is an adapted T o M -valued process on W(M). It is shown that there is a large class of processes h (called adapted vector fields) for which we may view X h as first-order differential operators acting on functions on W(M) . Moreover, if h and k are two such processes, then the commutator of X h with X k is again a vector field on W(M) of the same form

  11. "Chaos Rules" Revisited

    Science.gov (United States)

    Murphy, David

    2011-01-01

    About 20 years ago, while lost in the midst of his PhD research, the author mused over proposed titles for his thesis. He was pretty pleased with himself when he 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." He…

  12. Chaos Modelling with Computers

    Indian Academy of Sciences (India)

    Chaos is one of the major scientific discoveries of our times. In fact many scientists ... But there are other natural phenomena that are not predictable though ... characteristics of chaos. ... The position and velocity are all that are needed to determine the motion of a .... a system of equations that modelled the earth's weather ...

  13. Improved particle swarm optimization combined with chaos

    International Nuclear Information System (INIS)

    Liu Bo; Wang Ling; Jin Yihui; Tang Fang; Huang Dexian

    2005-01-01

    As a novel optimization technique, chaos has gained much attention and some applications during the past decade. For a given energy or cost function, by following chaotic ergodic orbits, a chaotic dynamic system may eventually reach the global optimum or its good approximation with high probability. To enhance the performance of particle swarm optimization (PSO), which is an evolutionary computation technique through individual improvement plus population cooperation and competition, hybrid particle swarm optimization algorithm is proposed by incorporating chaos. Firstly, adaptive inertia weight factor (AIWF) is introduced in PSO to efficiently balance the exploration and exploitation abilities. Secondly, PSO with AIWF and chaos are hybridized to form a chaotic PSO (CPSO), which reasonably combines the population-based evolutionary searching ability of PSO and chaotic searching behavior. Simulation results and comparisons with the standard PSO and several meta-heuristics show that the CPSO can effectively enhance the searching efficiency and greatly improve the searching quality

  14. Paths to chaos

    International Nuclear Information System (INIS)

    Friedrich, H.

    1992-01-01

    Rapid growth in the study of nonlinear dynamics and chaos in classical mechanics, has led physicists to reappraise their abandonment of this definition of atomic theory in favour of quantum mechanics adopted earlier this century. The concept of chaos in classical mechanics is examined in this paper and manifestations of chaos in quantum mechanics are explored. While quantum mechanics teaches that atomic particles must not be pictured as moving sharply in defined orbits, these precise orbits can be used to describe essential features of the measurable quantum mechanical spectra. (UK)

  15. Chaos applications in telecommunications

    CERN Document Server

    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

  16. A bound on chaos

    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.

  17. Colpitts and Chaos

    DEFF Research Database (Denmark)

    Lindberg, Erik

    1996-01-01

    The chaotic behaviour of the Colpitts oscillator reported by M.P. Kennedy is further investigated by means of PSpice simulations. Chaos is also observed with the default Ebers-Moll BJT transistor model with no memory. When the model is extended with memory and losses chaos do not occur and a 3'rd...... 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...

  18. Measurements of Wiener spectra of laser printer in a computed radiography

    International Nuclear Information System (INIS)

    Yamauchi, Syuichi; Ueda, Katsuhiko; Nishihara, Sadamitsu; Ohtsuka, Akiyoshi; Fujita, Hiroshi; Morishita, Junji; Fujikawa, Tsuyoshi.

    1992-01-01

    Sources of noise in a computed radiography (CR) were investigated by measuring three different Wiener spectra: 1) laser printer Wiener spectra including CR film, 2) Wiener spectrum of CR film (single emulsion), and 3) overall Wiener spectra. To measure the noise contributed by the laser printer, 'image data' (i.e., image having a constant pixel value) were produced on a personal computer and were sent to the laser printer in the CR system. The noise level of laser printer was comparable to that of the CR film at low spatial frequencies ( 4 cycle/mm) was higher than that of the film. Laser printer Wiener spectra obtained in the perpendicular direction relative to the laser beam scanning direction were comparable at low spatial frequencies, but greater at high spatial frequencies, to those obtained in the parallel direction. And a spectral peak around 10 cycle/mm was obtained in the Wiener spectrum in the perpendicular direction. The peak is caused mainly by a banding artifact. Overall Wiener spectra in the parallel and perpendicular directions show the same tendency as those of the laser printer, but the noise level of the overall Wiener spectrum was increased mainly by X-ray quantum mottle at low spatial frequencies. In conclusion, the noise of laser printer greatly increases the overall Wiener spectrum at high spatial frequencies. (author)

  19. Restoration of nuclear medicine images using adaptive Wiener filters

    International Nuclear Information System (INIS)

    Meinel, G.

    1989-01-01

    An adaptive Wiener filter implementation for restoration of nuclear medicine images is described. These are considerably disturbed both deterministically (definition) and stochastically (Poisson's quantum noise). After introduction of an image model, description of necessary parameter approximations and information on optimum design methods the implementation is described. The filter operates adaptively as concerns the local signal-to-noise ratio and is based on a filter band concept. To verify the restoration effect size numbers are introduced and the filter is tested against these numbers. (author)

  20. 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.

  1. Chaos: Choto delat?

    Science.gov (United States)

    Campbell, David

    1987-11-01

    I provide a brief overview of the current status of the field of deterministic "chaos" stressing its interrelations and applications to other fields and suggesting a number of important open problems for future study.

  2. Quantum manifestations of chaos

    International Nuclear Information System (INIS)

    Borondo, F.; Benito, R.M.

    1998-01-01

    The correspondence between classical and quantum mechanics is considered both in the regular and chaotic regimes, and the main results regarding the quantum manifestations of chaos are reviewed. (Author) 16 refs

  3. Channeling and dynamic chaos

    Energy Technology Data Exchange (ETDEWEB)

    Bolotin, IU L; Gonchar, V IU; Truten, V I; Shulga, N F

    1986-01-01

    It is shown that axial channeling of relativistic electrons can give rise to the effect of dynamic chaos which involves essentially chaotic motion of a particle in the channel. The conditions leading to the effect of dynamic chaos and the manifestations of this effect in physical processes associated with the passage of particles through a crystal are examined using a silicon crystal as an example. 7 references.

  4. 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.

  5. Exploiting chaos for applications.

    Science.gov (United States)

    Ditto, William L; Sinha, Sudeshna

    2015-09-01

    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.

  6. Wiener discrete cosine transform-based image filtering

    Science.gov (United States)

    Pogrebnyak, Oleksiy; Lukin, Vladimir V.

    2012-10-01

    A classical problem of additive white (spatially uncorrelated) Gaussian noise suppression in grayscale images is considered. The main attention is paid to discrete cosine transform (DCT)-based denoising, in particular, to image processing in blocks of a limited size. The efficiency of DCT-based image filtering with hard thresholding is studied for different sizes of overlapped blocks. A multiscale approach that aggregates the outputs of DCT filters having different overlapped block sizes is proposed. Later, a two-stage denoising procedure that presumes the use of the multiscale DCT-based filtering with hard thresholding at the first stage and a multiscale Wiener DCT-based filtering at the second stage is proposed and tested. The efficiency of the proposed multiscale DCT-based filtering is compared to the state-of-the-art block-matching and three-dimensional filter. Next, the potentially reachable multiscale filtering efficiency in terms of output mean square error (MSE) is studied. The obtained results are of the same order as those obtained by Chatterjee's approach based on nonlocal patch processing. It is shown that the ideal Wiener DCT-based filter potential is usually higher when noise variance is high.

  7. A General Accelerated Degradation Model Based on the Wiener Process

    Directory of Open Access Journals (Sweden)

    Le Liu

    2016-12-01

    Full Text Available Accelerated degradation testing (ADT is an efficient tool to conduct material service reliability and safety evaluations by analyzing performance degradation data. Traditional stochastic process models are mainly for linear or linearization degradation paths. However, those methods are not applicable for the situations where the degradation processes cannot be linearized. Hence, in this paper, a general ADT model based on the Wiener process is proposed to solve the problem for accelerated degradation data analysis. The general model can consider the unit-to-unit variation and temporal variation of the degradation process, and is suitable for both linear and nonlinear ADT analyses with single or multiple acceleration variables. The statistical inference is given to estimate the unknown parameters in both constant stress and step stress ADT. The simulation example and two real applications demonstrate that the proposed method can yield reliable lifetime evaluation results compared with the existing linear and time-scale transformation Wiener processes in both linear and nonlinear ADT analyses.

  8. Identificación Robusta de Modelos Wiener y Hammerstein

    Directory of Open Access Journals (Sweden)

    Silvina I. Biagiola

    2009-04-01

    Full Text Available Resumen: Los modelos orientados a bloques han mostrado ser útiles y eficaces como representaciones no lineales en muchas aplicaciones. Son modelos simples y a la vez válidos en una región más amplia que un modelo lineal invariante en el tiempo. En cuanto a su estructura, consisten en una cascada integrada por una dinámica lineal y un bloque estático no lineal.Si bien existen en la literatura numerosos trabajos que abordan la identificación nominal de estos modelos, el problema de identificación robusta en presencia de incertidumbre no ha sido cabalmente tratado.En este trabajo, se consideran dos clases de modelos orientados a bloques: modelos Wiener y Hammerstein. Empleando una representación paramétrica, se propone describir la incertidumbre como un conjunto de parámetros, cuyos valores se obtienen resolviendo un problema de optimización. El algoritmo de identificación desarrollado se ilustra mediante ejemplos de simulación. Palabras clave: Wiener, Hammerstein, Identificación, Incertidumbre, Optimización

  9. Chaotic System Identification Based on a Fuzzy Wiener Model with Particle Swarm Optimization

    International Nuclear Information System (INIS)

    Yong, Li; Ying-Gan, Tang

    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

  10. Correction Method of Wiener Spectrum (WS) on Digital Medical Imaging Systems

    International Nuclear Information System (INIS)

    Kim, Jung Min; Lee, Ki Sung; Kim, You Hyun

    2009-01-01

    Noise evaluation for an image has been performed by root mean square (RMS) granularity, autocorrelation function (ACF), and Wiener spectrum. RMS granularity stands for standard deviation of photon data and ACF is acquired by integration of 1 D function of distance variation. Fourier transform of ACF results in noise power spectrum which is called Wiener spectrum in image quality evaluation. Wiener spectrum represents noise itself. In addition, along with MTF, it is an important factor to produce detective quantum efficiency (DQE). The proposed evaluation method using Wiener spectrum is expected to contribute to educate the concept of Wiener spectrum in educational organizations, choose the appropriate imaging detectors for clinical applications, and maintain image quality in digital imaging systems.

  11. Nonlinear chaos control and synchronization

    NARCIS (Netherlands)

    Huijberts, H.J.C.; Nijmeijer, H.; Schöll, E.; Schuster, H.G.

    2007-01-01

    This chapter contains sections titled: Introduction Nonlinear Geometric Control Some Differential Geometric Concepts Nonlinear Controllability Chaos Control Through Feedback Linearization Chaos Control Through Input-Output Linearization Lyapunov Design Lyapunov Stability and Lyapunov's First Method

  12. Stochastic Estimation via Polynomial Chaos

    Science.gov (United States)

    2015-10-01

    AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

  13. 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.

  14. Model for Shock Wave Chaos

    KAUST Repository

    Kasimov, Aslan R.; Faria, Luiz; Rosales, Rodolfo R.

    2013-01-01

    : 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

  15. An Extension of SIC Predictions to the Wiener Coactive Model.

    Science.gov (United States)

    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.

  16. A vector Wiener filter for dual-radionuclide imaging

    International Nuclear Information System (INIS)

    Links, J.M.; Prince, J.L.; Gupta, S.N.

    1996-01-01

    The routine use of a single radionuclide for patient imaging in nuclear medicine can be complemented by studies employing two tracers to examine two different processes in a single organ, most frequently by simultaneous imaging of both radionuclides in two different energy windows. In addition, simultaneous transmission/emission imaging with dual-radionuclides has been described, with one radionuclide used for the transmission study and a second for the emission study. There is thus currently considerable interest in dual-radionuclide imaging. A major problem with all dual-radionuclide imaging is the crosstalk between the two radionuclides. Such crosstalk frequently occurs, because scattered radiation from the higher energy radionuclide is detected in the lower energy window, and because the lower energy radionuclide may have higher energy emissions which are detected in the higher energy window. The authors have previously described the use of Fourier-based restoration filtering in single photon emission computed tomography (SPECT) and positron emission tomography (PET) to improve quantitative accuracy by designing a Wiener or other Fourier filter to partially restore the loss of contrast due to scatter and finite spatial resolution effects. The authors describe here the derivation and initial validation of an extension of such filtering for dual-radionuclide imaging that simultaneously (1) improves contrast in each radionuclide's direct image, (2) reduces image noise, and (3) reduces the crosstalk contribution from the other radionuclide. This filter is based on a vector version of the Wiener filter, which is shown to be superior [in the minimum mean square error (MMSE) sense] to the sequential application of separate crosstalk and restoration filters

  17. Chaos in collective nuclei

    International Nuclear Information System (INIS)

    Whelan, N.D.

    1993-01-01

    Random Matrix Theory successfully describes the statistics of the low-lying spectra of some nuclei but not of others. It is currently believed that this theory applies to systems in which the corresponding classical motion is chaotic. This conjecture is tested for collective nuclei by studying the Interacting Boson Model. Quantum and classical measures of chaos are proposed and found to be in agreement throughout the parameter space of the model. For some parameter values the measures indicate the presence of a previously unknown approximate symmetry. A phenomenon called partial dynamical symmetry is explored and shown to lead to a suppression of chaos. A time dependent function calculated from the quantum spectrum is discussed. This function is sensitive to the extent of chaos and provides a robust method of analyzing experimental spectra

  18. Chaos and noise.

    Science.gov (United States)

    He, Temple; Habib, Salman

    2013-09-01

    Simple dynamical systems--with a small number of degrees of freedom--can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small number of dynamical degrees of freedom in a realistically coupled system generically yields reduced equations with terms that can have a stochastic interpretation. In situations where both noise and chaos can potentially exist, it is not immediately obvious how Lyapunov exponents, key to characterizing chaos, should be properly defined. In this paper, we show how to do this in a class of well-defined noise-driven dynamical systems, derived from an underlying Hamiltonian model.

  19. Chaos Modelling with Computers

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 5. Chaos Modelling with Computers Unpredicatable Behaviour of Deterministic Systems. Balakrishnan Ramasamy T S K V Iyer. General Article Volume 1 Issue 5 May 1996 pp 29-39 ...

  20. Neural chaos and schizophrenia

    Czech Academy of Sciences Publication Activity Database

    Bob, P.; Chládek, Jan; Šusta, M.; Glaslová, K.; Jagla, F.; Kukleta, M.

    2007-01-01

    Roč. 26, č. 4 (2007), s. 298-305 ISSN 0231-5882 Institutional research plan: CEZ:AV0Z20650511 Keywords : EDA * Lyapunov exponent * schizophrenia * chaos Subject RIV: FL - Psychiatry, Sexuology Impact factor: 1.286, year: 2007

  1. Patterns in chaos

    International Nuclear Information System (INIS)

    Chirikov, B.V.

    1990-01-01

    Classification of chaotic patterns in classical Hamiltonian systems is given as a series of levels with increasing disorder. Hamiltonian dynamics is presented, including the renormalization chaos, based upon the fairly simple resonant theory. First estimates for the critical structure and related statistical anomalies in arbitrary dimensions are discussed. 49 refs

  2. Chaos at High School

    Directory of Open Access Journals (Sweden)

    Tamás Meszéna

    2017-04-01

    Full Text Available We are faced with chaotic processes in many segments of our life: meteorology, environmental pollution, financial and economic processes, sociology, mechanics, electronics, biology, chemistry. The spreading of high-performance computers and the development of simulation methods made the examination of these processes easily available. Regular, periodic motions (pendulum, harmonic oscillatory motion, bouncing ball, as taught at secondary level, become chaotic even due minor changes. If it is true that the most considerable achievements of twentieth century physics were the theory of relativity, quantum mechanics and chaos theory, then it is presumably time to think about, examine and test how and to what extent chaos can be presented to the students. Here I would like to introduce a 12 lesson long facultative curriculum framework on chaos designed for students aged seventeen. The investigation of chaos phenomenon in this work is based on a freeware, “Dynamics Solver”. This software, with some assistance from the teacher, is suitable for classroom use at secondary level.

  3. Survival and weak chaos.

    Science.gov (United States)

    Nee, Sean

    2018-05-01

    Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as 'infant mortality'. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality- sensu engineering-without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy.

  4. Chaos in drive systems

    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.

  5. User-Driven Chaos

    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...

  6. Metadata in CHAOS

    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...

  7. Chaos and insect ecology

    Science.gov (United States)

    Jesse A. Logan; Fred P. Hain

    1990-01-01

    Recent advances in applied mathematical analysis have uncovered a fascinating and unexpected dynamical richness that underlies behavior of even the simplest non-linear mathematical models. Due to the complexity of solutions to these non-linear equations, a new mathematical term, chaos, has been coined to describe the resulting dynamics. This term captures the notion...

  8. 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...... structure of a molecule such that this value (hopefully) correlates with physical and/or chemical properties of the molecule. The Wiener index is perhaps the most studied molecular topological index with more than a thousand publications. It is open whether the Wiener index of a planar graph can be obtained...... in subquadratic time. In my talk, I will solve this open problem by exhibiting an O(n2 log log n / log n) time algorithm, where n is the size of the graph. A simple modification yields an algorithm with the same time bound that computes the diameter (maximum distance between any vertex pair) of a planar graph. I...

  9. Chaos in neurons and its application: perspective of chaos engineering.

    Science.gov (United States)

    Hirata, Yoshito; Oku, Makito; Aihara, Kazuyuki

    2012-12-01

    We review our recent work on chaos in neurons and its application to neural networks from perspective of chaos engineering. Especially, we analyze a dataset of a squid giant axon by newly combining our previous work of identifying Devaney's chaos with surrogate data analysis, and show that an axon can behave chaotically. Based on this knowledge, we use a chaotic neuron model to investigate possible information processing in the brain.

  10. Wiener-Hopf operators on spaces of functions on R+ with values in a Hilbert space

    OpenAIRE

    Petkova, Violeta

    2006-01-01

    A Wiener-Hopf operator on a Banach space of functions on R+ is a bounded operator T such that P^+S_{-a}TS_a=T, for every positive a, where S_a is the operator of translation by a. We obtain a representation theorem for the Wiener-Hopf operators on a large class of functions on R+ with values in a separable Hilbert space.

  11. A note about Norbert Wiener and his contribution to Harmonic Analysis and Tauberian Theorems

    Science.gov (United States)

    Almira, J. M.; Romero, A. E.

    2009-05-01

    In this note we explain the main motivations Norbert Wiener had for the creation of his Generalized Harmonic Analysis [13] and his Tauberian Theorems [14]. Although these papers belong to the most pure mathematical tradition, they were deeply based on some Engineering and Physics Problems and Wiener was able to use them for such diverse areas as Optics, Brownian motion, Filter Theory, Prediction Theory and Cybernetics.

  12. An interview with Murray Jackson by Jan Wiener.

    Science.gov (United States)

    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. © 2011, The Society of Analytical Psychology.

  13. Spontaneous emission of the non-Wiener type

    International Nuclear Information System (INIS)

    Basharov, A. M.

    2011-01-01

    The spontaneous emission of a quantum particle and superradiation of an ensemble of identical quantum particles in a vacuum electromagnetic field with zero photon density are examined under the conditions of significant Stark particle and field interaction. New fundamental effects are established: suppression of spontaneous emission by the Stark interaction, an additional “decay” shift in energy of the decaying level as a consequence of Stark interaction unrelated to the Lamb and Stark level shifts, excitation conservation phenomena in a sufficiently dense ensemble of identical particles and suppression of superradiaton in the decay of an ensemble of excited quantum particles of a certain density. The main equations describing the emission processes under conditions of significant Stark interaction are obtained in the effective Hamiltonian representation of quantum stochastic differential equations. It is proved that the Stark interaction between a single quantum particle and a broadband electromagnetic field is represented as a quantum Poisson process and the stochastic differential equations are of the non-Wiener (generalized Langevin) type. From the examined case of spontaneous emission of a quantum particle, the main rules are formulated for studying open systems in the effective Hamiltonian representation.

  14. The joy of transient chaos

    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.

  15. The joy of transient chaos.

    Science.gov (United States)

    Tél, Tamás

    2015-09-01

    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.

  16. Gullies of Gorgonus Chaos

    Science.gov (United States)

    2002-01-01

    (Released 11 June 2002) The Science This fractured surface belongs to a portion of a region called Gorgonum Chaos located in the southern hemisphere of Mars. Gorgonum Chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars and lolling tongues who lived in caves. As it turns out this is indeed a fitting name for this region of Mars because it contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of chaos. Upon closer examination one finds that these gullies and alluvial deposits, initially discovered by Mars Global Surveyor, are visible on the trough walls (best seen near the bottom of the image). These gullies appear to emanate from a specific layer in the walls. The gullies have been proposed to have formed by the subsurface release of water. The Story This fractured, almost spooky-looking surface belongs to a region called Gorgonum Chaos in the southern hemisphere of Mars. Chaos is a term used for regions of Mars with distinctive areas of broken terrain like the one seen above. This area of Martian chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars, and lolling tongues, who lived in caves. The Gorgons, including famous sister Medusa, could turn a person to stone, and their writhing, snakelike locks cause revulsion to this day. Given the afflicted nature of this contorted terrain, with all of its twisted, branching channels and hard, stony-looking hills in the top half of the image, this is indeed a fitting name for this region of Mars. The name also has great appeal, because the area contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of Martian chaos. Gullies are trenches cut into the land as accelerated streams of water (or another liquid) erode the surface. To see these, click on the

  17. Controlling chaos faster

    International Nuclear Information System (INIS)

    Bick, Christian; Kolodziejski, Christoph; Timme, Marc

    2014-01-01

    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

  18. Handbook of Chaos Control

    CERN Document Server

    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

  19. Chaos in quantum channels

    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.

  20. Fascination of chaos

    International Nuclear Information System (INIS)

    Loskutov, Alexander

    2010-01-01

    This review introduces most of the concepts used in the study of chaotic phenomena in nonlinear systems and has as its objective to summarize the current understanding of results from the theory of chaotic dynamical systems and to describe the original ideas underlying the study of deterministic chaos. The presentation relies on informal analysis, with abstract mathematical ideas visualized geometrically or by examples from physics. Hyperbolic dynamics, homoclinic trajectories and tangencies, wild hyperbolic sets, and different types of attractors which appear in dynamical systems are considered. The key aspects of ergodic theory are discussed, and the basic statistical properties of chaotic dynamical systems are described. The fundamental difference between stochastic dynamics and deterministic chaos is explained. The review concludes with an investigation of the possibility of studying complex systems on the basis of the analysis of registered signals, i.e. the generated time series. (reviews of topical problems)

  1. Controlling chaos faster.

    Science.gov (United States)

    Bick, Christian; Kolodziejski, Christoph; Timme, Marc

    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.

  2. Chaos detection and predictability

    CERN Document Server

    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...

  3. Controlling chaos faster

    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.

  4. Noise tolerant spatiotemporal chaos computing.

    Science.gov (United States)

    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.

  5. Chaos on hyperspace

    Czech Academy of Sciences Publication Activity Database

    Beran, Zdeněk; Čelikovský, Sergej

    2013-01-01

    Roč. 23, č. 5 (2013), 1350084-1-1350084-9 ISSN 0218-1274 R&D Projects: GA ČR GA13-20433S Institutional support: RVO:67985556 Keywords : Hyperspace * chaos * shadowing * Bernoulli shift Subject RIV: BC - Control Systems Theory Impact factor: 1.017, year: 2013 http://library.utia.cas.cz/separaty/2013/TR/beran-0392926.pdf

  6. Aram Chaos Rocks

    Science.gov (United States)

    2005-01-01

    8 September 2005 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows outcrops of light-toned, sedimentary rock among darker-toned mesas in Aram Chaos. Dark, windblown megaripples -- large ripples -- are also present at this location. Location near: 3.0oN, 21.6oW Image width: width: 3 km (1.9 mi) Illumination from: lower left Season: Northern Autumn

  7. Fractals and chaos

    CERN Document Server

    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...

  8. Chaos on the interval

    CERN Document Server

    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...

  9. Polynomiography and Chaos

    Science.gov (United States)

    Kalantari, Bahman

    Polynomiography is the algorithmic visualization of iterative systems for computing roots of a complex polynomial. It is well known that iterations of a rational function in the complex plane result in chaotic behavior near its Julia set. In one scheme of computing polynomiography for a given polynomial p(z), we select an individual member from the Basic Family, an infinite fundamental family of rational iteration functions that in particular include Newton's. Polynomiography is an excellent means for observing, understanding, and comparing chaotic behavior for variety of iterative systems. Other iterative schemes in polynomiography are possible and result in chaotic behavior of different kinds. In another scheme, the Basic Family is collectively applied to p(z) and the iterates for any seed in the Voronoi cell of a root converge to that root. Polynomiography reveals chaotic behavior of another kind near the boundary of the Voronoi diagram of the roots. We also describe a novel Newton-Ellipsoid iterative system with its own chaos and exhibit images demonstrating polynomiographies of chaotic behavior of different kinds. Finally, we consider chaos for the more general case of polynomiography of complex analytic functions. On the one hand polynomiography is a powerful medium capable of demonstrating chaos in different forms, it is educationally instructive to students and researchers, also it gives rise to numerous research problems. On the other hand, it is a medium resulting in images with enormous aesthetic appeal to general audiences.

  10. Chaos in hadrons

    International Nuclear Information System (INIS)

    Muñoz, L; Fernández-Ramírez, C; Relaño, A; Retamosa, J

    2012-01-01

    In the last decade quantum chaos has become a well established discipline with outreach to different fields, from condensed-matter to nuclear physics. The most important signature of quantum chaos is the statistical analysis of the energy spectrum, which distinguishes between systems with integrable and chaotic classical analogues. In recent years, spectral statistical techniques inherited from quantum chaos have been applied successfully to the baryon spectrum revealing its likely chaotic behaviour even at the lowest energies. However, the theoretical spectra present a behaviour closer to the statistics of integrable systems which makes theory and experiment statistically incompatible. The usual statement of missing resonances in the experimental spectrum when compared to the theoretical ones cannot account for the discrepancies. In this communication we report an improved analysis of the baryon spectrum, taking into account the low statistics and the error bars associated with each resonance. Our findings give a major support to the previous conclusions. Besides, analogue analyses are performed in the experimental meson spectrum, with comparison to theoretical models.

  11. Stochastic analysis for Poisson point processes Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry

    CERN Document Server

    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...

  12. Universal signatures of quantum chaos

    International Nuclear Information System (INIS)

    Aurich, R.; Bolte, J.; Steiner, F.

    1994-02-01

    We discuss fingerprints of classical chaos in spectra of the corresponding bound quantum systems. A novel quantity to measure quantum chaos in spectra is proposed and a conjecture about its universal statistical behaviour is put forward. Numerical as well as theoretical evidence is provided in favour of the conjecture. (orig.)

  13. Chaos Theory and Post Modernism

    Science.gov (United States)

    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…

  14. Death and revival of chaos.

    Science.gov (United States)

    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.

  15. Chaos Criminology: A critical analysis

    Science.gov (United States)

    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.

  16. [Shedding light on chaos theory].

    Science.gov (United States)

    Chou, Shieu-Ming

    2004-06-01

    Gleick (1987) said that only three twentieth century scientific theories would be important enough to continue be of use in the twenty-first century: The Theory of Relativity, Quantum Theory, and Chaos Theory. Chaos Theory has become a craze which is being used to forge a new scientific system. It has also been extensively applied in a variety of professions. The purpose of this article is to introduce chaos theory and its nursing applications. Chaos is a sign of regular order. This is to say that chaos theory emphasizes the intrinsic potential for regular order within disordered phenomena. It is to be hoped that this article will inspire more nursing scientists to apply this concept to clinical, research, or administrative fields in our profession.

  17. Remaining useful life prediction based on the Wiener process for an aviation axial piston pump

    Directory of Open Access Journals (Sweden)

    Xingjian Wang

    2016-06-01

    Full Text Available 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 characteristics 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 according to the performance degradation model based on the Wiener process. Experimental results indicate 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.

  18. Shear-induced chaos

    International Nuclear Information System (INIS)

    Lin, Kevin K; Young, Lai-Sang

    2008-01-01

    Guided by a geometric understanding developed in earlier works of Wang and Young, we carry out numerical studies of shear-induced chaos in several parallel but different situations. The settings considered include periodic kicking of limit cycles, random kicks at Poisson times and continuous-time driving by white noise. The forcing of a quasi-periodic model describing two coupled oscillators is also investigated. In all cases, positive Lyapunov exponents are found in suitable parameter ranges when the forcing is suitably directed

  19. Shear-induced chaos

    Science.gov (United States)

    Lin, Kevin K.; Young, Lai-Sang

    2008-05-01

    Guided by a geometric understanding developed in earlier works of Wang and Young, we carry out numerical studies of shear-induced chaos in several parallel but different situations. The settings considered include periodic kicking of limit cycles, random kicks at Poisson times and continuous-time driving by white noise. The forcing of a quasi-periodic model describing two coupled oscillators is also investigated. In all cases, positive Lyapunov exponents are found in suitable parameter ranges when the forcing is suitably directed.

  20. Eos Chaos Rocks

    Science.gov (United States)

    2006-01-01

    11 January 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows light-toned, layered rock outcrops in Eos Chaos, located near the east end of the Valles Marineris trough system. The outcrops occur in the form of a distinct, circular butte (upper half of image) and a high slope (lower half of image). The rocks might be sedimentary rocks, similar to those found elsewhere exposed in the Valles Marineris system and the chaotic terrain to the east of the region. Location near: 12.9oS, 49.5oW Image width: 3 km (1.9 mi) Illumination from: lower left Season: Southern Summer

  1. Application of Chaos Theory to Engine Systems

    OpenAIRE

    Matsumoto, Kazuhiro; Diebner, Hans H.; Tsuda, Ichiro; Hosoi, Yukiharu

    2008-01-01

    We focus on the control issue for engine systems from the perspective of chaos theory, which is based on the fact that engine systems have a low-dimensional chaotic dynamics. Two approaches are discussed: controlling chaos and harnessing chaos, respectively. We apply Pyragas' chaos control method to an actual engine system. The experimental results show that the chaotic motion of an engine system may be stabilized to a periodic motion. Alternatively, harnessing chaos for engine systems is add...

  2. WH-EA: An Evolutionary Algorithm for Wiener-Hammerstein System Identification

    Directory of Open Access Journals (Sweden)

    J. Zambrano

    2018-01-01

    Full Text Available Current methods to identify Wiener-Hammerstein systems using Best Linear Approximation (BLA involve at least two steps. First, BLA is divided into obtaining front and back linear dynamics of the Wiener-Hammerstein model. Second, a refitting procedure of all parameters is carried out to reduce modelling errors. In this paper, a novel approach to identify Wiener-Hammerstein systems in a single step is proposed. This approach is based on a customized evolutionary algorithm (WH-EA able to look for the best BLA split, capturing at the same time the process static nonlinearity with high precision. Furthermore, to correct possible errors in BLA estimation, the locations of poles and zeros are subtly modified within an adequate search space to allow a fine-tuning of the model. The performance of the proposed approach is analysed by using a demonstration example and a nonlinear system identification benchmark.

  3. Security analysis of chaotic communication systems based on Volterra-Wiener-Korenberg model

    International Nuclear Information System (INIS)

    Lei Min; Meng Guang; Feng Zhengjin

    2006-01-01

    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

  4. Quantum chaos: entropy signatures

    International Nuclear Information System (INIS)

    Miller, P.A.; Sarkar, S.; Zarum, R.

    1998-01-01

    A definition of quantum chaos is given in terms of entropy production rates for a quantum system coupled weakly to a reservoir. This allows the treatment of classical and quantum chaos on the same footing. In the quantum theory the entropy considered is the von Neumann entropy and in classical systems it is the Gibbs entropy. The rate of change of the coarse-grained Gibbs entropy of the classical system with time is given by the Kolmogorov-Sinai (KS) entropy. The relation between KS entropy and the rate of change of von Neumann entropy is investigated for the kicked rotator. For a system which is classically chaotic there is a linear relationship between these two entropies. Moreover it is possible to construct contour plots for the local KS entropy and compare it with the corresponding plots for the rate of change of von Neumann entropy. The quantitative and qualitative similarities of these plots are discussed for the standard map (kicked rotor) and the generalised cat maps. (author)

  5. Quantum mechanical suppression of chaos

    International Nuclear Information System (INIS)

    Bluemel, R.; Smilansky, U.

    1990-01-01

    The relation between determinism and predictability is the central issue in the study of 'deterministic chaos'. Much knowledge has been accumulated in the past 10 years about the chaotic dynamics of macroscopic (classical) systems. The implications of chaos in the microscopic quantum world is examined, in other words, how to reconcile the correspondence principle with the inherent uncertainties which reflect the wave nature of quantum dynamics. Recent atomic physics experiments demonstrate clearly that chaos is relevant to the microscopic world. In particular, such experiments emphasise the urgent need to clarify the genuine quantum mechanism which imposes severe limitations on quantum dynamics, and renders it so very different from its classical counterpart. (author)

  6. Application of wavelet domain wiener filter in denoising of airborne γ-ray data

    International Nuclear Information System (INIS)

    Luo Yaoyao; Ge Liangquan; Xiong Chao; Xu Lipeng; Hua Yongtao

    2012-01-01

    The wavelet domain Wiener filter method, which combines the traditional wavelet method and the wiener filter, is established at CUT to reduce noising in as-recorded airborne gamma-ray spectra. It was used to treat an airborne gamma-ray data collected from an area m Inner Mongolia. The results showed that using this method, statistical noise could be greatly removed from the raw airborne gamma-ray spectra, and quality of the processed data is much better than those by conventional spectral denoising methods. (authors)

  7. Nonlinear Model Predictive Control for Solid Oxide Fuel Cell System Based On Wiener Model

    OpenAIRE

    T. H. Lee; J. H. Park; S. M. Lee; S. C. Lee

    2010-01-01

    In this paper, we consider Wiener nonlinear model for solid oxide fuel cell (SOFC). The Wiener model of the SOFC consists of a linear dynamic block and a static output non-linearity followed by the block, in which linear part is approximated by state-space model and the nonlinear part is identified by a polynomial form. To control the SOFC system, we have to consider various view points such as operating conditions, another constraint conditions, change of load current and so on. A change of ...

  8. 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.

  9. La factorización de una transformada de Fourier en el método de Wiener-Hopf

    OpenAIRE

    José Rosales-Ortega; Carlos Márquez Rivera

    2009-01-01

    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.

  10. Recent development of chaos theory in topological dynamics

    OpenAIRE

    Li, Jian; Ye, Xiangdong

    2015-01-01

    We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.

  11. Ancient and Current Chaos Theories

    Directory of Open Access Journals (Sweden)

    Güngör Gündüz

    2006-07-01

    Full Text Available Chaos theories developed in the last three decades have made very important contributions to our understanding of dynamical systems and natural phenomena. The meaning of chaos in the current theories and in the past is somewhat different from each other. In this work, the properties of dynamical systems and the evolution of chaotic systems were discussed in terms of the views of ancient philosophers. The meaning of chaos in Anaximenes’ philosophy and its role in the Ancient natural philosophy has been discussed in relation to other natural philosophers such as of Anaximander, Parmenides, Heraclitus, Empedocles, Leucippus (i.e. atomists and Aristotle. In addition, the fundamental concepts of statistical mechanics and the current chaos theories were discussed in relation to the views in Ancient natural philosophy. The roots of the scientific concepts such as randomness, autocatalysis, nonlinear growth, information, pattern, etc. in the Ancient natural philosophy were investigated.

  12. Quantum Instantons and Quantum Chaos

    OpenAIRE

    Jirari, H.; Kröger, H.; Luo, X. Q.; Moriarty, K. J. M.; Rubin, S. G.

    1999-01-01

    Based on a closed form expression for the path integral of quantum transition amplitudes, we suggest rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.

  13. Cryptography with chaos and shadowing

    International Nuclear Information System (INIS)

    Smaoui, Nejib; Kanso, Ali

    2009-01-01

    In this paper, we present a novel approach to encrypt a message (a text composed by some alphabets) using chaos and shadowing. First, we generate a numerical chaotic orbit based on the logistic map, and use the shadowing algorithm of Smaoui and Kostelich [Smaoui N, Kostelich E. Using chaos to shadow the quadratic map for all time. Int J Comput Math 1998;70:117-29] to show that there exists a finite number of true orbits that shadow the numerical orbit. Then, the finite number of maps generated is used in Baptista's algorithm [Baptista MS. Cryptography with chaos. Phys Lett A 1998;240:50-4] to encrypt each character of the message. It is shown that the use of chaos and shadowing in the encryption process enhances the security level.

  14. Chaos and complexity by design

    Energy Technology Data Exchange (ETDEWEB)

    Roberts, Daniel A. [Center for Theoretical Physics and Department of Physics,Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Yoshida, Beni [Perimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5 (Canada)

    2017-04-20

    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 kth 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.

  15. Chaos and complexity by design

    International Nuclear Information System (INIS)

    Roberts, Daniel A.; Yoshida, Beni

    2017-01-01

    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 kth 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.

  16. Experimental Induction of Genome Chaos.

    Science.gov (United States)

    Ye, Christine J; Liu, Guo; Heng, Henry H

    2018-01-01

    Genome chaos, or karyotype chaos, represents a powerful survival strategy for somatic cells under high levels of stress/selection. Since the genome context, not the gene content, encodes the genomic blueprint of the cell, stress-induced rapid and massive reorganization of genome topology functions as a very important mechanism for genome (karyotype) evolution. In recent years, the phenomenon of genome chaos has been confirmed by various sequencing efforts, and many different terms have been coined to describe different subtypes of the chaotic genome including "chromothripsis," "chromoplexy," and "structural mutations." To advance this exciting field, we need an effective experimental system to induce and characterize the karyotype reorganization process. In this chapter, an experimental protocol to induce chaotic genomes is described, following a brief discussion of the mechanism and implication of genome chaos in cancer evolution.

  17. Encounters with chaos and fractals

    CERN Document Server

    Gulick, Denny

    2012-01-01

    Periodic Points Iterates of Functions Fixed Points Periodic Points Families of Functions The Quadratic Family Bifurcations Period-3 Points The Schwarzian Derivative One-Dimensional Chaos Chaos Transitivity and Strong Chaos Conjugacy Cantor Sets Two-Dimensional Chaos Review of Matrices Dynamics of Linear FunctionsNonlinear Maps The Hénon Map The Horseshoe Map Systems of Differential Equations Review of Systems of Differential Equations Almost Linearity The Pendulum The Lorenz System Introduction to Fractals Self-Similarity The Sierpiński Gasket and Other "Monsters"Space-Filling Curves Similarity and Capacity DimensionsLyapunov Dimension Calculating Fractal Dimensions of Objects Creating Fractals Sets Metric Spaces The Hausdorff Metric Contractions and Affine Functions Iterated Function SystemsAlgorithms for Drawing Fractals Complex Fractals: Julia Sets and the Mandelbrot Set Complex Numbers and Functions Julia Sets The Mandelbrot Set Computer Programs Answers to Selected Exercises References Index.

  18. Cryptography with chaos and shadowing

    Energy Technology Data Exchange (ETDEWEB)

    Smaoui, Nejib [Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail: nsmaoui64@yahoo.com; Kanso, Ali [Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail: akanso@hotmail.com

    2009-11-30

    In this paper, we present a novel approach to encrypt a message (a text composed by some alphabets) using chaos and shadowing. First, we generate a numerical chaotic orbit based on the logistic map, and use the shadowing algorithm of Smaoui and Kostelich [Smaoui N, Kostelich E. Using chaos to shadow the quadratic map for all time. Int J Comput Math 1998;70:117-29] to show that there exists a finite number of true orbits that shadow the numerical orbit. Then, the finite number of maps generated is used in Baptista's algorithm [Baptista MS. Cryptography with chaos. Phys Lett A 1998;240:50-4] to encrypt each character of the message. It is shown that the use of chaos and shadowing in the encryption process enhances the security level.

  19. Optical digital chaos cryptography

    Science.gov (United States)

    Arenas-Pingarrón, Álvaro; González-Marcos, Ana P.; Rivas-Moscoso, José M.; Martín-Pereda, José A.

    2007-10-01

    In this work we present a new way to mask the data in a one-user communication system when direct sequence - code division multiple access (DS-CDMA) techniques are used. The code is generated by a digital chaotic generator, originally proposed by us and previously reported for a chaos cryptographic system. It is demonstrated that if the user's data signal is encoded with a bipolar phase-shift keying (BPSK) technique, usual in DS-CDMA, it can be easily recovered from a time-frequency domain representation. To avoid this situation, a new system is presented in which a previous dispersive stage is applied to the data signal. A time-frequency domain analysis is performed, and the devices required at the transmitter and receiver end, both user-independent, are presented for the optical domain.

  20. SPICE and Chaos

    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...... in the right half plane. (2) "Chaotic" steady state behaviour of a non-chaotic dc power supply. (3) Analysis of a Colpitts oscillator with chaotic behaviour. In order to obtain reliable results from the SPICE simulators the users of these programs need insight not only in the use of the programs but also...... in the models of the circuits to be analyzed. If trimmed properly SPICE normally gives the correct result....

  1. Hasard et chaos

    CERN Document Server

    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.

  2. Speech enhancement via Mel-scale Wiener filtering with a frequency-wise voice activity detector

    International Nuclear Information System (INIS)

    Kim, Han Jun; Kim, Hwa Soo; Cho, Young Man

    2007-01-01

    This paper presents a speech enhancement system that enables a comfortable communication inside an automobile. A couple of novel concepts are proposed in an effort to improve two major building blocks in the existing speech enhancement systems: a voice activity detector (VAD) and a noise filtering algorithm. The proposed VAD classifies a given data frame as speech or noise at each frequency, enabling the frequency-wise updates of noise statistics and thereby improving the effectiveness of the noise filtering algorithms by providing more up-to-date noise statistics. The celebrated Wiener filter is adopted in this paper as the accompanying noise filtering algorithm, which results in significant noise suppression. Yet, the musical noise present in most Wiener filter-based systems prompts the idea of applying the Wiener filter in the Mel-scale in which the human auditory system responds to the external stimulation. It turns out that the Mel-scale Wiener filter creates some masking effects and thereby reduces musical noise significantly, leading to smooth transition between data frames

  3. Optimization of the reconstruction and anti-aliasing filter in a Wiener filter system

    NARCIS (Netherlands)

    Wesselink, J.M.; Berkhoff, Arthur 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

  4. State Estimation for Linear Systems Driven Simultaneously by Wiener and Poisson Processes.

    Science.gov (United States)

    1978-12-01

    The state estimation problem of linear stochastic systems driven simultaneously by Wiener and Poisson processes is considered, especially the case...where the incident intensities of the Poisson processes are low and the system is observed in an additive white Gaussian noise. The minimum mean squared

  5. Deconvolution of Defocused Image with Multivariate Local Polynomial Regression and Iterative Wiener Filtering in DWT Domain

    Directory of Open Access Journals (Sweden)

    Liyun Su

    2010-01-01

    obtaining the point spread function (PSF parameter, iterative wiener filter is adopted to complete the restoration. We experimentally illustrate its performance on simulated data and real blurred image. Results show that the proposed PSF parameter estimation technique and the image restoration method are effective.

  6. Quantum mechanical path integrals with Wiener measures for all polynomial Hamiltonians

    International Nuclear Information System (INIS)

    Klauder, J.R.; Daubechies, I.

    We construct arbitrary matrix elements of the quantum evolution operator for a wide class of self-adjoint canonical Hamiltonians, including those which are polynomial in the Heisenberg operators, as the limit of well-defined path integrals involving Wiener measure on phase space, as a diffusion constant diverges. A related construction achieves a similar result for an arbitrary spin Hamiltonian. (orig.)

  7. Combined adaptive multiple subtraction based on optimized event tracing and extended wiener filtering

    Science.gov (United States)

    Tan, Jun; Song, Peng; Li, Jinshan; Wang, Lei; Zhong, Mengxuan; Zhang, Xiaobo

    2017-06-01

    The surface-related multiple elimination (SRME) method is based on feedback formulation and has become one of the most preferred multiple suppression methods used. However, some differences are apparent between the predicted multiples and those in the source seismic records, which may result in conventional adaptive multiple subtraction methods being barely able to effectively suppress multiples in actual production. This paper introduces a combined adaptive multiple attenuation method based on the optimized event tracing technique and extended Wiener filtering. The method firstly uses multiple records predicted by SRME to generate a multiple velocity spectrum, then separates the original record to an approximate primary record and an approximate multiple record by applying the optimized event tracing method and short-time window FK filtering method. After applying the extended Wiener filtering method, residual multiples in the approximate primary record can then be eliminated and the damaged primary can be restored from the approximate multiple record. This method combines the advantages of multiple elimination based on the optimized event tracing method and the extended Wiener filtering technique. It is an ideal method for suppressing typical hyperbolic and other types of multiples, with the advantage of minimizing damage of the primary. Synthetic and field data tests show that this method produces better multiple elimination results than the traditional multi-channel Wiener filter method and is more suitable for multiple elimination in complicated geological areas.

  8. Medienerziehung im Vorschulbereich - Zum Projekt Mediengarten der Wiener Medienpädagogik

    Directory of Open Access Journals (Sweden)

    Gudrun Kern

    2010-09-01

    Full Text Available Im Zuge des Projekts Mediengarten der Wiener Medienpädagogik wurde in Kooperation mit angehenden KindergartenpädagogInnen eine Medienerziehung im Sinne einer Auseinandersetzung über Medien im Vorschulbereich anhand konkreter Angebote in Kindergärten konzipiert. Im folgenden Artikel werden die Schwerpunktsetzungen dieses Konzepts vorgestellt und durch praktische Beispiele verdeutlicht.

  9. 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.

  10. Degradation data analysis based on a generalized Wiener process subject to measurement error

    Science.gov (United States)

    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.

  11. Speech Enhancement by Classification of Noisy Signals Decomposed Using NMF and Wiener Filtering

    DEFF Research Database (Denmark)

    Fakhry, Mahmoud; Poorjam, Amir Hossein; Christensen, Mads Græsbøll

    2018-01-01

    are identified in the cepstral domain using the trained classifier. We apply unsupervised NMF followed by Wiener filtering for the decomposition, and use a support vector machine trained on the mel-frequency cepstral coefficients of the parts of training speech and noise signals for the classification...

  12. Nonintrusive Polynomial Chaos Expansions for Sensitivity Analysis in Stochastic Differential Equations

    KAUST Repository

    Jimenez, M. Navarro; Le Maî tre, O. P.; Knio, Omar

    2017-01-01

    A Galerkin polynomial chaos (PC) method was recently proposed to perform variance decomposition and sensitivity analysis in stochastic differential equations (SDEs), driven by Wiener noise and involving uncertain parameters. The present paper extends the PC method to nonintrusive approaches enabling its application to more complex systems hardly amenable to stochastic Galerkin projection methods. We also discuss parallel implementations and the variance decomposition of the derived quantity of interest within the framework of nonintrusive approaches. In particular, a novel hybrid PC-sampling-based strategy is proposed in the case of nonsmooth quantities of interest (QoIs) but smooth SDE solution. Numerical examples are provided that illustrate the decomposition of the variance of QoIs into contributions arising from the uncertain parameters, the inherent stochastic forcing, and joint effects. The simulations are also used to support a brief analysis of the computational complexity of the method, providing insight on the types of problems that would benefit from the present developments.

  13. Nonintrusive Polynomial Chaos Expansions for Sensitivity Analysis in Stochastic Differential Equations

    KAUST Repository

    Jimenez, M. Navarro

    2017-04-18

    A Galerkin polynomial chaos (PC) method was recently proposed to perform variance decomposition and sensitivity analysis in stochastic differential equations (SDEs), driven by Wiener noise and involving uncertain parameters. The present paper extends the PC method to nonintrusive approaches enabling its application to more complex systems hardly amenable to stochastic Galerkin projection methods. We also discuss parallel implementations and the variance decomposition of the derived quantity of interest within the framework of nonintrusive approaches. In particular, a novel hybrid PC-sampling-based strategy is proposed in the case of nonsmooth quantities of interest (QoIs) but smooth SDE solution. Numerical examples are provided that illustrate the decomposition of the variance of QoIs into contributions arising from the uncertain parameters, the inherent stochastic forcing, and joint effects. The simulations are also used to support a brief analysis of the computational complexity of the method, providing insight on the types of problems that would benefit from the present developments.

  14. The impact of high hydrostatic pressure on the functionality and consumer acceptability of reduced sodium naturally cured wieners.

    Science.gov (United States)

    Pietrasik, Z; Gaudette, N J; Johnston, S P

    2017-07-01

    The effects of high pressure processing (HPP; 600MPa for 3min at 8°C) on the quality and shelf life of reduced sodium naturally-cured wieners was studied. HPP did not negatively impact processing characteristics and assisted in extending shelf life of all wiener treatments up to a 12week storage period. At week 8, HPP wieners received higher acceptability scores, indicating HPP can effectively extend the sensory quality of products, including sodium reduced formulations containing natural forms of nitrite. Substitution of 50% NaCl with modified KCl had negative effect on textural characteristics of conventionally cured wieners but not those processed with celery powder as a source of nitrite. Celery powder favorably affected hydration of textural properties of wieners, and consumer acceptability of juiciness and texture was higher compared to nitrite. Sodium reduction, independent of curing agent, negatively impacted flavor acceptability, while only nitrite containing reduced sodium wieners scored significantly lower than both regular salt wieners for texture, juiciness and saltiness. Copyright © 2017 Elsevier Ltd. All rights reserved.

  15. 2012 Symposium on Chaos, Complexity and Leadership

    CERN Document Server

    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.

  16. Quantum chaos: Statistical relaxation in discrete spectrum

    International Nuclear Information System (INIS)

    Chirikov, B.V.

    1991-01-01

    The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Various mechanisms of the quantum suppression of classical chaos are considered with an application to the excitation and ionization of Rydberg atoms in a microwave field. Several definitions of the quantum chaos are discussed. (author). 27 refs

  17. Decoherence, determinism and chaos

    International Nuclear Information System (INIS)

    Noyes, H.P.

    1994-01-01

    The author claims by now to have made his case that modern work on fractals and chaos theory has already removed the presumption that classical physics is 'deterministic'. Further, he claims that in so far as classical relativistic field theory (i.e. electromagnetism and gravitation) are scale invariant, they are self-consistent only if the idea of 'test-particle' is introduced from outside the theory. Einstein spent the last years of his life trying to use singularities in the metric as 'particles' or to get them out of the non-linearities in a grand unified theory -- in vain. So classical physics in this sense cannot be the fundamental theory. However, the author claims to have shown that if he introduces a 'scale invariance bounded from below' by measurement accuracy, then Tanimura's generalization of the Feynman proof as reconstructed by Dyson allows him to make a consistent classical theory for decoherent sources sinks. Restoring coherence to classical physics via relativistic action-at-a distance is left as a task for the future. Relativistic quantum mechanics, properly reconstructed from a finite and discrete basis, emerges in much better shape. The concept of 'particles has to be replaced by NO-YES particulate events, and particle-antiparticle pair creation and annihilation properly formulated

  18. Quasiperiodic transition to chaos in a plasma

    International Nuclear Information System (INIS)

    Weixing, D.; Huang Wei; Wang Xiaodong; Yu, C.X.

    1993-01-01

    The quasiperiodic transition to chaos in an undriven discharge plasma has been investigated. Results from the power spectrum and Lyapunov exponents quantitatively confirm the transition to chaos through quasiperiodicity. A low-dimension strange attractor has been found for this kind of plasma chaos

  19. Further discussion on chaos in duopoly games

    International Nuclear Information System (INIS)

    Lu, Tianxiu; Zhu, Peiyong

    2013-01-01

    In this paper, we study Li–Yorke chaos, distributional chaos in a sequence, Li–Yorke sensitivity, sensitivity and distributional chaos of two-dimensional dynamical system of the form Φ(x, y) = (f(y), g(x))

  20. Puzzles in studies of quantum chaos

    International Nuclear Information System (INIS)

    Xu Gongou

    1994-01-01

    Puzzles in studies of quantum chaos are discussed. From the view of global properties of quantum states, it is clarified that quantum chaos originates from the break-down of invariant properties of quantum canonical transformations. There exist precise correspondences between quantum and classical chaos

  1. Towards chaos criterion in quantum field theory

    OpenAIRE

    Kuvshinov, V. I.; Kuzmin, A. V.

    2002-01-01

    Chaos criterion for quantum field theory is proposed. Its correspondence with classical chaos criterion in semi-classical regime is shown. It is demonstrated for real scalar field that proposed chaos criterion can be used to investigate stability of classical solutions of field equations.

  2. Quantum chaos: statistical relaxation in discrete spectrum

    International Nuclear Information System (INIS)

    Chirikov, B.V.

    1990-01-01

    The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Several definitions of the quantum chaos are discussed. 27 refs

  3. Hastily Formed Networks-Chaos to Recovery

    Science.gov (United States)

    2015-09-01

    NETWORKS— CHAOS TO RECOVERY by Mark Arezzi September 2015 Thesis Co-Advisors: Douglas J. MacKinnon Brian Steckler THIS PAGE......systems to self-organize, adapt, and exert control over the chaos . Defining the role of communications requires an understanding of complexity, chaos

  4. Chaos in the atomic and subatomic world

    International Nuclear Information System (INIS)

    Nussenzveig, H.M.

    1992-01-01

    This work discusses the possibility of the existence of chaos in the quantum level. In the macroscopic scale, chaos can be explained by the use of classical mechanics. The problem is to know whether there is any manifestation of chaos in the evolution of a system following the quantum mechanical laws. (A.C.A.S.)

  5. !CHAOS: A cloud of controls

    International Nuclear Information System (INIS)

    Angius, S.; Bisegni, C.; Ciuffetti, P.

    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 abstraction, 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.

  6. !CHAOS: A cloud of controls

    Science.gov (United States)

    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.

  7. Order against chaos in nuclei

    International Nuclear Information System (INIS)

    Soloviev, V.G.

    1995-01-01

    Order and chaos and order-to-chaos transition are treated in terms of nuclear wave functions. A quasiparticle-phonon interaction is responsible for the fragmentation of one- and many-quasiparticle and phonon states and for the mixing of closely spaced states. Complete damping of one-quasiparticle states cannot be considered as a transition to chaos due to large many-quasiparticle or quasiparticle-phonon terms in their wave functions. An experimental investigation of the strength distribution of many-quasiparticle and quasiparticle-phonon states should uncover a new region of a regularity in nuclei at intermediate excitation energy. A chaotic behaviour of nuclear states can be shifted to higher excitation energies. ((orig.))

  8. On CFT and quantum chaos

    Energy Technology Data Exchange (ETDEWEB)

    Turiaci, Gustavo J. [Physics Department, Princeton University,Princeton NJ 08544 (United States); Verlinde, Herman [Physics Department, Princeton University,Princeton NJ 08544 (United States); Princeton Center for Theoretical Science, Princeton University,Princeton NJ 08544 (United States)

    2016-12-21

    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.

  9. Chaos, decoherence and quantum cosmology

    International Nuclear Information System (INIS)

    Calzetta, Esteban

    2012-01-01

    In this topical review we discuss the connections between chaos, decoherence and quantum cosmology. We understand chaos as classical chaos in systems with a finite number of degrees of freedom, decoherence as environment induced decoherence and quantum cosmology as the theory of the Wheeler-DeWitt equation or else the consistent history formulation thereof, first in mini super spaces and later through its extension to midi super spaces. The overall conclusion is that consideration of decoherence is necessary (and probably sufficient) to sustain an interpretation of quantum cosmology based on the wavefunction of the Universe adopting a Wentzel-Kramers-Brillouin form for large Universes, but a definitive account of the semiclassical transition in classically chaotic cosmological models is not available in the literature yet. (topical review)

  10. On CFT and quantum chaos

    International Nuclear Information System (INIS)

    Turiaci, Gustavo J.; Verlinde, Herman

    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.

  11. Nuclear spectroscopy and quantum chaos

    International Nuclear Information System (INIS)

    Sakata, Fumihiko; Marumori, Toshio; Hashimoto, Yukio; Yamamoto, Yoshifumi; Tsukuma, Hidehiko; Iwasawa, Kazuo.

    1990-05-01

    In this paper, a recent development of INS-TSUKUBA joint research project on large-amplitude collective motion is summerized. The classical theory of nuclear collective dynamics formulated within the time-dependent Hartree-Fock theory is recapitulated and decisive role of the level crossing in the single-particle dynamics on the order-to-chaos transition of collective motion is discussed in detail. Extending the basic idea of the classical theory, we discuss a quantum theory of nuclear collective dynamics which allows us to properly define a concept of quantum chaos for each eigenfunction. By using numerical calculation, we illustrate what the quantum chaos for each eigenfunction means and its relation to usual definition based on the random matrix theory. (author)

  12. L'ordre du chaos

    CERN Document Server

    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.

  13. Some new surprises in chaos.

    Science.gov (United States)

    Bunimovich, Leonid A; Vela-Arevalo, Luz V

    2015-09-01

    "Chaos is found in greatest abundance wherever order is being sought.It always defeats order, because it is better organized"Terry PratchettA 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.

  14. Blurred image restoration using knife-edge function and optimal window Wiener filtering

    Science.gov (United States)

    Zhou, Shudao; Yan, Wei

    2018-01-01

    Motion blur in images is usually modeled as the convolution of a point spread function (PSF) and the original image represented as pixel intensities. The knife-edge function can be used to model various types of motion-blurs, and hence it allows for the construction of a PSF and accurate estimation of the degradation function without knowledge of the specific degradation model. This paper addresses the problem of image restoration using a knife-edge function and optimal window Wiener filtering. In the proposed method, we first calculate the motion-blur parameters and construct the optimal window. Then, we use the detected knife-edge function to obtain the system degradation function. Finally, we perform Wiener filtering to obtain the restored image. Experiments show that the restored image has improved resolution and contrast parameters with clear details and no discernible ringing effects. PMID:29377950

  15. Solution of Stochastic Nonlinear PDEs Using Automated Wiener-Hermite Expansion

    KAUST Repository

    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].

  16. A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems.

    Science.gov (United States)

    Kazemi, Mahdi; Arefi, Mohammad Mehdi

    2017-03-01

    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. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  17. On the improvement of Wiener attack on RSA with small private exponent.

    Science.gov (United States)

    Wu, Mu-En; Chen, Chien-Ming; Lin, Yue-Hsun; Sun, Hung-Min

    2014-01-01

    RSA system is based on the hardness of the integer factorization problem (IFP). Given an RSA modulus N = pq, it is difficult to determine the prime factors p and q efficiently. One of the most famous short exponent attacks on RSA is the Wiener attack. In 1997, Verheul and van Tilborg use an exhaustive search to extend the boundary of the Wiener attack. Their result shows that the cost of exhaustive search is 2r + 8 bits when extending the Weiner's boundary r bits. In this paper, we first reduce the cost of exhaustive search from 2r + 8 bits to 2r + 2 bits. Then, we propose a method named EPF. With EPF, the cost of exhaustive search is further reduced to 2r - 6 bits when we extend Weiner's boundary r bits. It means that our result is 2(14) times faster than Verheul and van Tilborg's result. Besides, the security boundary is extended 7 bits.

  18. Model-based Acceleration Control of Turbofan Engines with a Hammerstein-Wiener Representation

    Science.gov (United States)

    Wang, Jiqiang; Ye, Zhifeng; Hu, Zhongzhi; Wu, Xin; Dimirovsky, Georgi; Yue, Hong

    2017-05-01

    Acceleration control of turbofan engines is conventionally designed through either schedule-based or acceleration-based approach. With the widespread acceptance of model-based design in aviation industry, it becomes necessary to investigate the issues associated with model-based design for acceleration control. In this paper, the challenges for implementing model-based acceleration control are explained; a novel Hammerstein-Wiener representation of engine models is introduced; based on the Hammerstein-Wiener model, a nonlinear generalized minimum variance type of optimal control law is derived; the feature of the proposed approach is that it does not require the inversion operation that usually upsets those nonlinear control techniques. The effectiveness of the proposed control design method is validated through a detailed numerical study.

  19. On the Improvement of Wiener Attack on RSA with Small Private Exponent

    Directory of Open Access Journals (Sweden)

    Mu-En Wu

    2014-01-01

    Full Text Available RSA system is based on the hardness of the integer factorization problem (IFP. Given an RSA modulus N=pq, it is difficult to determine the prime factors p and q efficiently. One of the most famous short exponent attacks on RSA is the Wiener attack. In 1997, Verheul and van Tilborg use an exhaustive search to extend the boundary of the Wiener attack. Their result shows that the cost of exhaustive search is 2r+8 bits when extending the Weiner's boundary r bits. In this paper, we first reduce the cost of exhaustive search from 2r+8 bits to 2r+2 bits. Then, we propose a method named EPF. With EPF, the cost of exhaustive search is further reduced to 2r-6 bits when we extend Weiner's boundary r bits. It means that our result is 214 times faster than Verheul and van Tilborg's result. Besides, the security boundary is extended 7 bits.

  20. 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.

  1. Recursive parameter estimation for Hammerstein-Wiener systems using modified EKF algorithm.

    Science.gov (United States)

    Yu, Feng; Mao, Zhizhong; Yuan, Ping; He, Dakuo; Jia, Mingxing

    2017-09-01

    This paper focuses on the recursive parameter estimation for the single input single output Hammerstein-Wiener system model, and the study is then extended to a rarely mentioned multiple input single output Hammerstein-Wiener system. Inspired by the extended Kalman filter algorithm, two basic recursive algorithms are derived from the first and the second order Taylor approximation. Based on the form of the first order approximation algorithm, a modified algorithm with larger parameter convergence domain is proposed to cope with the problem of small parameter convergence domain of the first order one and the application limit of the second order one. The validity of the modification on the expansion of convergence domain is shown from the convergence analysis and is demonstrated with two simulation cases. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  2. Combination of Wiener filtering and singular value decomposition filtering for volume imaging PET

    International Nuclear Information System (INIS)

    Shao, L.; Lewitt, R.M.; Karp, J.S.

    1995-01-01

    Although the three-dimensional (3D) multi-slice rebinning (MSRB) algorithm in PET is fast and practical, and provides an accurate reconstruction, the MSRB image, in general, suffers from the noise amplified by its singular value decomposition (SVD) filtering operation in the axial direction. Their aim in this study is to combine the use of the Wiener filter (WF) with the SVD to decrease the noise and improve the image quality. The SVD filtering ''deconvolves'' the spatially variant axial response function while the WF suppresses the noise and reduces the blurring not modeled by the axial SVD filter but included in the system modulation transfer function. Therefore, the synthesis of these two techniques combines the advantages of both filters. The authors applied this approach to the volume imaging HEAD PENN-PET brain scanner with an axial extent of 256 mm. This combined filter was evaluated in terms of spatial resolution, image contrast, and signal-to-noise ratio with several phantoms, such as a cold sphere phantom and 3D brain phantom. Specifically, the authors studied both the SVD filter with an axial Wiener filter and the SVD filter with a 3D Wiener filter, and compared the filtered images to those from the 3D reprojection (3DRP) reconstruction algorithm. Their results indicate that the Wiener filter increases the signal-to-noise ratio and also improves the contrast. For the MSRB images of the 3D brain phantom, after 3D WF, both the Gray/White and Gray/Ventricle ratios were improved from 1.8 to 2.8 and 2.1 to 4.1, respectively. In addition, the image quality with the MSRB algorithm is close to that of the 3DRP algorithm with 3D WF applied to both image reconstructions

  3. A new non-commutative representation of the Wiener and Poisson processes

    International Nuclear Information System (INIS)

    Privault, N.

    1996-01-01

    Using two different constructions of the chaotic and variational calculus on Poisson space, we show that the Wiener and Poisson processes have a non-commutative representation which is different from the one obtained by transfer of the Fock space creation and annihilation operators. We obtain in this way an extension of the non-commutative It calculus. The associated commutation relations show a link between the geometric and exponential distributions. (author). 11 refs

  4. Effect of Sodium Nitrite and Sodium Nitrate on Botulinal Toxin Production and Nitrosamine Formation in Wieners

    Science.gov (United States)

    Hustad, Gerald O.; Cerveny, John G.; Trenk, Hugh; Deibel, Robert H.; Kautter, Donald A.; Fazio, Thomas; Johnston, Ralph W.; Kolari, Olaf E.

    1973-01-01

    Wieners were formulated and processed approximating commercial conditions as closely as possible. Twenty-four batches of product were made with the addition of six levels of sodium nitrite (0, 50, 100, 150, 200, and 300 μg/g), four levels of sodium nitrate (0, 50, 150, and 450 μg/g), and two levels of Clostridium botulinum (0 and 620 spores/g). After formulation, processing, and vacuum packaging, portions of each batch were incubated at 27 C or held for 21 days at 7 C followed by incubation at 27 C for 56 days. The latter storage condition approximated distribution of product through commercial channels and potential temperature abuse at the consumer level. Samples were analyzed for botulinal toxin, nitrite, and nitrate levels after 3, 7, 14, 21, 28, and 56 days of incubation. When nitrite was not added, toxic samples were detected after 14 days of incubation at 27 C. At the lowest level of nitrite added (50 μg/g), no toxic samples were observed until 56 days of incubation. Higher levels of nitrite completely inhibited toxin production throughout the incubation period. Nine uninoculated samples, representing various levels and combinations of nitrite and nitrate, were evaluated organoleptically. The flavor quality of wieners made with nitrite was judged significantly higher (P = 0.05) than of wieners made without nitrite. The nine samples were negative for 14 volatile nitrosamines at a sensitivity level of 10 ng/g. The results indicated that nitrite effectively inhibited botulinal toxin formation at commercially employed levels in wieners and that detectable quantities of nitrosamines were not produced during preparation and processing of the product for consumption. PMID:4580194

  5. Use of wiener nonlinear MPC to control a CSTR with multiple steady state

    OpenAIRE

    Lusson Cervantes, A.; Agamennoni, O.E.; Figueroa, J.L.

    2003-01-01

    In this paper a Nonlinear Model Predictive Control based on a Wiener Model with a Piecewise Linear gain is presented. The major advantages of this algorithm is that it retains all the interesting properties of the classical linear MPC and the computations are easy to solve due to the canonical structure of the nonlinear gain. The proposed control scheme is applied to a nonlinear CSTR that presents multiple steady states.

  6. Image restoration by Wiener filtering in the presence of signal-dependent noise.

    Science.gov (United States)

    Kondo, K; Ichioka, Y; Suzuki, T

    1977-09-01

    An optimum filter to restore the degraded image due to blurring and the signal-dependent noise is obtained on the basis of the theory of Wiener filtering. Computer simulations of image restoration using signal-dependent noise models are carried out. It becomes clear that the optimum filter, which makes use of a priori information on the signal-dependent nature of the noise and the spectral density of the signal and the noise showing significant spatial correlation, is potentially advantageous.

  7. Active polymers containing Lactobacillus curvatus CRL705 bacteriocins: effectiveness assessment in Wieners.

    Science.gov (United States)

    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. Copyright © 2014 Elsevier B.V. All rights reserved.

  8. Distributional chaos for linear operators

    Czech Academy of Sciences Publication Activity Database

    Bernardes Jr., N.C.; Bonilla, A.; Müller, Vladimír; Peris, A.

    2013-01-01

    Roč. 265, č. 9 (2013), s. 2143-2163 ISSN 0022-1236 R&D Projects: GA ČR GA201/09/0473 Institutional support: RVO:67985840 Keywords : distributional chaos * hypercyclic operators * irregular vectors Subject RIV: BA - General Mathematics Impact factor: 1.152, year: 2013 http://www.sciencedirect.com/science/article/pii/S0022123613002450

  9. Solitons and chaos in plasma

    International Nuclear Information System (INIS)

    Ichikawa, Y.H.

    1990-09-01

    Plasma exhibits a full of variety of nonlinear phenomena. Active research in nonlinear plasma physics contributed to explore the concepts of soliton and chaos. Structure of soliton equations and dynamics of low dimensional Hamiltonian systems are discussed to emphasize the universality of these novel concepts in the wide branch of science and engineering. (author) 52 refs

  10. Chaos Theory and International Relations

    Science.gov (United States)

    2016-12-01

    King Oscar II 12 James E. Glenn, Chaos Theory: The Essentials for Military Applications (Newport, RI...Adolf Hitler in Germany, Alexander’s conquest of the Persian Empire, the arrival of Attila to Europe, the onset of the two Gulf Wars, the Arab Spring

  11. The Chaos Theory of Careers

    Science.gov (United States)

    Bright, Jim E. H.; Pryor, Robert G. L.

    2011-01-01

    The Chaos Theory of Careers (CTC; Pryor & Bright, 2011) construes both individuals and the contexts in which they develop their careers in terms of complex dynamical systems. Such systems perpetually operate under influences of stability and change both internally and in relation to each other. The CTC introduces new concepts to account for…

  12. 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...

  13. Chaos in the Solar System

    Science.gov (United States)

    Lecar, Myron; Franklin, Fred A.; Holman, Matthew J.; Murray, Norman J.

    2001-01-01

    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-peroid" 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 1012 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 109 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!

  14. Chaos and remedial investigations

    International Nuclear Information System (INIS)

    Galbraith, R.M.

    1991-01-01

    Current research into the nature of chaos indicates that even for systems that are well known and easily modeled, slight changes in the scale used to measure the input have unpredictable results in the model output. The conduct of a remedial investigation (RI) is dictated by well-established rules of investigation and management, yet small changes in project orientation, regulatory environment, or site conditions have unpredictable consequences to the project. The consequences can lead to either brilliant success or utter failure. The chaotic effect of a change in scale is most often illustrated by an exercise in measuring the length of the coast of Great Britain. If a straight ruler 10-kilometers long is used, the sum of the 10-kilometer increments gives the length of the coast. If the ruler is changed to five kilometers long and the exercise is repeated, the sum of the five-kilometer increments will not be the same as the sum of the 10-kilometer increments. Nor is there a way to predict what the length of the coast will be using any other scale. Several examples from the Fernald Project RI are used to illustrate open-quotes changes in scaleclose quotes in both technical and management situations. Given that there is no way to predict the outcome of scale changes in a RI, technical and project management must be alert to the fact that a scale has changed and the investigation is no longer on the path it was thought to be on. The key to success, therefore, is to develop specific units of measure for a number of activities, in addition to cost and schedule, and track them regularly. An example for tracking a portion of the field investigation is presented. The determination of effective units of measure is perhaps the most difficult aspect of any project. Changes in scale sometimes go unnoticed until suddenly the budget is expended and only a portion of the work is completed. Remedial investigations on large facilities provide new and complex challenges

  15. Hamiltonian Chaos and Fractional Dynamics

    International Nuclear Information System (INIS)

    Combescure, M

    2005-01-01

    This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on. Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are: - the failure of the traditional description of chaotic dynamics in terms of diffusion equations; - he fractional kinematics, its foundation and renormalization group analysis; - 'pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents; - directional complexity and entropy. The purpose of this book is to provide researchers and students in physics, mathematics and engineering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and 'further reading'. Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject. My one regret is that the book does not

  16. Meaning Finds a Way: Chaos (Theory) and Composition

    Science.gov (United States)

    Kyburz, Bonnie Lenore

    2004-01-01

    The explanatory power provided by the chaos theory is explored. A dynamic and reciprocal relationship between culture and chaos theory indicates that the progressive cultural work may be formed by the cross-disciplinary resonance of chaos theory.

  17. Chaos, Chaos Control and Synchronization of a Gyrostat System

    Science.gov (United States)

    GE, Z.-M.; LIN, T.-N.

    2002-03-01

    The dynamic behavior of a gyrostat system subjected to external disturbance is studied in this paper. By applying numerical results, phase diagrams, power spectrum, period-T maps, and Lyapunov exponents are presented to observe periodic and choatic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. For global analysis, the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping (MICM) method. Several methods, the delayed feedback control, the addition of constant torque, the addition of periodic force, the addition of periodic impulse torque, injection of dither signal control, adaptive control algorithm (ACA) control and bang-bang control are used to control chaos effectively. Finally, synchronization of chaos in the gyrostat system is studied.

  18. Does chaos assist localization or delocalization?

    Science.gov (United States)

    Tan, Jintao; Lu, Gengbiao; Luo, Yunrong; Hai, Wenhua

    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.

  19. Advances in chaos theory and intelligent control

    CERN Document Server

    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...

  20. Early Exposure to Environmental Chaos and Children’s Physical and Mental Health

    Science.gov (United States)

    Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa

    2015-01-01

    Environmental chaos has been proposed as a central influence impeding children’s health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children’s physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children’s functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children’s functioning. PMID:25844016

  1. Early Exposure to Environmental Chaos and Children's Physical and Mental Health.

    Science.gov (United States)

    Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa

    Environmental chaos has been proposed as a central influence impeding children's health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children's physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children's functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children's functioning.

  2. Quantum chaos: diffusion photoeffect in hydrogen

    Energy Technology Data Exchange (ETDEWEB)

    Shepelyanskij, D L

    1987-05-01

    Ionization process in highly excited hydrogen atom in electromagnetic field is presented in the form of an extraordinary photoeffect, in which ionization at the frequency, being much lower than ionization energy, occurs much quicker than single-photon one. Such a quick ionization is explained by dynamic chaos occurence. Question, related to quantum effect influence on chaotic movement of the electron (quantum chaos) is considered. Electron excitation in the chaos area is described by a diffusional equation.

  3. Discursive Maps at the Edge of Chaos

    Science.gov (United States)

    2017-05-25

    Discursive Maps at the Edge of Chaos A Monograph by Major Mathieu Primeau Canadian Army, Royal Canadian Engineer School of Advanced Military...Master’s Thesis 3. DATES COVERED (From - To) JUN 2016 – MAY 2017 4. TITLE AND SUBTITLE Discursive Maps at the Edge of Chaos 5a. CONTRACT NUMBER 5b...meaning of boundaries and polarize conflict towards violence. The edge of chaos is the fine line between disorder and coherence. Discursive maps

  4. Controlling Mackey-Glass chaos

    Science.gov (United States)

    Kiss, Gábor; Röst, Gergely

    2017-11-01

    The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.

  5. A quantum correction to chaos

    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.

  6. Spatiotemporal chaos from bursting dynamics

    International Nuclear Information System (INIS)

    Berenstein, Igal; De Decker, Yannick

    2015-01-01

    In this paper, we study the emergence of spatiotemporal chaos from mixed-mode oscillations, by using an extended Oregonator model. We show that bursting dynamics consisting of fast/slow mixed mode oscillations along a single attractor can lead to spatiotemporal chaotic dynamics, although the spatially homogeneous solution is itself non-chaotic. This behavior is observed far from the Hopf bifurcation and takes the form of a spatiotemporal intermittency where the system locally alternates between the fast and the slow phases of the mixed mode oscillations. We expect this form of spatiotemporal chaos to be generic for models in which one or several slow variables are coupled to activator-inhibitor type of oscillators

  7. A quantum correction to chaos

    International Nuclear Information System (INIS)

    Fitzpatrick, A. Liam; 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=((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_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.

  8. A history of chaos theory.

    Science.gov (United States)

    Oestreicher, Christian

    2007-01-01

    Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century, when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely, although they can be predicted to some extent, in line with the chaos theory. Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory. This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms.

  9. Magnetic field induced dynamical chaos.

    Science.gov (United States)

    Ray, Somrita; Baura, Alendu; Bag, Bidhan Chandra

    2013-12-01

    In this article, we have studied the dynamics of a particle having charge in the presence of a magnetic field. The motion of the particle is confined in the x-y plane under a two dimensional nonlinear potential. We have shown that constant magnetic field induced dynamical chaos is possible even for a force which is derived from a simple potential. For a given strength of the magnetic field, initial position, and velocity of the particle, the dynamics may be regular, but it may become chaotic when the field is time dependent. Chaotic dynamics is very often if the field is time dependent. Origin of chaos has been explored using the Hamiltonian function of the dynamics in terms of action and angle variables. Applicability of the present study has been discussed with a few examples.

  10. Controlling Mackey-Glass chaos.

    Science.gov (United States)

    Kiss, Gábor; Röst, Gergely

    2017-11-01

    The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.

  11. A history of chaos theory

    Science.gov (United States)

    Oestreicher, Christian

    2007-01-01

    Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely although they can be predicted to some extent in line with the chaos theory Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory, A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms. PMID:17969865

  12. On the definition of 'chaos'

    International Nuclear Information System (INIS)

    Kolesov, Andrei Yu; Rozov, Nikolai Kh

    2009-01-01

    A new definition of a chaotic invariant set is given for a continuous semiflow in a metric space. It generalizes the well-known definition due to Devaney and allows one to take into account a special feature occurring in the non-compact infinite-dimensional case: so-called turbulent chaos. The paper consists of two sections. The first contains several well-known facts from chaotic dynamics, together with new definitions and results. The second presents a concrete example demonstrating that our definition of chaos is meaningful. Namely, an infinite-dimensional system of ordinary differential equations is investigated having an attractor that is chaotic in the sense of the new definition but not in the sense of Devaney or Knudsen. Bibliography: 65 titles.

  13. 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...... interaction among the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional time-discrete Kuramoto model, we outline the region of phase chaos in the parameter plane and determine the regions where phase chaos coexists with different periodic...

  14. 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...... to the core field, but the high-degree lithospheric field is regularized for n > 85. CHAOS-4 model is derived by merging two submodels: its low-degree part has been derived using similar model parametrization and data sets as used for previous CHAOS models (but of course including more recent data), while its...

  15. 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...... between the coordinate systems of the vector magnetometer and of the star sensor providing attitude information). The final CHAOS-4 model is derived by merging two sub-models: its low-degree part has been obtained using similar model parameterization and data sets as used for previous CHAOS models (but...

  16. A quantum harmonic oscillator and strong chaos

    International Nuclear Information System (INIS)

    Oprocha, Piotr

    2006-01-01

    It is known that many physical systems which do not exhibit deterministic chaos when treated classically may exhibit such behaviour if treated from the quantum mechanics point of view. In this paper, we will show that an annihilation operator of the unforced quantum harmonic oscillator exhibits distributional chaos as introduced in B Schweizer and J SmItal (1994 Trans. Am. Math. Soc. 344 737-54). Our approach strengthens previous results on chaos in this model and provides a very powerful tool to measure chaos in other (quantum or classical) models

  17. The chaos cookbook a practical programming guide

    CERN Document Server

    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

  18. Chaos in a complex plasma

    International Nuclear Information System (INIS)

    Sheridan, T.E.

    2005-01-01

    Chaotic dynamics is observed experimentally in a complex (dusty) plasma of three particles. A low-frequency sinusoidal modulation of the plasma density excites both the center-of-mass and breathing modes. Low-dimensional chaos is seen for a 1:2 resonance between these modes. A strange attractor with a dimension of 2.48±0.05 is observed. The largest Lyapunov exponent is positive

  19. Chaos, complexity, and random matrices

    Science.gov (United States)

    Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu; Yoshida, Beni

    2017-11-01

    Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an O(1) scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us computational traction is the Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics look the same in any basis. Motivated by this property of the GUE, we introduce k-invariance as a precise definition of what it means for the dynamics of a quantum system to be described by random matrix theory. We envision that the dynamical onset of approximate k-invariance will be a useful tool for capturing the transition from early-time chaos, as seen by OTOCs, to late-time chaos, as seen by random matrix theory.

  20. Model for Shock Wave Chaos

    KAUST Repository

    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.

  1. 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.

  2. Chaos desynchronization in strongly coupled systems

    International Nuclear Information System (INIS)

    Wu Ye; Liu Weiqing; Xiao, Jinghua; Zhan Meng

    2007-01-01

    The dynamics of chaos desynchronization in strongly coupled oscillator systems is studied. We find a new bifurcation from synchronous chaotic state, chaotic short wave bifurcation, i.e. a chaotic desynchronization attractor is new born in the systems due to chaos desynchronization. In comparison with the usual periodic short wave bifurcation, very rich but distinct phenomena are observed

  3. Galloping instability to chaos of cables

    CERN Document Server

    Luo, Albert C J

    2017-01-01

    This book provides students and researchers with a systematic solution for fluid-induced structural vibrations, galloping instability and the chaos of cables. They will also gain a better understanding of stable and unstable periodic motions and chaos in fluid-induced structural vibrations. Further, the results presented here will help engineers effectively design and analyze fluid-induced vibrations.

  4. Chaos and fractals. Applications to nuclear engineering

    International Nuclear Information System (INIS)

    Clausse, A.; Delmastro, D.F.

    1990-01-01

    This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author) [es

  5. Spontaneous Rayleigh-Brillouin scattering spectral analysis based on the Wiener filter

    Directory of Open Access Journals (Sweden)

    Tao Wu

    2018-01-01

    Full Text Available In this paper, a spontaneous Rayleigh-Brillouin scattering spectrometer is developed to measure the gaseous spontaneous Rayleigh-Brillouin scattering profiles over the pressure range from 1 to 5 atm for a wavelength of 532nm at a constant room temperature of 296K and a 90o scattering angle. In order to make a direct comparison between the experimentally obtained spectrum and the theoretical spectrum calculated from the Tenti S6 model, the measured spontaneous Rayleigh-Brillouin scattering signal is deconvolved by the Wiener filtering. The purpose is to remove the effect on the spectrum by the transmission function of the Fabry-Perrot scanning interferometer. The results of the comparison show that the deconvolved spectra are consistent with the theoretical spectra calculated from the Tenti S6 model, and thus confirm that the deconvolution based on the Wiener filter is able to process the measured spectra and improve the spectral resolution. Some factors that influence the accuracy of deconvolution are analyzed and discussed. At the same time, another comparison between the raw experimentally obtained spectra and the theoretical spectra calculated by convolving the Tenti S6 model with instrument function of the measurement system is performed in the same experimental condition. The results of the two comparisons show that, compared with the raw experimentally obtained spectrum, the deconvolved spectrum matches the theoretically calculated spectrum more accurately under lower pressure (≤2atm than under relative higher pressure (>2atm.

  6. Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise.

    Science.gov (United States)

    Leibovich, N; Dechant, A; Lutz, E; Barkai, E

    2016-11-01

    The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{β} noise. Aging 1/f^{β} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.

  7. Two-dimensional filtering of SPECT images using the Metz and Wiener filters

    International Nuclear Information System (INIS)

    King, M.A.; Schwinger, R.B.; Penney, B.C.; Doherty, P.W.

    1984-01-01

    Presently, single photon emission computed tomographic (SPECT) images are usually reconstructed by arbitrarily selecting a one-dimensional ''window'' function for use in reconstruction. A better method would be to automatically choose among a family of two-dimensional image restoration filters in such a way as to produce ''optimum'' image quality. Two-dimensional image processing techniques offer the advantages of a larger statistical sampling of the data for better noise reduction, and two-dimensional image deconvolution to correct for blurring during acquisition. An investigation of two such ''optimal'' digital image restoration techniques (the count-dependent Metz filter and the Wiener filter) was made. They were applied both as two-dimensional ''window'' functions for preprocessing SPECT images, and for filtering reconstructed images. Their performance was compared by measuring image contrast and per cent fractional standard deviation (% FSD) in multiple-acquisitions of the Jaszczak SPECT phantom at two different count levels. A statistically significant increase in image contrast and decrease in % FSD was observed with these techniques when compared to the results of reconstruction with a ramp filter. The adaptability of the techniques was manifested in a lesser % reduction in % FSD at the high count level coupled with a greater enhancement in image contrast. Using an array processor, processing time was 0.2 sec per image for the Metz filter and 3 sec for the Wiener filter. It is concluded that two-dimensional digital image restoration with these techniques can produce a significant increase in SPECT image quality

  8. Speech Enhancement Using Gaussian Mixture Models, Explicit Bayesian Estimation and Wiener Filtering

    Directory of Open Access Journals (Sweden)

    M. H. Savoji

    2014-09-01

    Full Text Available Gaussian Mixture Models (GMMs of power spectral densities of speech and noise are used with explicit Bayesian estimations in Wiener filtering of noisy speech. No assumption is made on the nature or stationarity of the noise. No voice activity detection (VAD or any other means is employed to estimate the input SNR. The GMM mean vectors are used to form sets of over-determined system of equations whose solutions lead to the first estimates of speech and noise power spectra. The noise source is also identified and the input SNR estimated in this first step. These first estimates are then refined using approximate but explicit MMSE and MAP estimation formulations. The refined estimates are then used in a Wiener filter to reduce noise and enhance the noisy speech. The proposed schemes show good results. Nevertheless, it is shown that the MAP explicit solution, introduced here for the first time, reduces the computation time to less than one third with a slight higher improvement in SNR and PESQ score and also less distortion in comparison to the MMSE solution.

  9. SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

    Energy Technology Data Exchange (ETDEWEB)

    Ahlfeld, R., E-mail: r.ahlfeld14@imperial.ac.uk; 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

  10. SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

    International Nuclear Information System (INIS)

    Ahlfeld, R.; Belkouchi, B.; Montomoli, F.

    2016-01-01

    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

  11. 4th international interdisciplinary chaos symposium

    CERN Document Server

    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...

  12. Chaos the science of predictable random motion

    CERN Document Server

    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.

  13. Semiconductor Lasers Stability, Instability and Chaos

    CERN Document Server

    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...

  14. Scaling of chaos in strongly nonlinear lattices.

    Science.gov (United States)

    Mulansky, Mario

    2014-06-01

    Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.

  15. Langevin equation with multiplicative white noise: Transformation of diffusion processes into the Wiener process in different prescriptions

    International Nuclear Information System (INIS)

    Kwok, Sau Fa

    2012-01-01

    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: ► Fokker–Planck equation corresponding to the Langevin equation with mul- tiplicative white noise is presented. ► Transformation of diffusion processes into the Wiener process in different prescriptions is provided. ► The prescription parameter is associated with the growth rate for a Gompertz-type model.

  16. Chaos and bifurcations in periodic windows observed in plasmas

    International Nuclear Information System (INIS)

    Qin, J.; Wang, L.; Yuan, D.P.; Gao, P.; Zhang, B.Z.

    1989-01-01

    We report the experimental observations of deterministic chaos in a steady-state plasma which is not driven by any extra periodic forces. Two routes to chaos have been found, period-doubling and intermittent chaos. The fine structures in chaos such as periodic windows and bifurcations in windows have also been observed

  17. Prediction based chaos control via a new neural network

    International Nuclear Information System (INIS)

    Shen Liqun; Wang Mao; Liu Wanyu; Sun Guanghui

    2008-01-01

    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

  18. Homoclinic tubes and chaos in perturbed sine-Gordon equation

    International Nuclear Information System (INIS)

    Li, Y. Charles

    2004-01-01

    Sine-Gordon equation under a quasi-periodic perturbation or a chaotic perturbation is studied. Existence of a homoclinic tube is proved. Established are chaos associated with the homoclinic tube, and 'chaos cascade' referring to the embeddings of smaller scale chaos in larger scale chaos

  19. Model for shock wave chaos.

    Science.gov (United States)

    Kasimov, Aslan R; Faria, Luiz M; Rosales, Rodolfo R

    2013-03-08

    We propose the following model equation, u(t) + 1/2(u(2)-uu(s))x = f(x,u(s)) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, xorder 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.

  20. Chaos control in duffing system

    International Nuclear Information System (INIS)

    Wang Ruiqi; Deng Jin; Jing Zhujun

    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

  1. Deterministic chaos in entangled eigenstates

    Science.gov (United States)

    Schlegel, K. G.; Förster, S.

    2008-05-01

    We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator.

  2. Deterministic chaos in entangled eigenstates

    Energy Technology Data Exchange (ETDEWEB)

    Schlegel, K.G. [Fakultaet fuer Physik, Universitaet Bielefeld, Postfach 100131, D-33501 Bielefeld (Germany)], E-mail: guenter.schlegel@arcor.de; Foerster, S. [Fakultaet fuer Physik, Universitaet Bielefeld, Postfach 100131, D-33501 Bielefeld (Germany)

    2008-05-12

    We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator.

  3. Deterministic chaos in entangled eigenstates

    International Nuclear Information System (INIS)

    Schlegel, K.G.; Foerster, S.

    2008-01-01

    We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator

  4. Decoherence, determinism and chaos revisited

    Energy Technology Data Exchange (ETDEWEB)

    Noyes, H.P.

    1994-11-15

    We suggest that the derivation of the free space Maxwell Equations for classical electromagnetism, using a discrete ordered calculus developed by L.H. Kauffman and T. Etter, necessarily pushes the discussion of determinism in natural science down to the level of relativistic quantum mechanics and hence renders the mathematical phenomena studied in deterministic chaos research irrelevant to the question of whether the world investigated by physics is deterministic. We believe that this argument reinforces Suppes` contention that the issue of determinism versus indeterminism should be viewed as a Kantian antinomy incapable of investigation using currently available scientific tools.

  5. Decoherence, determinism and chaos revisited

    International Nuclear Information System (INIS)

    Noyes, H.P.

    1994-01-01

    We suggest that the derivation of the free space Maxwell Equations for classical electromagnetism, using a discrete ordered calculus developed by L.H. Kauffman and T. Etter, necessarily pushes the discussion of determinism in natural science down to the level of relativistic quantum mechanics and hence renders the mathematical phenomena studied in deterministic chaos research irrelevant to the question of whether the world investigated by physics is deterministic. We believe that this argument reinforces Suppes' contention that the issue of determinism versus indeterminism should be viewed as a Kantian antinomy incapable of investigation using currently available scientific tools

  6. The organization of the chaos

    OpenAIRE

    Merxhani, Branko

    2012-01-01

    Title: Organizimi i Kaosit (The organization of the chaos) Originally Published: In the monthly review Neo-shqiptarisma, Nr. 1, Tirana, 1930 Language: Albanian The excerpts used are from A. Plasari ed., Formula të Neoshqiptarismës. Përmbledhje shkrimesh (Tirana: Apollonia, 1996), pp. 99–102. About the author Branko Merxhani [1894 Istanbul – 1981, Istanbul]: scholar and writer. He was born in Istanbul and educated in Germany. In all likelihood, only his father was Albanian. By the end of the 1...

  7. Quantifying chaos for ecological stoichiometry.

    Science.gov (United States)

    Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep

    2010-09-01

    The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincaré return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing δ1. However, for higher values of δ1 the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter ζ) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.

  8. Invoking the muse: Dada's chaos.

    Science.gov (United States)

    Rosen, Diane

    2014-07-01

    Dada, a self-proclaimed (anti)art (non)movement, took shape in 1916 among a group of writers and artists who rejected the traditions of a stagnating bourgeoisie. Instead, they adopted means of creative expression that embraced chaos, stoked instability and undermined logic, an outburst that overturned centuries of classical and Romantic aesthetics. Paradoxically, this insistence on disorder foreshadowed a new order in understanding creativity. Nearly one hundred years later, Nonlinear Dynamical Systems theory (NDS) gives renewed currency to Dada's visionary perspective on chance, chaos and creative cognition. This paper explores commonalities between NDS-theory and this early precursor of the nonlinear paradigm, suggesting that their conceptual synergy illuminates what it means to 'be creative' beyond the disciplinary boundaries of either. Key features are discussed within a 5P model of creativity based on Rhodes' 4P framework (Person, Process, Press, Product), to which I add Participant-Viewer for the interactivity of observer-observed. Grounded in my own art practice, several techniques are then put forward as non-methodical methods that invoke creative border zones, those regions where Dada's chance and design are wedded in a dialectical tension of opposites.

  9. Markov transitions and the propagation of chaos

    International Nuclear Information System (INIS)

    Gottlieb, A.

    1998-01-01

    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 show 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

  10. Using chaos theory: the implications for nursing.

    Science.gov (United States)

    Haigh, Carol

    2002-03-01

    The purpose of this paper is to review chaos theory and to examine the role that it may have in the discipline of nursing. In this paper, the fundamental ingredients of chaotic thinking are outlined. The earlier days of chaos thinking were characterized by an almost exclusively physiological focus. By the 21st century, nurse theorists were applying its principles to the organization and evaluation of care delivery with varying levels of success. Whilst the biological use of chaos has focused on pragmatic approaches to knowledge enhancement, nursing has often focused on the mystical aspects of chaos as a concept. The contention that chaos theory has yet to find a niche within nursing theory and practice is examined. The application of chaotic thinking across nursing practice, nursing research and statistical modelling is reviewed. The use of chaos theory as a way of identifying the attractor state of specific systems is considered and the suggestion is made that it is within statistical modelling of services that chaos theory is most effective.

  11. 3D pulsed chaos lidar system.

    Science.gov (United States)

    Cheng, Chih-Hao; Chen, Chih-Ying; Chen, Jun-Da; Pan, Da-Kung; Ting, Kai-Ting; Lin, Fan-Yi

    2018-04-30

    We develop an unprecedented 3D pulsed chaos lidar system for potential intelligent machinery applications. Benefited from the random nature of the chaos, conventional CW chaos lidars already possess excellent anti-jamming and anti-interference capabilities and have no range ambiguity. In our system, we further employ self-homodyning and time gating to generate a pulsed homodyned chaos to boost the energy-utilization efficiency. Compared to the original chaos, we show that the pulsed homodyned chaos improves the detection SNR by more than 20 dB. With a sampling rate of just 1.25 GS/s that has a native sampling spacing of 12 cm, we successfully achieve millimeter-level accuracy and precision in ranging. Compared with two commercial lidars tested side-by-side, namely the pulsed Spectroscan and the random-modulation continuous-wave Lidar-lite, the pulsed chaos lidar that is in compliance with the class-1 eye-safe regulation shows significantly better precision and a much longer detection range up to 100 m. Moreover, by employing a 2-axis MEMS mirror for active laser scanning, we also demonstrate real-time 3D imaging with errors of less than 4 mm in depth.

  12. How to test for partially predictable chaos.

    Science.gov (United States)

    Wernecke, Hendrik; Sándor, Bulcsú; Gros, Claudius

    2017-04-24

    For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. Both processes can be either of the same or of very different time scales. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and remain partially predictable. Standard tests for chaos widely use inter-orbital correlations as an indicator. However, testing partially predictable chaos yields mostly ambiguous results, as this type of chaos is characterized by attractors of fractally broadened braids. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test robustly discriminates chaos, including partially predictable chaos, from laminar flow. Additionally using the finite time cross-correlation of pairs of initially close trajectories, we are able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.

  13. 9 CFR 319.309 - Beans with frankfurters in sauce, sauerkraut with wieners and juice, and similar products.

    Science.gov (United States)

    2010-01-01

    ... 9 Animals and Animal Products 2 2010-01-01 2010-01-01 false Beans with frankfurters in sauce... STANDARDS OF IDENTITY OR COMPOSITION Canned, Frozen, or Dehydrated Meat Food Products § 319.309 Beans with frankfurters in sauce, sauerkraut with wieners and juice, and similar products. “Beans with Frankfurters in...

  14. Chaos as a psychological construct: historical roots, principal findings, and current growth directions.

    Science.gov (United States)

    Guastello, Stephen J

    2009-07-01

    The landmarks in the use of chaos and related constructs in psychology were entwined with the growing use of other nonlinear dynamical constructs, especially catastrophes and self-organization. The growth in substantive applications of chaos in psychology is partially related to the development of methodologies that work within the constraints of psychological data. The psychological literature includes rigorous theory with testable propositions, lighter-weight metaphorical uses of the construct, and colloquial uses of "chaos" with no particular theoretical intent. The current state of the chaos construct and supporting empirical research in psychological theory is summarized in neuroscience, psychophysics, psychomotor skill and other learning phenomena, clinical and abnormal psychology, and group dynamics and organizational behavior. Trends indicate that human systems do not remain chaotic indefinitely; they eventually self-organize, and the concept of the complex adaptive system has become prominent. Chaotic turbulence is generally higher in healthy systems compared to unhealthy systems, although opposite appears true in mood disorders. Group dynamics research shows trends consistent with the complex adaptive system, whereas organizational behavior lags behind in empirical studies relative to the quantity of its theory. Future directions for research involving the chaos construct and other nonlinear dynamics are outlined.

  15. Some remarks on chaos in topological dynamics

    Directory of Open Access Journals (Sweden)

    Huoyung Wang

    2011-10-01

    Full Text Available Bau-Sen Du introduced a notion of chaos which is stronger than Li-Yorke sensitivity. A TDS (X, f is called chaotic if there is a positive e such that for any x and any nonempty open set V of X there is a point y in V such that the pair (x, y is proximal but not e-asymptotic. In this article, we show that a TDS (T, f is transitive but not mixing if and only if (T, f is Li-Yorke sensitive but not chaotic, where T is a tree. Moreover, we compare such chaos with other notions of chaos.

  16. A-coupled-expanding and distributional chaos

    International Nuclear Information System (INIS)

    Kim, Cholsan; Ju, Hyonhui; Chen, Minghao; Raith, Peter

    2015-01-01

    The concept of A-coupled-expanding maps is one of the more natural and useful ideas generalized from the horseshoe map which is commonly known as a criterion of chaos. It is well known that distributional chaos is one of the concepts which reflect strong chaotic behavior. In this paper, we focus on the relationship between A-coupled-expanding and distributional chaos. We prove two theorems which give sufficient conditions for a strictly A-coupled-expanding map to be distributionally chaotic in the senses of two kinds, where A is an m × m irreducible transition matrix

  17. 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...

  18. Chaos from simple models to complex systems

    CERN Document Server

    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

  19. Some open questions in 'wave chaos'

    International Nuclear Information System (INIS)

    Nonnenmacher, Stéphane

    2008-01-01

    The subject area referred to as 'wave chaos', 'quantum chaos' or 'quantum chaology' has been investigated mostly by the theoretical physics community in the last 30 years. The questions it raises have more recently also attracted the attention of mathematicians and mathematical physicists, due to connections with number theory, graph theory, Riemannian, hyperbolic or complex geometry, classical dynamical systems, probability, etc. After giving a rough account on 'what is quantum chaos?', I intend to list some pending questions, some of them having been raised a long time ago, some others more recent. The choice of problems (and of references) is of course partial and personal. (open problem)

  20. Nuclear physics, symmetries, and quantum chaos

    International Nuclear Information System (INIS)

    Bunakov, V.E.

    1999-01-01

    The reasons why the problem of chaos is of great topical interest in modern physics are briefly summarized, and it is indicated that ambiguities in the concept of quantum chaos present the greatest difficulties in these realms. The theory of random matrices and strength functions are generalized to demonstrate that chaotization of a system is associated with the violation of its symmetries. A criterion of quantum chaoticity is formulated in terms of the spreading width Γ spr . In the classical limit, this criterion reduces to Lyapunov's stability criteria. It is shown that the proposed criterion is applicable to standard problems of the modern theory of dynamical chaos

  1. Semiconductor Lasers Stability, Instability and Chaos

    CERN Document Server

    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.

  2. Quantum chaos in the Heisenberg picture

    International Nuclear Information System (INIS)

    McKellar, B.H.J.; Lancaster, M.; McCaw, J.

    2000-01-01

    Full text: We explore the possibility of defining quantum chaos in the algebra of quantum mechanical operators. The simple definition of the Lyapunov exponent in terms of a metric on that algebra has the expected properties for the quantum logistic map, as we confirm for the simple spin 1 system. We then show numerically and analytically that the Hamiltonian evolution of finite spin systems does not lead to chaos in this definition, and investigate alternative definitions of quantum chaos in the algebra of operators

  3. Chaos in body-vortex interactions

    DEFF Research Database (Denmark)

    Pedersen, Johan Rønby; Aref, Hassan

    2010-01-01

    of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between...... rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos....

  4. Chua's circuit a paradigm for chaos

    CERN Document Server

    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

  5. Wiener-Hopf factorization of piecewise meromorphic matrix-valued functions

    International Nuclear Information System (INIS)

    Adukov, Victor M

    2009-01-01

    Let D + be a multiply connected domain bounded by a contour Γ, let D - be the complement of D + union Γ in C-bar=C union {∞}, and a(t) be a continuous invertible matrix-valued function on Γ which can be meromorphically extended into the open disconnected set D - (as a piecewise meromorphic matrix-valued function). An explicit solution of the Wiener-Hopf factorization problem for a(t) is obtained and the partial factorization indices of a(t) are calculated. Here an explicit solution of a factorization problem is meant in the sense of reducing it to the investigation of finitely many systems of linear algebraic equations with matrices expressed in closed form, that is, in quadratures. Bibliography: 15 titles.

  6. Percolation Analysis of a Wiener Reconstruction of the IRAS 1.2 Jy Redshift Catalog

    Science.gov (United States)

    Yess, Capp; Shandarin, Sergei F.; Fisher, Karl B.

    1997-01-01

    We present percolation analyses of Wiener reconstructions of the IRAS 1.2 Jy redshift survey. There are 10 reconstructions of galaxy density fields in real space spanning the range β = 0.1-1.0, where β = Ω0.6/b, Ω is the present dimensionless density, and b is the bias factor. Our method uses the growth of the largest cluster statistic to characterize the topology of a density field, where Gaussian randomized versions of the reconstructions are used as standards for analysis. For the reconstruction volume of radius R ~ 100 h-1 Mpc, percolation analysis reveals a slight ``meatball'' topology for the real space, galaxy distribution of the IRAS survey.

  7. Adaptive Kernel Canonical Correlation Analysis Algorithms for Nonparametric Identification of Wiener and Hammerstein Systems

    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.

  8. Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders

    KAUST Repository

    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.

  9. Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders

    KAUST Repository

    El Beltagy, Mohamed

    2016-01-01

    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.

  10. Wiener's Loop Filter for PLL-Based Carrier Recovery of OQPSK and MSK-Type Modulations

    Directory of Open Access Journals (Sweden)

    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.

  11. Modelling accelerated degradation data using Wiener diffusion with a time scale transformation.

    Science.gov (United States)

    Whitmore, G A; Schenkelberg, F

    1997-01-01

    Engineering degradation tests allow industry to assess the potential life span of long-life products that do not fail readily under accelerated conditions in life tests. A general statistical model is presented here for performance degradation of an item of equipment. The degradation process in the model is taken to be a Wiener diffusion process with a time scale transformation. The model incorporates Arrhenius extrapolation for high stress testing. The lifetime of an item is defined as the time until performance deteriorates to a specified failure threshold. The model can be used to predict the lifetime of an item or the extent of degradation of an item at a specified future time. Inference methods for the model parameters, based on accelerated degradation test data, are presented. The model and inference methods are illustrated with a case application involving self-regulating heating cables. The paper also discusses a number of practical issues encountered in applications.

  12. Analysis of moiré fringes by Wiener filtering: An extension to the Fourier method

    International Nuclear Information System (INIS)

    Harasse, Sébastien; Yashiro, Wataru; Momose, Atsushi

    2012-01-01

    In X-ray Talbot interferometry, tilting the phase grating with respect to the absorption grating results in the formation of spatial fringes. The analysis of this moiré pattern, classically performed by the Fourier method, allows the extraction of the sample phase shift information from a single image. In this context, an extension to the Fourier method is proposed. The filter used to extract the fringe information is chosen optimally in the least-squares sense, given models for the zeroth and first order modes, noise and the modulation transfer function. The latter is obtained by measuring the detector response to moiré fringes with increasing frequencies. The obtained Wiener filter allows a better reconstruction of the phase information at all fringe frequencies, compared to the usual box or gaussian filters. This is demonstrated quantitatively by experiments using synchrotron radiation.

  13. Median Modified Wiener Filter for nonlinear adaptive spatial denoising of protein NMR multidimensional spectra

    KAUST Repository

    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.

  14. Median Modified Wiener Filter for nonlinear adaptive spatial denoising of protein NMR multidimensional spectra

    KAUST Repository

    Cannistraci, Carlo Vittorio; Abbas, Ahmed; Gao, Xin

    2015-01-01

    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.

  15. Chaos excited chaos synchronizations of integral and fractional order generalized van der Pol systems

    International Nuclear Information System (INIS)

    Ge Zhengming; Hsu Maoyuan

    2008-01-01

    In this paper, chaos excited chaos synchronizations of generalized van der Pol systems with integral and fractional order are studied. Synchronizations of two identified autonomous generalized van der Pol chaotic systems are obtained by replacing their corresponding exciting terms by the same function of chaotic states of a third nonautonomous or autonomous generalized van der Pol system. Numerical simulations, such as phase portraits, Poincare maps and state error plots are given. It is found that chaos excited chaos synchronizations exist for the fractional order systems with the total fractional order both less than and more than the number of the states of the integer order generalized van der Pol system

  16. Leveraging Chaos in Continuous Thrust Trajectory Design

    Data.gov (United States)

    National Aeronautics and Space Administration — A trajectory design tool is sought to leverage chaos and nonlinear dynamics present in multi-body gravitational fields to design ultra-low energy transfer...

  17. A Chaos Theory Perspective on International Migration

    Directory of Open Access Journals (Sweden)

    Anca Tănasie

    2017-12-01

    Full Text Available This paper aims at providing a different approach to international migration analysis, beyond classical models previously proposed by specialized literature. Chaos theory is getting more and more applied into macroeconomics once traditional linear models or even previous dynamic analysis become less suitable. Modern science sees chaos as unpredictable evolution, maybe even disorder. Still, chaos has got its own rules and can describe many dynamic phenomena within our world. Thus, we test whether international migration data falls under the rules of chaos and whether recent developments within the “European migration crisis” (the total daily migration inflows towards the coasts of Italy, by sea, from January 2014 to April 2017 could be described as chaotic.

  18. Chaos concepts, control and constructive use

    CERN Document Server

    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...

  19. Homoclinic chaos and energy condition violation

    International Nuclear Information System (INIS)

    Heinzle, J. Mark; Roehr, Niklas; Uggla, Claes

    2006-01-01

    In this letter we discuss the connection between so-called homoclinic chaos and the violation of energy conditions in locally rotationally symmetric Bianchi type IX models, where the matter is assumed to be nontilted dust and a positive cosmological constant. We show that homoclinic chaos in these models is an artifact of unphysical assumptions: it requires that there exist solutions with positive matter energy density ρ>0 that evolve through the singularity and beyond as solutions with negative matter energy density ρ<0. Homoclinic chaos is absent when it is assumed that the dust particles always retain their positive mass. In addition, we discuss more general models: for solutions that are not locally rotationally symmetric we demonstrate that the construction of extensions through the singularity, which is required for homoclinic chaos, is not possible in general

  20. Searching for chaos on low frequency

    OpenAIRE

    Nicolas Wesner

    2004-01-01

    A new method for detecting low dimensional chaos in small sample sets is presented. The method is applied to financial data on low frequency (annual and monthly) for which few observations are available.

  1. Coherence and chaos in condensed matter

    International Nuclear Information System (INIS)

    Bishop, A.R.

    1989-01-01

    This paper discusses the following topics: nonlinearity in condensed matter; coherence and chaos in spatially extended condensed matter systems; nonlinearity and magnetism; and solitons and conducting polymers. 52 refs., 7 figs

  2. Semiconductor lasers stability, instability and chaos

    CERN Document Server

    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...

  3. Nuclear physics and ideas of quantum chaos

    International Nuclear Information System (INIS)

    Zelevinsky, V.G.

    2002-01-01

    The field nowadays called 'many-body quantum chaos' was started in 1939 with the article by I.I. Gurevich studying the regularities of nuclear spectra. The field has been extensively developed recently, both mathematically and in application to mesoscopic systems and quantum fields. We argue that nuclear physics and the theory of quantum chaos are mutually beneficial. Many ideas of quantum chaos grew up from the factual material of nuclear physics; this enrichment still continues to take place. On the other hand, many phenomena in nuclear structure and reactions, as well as the general problem of statistical physics of finite strongly interacting systems, can be understood much deeper with the help of ideas and methods borrowed from the field of quantum chaos. A brief review of the selected topics related to the recent development is presented

  4. Chaos on the conveyor belt.

    Science.gov (United States)

    Sándor, Bulcsú; Járai-Szabó, Ferenc; Tél, Tamás; Néda, Zoltán

    2013-04-01

    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 a 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 be achieved only 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).

  5. From classical to quantum chaos

    International Nuclear Information System (INIS)

    Zaslavsky, G.M.

    1991-01-01

    The analysis is done for the quantum properties of systems that possess dynamical chaos in classical limit. Two main topics are considered: (i) the problem of quantum macroscopical description of the system and the Ehrenfest-Einstein problem of the validity of the classical approximation; and (ii) the problem of levels spacing distribution for the nonintegrable case. For the first topic the method of projecting on the coherent states base is considered and the ln 1/(h/2π) time for the quasiclassical approximation breaking is described. For the second topic the discussion of GOE and non-GOE distributions is done and estimations and simulations for the non-GOE case are reviewed. (author). 44 refs, 2 figs

  6. Distributional chaos for triangular maps

    International Nuclear Information System (INIS)

    Smital, Jaroslav; Stefankova, Marta

    2004-01-01

    In this paper we exhibit a triangular map F of the square with the following properties: (i) F is of type 2 ∞ but has positive topological entropy; we recall that similar example was given by Kolyada in 1992, but our argument is much simpler. (ii) F is distributionally chaotic in the wider sense, but not distributionally chaotic in the sense introduced by Schweizer and Smital [Trans. Amer. Math. Soc. 344 (1994) 737]. In other words, there are lower and upper distribution functions PHI xy and PHI xy * generated by F such that PHI xy * ≡1 and PHI xy (0 + ) uv , and PHI uv * such that PHI uv * ≡1 and PHI uv (t)=0 whenever 0 0. We also show that the two notions of distributional chaos used in the paper, for continuous maps of a compact metric space, are invariants of topological conjugacy

  7. Chaos, Fractals and Their Applications

    Science.gov (United States)

    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.

  8. A new interpretation of chaos

    International Nuclear Information System (INIS)

    Luo Chuanwen; Wang Gang; Wang Chuncheng; Wei Junjie

    2009-01-01

    The concepts of uniform index and expectation uniform index are two mathematical descriptions of the uniformity and the mean uniformity of a finite set in a polyhedron. The concepts of instantaneous chaometry (ICM) and k step chaometry (k SCM) are introduced in order to apply the method in statistics for studying the nonlinear difference equations. It is found that k step chaometry is an indirect estimation of the expectation uniform index. The simulation illustrate that the expectation uniform index for the Lorenz System is increasing linearly, but increasing nonlinearly for the Chen's System with parameter b. In other words, the orbits for each system become more and more uniform with parameter b increasing. Finally, a conjecture is also brought forward, which implies that chaos can be interpreted by its orbit's mean uniformity described by the expectation uniform index and indirectly estimated by k SCM. The k SCM of the heart rate showes the feeble and old process of the heart.

  9. Control of collective network chaos.

    Science.gov (United States)

    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.

  10. Quantum chaos on discrete graphs

    International Nuclear Information System (INIS)

    Smilansky, Uzy

    2007-01-01

    Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of ζ functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)

  11. Menstruation, perimenopause, and chaos theory.

    Science.gov (United States)

    Derry, Paula S; Derry, Gregory N

    2012-01-01

    This article argues that menstruation, including the transition to menopause, results from a specific kind of complex system, namely, one that is nonlinear, dynamical, and chaotic. A complexity-based perspective changes how we think about and research menstruation-related health problems and positive health. Chaotic systems are deterministic but not predictable, characterized by sensitivity to initial conditions and strange attractors. Chaos theory provides a coherent framework that qualitatively accounts for puzzling results from perimenopause research. It directs attention to variability within and between women, adaptation, lifespan development, and the need for complex explanations of disease. Whether the menstrual cycle is chaotic can be empirically tested, and a summary of our research on 20- to 40-year-old women is provided.

  12. True quantum chaos? An instructive example

    International Nuclear Information System (INIS)

    Berry, M.V.

    1992-01-01

    Any chaotic classical system can be transformed into a quantum system that preserves the chaos, because the classical Liouville equation involving 2Ν phase-space variables q ,p has the form of a 'Schroedinger equation' with 'coordinates' Q=[q,p]. The feature of this quantum system that allows chaos to persist is linarity of the Hamiltonian' in the 2Ν 'momentum' operators conjugate to Q. (orig.)

  13. Scaling properties of localized quantum chaos

    International Nuclear Information System (INIS)

    Izrailev, F.M.

    1991-01-01

    Statistical properties of spectra and eigenfunctions are studied for the model of quantum chaos in the presence of dynamical localization. The main attention is paid to the scaling properties of localization length and level spacing distribution in the intermediate region between Poissonian and Wigner-Dyson statistics. It is shown that main features of such localized quantum chaos are well described by the introduced ensemble of band random matrices. 28 refs.; 7 figs

  14. Deterministic chaos in the processor load

    International Nuclear Information System (INIS)

    Halbiniak, Zbigniew; Jozwiak, Ireneusz J.

    2007-01-01

    In this article we present the results of research whose purpose was to identify the phenomenon of deterministic chaos in the processor load. We analysed the time series of the processor load during efficiency tests of database software. Our research was done on a Sparc Alpha processor working on the UNIX Sun Solaris 5.7 operating system. The conducted analyses proved the presence of the deterministic chaos phenomenon in the processor load in this particular case

  15. Chaos control of Chen chaotic dynamical system

    International Nuclear Information System (INIS)

    Yassen, M.T.

    2003-01-01

    This paper is devoted to study the problem of controlling chaos in Chen chaotic dynamical system. Two different methods of control, feedback and nonfeedback methods are used to suppress chaos to unstable equilibria or unstable periodic orbits (UPO). The Lyapunov direct method and Routh-Hurwitz criteria are used to study the conditions of the asymptotic stability of the steady states of the controlled system. Numerical simulations are presented to show these results

  16. Chaos control using sliding-mode theory

    International Nuclear Information System (INIS)

    Nazzal, Jamal M.; Natsheh, Ammar N.

    2007-01-01

    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

  17. Chaos

    Indian Academy of Sciences (India)

    K Krishan1 Manu2 R Ramaswamy2. Department of Physics, Indian Institute of Technology, Kanpur 208 016, India; School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India. Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 4 · Current Issue Volume 23 | Issue 4. April 2018.

  18. Chaos in World Politics: A Reflection

    Science.gov (United States)

    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.

  19. Purification of leucocin A for use on wieners to inhibit Listeria monocytogenes in the presence of spoilage organisms.

    Science.gov (United States)

    Balay, Danielle R; Dangeti, Ramana V; Kaur, Kamaljit; McMullen, Lynn M

    2017-08-16

    The aims of this study were to improve the method for purification of leucocin A to increase yield of peptide and to evaluate the efficacy of leucocin A and an analogue of leucocin A (leucocin N17L) to inhibit the growth of Listeria monocytogenes on wieners in the presence of spoilage organisms. Leucocin A was produced by Leuconostoc gelidum UAL187 and purified with a five-fold increase in yield; leucocin N17L was synthesized replacing asparagine at residue 17 with leucine. Five strains of L. monocytogenes associated with foodborne illness were used to assess bacteriocin efficacy in vitro and in situ. Minimum inhibitory concentrations could not be determined in broth; however, on agar the minimum inhibitory concentrations ranged from 11.7-62.5μM and 62.5->500μM for leucocin A and leucocin N17L, respectively. Leucocin N17L was less effective than the native bacteriocin at controlling the growth of L. monocytogenes. The inactivation profiles of L. monocytogenes in broth in the presence of leucocin A suggested each isolate had different levels of resistance to the bacteriocin as determined by the initial bactericidal effect. The formation of spontaneously resistance subpopulations were also observed for each strain of L. monocytogenes. In situ, wieners were inoculated with the spoilage organisms, Carnobacterium divergens and Brochothrix thermosphacta, followed by surface application of purified leucocin A, and inoculated with a cocktail of L. monocytogenes. Wieners were vacuum packaged and stored at 7°C for 16d. Leucocin A reduced the counts L. monocytogenes on wieners during storage, regardless of the presence of C. divergens. B. thermosphacta was unaffected by the presence of leucocin A on wieners over the duration of storage. This study suggests that leucocin A may be beneficial to industry as a surface application on wieners to help reduce L. monocytogenes counts due to post-processing contamination even in the presence of spoilage organisms. However, further

  20. Li-Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice

    International Nuclear Information System (INIS)

    Khellat, Farhad; Ghaderi, Akashe; Vasegh, Nastaran

    2011-01-01

    Highlights: → A globally nonlocal coupled map lattice is introduced. → A sufficient condition for the existence of Li-Yorke chaos is determined. → A sufficient condition for synchronous behaviors is obtained. - Abstract: This paper investigates a globally nonlocal coupled map lattice. A rigorous proof to the existence of chaos in the scene of Li-Yorke in that system is presented in terms of the Marotto theorem. Analytical sufficient conditions under which the system is chaotic, and has synchronous behaviors are determined, respectively. The wider regions associated with chaos and synchronous behaviors are shown by simulations. Spatiotemporal chaos, synchronous chaos and some other synchronous behaviors such as fixed points, 2-cycles and 2 2 -cycles are also shown by simulations for some values of the parameters.

  1. Genome chaos: survival strategy during crisis.

    Science.gov (United States)

    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.

  2. Particle ratios, quarks, and Chao-Yang statistics

    Energy Technology Data Exchange (ETDEWEB)

    Chew, C K; Low, G B; Lo, S Y [Nanyang Univ. (Singapore). Dept. of Physics; Phua, K K [Argonne National Lab., IL (USA)

    1980-01-01

    By introducing quarks into Chao-Yang statistics for 'violent' collisions, particle ratios are obtained which are consistent with the Chao-Yang results. The present method can also be extended to baryon-meson and baryon-antibaryon ratios.

  3. Digital Communication Devices Based on Nonlinear Dynamics and Chaos

    National Research Council Canada - National Science Library

    Larson, Lawrence

    2003-01-01

    The final report of the ARO MURI "Digital Communications Based on Chaos and Nonlinear Dynamics" contains research results in the areas of chaos and nonlinear dynamics applied to wireless and optical communications...

  4. Quantum chaos in atom optics

    International Nuclear Information System (INIS)

    D'Arcy, Michael Brendan

    2002-01-01

    This thesis presents an account of experimental and numerical investigations of two quantum systems whose respective classical analogues are chaotic. These are the δ-kicked rotor, a paradigm in classical chaos theory, and the novel δ-kicked accelerator, created by application of a constant external acceleration or torque to the rotor. The experimental realisation of these systems has been achieved by the exposure of laser-cooled caesium atoms to approximate δ-kicks from a pulsed, high-intensity, vertical standing wave of laser light. Gravity's effect on the atoms can be controlled by appropriate shifting of the profile of the standing wave. Numerical simulations of the systems are based on a diffractive model of the potential's effect. Each system's dynamics are characterised by the final form of the momentum distribution and the dependence of the atoms' mean kinetic energy on the number and time period of the δ-kicks. The phenomena of dynamical localisation and quantum resonances in the δ-kicked rotor, which have no counterparts in the system's classical analogue, are observed and investigated. Similar experiments on the δ-kicked accelerator reveal the striking phenomenon of the quantum accelerator mode, in which a large momentum is transferred to a substantial fraction of the atomic ensemble. This feature, absent in the system's classical analogue, is characterised and an analytic explanation is presented. The effect on each quantum system of decoherence, introduced through spontaneous emission in the atoms, is examined and comparison is made with the results of classical simulations. While having little effect on the classical systems, the level of decoherence used is found to degrade quantum signatures of behaviour. Classical-like behaviour is, to some extent, restored, although significant quantum features remain. Possible applications of the quantum accelerator mode are discussed. These include use as a tool in atom optics and interferometry, a

  5. 2nd International Symposium on Chaos, Complexity and Leadership

    CERN Document Server

    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.

  6. Chaos of discrete dynamical systems in complete metric spaces

    International Nuclear Information System (INIS)

    Shi Yuming; Chen Guanrong

    2004-01-01

    This paper is concerned with chaos of discrete dynamical systems in complete metric spaces. Discrete dynamical systems governed by continuous maps in general complete metric spaces are first discussed, and two criteria of chaos are then established. As a special case, two corresponding criteria of chaos for discrete dynamical systems in compact subsets of metric spaces are obtained. These results have extended and improved the existing relevant results of chaos in finite-dimensional Euclidean spaces

  7. Quantum theory of open systems based on stochastic differential equations of generalized Langevin (non-Wiener) type

    Energy Technology Data Exchange (ETDEWEB)

    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.

  8. Quantum theory of open systems based on stochastic differential equations of generalized Langevin (non-Wiener) type

    International Nuclear Information System (INIS)

    Basharov, A. M.

    2012-01-01

    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.

  9. Optimal Constant-Stress Accelerated Degradation Test Plans Using Nonlinear Generalized Wiener Process

    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.

  10. A generic EEG artifact removal algorithm based on the multi-channel Wiener filter

    Science.gov (United States)

    Somers, Ben; Francart, Tom; Bertrand, Alexander

    2018-06-01

    Objective. The electroencephalogram (EEG) is an essential neuro-monitoring tool for both clinical and research purposes, but is susceptible to a wide variety of undesired artifacts. Removal of these artifacts is often done using blind source separation techniques, relying on a purely data-driven transformation, which may sometimes fail to sufficiently isolate artifacts in only one or a few components. Furthermore, some algorithms perform well for specific artifacts, but not for others. In this paper, we aim to develop a generic EEG artifact removal algorithm, which allows the user to annotate a few artifact segments in the EEG recordings to inform the algorithm. Approach. We propose an algorithm based on the multi-channel Wiener filter (MWF), in which the artifact covariance matrix is replaced by a low-rank approximation based on the generalized eigenvalue decomposition. The algorithm is validated using both hybrid and real EEG data, and is compared to other algorithms frequently used for artifact removal. Main results. The MWF-based algorithm successfully removes a wide variety of artifacts with better performance than current state-of-the-art methods. Significance. Current EEG artifact removal techniques often have limited applicability due to their specificity to one kind of artifact, their complexity, or simply because they are too ‘blind’. This paper demonstrates a fast, robust and generic algorithm for removal of EEG artifacts of various types, i.e. those that were annotated as unwanted by the user.

  11. Harmonies of disorder Norbert Wiener : a mathematician-philosopher of our time

    CERN Document Server

    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...

  12. A maintenance optimization model for mission-oriented systems based on Wiener degradation

    International Nuclear Information System (INIS)

    Guo, Chiming; Wang, Wenbin; Guo, Bo; Si, Xiaosheng

    2013-01-01

    Over the past few decades, condition-based maintenance (CBM) has attracted many researchers because of its effectiveness and practical significance. This paper deals with mission-oriented systems subject to gradual degradation modeled by a Wiener stochastic process within the context of CBM. For a mission-oriented system, the mission usually has constraints on availability/reliability, the opportunity for maintenance actions, and the monitoring type (continuous or discrete). Furthermore, in practice, a mission-oriented system may undertake some preventive maintenance (PM) and after such PM, the system may return to an intermediate state between an as-good-as new state and an as-bad-as old state, i.e., the PM is not perfect and only partially restores the system. However, very few CBM models integrated these mission constraints together with an imperfect nature of the PM into the course of optimizing the PM policy. This paper develops a model to optimize the PM policy in terms of the maintenance related cost jointly considering the mission constraints and the imperfect PM nature. A numerical example is presented to demonstrate the proposed model. The comparison with the simulated results and the sensitivity analysis show the usefulness of the optimization model for mission-oriented system maintenance presented in this paper.

  13. The three versions of distributional chaos

    International Nuclear Information System (INIS)

    Balibrea, F.; Smital, J.; Stefankova, M.

    2005-01-01

    The notion of distributional chaos was introduced by Schweizer and Smital [Trans. Amer. Math. Soc. 344 (1994) 737] for continuous maps of the interval. However, it turns out that, for continuous maps of a compact metric space three mutually nonequivalent versions of distributional chaos, DC1-DC3, can be considered. In this paper we consider the weakest one, DC3. We show that DC3 does not imply chaos in the sense of Li and Yorke. We also show that DC3 is not invariant with respect to topological conjugacy. In other words, there are lower and upper distribution functions Φ xy and Φxy* generated by a continuous map f of a compact metric space (M, ρ) such that Φxy*(t)>Φxy(t) for all t in an interval. However, f on the same space M, but with a metric ρ' generating the same topology as ρ is no more DC3.Recall that, contrary to this, either DC1 or DC2 is topological conjugacy invariant and implies Li and Yorke chaos (cf. [Chaos, Solitons and Fractals 21 (2004) 1125])

  14. Generic superweak chaos induced by Hall effect

    Science.gov (United States)

    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 κ2 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.

  15. 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. “System” will be rigorously defined. Can a low-informational rapid succession of Prigogine’s dissipative structures self-order into bona fide organization?

  16. Target-oriented chaos control

    International Nuclear Information System (INIS)

    Dattani, Justine; Blake, Jack C.H.; Hilker, Frank M.

    2011-01-01

    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.

  17. Symbolic dynamics of noisy chaos

    Energy Technology Data Exchange (ETDEWEB)

    Crutchfield, J P; Packard, N H

    1983-05-01

    One model of randomness observed in physical systems is that low-dimensional deterministic chaotic attractors underly the observations. A phenomenological theory of chaotic dynamics requires an accounting of the information flow fromthe observed system to the observer, the amount of information available in observations, and just how this information affects predictions of the system's future behavior. In an effort to develop such a description, the information theory of highly discretized observations of random behavior is discussed. Metric entropy and topological entropy are well-defined invariant measures of such an attractor's level of chaos, and are computable using symbolic dynamics. Real physical systems that display low dimensional dynamics are, however, inevitably coupled to high-dimensional randomness, e.g. thermal noise. We investigate the effects of such fluctuations coupled to deterministic chaotic systems, in particular, the metric entropy's response to the fluctuations. It is found that the entropy increases with a power law in the noise level, and that the convergence of the entropy and the effect of fluctuations can be cast as a scaling theory. It is also argued that in addition to the metric entropy, there is a second scaling invariant quantity that characterizes a deterministic system with added fluctuations: I/sub 0/, the maximum average information obtainable about the initial condition that produces a particular sequence of measurements (or symbols). 46 references, 14 figures, 1 table.

  18. Chaos and unpredictability in evolution.

    Science.gov (United States)

    Doebeli, Michael; Ispolatov, Iaroslav

    2014-05-01

    The possibility of complicated dynamic behavior driven by nonlinear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility of long-term evolutionary chaos is rarely considered. The concept of "survival of the fittest" is central to much evolutionary thinking and embodies a perspective of evolution as a directional optimization process exhibiting simple, predictable dynamics. This perspective is adequate for simple scenarios, when frequency-independent selection acts on scalar phenotypes. However, in most organisms many phenotypic properties combine in complicated ways to determine ecological interactions, and hence frequency-dependent selection. Therefore, it is natural to consider models for evolutionary dynamics generated by frequency-dependent selection acting simultaneously on many different phenotypes. Here we show that complicated, chaotic dynamics of long-term evolutionary trajectories in phenotype space is very common in a large class of such models when the dimension of phenotype space is large, and when there are selective interactions between the phenotypic components. Our results suggest that the perspective of evolution as a process with simple, predictable dynamics covers only a small fragment of long-term evolution. © 2014 The Author(s). Evolution © 2014 The Society for the Study of Evolution.

  19. Chaos for induced hyperspace maps

    International Nuclear Information System (INIS)

    Banks, John

    2005-01-01

    For (X,d) be a metric space, f:X->X a continuous map and (K(X),H) the space of non-empty compact subsets of X with the Hausdorff metric, one may study the dynamical properties of the induced map (*)f-bar :K(X)->K(X):A-bar f(A).H. Roman-Flores [A note on in set-valued discrete systems. Chaos, Solitons and Fractals 2003;17:99-104] has shown that if f-bar is topologically transitive then so is f, but that the reverse implication does not hold. This paper shows that the topological transitivity of f-bar is in fact equivalent to weak topological mixing on the part of f. This is proved in the more general context of an induced map on some suitable hyperspace H of X with the Vietoris topology (which agrees with the topology of the Hausdorff metric in the case discussed by Roman-Flores

  20. Deterministic Chaos - Complex Chance out of Simple Necessity ...

    Indian Academy of Sciences (India)

    This is a very lucid and lively book on deterministic chaos. Chaos is very common in nature. However, the understanding and realisation of its potential applications is very recent. Thus this book is a timely addition to the subject. There are several books on chaos and several more are being added every day. In spite of this ...

  1. Chaos Theory as a Model for Managing Issues and Crises.

    Science.gov (United States)

    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…

  2. God's Stuff: The Constructive Powers of Chaos for Teaching Religion

    Science.gov (United States)

    Willhauck, Susan

    2010-01-01

    Order and organization are valued in the classroom, and there is a prevailing understanding that chaos should be avoided. Yet chaos can also be potent space or a source from which new things spring forth. This article investigates biblical, scientific, and cultural understandings of chaos to discover how these contribute to a revelatory metaphor…

  3. Chaos in the fractional order Chen system and its control

    International Nuclear Information System (INIS)

    Li Chunguang; Chen Guanrong

    2004-01-01

    In this letter, we study the chaotic behaviors in the fractional order Chen system. We found that chaos exists in the fractional order Chen system with order less than 3. The lowest order we found to have chaos in this system is 2.1. Linear feedback control of chaos in this system is also studied

  4. The Nature (and Nurture) of Children's Perceptions of Family Chaos

    Science.gov (United States)

    Hanscombe, Ken B.; Haworth, Claire M. A.; Davis, Oliver S. P.; Jaffee, Sara R.; Plomin, Robert

    2010-01-01

    Chaos in the home is a key environment in cognitive and behavioural development. However, we show that children's experience of home chaos is partly genetically mediated. We assessed children's perceptions of household chaos at ages 9 and 12 in 2337 pairs of twins. Using child-specific reports allowed us to use structural equation modelling to…

  5. Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems

    International Nuclear Information System (INIS)

    Ge Zhengming; Chang Chingming; Chen Yensheng

    2006-01-01

    Anti-control of chaos of single time scale brushless dc motors (BLDCM) and chaos synchronization of different order systems are studied in this paper. By addition of an external nonlinear term, we can obtain anti-control of chaos. Then, by addition of the coupling terms, by the use of Lyapunov stability theorem and by the linearization of the error dynamics, chaos synchronization between a third-order BLDCM and a second-order Duffing system are presented

  6. Chaos to periodicity and periodicity to chaos by periodic perturbations in the Belousov-Zhabotinsky reaction

    International Nuclear Information System (INIS)

    Li Qianshu; Zhu Rui

    2004-01-01

    A three-variable model of the Belousov-Zhabotinsky reaction system subject to external sinusoidal perturbations is investigated by means of frequency spectrum analysis. In the period-1 window of the model, the transitions from periodicity to chaos are observed; in the chaotic window, the transitions from chaos to periodicity are found. The former might be understood by the circle map of two coupled oscillators, and the latter is partly explained by the resonance between the main frequency of the chaos and the frequency of the external periodic perturbations

  7. Hyperbolic Chaos A Physicist’s View

    CERN Document Server

    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.  

  8. Nonlinear dynamics and quantum chaos an introduction

    CERN Document Server

    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.

  9. Entanglement as a signature of quantum chaos.

    Science.gov (United States)

    Wang, Xiaoguang; Ghose, Shohini; Sanders, Barry C; Hu, Bambi

    2004-01-01

    We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter kappa in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both the bipartite and the pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is suppressed. Furthermore, we define a time-averaged entangling power and show that this entangling power changes markedly as kappa moves the system from being predominantly regular to being predominantly chaotic, thus sharply identifying the edge of chaos. When this entangling power is averaged over all states, it yields a signature of global chaos. The qualitative behavior of this global entangling power is similar to that of the classical Lyapunov exponent.

  10. Chaos Concepts, Control and Constructive Use

    CERN Document Server

    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...

  11. Polynomial chaos functions and stochastic differential equations

    International Nuclear Information System (INIS)

    Williams, M.M.R.

    2006-01-01

    The Karhunen-Loeve procedure and the associated polynomial chaos expansion have been employed to solve a simple first order stochastic differential equation which is typical of transport problems. Because the equation has an analytical solution, it provides a useful test of the efficacy of polynomial chaos. We find that the convergence is very rapid in some cases but that the increased complexity associated with many random variables can lead to very long computational times. The work is illustrated by exact and approximate solutions for the mean, variance and the probability distribution itself. The usefulness of a white noise approximation is also assessed. Extensive numerical results are given which highlight the weaknesses and strengths of polynomial chaos. The general conclusion is that the method is promising but requires further detailed study by application to a practical problem in transport theory

  12. Bifurcation and chaos in neural excitable system

    International Nuclear Information System (INIS)

    Jing Zhujun; Yang Jianping; Feng Wei

    2006-01-01

    In this paper, we investigate the dynamical behaviors of neural excitable system without periodic external current (proposed by Chialvo [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] and with periodic external current as system's parameters vary. The existence and stability of three fixed points, bifurcation of fixed points, the conditions of existences of fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using bifurcation theory and center manifold theorem. The chaotic existence in the sense of Marotto's definition of chaos is proved. We then give the numerical simulated results (using bifurcation diagrams, computations of Maximum Lyapunov exponent and phase portraits), which not only show the consistence with the analytic results but also display new and interesting dynamical behaviors, including the complete period-doubling and inverse period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, simultaneous occurrence of two different routes (invariant cycle and period-doubling bifurcations) to chaos for a given bifurcation parameter, sudden disappearance of chaos at one critical point, a great abundance of period windows (period 2 to 10, 12, 19, 20 orbits, and so on) in transient chaotic regions with interior crises, strange chaotic attractors and strange non-chaotic attractor. In particular, the parameter k plays a important role in the system, which can leave the chaotic behavior or the quasi-periodic behavior to period-1 orbit as k varies, and it can be considered as an control strategy of chaos by adjusting the parameter k. Combining the existing results in [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] with the new results reported in this paper, a more complete description of the system is now obtained

  13. Harnessing quantum transport by transient chaos.

    Science.gov (United States)

    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.

  14. Chaos synchronization of coupled hyperchaotic system

    International Nuclear Information System (INIS)

    Yang Lixin; Chu Yandong; Zhang Jiangang; Li Xianfeng

    2009-01-01

    Chaos synchronization, as an important topic, has become an active research subject in nonlinear science. Over the past two decades, chaos synchronization between nonlinear systems has been extensively studied, and many types of synchronization have been announced. This paper introduces synchronization of coupled hyperchaotic system, based on the Lapunov stability theory, asymptotic stability of the system is guaranteed by means of Lapunov function. The numerical simulation was provided in order to show the effectiveness of this method for the synchronization of the chaotic hyperchaotic Chen system and Rossler system.

  15. An introduction to chaos theory in CFD

    Science.gov (United States)

    Pulliam, Thomas H.

    1990-01-01

    The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.

  16. Chaos and random matrices in supersymmetric SYK

    Science.gov (United States)

    Hunter-Jones, Nicholas; Liu, Junyu

    2018-05-01

    We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. We find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.

  17. Shape of power spectrum of intermittent chaos

    International Nuclear Information System (INIS)

    So, B.C.; Mori, H.

    1984-01-01

    Power spectra of intermittent chaos are calculated analytically. It is found that the power spectrum near onset point consists of a large number of Lorentzian lines with two peaks around frequencies ω = 0 and ω = ω 0 , where ω 0 is a fundamental frequency of a periodic orbit before the onset point, and furthermore the envelope of lines around ω = 0 obeys the power law 1/ + ω +2 , whereas the envelope around ω 0 obeys 1/ + ω-ω 0 +4 . The universality of these power law dependence in a certain class of intermittent chaos are clarified from a phenomenological view point. (author)

  18. Signatures of chaos in the Brillouin zone.

    Science.gov (United States)

    Barr, Aaron; Barr, Ariel; Porter, Max D; Reichl, Linda E

    2017-10-01

    When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.

  19. Chaos in an imperfectly premixed model combustor.

    Science.gov (United States)

    Kabiraj, Lipika; Saurabh, Aditya; Karimi, Nader; Sailor, Anna; Mastorakos, Epaminondas; Dowling, Ann P; Paschereit, Christian O

    2015-02-01

    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.

  20. Chaotic dynamics and chaos control in nonlinear laser systems

    International Nuclear Information System (INIS)

    Fang Jinqing; Yao Weiguang

    2001-01-01

    Chaotic dynamics and chaos control have become a great challenge in nonlinear laser systems and its advances are reviewed mainly based on the ring cavity laser systems. The principle and stability conditions for time-delay feedback control are analyzed and applied to chaos control in the laser systems. Other advanced methods of chaos control, such as weak spatial perturbation and occasional proportional feedback technique, are discussed. Prospects of chaos control for application (such as improvement of laser power and performance, synchronized chaos secure communication and information processing) are pointed out finally

  1. Chaos and routes to chaos in coupled Duffing oscillators with multiple degrees of freedom

    International Nuclear Information System (INIS)

    Musielak, D.E.; Musielak, Z.E.; Benner, J.W.

    2005-01-01

    New results are reported on the routes to chaos in increasingly complex Duffing oscillator systems, which are formed by coupling several oscillators, thereby increasing the number of degrees of freedom. Other forms of increasing system complexity through distributed excitation, different forcing function phasing, different excitation frequency ratios, and higher order coupling are also studied. Changes in the quantitative aspects of the chaotic regions and in the routes to chaos of complex Duffing systems are investigated by performing numerical simulations. It is shown that the number of chaotic regions in these systems is significantly reduced when compared to the original Duffing system, and that crisis replaces period doubling as the dominant route to chaos when the number of degrees of freedom is increased. A new discovered phenomenon is that chaos emerges in the symmetrically and asymmetrically coupled Duffing oscillators only after the quasi-periodic torus breaks down through a 3-periodic and 2-periodic window, respectively

  2. Resurvey of order and chaos in spinning compact binaries

    International Nuclear Information System (INIS)

    Wu Xin; Xie Yi

    2008-01-01

    This paper is mainly devoted to applying the invariant, fast, Lyapunov indicator to clarify some doubt regarding the apparently conflicting results of chaos in spinning compact binaries at the second-order post-Newtonian approximation of general relativity from previous literatures. It is shown with a number of examples that no single physical parameter or initial condition can be described as responsible for causing chaos, but a complicated combination of all parameters and initial conditions is responsible. In other words, a universal rule for the dependence of chaos on each parameter or initial condition cannot be found in general. Chaos does not depend only on the mass ratio, and the maximal spins do not necessarily bring the strongest effect of chaos. Additionally, chaos does not always become drastic when the initial spin vectors are nearly perpendicular to the orbital plane, and the alignment of spins cannot trigger chaos by itself

  3. Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

    Directory of Open Access Journals (Sweden)

    Bin Wang

    2015-01-01

    Full Text Available This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.

  4. Torus Destruction and Chaos-Chaos Intermittency in a Commodity Distribution Chain

    DEFF Research Database (Denmark)

    Sosnovtseva, O.; Mosekilde, Erik

    1997-01-01

    The destruction of two-dimensional tori T2 and the transitions to chaos are studied in a high-dimensional model describing the decision-making behavior of human subjects in a simulated managerial environment (the beer production-distribution model). Two different routes from quasiperiodicity...... to chaos can be distinguished. Intermittency transitions between chaotic and hyperchaotic attractors are characterized, and transients in which the system "pursues the ghost" of a vanished hyperchaotic attractor are studied....

  5. Chaos, strange attractors, and fractal basin boundaries

    International Nuclear Information System (INIS)

    Grebogi, C.

    1989-01-01

    Even simple mathematical models of physical systems are often observed to exhibit rather complex time evolution. Upon observation, one often has the feeling that such complex time evolutions could, for most practical purposes, be best characterized by statistical properties rather than by detailed knowledge of the exact process. In such situations, the time evolution is often labeled chaotic or turbulent. The study of chaotic dynamics has recently undergone explosive growth. Motivation for this comes partly from the fact that chaotic dynamics is being found to be of fundamental importance in many branches of science and engineering. Examples illustrating the wide-ranging applications of chaotic dynamics to scientific and engineering problems are the following: fluid dynamics, biology, ecology, meteorology, optics, electronics, mechanical engineerings, physiology, economics, chemistry, accelerator technology, thermonuclear fusion, celestial mechanics, and oceanography. The common element in all of the above topics is that they involve nonlinearity in some way. Indeed chaos is expected to be common whenever nonlinearity plays a role. Since nonlinearity is inherent in so much of science and engineering, an understanding of chaos is essential. Given the varied nature of applications where chaos is important, it is natural that researchers in a broad range of fields have become interested in and have contributed to recent developments in chaos

  6. 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.

  7. Synchronization of chaos by nonlinear feedback

    International Nuclear Information System (INIS)

    Cheng Yanxiang

    1995-01-01

    The authors point out that synchronization of chaos may also be achieved by a nonlinear feedback without decomposing the original system. They apply the idea to the Lorentz system, and discuss several forms of nonlinear feedbacks by Lyapunov function and numerical method

  8. Chaos synchronization based on contraction principle

    International Nuclear Information System (INIS)

    Wang Junwei; Zhou Tianshou

    2007-01-01

    This paper introduces contraction principle. Based on such a principle, a novel scheme is proposed to synchronize coupled systems with global diffusive coupling. A rigorous sufficient condition on chaos synchronization is derived. As an example, coupled Lorenz systems with nearest-neighbor diffusive coupling are investigated, and numerical simulations are given to validate the proposed synchronization approach

  9. Importance of packing in spiral defect chaos

    Indian Academy of Sciences (India)

    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 ...

  10. Characterizing and quantifying quantum chaos with quantum ...

    Indian Academy of Sciences (India)

    We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under the application of the Floquet operator of a quantum map that possesses (or lacks) time-reversal ...

  11. Quantum Chaos via the Quantum Action

    OpenAIRE

    Kröger, H.

    2002-01-01

    We discuss the concept of the quantum action with the purpose to characterize and quantitatively compute quantum chaos. As an example we consider in quantum mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling - which is classically a chaotic system. We compare Poincar\\'e sections obtained from the quantum action with those from the classical action.

  12. Chaos in schizophrenia associations, reality or metaphor?

    Czech Academy of Sciences Publication Activity Database

    Bob, P.; Šusta, M.; Chládek, Jan; Glaslová, K.; Paluš, Milan

    2009-01-01

    Roč. 73, č. 3 (2009), s. 179-185 ISSN 0167-8760 Institutional research plan: CEZ:AV0Z20650511; CEZ:AV0Z10300504 Keywords : Chaos * Schizophrenia * Associations * Electrodermal activity * Lyapunov exponent Subject RIV: FH - Neurology Impact factor: 3.045, year: 2009

  13. Chaos synchronization of nonlinear Bloch equations

    International Nuclear Information System (INIS)

    Park, Ju H.

    2006-01-01

    In this paper, the problem of chaos synchronization of Bloch equations is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived

  14. Melnikov's vector - a 'measure of chaos'

    International Nuclear Information System (INIS)

    Haidegger, W.

    1990-01-01

    In this paper a method of global perturbation theory, the method of Melnikov, is introduced as a way of detecting Smale horseshoe chaos near homoclinic and heteroclinic orbits. Special emphasis is put on the point that Melnikov's method is of great practical value, as it yields computable, often even analytically solvable expressions. (Author) 18 refs

  15. Order, chaos and nuclear dynamics: An introduction

    International Nuclear Information System (INIS)

    Swiatecki, W.J.

    1990-08-01

    This is an introductory lecture illustrating by simple examples the anticipated effect on collective nuclear dynamics of a transition from order to chaos in the motions of nucleons inside an idealized nucleus. The destruction of order is paralleled by a transition from a rubber-like to a honey-like behaviour of the independent-particle nuclear model. 10 refs., 6 figs

  16. Chaos and fractals an elementary introduction

    CERN Document Server

    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.

  17. Chaos in Practice: Techniques for Career Counsellors

    Science.gov (United States)

    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…

  18. Controlling chaos in discontinuous dynamical systems

    International Nuclear Information System (INIS)

    Danca, Marius-F.

    2004-01-01

    In this paper we consider the possibility to implement the technique of changes in the system variables to control the chaos introduced by Gueemez and Matias for continuous dynamical systems to a class of discontinuous dynamical systems. The approach is realized via differential inclusions following the Filippov theory. Three practical examples are considered

  19. [Chaos theory: a fascinating concept for oncologists].

    Science.gov (United States)

    Denis, F; Letellier, C

    2012-05-01

    The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. Copyright © 2012 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.

  20. Chaos in nuclei: Theory and experiment

    Science.gov (United States)

    Muñoz, L.; Molina, R. A.; Gómez, J. M. G.

    2018-05-01

    During the last three decades the quest for chaos in nuclei has been quite intensive, both with theoretical calculations using nuclear models and with detailed analyses of experimental data. In this paper we outline the concept and characteristics of quantum chaos in two different approaches, the random matrix theory fluctuations and the time series fluctuations. Then we discuss the theoretical and experimental evidence of chaos in nuclei. Theoretical calculations, especially shell-model calculations, have shown a strongly chaotic behavior of bound states in regions of high level density. The analysis of experimental data has shown a strongly chaotic behavior of nuclear resonances just above the one-nucleon emission threshold. For bound states, combining experimental data of a large number of nuclei, a tendency towards chaotic motion is observed in spherical nuclei, while deformed nuclei exhibit a more regular behavior associated to the collective motion. On the other hand, it had never been possible to observe chaos in the experimental bound energy levels of any single nucleus. However, the complete experimental spectrum of the first 151 states up to excitation energies of 6.20 MeV in the 208Pb nucleus have been recently identified and the analysis of its spectral fluctuations clearly shows the existence of chaotic motion.

  1. Transient chaos in weakly coupled Josephson junctions

    Energy Technology Data Exchange (ETDEWEB)

    Koch, B P; Bruhn, B

    1988-01-01

    This paper considers periodic excitations and coupling of nonlinear Josephson oscillators. The Melnikov method is used to prove the existence of horseshoes in the dynamics. The coupling of two systems yields a reduction of the chaos threshold in comparison with the corresponding threshold of a single system. For some selected parameter values the theoretical predictions are checked by numerical methods.

  2. Quantum chaos of the 2-level atom

    Energy Technology Data Exchange (ETDEWEB)

    Graham, R; Hoehnerbach, M [Essen Univ. (Germany, F.R.). Fachbereich Physik

    1984-01-01

    Recent work on the two-level atom coupled to a single mode of the electromagnetic field is reviewed from the point of view of 'quantum chaos', defined as the quantum behavior of a dynamical system which is non-integrable in the classical limit. Spectral properties and the dynamics of occupation probabilities including their revivals are obtained without making the rotating wave approximation.

  3. A Framework for Chaos Theory Career Counselling

    Science.gov (United States)

    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,…

  4. Chaos theory: A fascinating concept for oncologists

    International Nuclear Information System (INIS)

    Denis, F.; Letellier, C.

    2012-01-01

    The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. (authors)

  5. Biologically inspired rate control of chaos.

    Science.gov (United States)

    Olde Scheper, Tjeerd V

    2017-10-01

    The overall intention of chaotic control is to eliminate chaos and to force the system to become stable in the classical sense. In this paper, I demonstrate a more subtle method that does not eliminate all traces of chaotic behaviour; yet it consistently, and reliably, can provide control as intended. The Rate Control of Chaos (RCC) method is derived from metabolic control processes and has several remarkable properties. RCC can control complex systems continuously, and unsupervised, it can also maintain control across bifurcations, and in the presence of significant systemic noise. Specifically, I show that RCC can control a typical set of chaotic models, including the 3 and 4 dimensional chaotic Lorenz systems, in all modes. Furthermore, it is capable of controlling spatiotemporal chaos without supervision and maintains control of the system across bifurcations. This property of RCC allows a dynamic system to operate in parameter spaces that are difficult to control otherwise. This may be particularly interesting for the control of forced systems or dynamic systems that are chaotically perturbed. These control properties of RCC are applicable to a range of dynamic systems, thereby appearing to have far-reaching effects beyond just controlling chaos. RCC may also point to the existence of a biochemical control function of an enzyme, to stabilise the dynamics of the reaction cascade.

  6. Meeting energy demands: chaos round the corner

    Energy Technology Data Exchange (ETDEWEB)

    Petrick, A J

    1976-02-01

    In this interview with Coal Gold and Base Minerals, Dr. Petrick talks about several aspects of his recent report and indicates that it will only be in the next 20 or 30 years that the real energy crisis will appear. He goes on to warn of possible chaos if energy is continually squandered throughout the world.

  7. CHAOS-BASED ADVANCED ENCRYPTION STANDARD

    KAUST Repository

    Abdulwahed, Naif B.

    2013-01-01

    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

  8. Analysis of chaos in plasma turbulence

    DEFF Research Database (Denmark)

    Pedersen, T.S.; Michelsen, Poul; Juul Rasmussen, J.

    1996-01-01

    -stationary turbulent state is reached in a finite time, independent of the initial conditions. Different regimes of the turbulent state can be obtained by varying the coupling parameter C, related to the parallel electron dynamics. The turbulence is described by using particle tracking and tools from chaos analysis...

  9. Chaos in plasma simulation and experiment

    International Nuclear Information System (INIS)

    Watts, C.; Sprott, J.C.

    1993-09-01

    We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos. These tools include phase portraits and Poincard sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are -the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low,dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system

  10. Chaos in plasma simulation and experiment

    Energy Technology Data Exchange (ETDEWEB)

    Watts, C. [Texas Univ., Austin, TX (United States). Fusion Research Center; Newman, D.E. [Oak Ridge National Lab., TN (United States); Sprott, J.C. [Wisconsin Univ., Madison, WI (United States). Plasma Physics Research

    1993-09-01

    We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos. These tools include phase portraits and Poincard sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are -the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low,dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.

  11. CHAOS-BASED ADVANCED ENCRYPTION STANDARD

    KAUST Repository

    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

  12. Chaos: A Very Short Introduction

    Energy Technology Data Exchange (ETDEWEB)

    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

  13. Chaos: A Very Short Introduction

    International Nuclear Information System (INIS)

    Klages, R

    2007-01-01

    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 field. I feel that occasionally the book

  14. THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT

    International Nuclear Information System (INIS)

    Lithwick, Yoram; Wu Yanqin

    2011-01-01

    We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, which dominate on long timescales. We first focus on the evolution of a test particle that is forced by multiple planets. To linear order in eccentricity and inclination, its orbit precesses with constant frequencies. But nonlinearities modify the frequencies, and can shift them into and out of resonance with either the planets' eigenfrequencies (forming eccentricity or inclination secular resonances), or with linear combinations of those frequencies (forming mixed high-order secular resonances). The overlap of these nonlinear secular resonances drives secular chaos. We calculate the locations and widths of nonlinear secular resonances, display them together on a newly developed map (the 'map of the mean momenta'), and find good agreement between analytical and numerical results. This map also graphically demonstrates how chaos emerges from overlapping secular resonances. We then apply this newfound understanding to Mercury to elucidate the origin of its orbital chaos. We find that since Mercury's two free precession frequencies (in eccentricity and inclination) lie within ∼25% of two other eigenfrequencies in the solar system (those of the Jupiter-dominated eccentricity mode and the Venus-dominated inclination mode), secular resonances involving these four modes overlap and cause Mercury's chaos. We confirm this with N-body integrations by showing that a slew of these resonant angles alternately librate and circulate. Our new analytical understanding allows us to calculate the criterion for Mercury to become chaotic: Jupiter and Venus must have eccentricity and inclination of a few percent. The timescale for Mercury's chaotic diffusion depends sensitively on the forcing. As it is, Mercury appears to be perched on the threshold for chaos, with an instability timescale comparable to the lifetime of the solar system.

  15. Phase Chaos and Multistability in the Discrete Kuramoto Model

    DEFF Research Database (Denmark)

    Maistrenko, V. L.; Vasylenko, A. A.; Maistrenko, Y. L.

    2008-01-01

    The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear interact......The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear...... interaction of the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional discrete Kuramoto model, we outline the region of phase chaos in the parameter plane, distinguish the region where the phase chaos coexists with other periodic attractors...

  16. Chaos in electric drive systems analysis control and application

    CERN Document Server

    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...

  17. Joint probabilities of noncommuting observables and the Einstein-Podolsky-Rosen question in Wiener-Siegel quantum theory

    International Nuclear Information System (INIS)

    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 α 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 α 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

  18. Reliability Analysis Based on a Jump Diffusion Model with Two Wiener Processes for Cloud Computing with Big Data

    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.

  19. Analysis of the power flow in nonlinear oscillators driven by random excitation using the first Wiener kernel

    Science.gov (United States)

    Hawes, D. H.; Langley, R. S.

    2018-01-01

    Random excitation of mechanical systems occurs in a wide variety of structures and, in some applications, calculation of the power dissipated by such a system will be of interest. In this paper, using the Wiener series, a general methodology is developed for calculating the power dissipated by a general nonlinear multi-degree-of freedom oscillatory system excited by random Gaussian base motion of any spectrum. The Wiener series method is most commonly applied to systems with white noise inputs, but can be extended to encompass a general non-white input. From the extended series a simple expression for the power dissipated can be derived in terms of the first term, or kernel, of the series and the spectrum of the input. Calculation of the first kernel can be performed either via numerical simulations or from experimental data and a useful property of the kernel, namely that the integral over its frequency domain representation is proportional to the oscillating mass, is derived. The resulting equations offer a simple conceptual analysis of the power flow in nonlinear randomly excited systems and hence assist the design of any system where power dissipation is a consideration. The results are validated both numerically and experimentally using a base-excited cantilever beam with a nonlinear restoring force produced by magnets.

  20. Approximate motion integrals and the quantum chaos problem

    International Nuclear Information System (INIS)

    Bunakov, V.E.; Ivanov, I.B.

    2001-01-01

    One discusses the problem of occurrence and seek for the motion integrals in the stationary quantum mechanics and its relation to the quantum chaos. One studies decomposition of quantum numbers and derives the criterion of chaos. To seek the motion integrals one applies the convergence method. One derived the approximate integrals in the Hennone-Hales problem. One discusses the problem of compatibility of chaos and integrability [ru

  1. Nonlinear physics: Catastrophe, chaos and complexity

    International Nuclear Information System (INIS)

    Arecchi, F.T.

    1992-01-01

    Currently in the world of physics, there is open debate on the role of the three C's - catastrophe, chaos and complexity. Seen as new ideas or paradigms, incapable of being harmonized within the realm of traditional physics, these terms seem to be creating turmoil in the classical physics establishment whose foundations date back to the early seventeenth century. This paper first defines catastrophe, chaos and complexity and shows how these terms are all connected to nonlinear dynamics and how they have long since been present within scientific treatises. It also evidences the relationship of the three C's with the concept of organization, inappropriately called self-organization, and with recognition and decisional strategies of cognitive systems. Relevant to natural science, the development of these considerations is necessitating the re-examination of the role and capabilities of human knowledge and a return to inter-disciplinary scientific-philosophical debate

  2. Communication with spatial periodic chaos synchronization

    International Nuclear Information System (INIS)

    Zhou, J.; Huang, H.B.; Qi, G.X.; Yang, P.; Xie, X.

    2005-01-01

    Based on the spatial periodic chaos synchronization in coupled ring and linear arrays, we proposed a random high-dimensional chaotic encryption scheme. The transmitter can choose hyperchaotic signals randomly from the ring at any different time and simultaneously transmit the information of chaotic oscillators in the ring to receiver through public channel, so that the message can be masked by different hyperchaotic signals in different time intervals during communication, and the receiver can decode the message based on chaos synchronization but the attacker does not know the random hyperchaotic dynamics and cannot decode the message. Furthermore, the high sensitivity to the symmetry of the coupling structure makes the attacker very difficult to obtain any useful message from the channel

  3. An exploration of dynamical systems and chaos

    CERN Document Server

    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...

  4. Inequivalent topologies of chaos in simple equations

    International Nuclear Information System (INIS)

    Letellier, Christophe; Roulin, Elise; Roessler, Otto E.

    2006-01-01

    In the 1970, one of us introduced a few simple sets of ordinary differential equations as examples showing different types of chaos. Most of them are now more or less forgotten with the exception of the so-called Roessler system published in [Roessler OE. An equation for continuous chaos. Phys Lett A 1976;57(5):397-8]. In the present paper, we review most of the original systems and classify them using the tools of modern topological analysis, that is, using the templates and the bounding tori recently introduced by Tsankov and Gilmore in [Tsankov TD, Gilmore R. Strange attractors are classified by bounding tori. Phys Rev Lett 2003;91(13):134104]. Thus, examples of inequivalent topologies of chaotic attractors are provided in modern spirit

  5. Order in nuclei and transition to chaos

    International Nuclear Information System (INIS)

    Soloviev, V.G.

    1995-01-01

    Based on the statement that there is order in the large and chaos in the small components of nuclear wave functions, the order-to-chaos transition is treated as a transition from the large to small components of wave functions. Therefore, experimental investigation of fragmentation of the many-quasiparticle and quasiparticle-phonon states plays a decisive role. The mixing of closely-spaced states having the same K π in the doubly even well-deformed nuclei is investigated. The quasiparticle-phonon interaction is responsible for fragmentation of the quasiparticle and phonon states and therefore for their mixing. Experimental investigation of the strength distribution of the many-quasiparticle and quasiparticle-phonon states should discover a new region of regularity in nuclei at intermediate excitation energies. A chaotic behaviour of nuclear states can be shifted to higher excitation energies. (author). 21 refs., 1 fig., 1 tab

  6. Order in nuclei and transition to chaos

    International Nuclear Information System (INIS)

    Soloviev, V.G.

    1995-01-01

    Based on the statement that there is order in the large and chaos in the small components of nuclear wave functions, the order-to-chaos transition is treated as a transition from the large to small components of wave functions. Therefore, experimental investigation of fragmentation of the many-quasiparticle and quasiparticle-phonon states a decisive role. The mixing of closely-spaced states having the same K π in the doubly even well-deformed nuclei is investigated. The quasiparticle-phonon interaction is responsible for fragmentation of the quasiparticle and phonon states and therefore for their mixing. Experimental investigation of the strength distribution of the many-quasiparticle and quasiparticle-phonon states should discover a new region of regularity in nuclei at intermediate excitation energies. A chaotic behaviour of nuclear states can be shifted to higher excitation energies. (author). 21 refs., 1 fig., 1 tab

  7. Tuning quantum measurements to control chaos.

    Science.gov (United States)

    Eastman, Jessica K; Hope, Joseph J; Carvalho, André R R

    2017-03-20

    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.

  8. Kac-Moody algebras and controlled chaos

    International Nuclear Information System (INIS)

    Wesley, Daniel H

    2007-01-01

    Compactification can control chaotic Mixmaster behaviour 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 Lorentzian (but not 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. (fast track communication)

  9. Chaos theory perspective for industry clusters development

    Science.gov (United States)

    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.

  10. 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.

  11. Poincaré chaos and unpredictable functions

    Science.gov (United States)

    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.

  12. Controllable chaos in hybrid electro-optomechanical systems

    Science.gov (United States)

    Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying

    2016-01-01

    We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication. PMID:26948505

  13. Controllable chaos in hybrid electro-optomechanical systems.

    Science.gov (United States)

    Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying

    2016-03-07

    We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication.

  14. Congenital high airway obstruction syndrome (CHAOS) associated with cervical myelomeningocele.

    Science.gov (United States)

    Adin, Mehmet Emin

    2017-10-01

    Congenital high airway obstruction syndrome (CHAOS) is a rare and potentially fatal entity resulting from complete or near complete developmental airway obstruction. Although most reported cases of CHAOS are sporadic, the condition may also be associated with certain syndromes and a variety of cervical masses. Meningocele and myelomeningocele have not yet been reported in association with CHAOS. We describe the typical constellation of sonographic findings in a case of early diagnosis of CHAOS associated with cervical myelomeningocele. © 2016 Wiley Periodicals, Inc. J Clin Ultrasound 45:507-510, 2017. © 2016 Wiley Periodicals, Inc.

  15. Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons

    OpenAIRE

    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.

  16. Robinson's chaos in set-valued discrete systems

    International Nuclear Information System (INIS)

    Roman-Flores, Heriberto; Chalco-Cano, Y.

    2005-01-01

    Let (X,d) be a compact metric space and f:X->X a continuous function. If we consider the space (K(X),H) of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and f-bar :K(X)->K(X), f-bar (A)={f(a)/a-bar A}, then the aim of this work is to show that Robinson's chaos in f-bar implies Robinson's chaos in f. Also, we give an example showing that R-chaos in f does not implies R-chaos in f-bar

  17. Chaos theory in geophysics: past, present and future

    International Nuclear Information System (INIS)

    Sivakumar, B.

    2004-01-01

    The past two decades of research on chaos theory in geophysics has brought about a significant shift in the way we view geophysical phenomena. Research on chaos theory in geophysics continues to grow at a much faster pace, with applications to a wide variety of geophysical phenomena and geophysical problems. In spite of our success in understanding geophysical phenomena also from a different (i.e. chaotic) perspective, there still seems to be lingering suspicions on the scope of chaos theory in geophysics. The goal of this paper is to present a comprehensive account of the achievements and status of chaos theory in geophysics, and to disseminate the hope and scope for the future. A systematic review of chaos theory in geophysics, covering a wide spectrum of geophysical phenomena studied (e.g. rainfall, river flow, sediment transport, temperature, pressure, tree ring series, etc.), is presented to narrate our past achievements not only in understanding and predicting geophysical phenomena but also in improving the chaos identification and prediction techniques. The present state of chaos research in geophysics (in terms of geophysical phenomena, problems, and chaos methods) and potential for future improvements (in terms of where, why and possibly how) are also highlighted. Our popular views of nature (i.e. stochastic and deterministic), and of geophysical phenomena in particular, are discussed, and the usefulness of chaos theory as a bridge between such views is also put forth

  18. Chaos synchronization of a new chaotic system via nonlinear control

    International Nuclear Information System (INIS)

    Zhang Qunjiao; Lu Junan

    2008-01-01

    This paper investigates chaos synchronization of a new chaotic system [Lue J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507-37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons and Fractals 2005;25:579-84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method

  19. Chaos and creation in Fernando Pessoa

    Directory of Open Access Journals (Sweden)

    José Nuno Gil

    2016-07-01

    Full Text Available Fernando Pessoa's poem "A Múmia" describes a sort of psychotic experience, which shows the condition of the literary creation by itself. The poem springs from – and describes – the experience of psychic and existential chaos: criticism and clinic overlap in the making and analysis of "A Múmia" This critical reading aims at bringing some intelligibility to the creative processes and, in particular, to Pessoa's heteronyms.

  20. Bifurcations and chaos of DNA solitonic dynamics

    International Nuclear Information System (INIS)

    Gonzalez, J.A.; Martin-Landrove, M.; Carbo, J.R.; Chacon, M.

    1994-09-01

    We investigated the nonlinear DNA torsional equations proposed by Yakushevich in the presence of damping and external torques. Analytical expressions for some solutions are obtained in the case of the isolated chain. Special attention is paid to the stability of the solutions and the range of soliton interaction in the general case. The bifurcation analysis is performed and prediction of chaos is obtained for some set of parameters. Some biological implications are suggested. (author). 11 refs, 13 figs

  1. Li-Yorke chaos in linear dynamics

    Czech Academy of Sciences Publication Activity Database

    Bernardes Jr., N.C.; Bonilla, A.; Müller, Vladimír; Peris, A.

    2015-01-01

    Roč. 35, č. 6 (2015), s. 1723-1745 ISSN 0143-3857 R&D Projects: GA ČR GA201/09/0473; GA AV ČR IAA100190903 Institutional support: RVO:67985840 Keywords : Li-York chaos * Banach space * Fréchet space Subject RIV: BA - General Mathematics Impact factor: 0.983, year: 2015 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9884748&fileId=S0143385714000200

  2. The chaos theory and the quality assurance

    International Nuclear Information System (INIS)

    Aguilar, Omar; Domech More, Jesus

    1999-01-01

    In the present paper we suggest the importance that the new science of chaos offers in the analysis,design and improvement processes in the production of gamma shielding devices as part of the quality assurance system. A brief analysis of the influence of the errors of measures, the interactions between the process and its environment in determining of the basic behaviour of the process and its stability is done.(author)

  3. Coherence and chaos in extended dynamical systems

    International Nuclear Information System (INIS)

    Bishop, A.R.

    1994-01-01

    Coherence, chaos, and pattern formation are characteristic elements of the nonequilibrium statistical mechanics controlling mesoscopic order and disorder in many-degree-of-freedom nonlinear dynamical systems. Competing length scales and/or time scales are the underlying microscopic driving forces for many of these aspects of ''complexity.'' We illustrate the basic concepts with some model examples of classical and quantum, ordered and disordered, nonlinear systems

  4. Classical and Quantum Chaos in Atom Optics

    OpenAIRE

    Saif, Farhan

    2006-01-01

    The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits ...

  5. Wave Chaos and Coupling to EM Structures

    Science.gov (United States)

    2006-07-01

    Antonsen, E. Ott and S. Anlage, Aspects of the Scattering and Impedance Properties of Chaotic Microwave Cavities, Acta Physica Polonica A 109, 65...other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a ...currently valid OMB control number. 1. REPORT DATE JUL 2006 2. REPORT TYPE N/ A 3. DATES COVERED - 4. TITLE AND SUBTITLE Wave Chaos and Coupling

  6. Complex motions and chaos in nonlinear systems

    CERN Document Server

    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.

  7. Effect of smoothing on robust chaos.

    Science.gov (United States)

    Deshpande, Amogh; Chen, Qingfei; Wang, Yan; Lai, Ying-Cheng; Do, Younghae

    2010-08-01

    In piecewise-smooth dynamical systems, situations can arise where the asymptotic attractors of the system in an open parameter interval are all chaotic (e.g., no periodic windows). This is the phenomenon of robust chaos. Previous works have established that robust chaos can occur through the mechanism of border-collision bifurcation, where border is the phase-space region where discontinuities in the derivatives of the dynamical equations occur. We investigate the effect of smoothing on robust chaos and find that periodic windows can arise when a small amount of smoothness is present. We introduce a parameter of smoothing and find that the measure of the periodic windows in the parameter space scales linearly with the parameter, regardless of the details of the smoothing function. Numerical support and a heuristic theory are provided to establish the scaling relation. Experimental evidence of periodic windows in a supposedly piecewise linear dynamical system, which has been implemented as an electronic circuit, is also provided.

  8. Dynamics and chaos control of gyrostat satellite

    International Nuclear Information System (INIS)

    Aslanov, Vladimir; Yudintsev, Vadim

    2012-01-01

    Highlights: ► Free dual-spin gyrostat with a small rotor asymmetry is considered. ► Equations in Andoyer-Deprit canonical dimensionless variables are obtained. ► Phase space heteroclinic and homoclinic trajectories are written in closed form. ► Modified Melnikov function is used to construct the control that eliminates chaos. - Abstract: We consider the chaotic motion of the free gyrostat consisting of a platform with a triaxial inertia ellipsoid and a rotor with a small asymmetry with respect to the axis of rotation. Dimensionless equations of motion of the system with perturbations caused by small asymmetries of the rotor are written in Andoyer-Deprit variables. These perturbations lead to separatrix chaos. For gyrostats with different ratios of moments of inertia heteroclinic and homoclinic trajectories are written in closed-form. These trajectories are used for constructing modified Melnikov function, which is used for determine the control that eliminates separatrix chaos. Melnikov function and phase space trajectory are built to show the effectiveness of the control.

  9. Chaos and Structures in Nonlinear Plasmas

    Science.gov (United States)

    Chen, James

    In recent decades, the concepts and applications of chaos, complexity, and nonlinear dynamics have profoundly influenced scientific as well as literary thinking. Some aspects of these concepts are used in almost all of the geophysical disciplines. Chaos and Structures in Nonlinear Plasmas, written by two respected plasma physicists, focuses on nonlinear phenomena in laboratory and space plasmas, which are rich in nonlinear and complex collective effects. Chaos is treated only insofar as it relates to some aspects of nonlinear plasma physics.At the outset, the authors note that plasma physics research has made fundamental contributions to modern nonlinear sciences. For example, the Poincare surface of section technique was extensively used in studies of stochastic field lines in magnetically confined plasmas and turbulence. More generally, nonlinearity in plasma waves and wave-wave and wave-particle interactions critically determines the propagation of energy through a plasma medium. The book also makes it clear that the importance of understanding nonlinear waves goes beyond plasma physics, extending to such diverse fields as solid state physics, fluid dynamics, atmospheric physics, and optics. In space physics, non-linear plasma physics is essential for interpreting in situ as well as remote-sensing data.

  10. Dynamical chaos: systems of classical mechanics

    International Nuclear Information System (INIS)

    Loskutov, A Yu

    2007-01-01

    This article is a methodological manual for those who are interested in chaotic dynamics. An exposition is given on the foundations of the theory of deterministic chaos that originates in classical mechanics systems. Fundamental results obtained in this area are presented, such as elements of the theory of nonlinear resonance and the Kolmogorov-Arnol'd-Moser theory, the Poincare-Birkhoff fixed-point theorem, and the Mel'nikov method. Particular attention is given to the analysis of the phenomena underlying the self-similarity and nature of chaos: splitting of separatrices and homoclinic and heteroclinic tangles. Important properties of chaotic systems - unpredictability, irreversibility, and decay of temporal correlations - are described. Models of classical statistical mechanics with chaotic properties, which have become popular in recent years - billiards with oscillating boundaries - are considered. It is shown that if a billiard has the property of well-developed chaos, then perturbations of its boundaries result in Fermi acceleration. But in nearly-integrable billiard systems, excitations of the boundaries lead to a new phenomenon in the ensemble of particles, separation of particles in accordance their velocities. If the initial velocity of the particles exceeds a certain critical value characteristic of the given billiard geometry, the particles accelerate; otherwise, they decelerate. (methodological notes)

  11. Detecting chaos in irregularly sampled time series.

    Science.gov (United States)

    Kulp, C W

    2013-09-01

    Recently, Wiebe and Virgin [Chaos 22, 013136 (2012)] developed an algorithm which detects chaos by analyzing a time series' power spectrum which is computed using the Discrete Fourier Transform (DFT). Their algorithm, like other time series characterization algorithms, requires that the time series be regularly sampled. Real-world data, however, are often irregularly sampled, thus, making the detection of chaotic behavior difficult or impossible with those methods. In this paper, a characterization algorithm is presented, which effectively detects chaos in irregularly sampled time series. The work presented here is a modification of Wiebe and Virgin's algorithm and uses the Lomb-Scargle Periodogram (LSP) to compute a series' power spectrum instead of the DFT. The DFT is not appropriate for irregularly sampled time series. However, the LSP is capable of computing the frequency content of irregularly sampled data. Furthermore, a new method of analyzing the power spectrum is developed, which can be useful for differentiating between chaotic and non-chaotic behavior. The new characterization algorithm is successfully applied to irregularly sampled data generated by a model as well as data consisting of observations of variable stars.

  12. Chaos, dynamical structure and climate variability

    Energy Technology Data Exchange (ETDEWEB)

    Stewart, H.B. [Brookhaven National Lab., Upton, NY (United States). Dept. of Applied Science

    1995-09-01

    Deterministic chaos in dynamical systems offers a new paradigm for understanding irregular fluctuations. Techniques for identifying deterministic chaos from observed data, without recourse to mathematical models, are being developed. Powerful methods exist for reconstructing multidimensional phase space from an observed time series of a single scalar variable; these methods are invaluable when only a single scalar record of the dynamics is available. However, in some applications multiple concurrent time series may be available for consideration as phase space coordinates. Here the authors propose some basic analytical tools for such multichannel time series data, and illustrate them by applications to a simple synthetic model of chaos, to a low-order model of atmospheric circulation, and to two high-resolution paleoclimate proxy data series. The atmospheric circulation model, originally proposed by Lorenz, has 27 principal unknowns; they establish that the chaotic attractor can be embedded in a subspace of eight dimensions by exhibiting a specific subset of eight unknowns which pass multichannel tests for false nearest neighbors. They also show that one of the principal unknowns in the 27-variable model--the global mean sea surface temperature--is of no discernible usefulness in making short-term forecasts.

  13. 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.

  14. Application of Chaos Theory to Psychological Models

    Science.gov (United States)

    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

  15. Household chaos and family sleep during infants' first year.

    Science.gov (United States)

    Whitesell, Corey J; Crosby, Brian; Anders, Thomas F; Teti, Douglas M

    2018-05-21

    Household chaos has been linked with dysregulated family and individual processes. The present study investigated linkages between household chaos and infant and parent sleep, a self-regulated process impacted by individual, social, and environmental factors. Studies of relations between household chaos and child sleep have focused on older children and teenagers, with little attention given to infants or parent sleep. This study examines these relationships using objective measures of household chaos and sleep while controlling for, respectively, maternal emotional availability at bedtime and martial adjustment, in infant and parent sleep. Multilevel modeling examined mean and variability of sleep duration and fragmentation for infants, mothers, and fathers when infants were 1, 3, 6, 9, and 12 months (N = 167). Results indicated infants in higher chaos homes experienced delays in sleep consolidation patterns, with longer and more variable sleep duration, and greater fragmentation. Parent sleep was also associated with household chaos such that in higher chaos homes, mothers and fathers experienced greater variability in sleep duration, which paralleled infant findings. In lower chaos homes, parents' sleep fragmentation mirrored infants' decreasingly fragmented sleep across the first year and remained lower at all timepoints compared to parents and infants in high chaos homes. Collectively, these findings indicate that after controlling for maternal emotional availability and marital adjustment (respectively) household chaos has a dysregulatory impact on infant and parent sleep. Results are discussed in terms of the potential for chaos-induced poor sleep to dysregulate daytime functioning and, in turn, place parent-infant relationships at risk. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

  16. Chaos controlling problems for circuit systems with Josephson junction

    International Nuclear Information System (INIS)

    Gou, X-F; Wang, X; Xie, J-L

    2008-01-01

    The complex dynamical characters of the Josephson junction circuit system are studied and the tunnel effect is considered. The dynamical equation of the system is established. The route from periodic motion to chaos is illustrated using bifurcation diagram. An adscititious coupling controller is constructed to control the chaos

  17. Synchronization and suppression of chaos in non-locally coupled ...

    Indian Academy of Sciences (India)

    Coupled map lattices have been intensively investigated as models to understand many spatiotemporal phenomena observed in extended system, and consequently spatiotemporal chaos. We used the complex order parameter to quantify chaos synchronization for a one-dimensional chain of coupled logistic maps with a ...

  18. On the efficiency of chaos optimization algorithms for global optimization

    International Nuclear Information System (INIS)

    Yang Dixiong; Li Gang; Cheng Gengdong

    2007-01-01

    Chaos optimization algorithms as a novel method of global optimization have attracted much attention, which were all based on Logistic map. However, we have noticed that the probability density function of the chaotic sequences derived from Logistic map is a Chebyshev-type one, which may affect the global searching capacity and computational efficiency of chaos optimization algorithms considerably. Considering the statistical property of the chaotic sequences of Logistic map and Kent map, the improved hybrid chaos-BFGS optimization algorithm and the Kent map based hybrid chaos-BFGS algorithm are proposed. Five typical nonlinear functions with multimodal characteristic are tested to compare the performance of five hybrid optimization algorithms, which are the conventional Logistic map based chaos-BFGS algorithm, improved Logistic map based chaos-BFGS algorithm, Kent map based chaos-BFGS algorithm, Monte Carlo-BFGS algorithm, mesh-BFGS algorithm. The computational performance of the five algorithms is compared, and the numerical results make us question the high efficiency of the chaos optimization algorithms claimed in some references. It is concluded that the efficiency of the hybrid optimization algorithms is influenced by the statistical property of chaotic/stochastic sequences generated from chaotic/stochastic algorithms, and the location of the global optimum of nonlinear functions. In addition, it is inappropriate to advocate the high efficiency of the global optimization algorithms only depending on several numerical examples of low-dimensional functions

  19. Research on a family of n-scroll chaos generators

    International Nuclear Information System (INIS)

    Zhang, G; Yang, S-Z; He, L-F

    2008-01-01

    This paper studies a family of n-scroll chaos generators using a modified Chua's circuit. A mathematic model of the generators is established, the relationship between equilibrium points and scrolls is also analyzed, and a general theorem for generation of n-scroll chaos attractors is given. Numerical simulation is illustrated, showing excellent agreement with our theoretical predictions

  20. On the suppression of chaos in quantum and classical physics

    International Nuclear Information System (INIS)

    Fried, H.M.; Gabellini, Y.

    1997-01-01

    A brief outline is presented of an example of potential-theory quantum chaos, which is suppressed by the full radiative corrections of quantum field theory. A similar mechanism may be devised and applied to classically chaotic systems, and provides an example in which an explicit diminution of the original chaos becomes apparent. (author)

  1. Applying Chaos Theory to Lesson Planning and Delivery

    Science.gov (United States)

    Cvetek, Slavko

    2008-01-01

    In this article, some of the ways in which thinking about chaos theory can help teachers and student-teachers to accept uncertainty and randomness as natural conditions in the classroom are considered. Building on some key features of complex systems commonly attributed to chaos theory (e.g. complexity, nonlinearity, sensitivity to initial…

  2. The Chaos Theory of Careers: A User's Guide

    Science.gov (United States)

    Bright, Jim E. H.; Pryor, Robert G. L.

    2005-01-01

    The purpose of this article is to set out the key elements of the Chaos Theory of Careers. The complexity of influences on career development presents a significant challenge to traditional predictive models of career counseling. Chaos theory can provide a more appropriate description of career behavior, and the theory can be applied with clients…

  3. Switching control of linear systems for generating chaos

    International Nuclear Information System (INIS)

    Liu Xinzhi; Teo, Kok-Lay; Zhang Hongtao; Chen Guanrong

    2006-01-01

    In this paper, a new switching method is developed, which can be applied to generating different types of chaos or chaos-like dynamics from two or more linear systems. A numerical simulation is given to illustrate the generated chaotic dynamic behavior of the systems with some variable parameters. Finally, a circuit is built to realize various chaotic dynamical behaviors

  4. Chaos: A Topic for Interdisciplinary Education in Physics

    Science.gov (United States)

    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…

  5. Chaos and the classical limit of quantum systems

    Energy Technology Data Exchange (ETDEWEB)

    Hogg, T; Huberman, B A [Xerox Palo Alto Research Center, CA (USA)

    1984-10-01

    The authors discuss the question of whether experiments can be designed to test the existence of quantum chaos. In particular, they show that high energies are not sufficient to guarantee that an initially localized wave packet will behave classically for long times. Computer simulations illustrating these ideas are presented and the question whether experiments can be designed to observe quantum chaos is commented on.

  6. Specifying the Links between Household Chaos and Preschool Children's Development

    Science.gov (United States)

    Martin, Anne; Razza, Rachel A.; Brooks-Gunn, Jeanne

    2012-01-01

    Household chaos has been linked to poorer cognitive, behavioural, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family…

  7. Common Core State Standards and Teacher Effectiveness. Q&A with Ross Wiener, Ph.D. REL Mid-Atlantic Teacher Effectiveness Webinar Series

    Science.gov (United States)

    Regional Educational Laboratory Mid-Atlantic, 2013

    2013-01-01

    In this REL Mid-Atlantic webinar, Dr. Ross Wiener, Vice President and Executive Director of the Education and Society Program, Aspen Institute, discussed strategies for integrating the Common Core State Standards (CCSS) into teacher effectiveness systems, including ways in which the CCSS can support professional growth and inform teacher…

  8. Generalized treatment of point reactor kinetics driven by random reactivity fluctuations via the Wiener-Hermite functional method

    International Nuclear Information System (INIS)

    Behringer, K.

    1991-02-01

    In a recent paper by Behringer et al. (1990), the Wiener-Hermite Functional (WHF) method has been applied to point reactor kinetics excited by Gaussian random reactivity noise under stationary conditions, in order to calculate the neutron steady-state value and the neutron power spectral density (PSD) in a second-order (WHF-2) approximation. For simplicity, delayed neutrons and any feedback effects have been disregarded. The present study is a straightforward continuation of the previous one, treating the problem more generally by including any number of delayed neutron groups. For the case of white reactivity noise, the accuracy of the approach is determined by comparison with the exact solution available from the Fokker-Planck method. In the numerical comparisons, the first-oder (WHF-1) approximation of the PSD is also considered. (author) 4 figs., 10 refs

  9. Application of the Wiener-Hermite functional method to point reactor kinetics driven by random reactivity fluctuations

    International Nuclear Information System (INIS)

    Behringer, K.; Pineyro, J.; Mennig, J.

    1990-06-01

    The Wiener-Hermite functional (WHF) method has been applied to the point reactor kinetic equation excited by Gaussian random reactivity noise under stationary conditions. Delayed neutrons and any feedback effects are disregarded. The neutron steady-state value and the power spectral density (PSD) of the neutron flux have been calculated in a second order (WHF-2) approximation. Two cases are considered: in the first case, the noise source is low-pass white noise. In both cases the WHF-2 approximation of the neutron PSDs leads to relatively simple analytical expressions. The accuracy of the approach is determined by comparison with exact solutions of the problem. The investigations show that the WHF method is a powerful approximative tool for studying the nonlinear effects in the stochastic differential equation. (author) 5 figs., 29 refs

  10. Random matrices and chaos in nuclear physics: Nuclear structure

    International Nuclear Information System (INIS)

    Weidenmueller, H. A.; Mitchell, G. E.

    2009-01-01

    Evidence for the applicability of random-matrix theory to nuclear spectra is reviewed. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately, quantum chaos) in nuclei whenever random-matrix predictions are fulfilled. An introduction into the basic concepts of random-matrix theory is followed by a survey over the extant experimental information on spectral fluctuations, including a discussion of the violation of a symmetry or invariance property. Chaos in nuclear models is discussed for the spherical shell model, for the deformed shell model, and for the interacting boson model. Evidence for chaos also comes from random-matrix ensembles patterned after the shell model such as the embedded two-body ensemble, the two-body random ensemble, and the constrained ensembles. All this evidence points to the fact that chaos is a generic property of nuclear spectra, except for the ground-state regions of strongly deformed nuclei.

  11. Replication of chaos in neural networks, economics and physics

    CERN Document Server

    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.

  12. Strong chaos in one-dimensional quantum system

    International Nuclear Information System (INIS)

    Yang, C.-D.; Wei, C.-H.

    2008-01-01

    According to the Poincare-Bendixson theorem, a minimum of three autonomous equations is required to exhibit deterministic chaos. Because a one-dimensional quantum system is described by only two autonomous equations using de Broglie-Bohm's trajectory interpretation, chaos in one-dimensional quantum systems has long been considered impossible. We will prove in this paper that chaos phenomenon does exist in one-dimensional quantum systems, if the domain of quantum motions is extended to complex space by noting that the quantum world is actually characterized by a four-dimensional complex spacetime according to the E (∞) theory. Furthermore, we point out that the interaction between the real and imaginary parts of complex trajectories produces a new chaos phenomenon unique to quantum systems, called strong chaos, which describes the situation that quantum trajectories may emerge and diverge spontaneously without any perturbation in the initial position

  13. Relativistic quantum chaos-An emergent interdisciplinary field.

    Science.gov (United States)

    Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

    2018-05-01

    Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

  14. A new approach for realizing electronic chaos generators

    International Nuclear Information System (INIS)

    Elwakeel, A.E.

    1997-01-01

    A dictionary definition of chaos is a 'formless primordial matter, utter confusion' [1]. The study of chaos is part of a larger program of study of so-called strongly nonlinear systems. No strict definition of chaos yet exists, however, nonrandom complicated motions that exhibit a very rapid growth of errors and that, despite perfect determinism, inhibit any ability to render accurate long-term prediction are usually termed chaotic. In other words, chaos may be referred to as deterministic randomness since it is the phenomenon where deterministic laws, are sometimes extremely simple, show random (or random-like) behaviours while random (or random-like) motions happen to follow strict deterministic laws. The sense of order in chaos can be usually observed in the space of dimensions where time is not a dimension, while the sense of randomness is usually evident when time is incorporated. 10 refs., 29 figs

  15. Elimination of spiral chaos by periodic force for the Aliev-Panfilov model

    OpenAIRE

    Sakaguchi, Hidetsugu; Fujimoto, Takefumi

    2003-01-01

    Spiral chaos appears in the two dimensional Aliev-Panfilov model. The generation mechanism of the spiral chaos is related to the breathing instability of pulse trains. The spiral chaos can be eliminated by applying periodic force uniformly. The elimination of spiral chaos is most effective, when the frequency of the periodic force is close to that of the breathing motion.

  16. Chaos and its Role in Design and Simulation of Railway Vehicles

    DEFF Research Database (Denmark)

    True, Hans

    1996-01-01

    First certain important properties of nonlinear problems are discussed. Thenthe concept of chaos is described. It can only appear in nonlinear systemsand it is very common in the real world. Certain characteristic features ofdeterministic chaos and in relation hereto tests for the existence...... of chaos indynamical systems are presented.\\ Next the relevance of chaos for railwaydynamics is discussed and examples of chaotic oscillations in railwaydynamical model are shown, whereby the distinction between a chaoticattractor and transient chaos is introduces. Some causes of chaos in railwaytechnology...... are discussed. Finally the effects of chaos on field tests andnumerical simulations are discussed....

  17. Method of controlling chaos in laser equations

    International Nuclear Information System (INIS)

    Duong-van, M.

    1993-01-01

    A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang, and Bau [Phys. Rev. Lett. 66, 1123 (1991)]. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the laser equations are isomorphic to the Lorenz equations we use this method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential laser controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills, and Hunt [Phys. Rev. Lett. 68, 1259 (1992)

  18. Chaos of several typical asymmetric systems

    International Nuclear Information System (INIS)

    Feng Jingjing; Zhang Qichang; Wang Wei

    2012-01-01

    The threshold for the onset of chaos in asymmetric nonlinear dynamic systems can be determined using an extended Padé method. In this paper, a double-well asymmetric potential system with damping under external periodic excitation is investigated, as well as an asymmetric triple-well potential system under external and parametric excitation. The integrals of Melnikov functions are established to demonstrate that the motion is chaotic. Threshold values are acquired when homoclinic and heteroclinic bifurcations occur. The results of analytical and numerical integration are compared to verify the effectiveness and feasibility of the analytical method.

  19. Method of controlling chaos in laser equations

    Science.gov (United States)

    Duong-van, Minh

    1993-01-01

    A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang, and Bau [Phys. Rev. Lett. 66, 1123 (1991)]. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the laser equations are isomorphic to the Lorenz equations we use this method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential laser controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills, and Hunt [Phys. Rev. Lett. 68, 1259 (1992)].

  20. Controlling chaos in Internet congestion control model

    International Nuclear Information System (INIS)

    Chen Liang; Wang Xiaofan; Han Zhengzhi

    2004-01-01

    The TCP end-to-end congestion control plus RED router queue management can be modeled as a discrete-time dynamical system, which may create complex bifurcating and chaotic behavior. Based on the basic features of the TCP-RED model, we propose a time-dependent delayed feedback control algorithm to control chaos in the system by perturbing the accessible RED parameter p max . This method is able to stabilized a router queue occupancy at a level without knowing the exact knowledge of the network. Further, we study the situation of the presence of the UDP traffic

  1. Experimental chaos in nonlinear vibration isolation system

    International Nuclear Information System (INIS)

    Lou Jingjun; Zhu Shijian; He Lin; He Qiwei

    2009-01-01

    The chaotic vibration isolation method was studied thoroughly from an experimental perspective. The nonlinear load-deflection characteristic of the conical coil spring used in the experiment was surveyed. Chaos and subharmonic responses including period-2 and period-6 motions were observed. The line spectrum reduction and the drop of the acceleration vibration level in chaotic state and that in non-chaotic state were compared, respectively. It was concluded from the experiment that the nonlinear vibration isolation system in chaotic state has strong ability in line spectrum reduction.

  2. Quantum chaos and the black hole horizon

    CERN Multimedia

    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)

  3. Cryptography with chaos at the physical level

    International Nuclear Information System (INIS)

    Machado, Romuel F.; Baptista, Murilo S.; Grebogi, C.

    2004-01-01

    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

  4. Topological organization of (low-dimensional) chaos

    International Nuclear Information System (INIS)

    Tufillaro, N.B.

    1992-01-01

    Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template describes the primary folding and stretching mechanisms of phase space responsible for the chaotic motion. Topological invariants of the unstable periodic orbits in the closure of the strange set are calculated from the (reconstructed) template. These topological invariants must be consistent with ampersand ny model put forth to describe the time series data, and are useful in invalidating (or gaining confidence in) any model intended to describe the dynamical system generating the time series

  5. Quantum chaos and nuclear mass systematics

    International Nuclear Information System (INIS)

    Hirsch, Jorge G.; Velazquez, Victor; Frank, Alejandro

    2004-01-01

    The presence of quantum chaos in nuclear mass systematics is analyzed by considering the differences between measured and calculated nuclear masses as a time series described by the power law 1fα. While for the liquid droplet model plus shell corrections a quantum chaotic behavior α∼1 is found, errors in the microscopic mass formula have α∼0.5, closer to white noise. The chaotic behavior seems to arise from many body effects not included in the mass formula

  6. Conduction at the onset of chaos

    Science.gov (United States)

    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.

  7. Order, disorder and chaos in crystal lattice

    International Nuclear Information System (INIS)

    Oliveira, M.J. de; Salinas, S.R.A.

    1985-01-01

    The properties of two two-dimensional mappings corresponding to the solutions of spin models on a Cayley tree in infinite coordination limit are analised in detail. The models under consideration are related to some mechanisms which were proposed to explain the occurrence of modulated phases in magnetic crystals. The existence of devil's staircases characterized by fractal dimensionalities which increase with temperature is shown. Numerical evidences to support the existence of a strange attractor, of a fractal character, in the Ising model with competing interactions restricted to the branches of a Cayley tree are presented. The route to chaos agrees with the scenario of Feigenbaum. (Author) [pt

  8. Classical and quantum chaos in atom optics

    International Nuclear Information System (INIS)

    Saif, Farhan

    2005-01-01

    The interaction of an atom with an electro-magnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electro-magnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits dynamical localization and quantum recurrences

  9. 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.

  10. Pattern formation and chaos in synergetic systems

    Energy Technology Data Exchange (ETDEWEB)

    Haken, H

    1985-01-01

    A general approach to the reduction of the equations of systems composed of many subsystems of equations for, in general, few order parameters at instability points is sketched. As special case generalized Ginzburg-Landau equations are obtained. Recent results based on these equations, showing pattern formation in the convection instability and flames, are presented. Bifurcations from tori to other tori are treated, and some general conclusions are drawn. Analogies between fluid dynamics and lasers which led to the prediction of laser light chaos by Haken (1975) are pointed out. Finally the suspension of a class of discrete one-dimensional maps is discussed and explicitly presented for a typical case. 21 references.

  11. Chaos synchronization of the energy resource system

    International Nuclear Information System (INIS)

    Li Xiuchun; Xu Wei; Li Ruihong

    2009-01-01

    This paper presents the chaos synchronization problem for new dynamical system (that is, energy resource demand-supply system), where the controller is designed using two different control methods. Firstly, based on stability criterion of linear system, chaotic synchronization is achieved with the help of the active theory, and accordingly, the simulation results are given for verifying the feasibility of the method. Secondly, based on Lyapunov stability theory, on the assumption that all the parameters of the system are unknown, adaptive control approach is proposed to make the states of two chaotic systems asymptotic synchronization. In the end, numerical simulations are used to show the effectiveness of the proposed control method.

  12. Chaos in Kaluza-Klein models

    Energy Technology Data Exchange (ETDEWEB)

    Elskens, Yves; Henneaux, Marc

    1987-09-01

    Kaluza-Klein cosmological models are investigated in the vicinity of a spacelike singularity. A new parametrisation of the Kasner exponents is given for any spacetime dimension, which reduces the mixmaster dynamics to a combination of a translation and an isometry or a dilating inversion. Using this parametrisation, chaos is proven to hold for spacetime dimension n <= 10. For n >= 11, the chaotic behaviour is shown to become unstable and to be replaced by monotonic Kasner asymptotics. These results explicitly establish conjectures formulated in previous work.

  13. Order out of chaos in atomic nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Rotter, I

    1988-07-01

    The transition from the resonance reaction mechanism at low level density to the direct reaction mechanism at high level density is investigated by means of numerical results obtained from microscopic calculations for nucleon-induced reactions. The transition takes place rather sharply at GAMMA approx. = D-bar. Here, two types of motion of the nucleons exist simultaneously: a motion in long-living states which are near equilibrium and a motion in short-living states which are far from equilibrium. A formation of order out of chaos takes place only in the open quantum mechanical nuclear system. It is caused by quantum fluctuations via the continuum.

  14. From Cool Cash to Coded Chaos

    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...... of Denmark (called New Wage), this paper theorizes this complexity in terms of Niklas Luhmann's systems theory. It identifies four wholly different `codes' of communication: legal, economic, pedagogical and intimate. Each of them shapes the phenomena of `pay', the construal of the employee and the form...

  15. Pulsating instabilities and chaos in lasers

    Energy Technology Data Exchange (ETDEWEB)

    Harrison, R G; Biswas, D J

    1985-01-01

    A detailed state of the art survey of deterministic chaos in laser systems is presented. The mechanism of single mode instability is discussed, including spontaneous and induced mode splitting and the threshold for laser instabilities. Single mode homogeneously broadened systems are addressed, including optically pumped far infrared lasers and near-resonantly pumped midinfrared systems. Single mode inhomogeneously broadened systems are considered, including the He-Xe laser and the He-Ne laser at 3.39 microns. Single mode lasers with external control parameter are discussed, as is the multimode laser. 297 references.

  16. Controlling chaos in Internet congestion control model

    Energy Technology Data Exchange (ETDEWEB)

    Chen Liang E-mail: chenmoon110@yahoo.com.cn; Wang Xiaofan; Han Zhengzhi

    2004-07-01

    The TCP end-to-end congestion control plus RED router queue management can be modeled as a discrete-time dynamical system, which may create complex bifurcating and chaotic behavior. Based on the basic features of the TCP-RED model, we propose a time-dependent delayed feedback control algorithm to control chaos in the system by perturbing the accessible RED parameter p{sub max}. This method is able to stabilized a router queue occupancy at a level without knowing the exact knowledge of the network. Further, we study the situation of the presence of the UDP traffic.

  17. Chaos as an intermittently forced linear system.

    Science.gov (United States)

    Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

    2017-05-30

    Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

  18. Quantum chaos and holographic tensor models

    Energy Technology Data Exchange (ETDEWEB)

    Krishnan, Chethan [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India); Sanyal, Sambuddha [International Center for Theoretical Sciences, Tata Institute of Fundamental Research,Bangalore 560089 (India); Subramanian, P.N. Bala [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India)

    2017-03-10

    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.

  19. Quantum chaos in a fermion system

    International Nuclear Information System (INIS)

    Pal, Santanu

    1992-01-01

    With the growing realisation that the dynamics of a system with a few degrees of freedom is chaotic more as a rule than an exception, the relevance of quantum chaos in nuclear single-particle motion is now receiving closer scrutinisation. This on one hand is helping to gain a deeper understanding of dissipative processes in nuclear dynamics as well as revealing certain interesting features of a fermion system on the other. In the present talk, we would discuss the chaotic features of the single-particle motion in a di nucleus with a view to study the signatures of an effective underlying classical dynamics in the system. As the present day understanding of quantum chaos relies quite heavily on the existence of classical trajectories, it is rather interesting to study how far such considerations can be pushed for systems which do not have a obvious classical analogue such as the spin-orbit interaction in our system. This question has been further investigated for a relativistic fermion system, similar to the Bogoliubov bag. This model is particularly suited as spin, without a classical analogue, has its natural place in the Dirac equation. The results of this study have been presented in the talk. (author). 25 refs., 14 figs

  20. RAPID DYNAMICAL CHAOS IN AN EXOPLANETARY SYSTEM

    Energy Technology Data Exchange (ETDEWEB)

    Deck, Katherine M.; Winn, Joshua N. [Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Holman, Matthew J.; Carter, Joshua A.; Ragozzine, Darin [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Agol, Eric [Department of Astronomy, Box 351580, University of Washington, Seattle, WA 98195 (United States); Lissauer, Jack J. [NASA Ames Research Center, Moffet Field, CA 94035 (United States)

    2012-08-10

    We report on the long-term dynamical evolution of the two-planet Kepler-36 system, which consists of a super-Earth and a sub-Neptune in a tightly packed orbital configuration. The orbits of the planets, which we studied through numerical integrations of initial conditions that are consistent with observations of the system, are chaotic with a Lyapunov time of only {approx}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 {approx}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 ({approx}200 million years). Restricting the orbits to this long-lived region allows a refinement of estimates of the masses and radii of the planets. We find that the long-lived region consists of the initial conditions that satisfy the Hill stability criterion by the largest margin. Any successful theory for the formation of this system will need to account for why its current state is so close to unstable regions of phase space.

  1. Quantum chaos and holographic tensor models

    International Nuclear Information System (INIS)

    Krishnan, Chethan; Sanyal, Sambuddha; Subramanian, P.N. Bala

    2017-01-01

    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.

  2. Collective diffusion and quantum chaos in holography

    Science.gov (United States)

    Wu, Shao-Feng; Wang, Bin; Ge, Xian-Hui; Tian, Yu

    2018-05-01

    We define a particular combination of charge and heat currents that is decoupled with the heat current. This "heat-decoupled" (HD) current can be transported by diffusion at long distances, when some thermoelectric conductivities and susceptibilities satisfy a simple condition. Using the diffusion condition together with the Kelvin formula, we show that the HD diffusivity can be same as the charge diffusivity and also the heat diffusivity. We illustrate that such mechanism is implemented in a strongly coupled field theory, which is dual to a Lifshitz gravity with the dynamical critical index z =2 . In particular, it is exhibited that both charge and heat diffusivities build the relationship to the quantum chaos. Moreover, we study the HD diffusivity without imposing the diffusion condition. In some homogeneous holographic lattices, it is found that the diffusivity/chaos relation holds independently of any parameters, including the strength of momentum relaxation, chemical potential, or temperature. We also show a counter example of the relation and discuss its limited universality.

  3. Control of chaos in a three-well duffing system

    International Nuclear Information System (INIS)

    Yang Jianping; Jing Zhujun

    2009-01-01

    Analytical and numerical results concerning control of chaos in a three-well duffing system with two external excitations are given by using the Melnikov methods proposed by Chacon et al. [Chacon R. General results on chaos suppression for biharmonically driven dissipative systems. Phys Lett A 1999;257:293-300, Chacon R, Palmero F, Balibrea F. Taming chaos in a driven Josephson Junction. Int J Bifurc Chaos 2001;11(7):1897-909, Chacon R. Role of ultrasubharmonic resonances in taming chaos by weak harmonic perturbations. Europhys Lett 2001;54(2):148C153]. We theoretically give the parameter-space region and intervals of initial phase difference for primary and subharmonic resonance and the necessary condition for the superharmonic and supersubharmonic resonance, where homoclinic chaos or heteroclinic chaos can be suppressed. Numerical simulations show the consistency and difference with theoretical analysis and the chaotic behavior can be converted to periodic orbits by adjusting amplitude and phase-difference of inhibiting excitation. Moreover, we consider the influence of parametric frequency on maximum Lyapunov exponent (LE) for different phase-differences, and give the distribution of maximum Lyapunov exponents in parameter-plane, which indicates the regions of non-chaotic states (non-positive LE) and chaotic states (positive LE).

  4. Chaos as a Social Determinant of Child Health: Reciprocal Associations?

    Science.gov (United States)

    Schmeer, Kammi K.; Taylor, Miles

    2013-01-01

    This study informs the social determinants of child health by exploring an understudied aspect of children’s social contexts: chaos. Chaos has been conceptualized as crowded, noisy, disorganized, unpredictable settings for child development (Evans et al., 2010). We measure chaos at two levels of children’s ecological environment - the microsystem (household) and the mesosystem (work-family-child care nexus) – and at two points in early childhood (ages 3 and 5). Using data from the Fragile Families and Child Wellbeing Study (N=3288), a study of predominantly low-income women and their partners in large US cities, we develop structural equation models that assess how maternal-rated child health (also assessed at ages 3 and 5) is associated with latent constructs of chaos, and whether there are important reciprocal effects. Autoregressive crosslagged path analysis suggest that increasing chaos (at both the household and maternal work levels) is associated with worse child health, controlling for key confounders like household economic status, family structure, and maternal health status. Child health has little effect on chaos, providing further support for the hypothesis that chaos is an important social determinant of child health in this sample of relatively disadvantaged children. This suggests child health may be improved by supporting families in ways that reduce chaos in their home and work/family environments, and that as researchers move beyond SES, race, and family structure to explore other sources of health inequalities, chaos and its proximate determinants may be a promising avenue for future research. PMID:23541250

  5. Error function attack of chaos synchronization based encryption schemes.

    Science.gov (United States)

    Wang, Xingang; Zhan, Meng; Lai, C-H; Gang, Hu

    2004-03-01

    Different chaos synchronization based encryption schemes are reviewed and compared from the practical point of view. As an efficient cryptanalysis tool for chaos encryption, a proposal based on the error function attack is presented systematically and used to evaluate system security. We define a quantitative measure (quality factor) of the effective applicability of a chaos encryption scheme, which takes into account the security, the encryption speed, and the robustness against channel noise. A comparison is made of several encryption schemes and it is found that a scheme based on one-way coupled chaotic map lattices performs outstandingly well, as judged from quality factor. Copyright 2004 American Institute of Physics.

  6. Controlling beam halo-chaos via backstepping design

    International Nuclear Information System (INIS)

    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

  7. From chaos to order methodologies, perspectives and applications

    CERN Document Server

    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

  8. Chaos-based hash function (CBHF) for cryptographic applications

    International Nuclear Information System (INIS)

    Amin, Mohamed; Faragallah, Osama S.; Abd El-Latif, Ahmed A.

    2009-01-01

    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.

  9. Global chaos synchronization with channel time-delay

    International Nuclear Information System (INIS)

    Jiang Guoping; Zheng Weixing; Chen Guanrong

    2004-01-01

    This paper addresses a practical issue in chaos synchronization where there is a time-delay in the receiver as compared with the transmitter. A new synchronization scheme and a general criterion for global chaos synchronization are proposed and developed from the approach of unidirectional linear error feedback coupling with time-delay. The chaotic Chua's circuit is used for illustration, where the coupling parameters are determined according to the criterion under which the global chaos synchronization of the time-delay coupled systems is achieved

  10. 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.

  11. Individual chaos implies collective chaos for weakly mixing discrete dynamical systems

    International Nuclear Information System (INIS)

    Liao Gongfu; Ma Xianfeng; Wang Lidong

    2007-01-01

    Let X be a metric space (X,f) a discrete dynamical system, where f:X->X is a continuous function. Let f-bar denote the natural extension of f to the space of all non-empty compact subsets of X endowed with Hausdorff metric induced by d. In this paper we investigate some dynamical properties of f and f-bar . It is proved that f is weakly mixing (mixing) if and only if f-bar is weakly mixing (mixing, respectively). From this, we deduce that weak-mixing of f implies transitivity of f-bar , further, if f is mixing or weakly mixing, then chaoticity of f (individual chaos) implies chaoticity of f-bar (collective chaos) and if X is a closed interval then f-bar is chaotic (in the sense of Devaney) if and only if f is weakly mixing

  12. Calculating topological entropy for transient chaos with an application to communicating with chaos

    International Nuclear Information System (INIS)

    Jacobs, J.; Ott, E.; Hunt, B.R.

    1998-01-01

    Recent work on communicating with chaos provides a practical motivation for being able to determine numerically the topological entropy for chaotic invariant sets. In this paper we discuss numerical methods for evaluating topological entropy. To assess the accuracy and convergence of the methods, we test them in situations where the topological entropy is known independently. We also discuss the entropy of invariant chaotic saddles formed by those points in a given attractor that never visit some forbidden 'gap' region. Such gaps have been proposed as a means of providing noise immunity in schemes for communication with chaos, and we discuss the dependence of the topological entropy on the size of the gap. copyright 1998 The American Physical Society

  13. Global chaos synchronization of three coupled nonlinear autonomous systems and a novel method of chaos encryption

    International Nuclear Information System (INIS)

    An Xinlei; Yu Jianning; Chu Yandong; Zhang Jiangang; Zhang Li

    2009-01-01

    In this paper, we discussed the fixed points and their linear stability of a new nonlinear autonomous system that introduced by J.C. Sprott. Based on Lyapunov stabilization theorem, a global chaos synchronization scheme of three coupled identical systems is investigated. By choosing proper coupling parameters, the states of all the three systems can be synchronized. Then this method was applied to secure communication through chaotic masking, used three coupled identical systems, propose a novel method of chaos encryption, after encrypting in the previous two transmitters, information signal can be recovered exactly at the receiver end. Simulation results show that the method can realize monotonous synchronization. Further more, the information signal can be recovered undistorted when applying this method to secure communication.

  14. Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos

    International Nuclear Information System (INIS)

    Zhang Fang-Fang; Liu Shu-Tang; Yu Wei-Yong

    2013-01-01

    To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors (CMPS) of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes. (general)

  15. The Strength of Chaos: Accurate Simulation of Resonant Electron Scattering by Many-Electron Ions and Atoms in the Presence of Quantum Chaos

    Science.gov (United States)

    2017-01-20

    AFRL-AFOSR-JP-TR-2017-0012 The Strength of Chaos : accurate simulation of resonant electron scattering by many-electron ions and atoms in the presence...of quantum chaos Igor Bray CURTIN UNIVERSITY OF TECHNOLOGY Final Report 01/20/2017 DISTRIBUTION A: Distribution approved for public release. AF...SUBTITLE The Strength of Chaos : accurate simulation of resonant electron scattering by many- electron ions and atoms in the presence of quantum chaos

  16. Chaos analysis of viscoelastic chaotic flows of polymeric fluids in a micro-channel

    Energy Technology Data Exchange (ETDEWEB)

    Lim, C. P.; Lam, Y. C., E-mail: myclam@ntu.edu.sg [School of Mechanical and Aerospace Engineering, Nanyang Technological University, 639798 (Singapore); BioSystems and Micromechanics (BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, 138602 (Singapore); Han, J. [BioSystems and Micromechanics (BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, 138602 (Singapore); Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)

    2015-07-15

    Many fluids, including biological fluids such as mucus and blood, are viscoelastic. Through the introduction of chaotic flows in a micro-channel and the construction of maps of characteristic chaos parameters, differences in viscoelastic properties of these fluids can be measured. This is demonstrated by creating viscoelastic chaotic flows induced in an H-shaped micro-channel through the steady infusion of a polymeric fluid of polyethylene oxide (PEO) and another immiscible fluid (silicone oil). A protocol for chaos analysis was established and demonstrated for the analysis of the chaotic flows generated by two polymeric fluids of different molecular weight but with similar relaxation times. The flows were shown to be chaotic through the computation of their correlation dimension (D{sub 2}) and the largest Lyapunov exponent (λ{sub 1}), with D{sub 2} being fractional and λ{sub 1} being positive. Contour maps of D{sub 2} and λ{sub 1} of the respective fluids in the operating space, which is defined by the combination of polymeric fluids and silicone oil flow rates, were constructed to represent the characteristic of the chaotic flows generated. It was observed that, albeit being similar, the fluids have generally distinct characteristic maps with some similar trends. The differences in the D{sub 2} and λ{sub 1} maps are indicative of the difference in the molecular weight of the polymers in the fluids because the driving force of the viscoelastic chaotic flows is of molecular origin. This approach in constructing the characteristic maps of chaos parameters can be employed as a diagnostic tool for biological fluids and, more generally, chaotic signals.

  17. Low-frequency Wiener spectra for homogenity analysis of image-forming films at imaging with film-foils systems in radiography

    International Nuclear Information System (INIS)

    Wolf, M.; Angerstein, W.

    1986-01-01

    A special photometer for the measurement of image Wiener spectra below spatial frequencies of 1 mm -1 is described. These low-frequency Wiener spectra allow a quantitative assessment of inhomogeneities of screens and films (such as clouds and coarse structures) introduced in the production process. Noise with frequencies below the usually measured frequency range of 1 to 7 mm -1 is decisive for the detection of the diagnostically important details greater than 1 mm. It appears, that the noise amplitudes and their differences between screens of the same type can be relatively high. This in accordance with the visual noise impression indicates, that low frequency noise is an important image quality factor for screen-film systems. (author)

  18. Ray and wave chaos in underwater acoustic waveguides

    International Nuclear Information System (INIS)

    Virovlyansky, Anatolii L; Makarov, Denis V; Prants, Sergei V

    2012-01-01

    In the 1990s, the study of the chaotic behavior of ray trajectories in inhomogeneous waveguides emerged as a new field in ocean acoustics. It turned out that at ranges on the order of or larger than 1000 km ray chaos is well developed and should be taken into account when describing long-range sound propagation in the ocean. The theoretical analysis of ray chaos and of its finite-wavelength manifestation, wave chaos, is to a large extent based on well-known methods and ideas from the theory of dynamical and quantum chaos. Concrete examples are used to review the results obtained in this field over the last two decades. (reviews of topical problems)

  19. Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals

    CERN Document Server

    Ivancevic, Vladimir G

    2008-01-01

    Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...

  20. Controlling chaos in the current-driven ion acoustic instability

    International Nuclear Information System (INIS)

    Fukuyama, T.; Taniguchi, K.; Kawai, Y.

    2002-01-01

    Control of intermittent chaos caused by the current-driven ion acoustic instability is attempted and the controlling mechanism is investigated. When a small negative dc voltage is applied to the chaotic system as a perturbation, the system changes from a chaotic state to a periodic state while maintaining the instability, indicating that the chaotic state caused by the ion acoustic instability is well controlled by applying a small negative dc voltage. A hysteresis structure is observed on the V-I curve of the mesh grid to which the negative dc voltage to control is applied. Furthermore, when a negative dc voltage is applied to the state which shows a laminar structure existing under same experimental conditions, the system becomes chaotic via a bifurcation. Driven-chaos is excited when a negative dc voltage is applied to the laminar state. Applying a small negative dc voltage leads to controlling intermittent chaos while exciting driven-chaos

  1. The transition to chaos conservative classical systems and quantum manifestations

    CERN Document Server

    Reichl, Linda E

    2004-01-01

    This book provides a thorough and comprehensive discussion of classical and quantum chaos theory for bounded systems and for scattering processes Specific discussions include • Noether’s theorem, integrability, KAM theory, and a definition of chaotic behavior • Area-preserving maps, quantum billiards, semiclassical quantization, chaotic scattering, scaling in classical and quantum dynamics, dynamic localization, dynamic tunneling, effects of chaos in periodically driven systems and stochastic systems • Random matrix theory and supersymmetry The book is divided into several parts Chapters 2 through 4 deal with the dynamics of nonlinear conservative classical systems Chapter 5 and several appendices give a thorough grounding in random matrix theory and supersymmetry techniques Chapters 6 and 7 discuss the manifestations of chaos in bounded quantum systems and open quantum systems respectively Chapter 8 focuses on the semiclassical description of quantum systems with underlying classical chaos, and Chapt...

  2. Colloquium: Random matrices and chaos in nuclear spectra

    International Nuclear Information System (INIS)

    Papenbrock, T.; Weidenmueller, H. A.

    2007-01-01

    Chaos occurs in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean-field theory) plus a residual interaction. The question is answered using a statistical approach (the two-body random ensemble): The matrix elements of the residual interaction are taken to be random variables. Chaos is shown to be a generic feature of the ensemble and some of its properties are displayed, emphasizing those which differ from standard random-matrix theory. In particular, the existence of correlations among spectra carrying different quantum numbers is demonstrated. These are subject to experimental verification

  3. Discrete chaos with applications in science and engineering

    CERN Document Server

    Elaydi, Saber N

    2007-01-01

    PREFACE FOREWORD The Stability of One-Dimensional Maps Introduction Maps vs. Difference Equations Maps vs. Differential Equations Linear Maps/Difference Equations Fixed (Equilibrium) Points Graphical Iteration and Stability Criteria for Stability Periodic Points and Their Stability The Period-Doubling Route to Chaos Applications Attraction and Bifurcation Introduction Basin of Attraction of Fixed Points Basin of Attraction of Periodic Orbits Singer's Theorem Bifurcation Sharkovsky's Theorem The Lorenz Map Period-Doubling in the Real World Poincaré Section/Map Appendix Chaos in One Dimension Introduction Density of the Set of Periodic Points Transitivity Sensitive Dependence Definition of Chaos Cantor Sets Symbolic Dynamics Conjugacy Other Notions of Chaos Rössler's Attractor Saturn's Rings Stability of Two-Dimensional Maps Linear Maps vs. Linear Systems Computing An Fundamental Set of Solutions Second-Order Difference Equations Phase Space ...

  4. Random number generation based on digital differential chaos

    KAUST Repository

    Zidan, Mohammed A.; Radwan, Ahmed G.; Salama, Khaled N.

    2012-01-01

    In this paper, we present a fully digital differential chaos based random number generator. The output of the digital circuit is proved to be chaotic by calculating the output time series maximum Lyapunov exponent. We introduce a new post processing

  5. Extension of spatiotemporal chaos in glow discharge-semiconductor systems.

    Science.gov (United States)

    Akhmet, Marat; Rafatov, Ismail; Fen, Mehmet Onur

    2014-12-01

    Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528-4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).].

  6. Exploring chaos a guide to the new science of disorder

    CERN Document Server

    1994-01-01

    Chaos Theory is giving scientists fresh insights into all sorts of unruly phenomena--from dripping faucets to swinging pendulums, from the vagaries of the weather to the movements of the planets, from heart rhythms to gold futures.

  7. Extension of spatiotemporal chaos in glow discharge-semiconductor systems

    International Nuclear Information System (INIS)

    Akhmet, Marat; Fen, Mehmet Onur; Rafatov, Ismail

    2014-01-01

    Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528–4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).

  8. Hardware Realization of Chaos Based Symmetric Image Encryption

    KAUST Repository

    Barakat, Mohamed L.

    2012-01-01

    This thesis presents a novel work on hardware realization of symmetric image encryption utilizing chaos based continuous systems as pseudo random number generators. Digital implementation of chaotic systems results in serious degradations

  9. Nonlinear effects on Turing patterns: Time oscillations and chaos

    KAUST Repository

    Aragó n, J. L.; Barrio, R. A.; Woolley, T. E.; Baker, R. E.; Maini, P. K.

    2012-01-01

    consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos

  10. Biological conditions for oscillations and chaos generated by multispecies competition

    NARCIS (Netherlands)

    Huisman, J; Weissing, FJ

    2001-01-01

    We investigate biological mechanisms that generate oscillations and chaos in multispecies competition models. For this purpose, we use a competition model concerned with competition for abiotic essential resources. Because phytoplankton and plants consume quite a number of abiotic essential

  11. Hardware Realization of Chaos-based Symmetric Video Encryption

    KAUST Repository

    Ibrahim, Mohamad A.

    2013-01-01

    This thesis reports original work on hardware realization of symmetric video encryption using chaos-based continuous systems as pseudo-random number generators. The thesis also presents some of the serious degradations caused by digitally

  12. Wave chaos in acoustics and elasticity

    International Nuclear Information System (INIS)

    Tanner, Gregor; Soendergaard, Niels

    2007-01-01

    Interpreting wave phenomena in terms of an underlying ray dynamics adds a new dimension to the analysis of linear wave equations. Forming explicit connections between spectra and wavefunctions on the one hand and the properties of a related ray dynamics on the other hand is a comparatively new research area, especially in elasticity and acoustics. The theory has indeed been developed primarily in a quantum context; it is increasingly becoming clear, however, that important applications lie in the field of mechanical vibrations and acoustics. We provide an overview over basic concepts in this emerging field of wave chaos. This ranges from ray approximations of the Green function to periodic orbit trace formulae and random matrix theory and summarizes the state of the art in applying these ideas in acoustics-both experimentally and from a theoretical/numerical point of view. (topical review)

  13. Computational chaos in massively parallel neural networks

    Science.gov (United States)

    Barhen, Jacob; Gulati, Sandeep

    1989-01-01

    A fundamental issue which directly impacts the scalability of current theoretical neural network models to massively parallel embodiments, in both software as well as hardware, is the inherent and unavoidable concurrent asynchronicity of emerging fine-grained computational ensembles and the possible emergence of chaotic manifestations. Previous analyses attributed dynamical instability to the topology of the interconnection matrix, to parasitic components or to propagation delays. However, researchers have observed the existence of emergent computational chaos in a concurrently asynchronous framework, independent of the network topology. Researcher present a methodology enabling the effective asynchronous operation of large-scale neural networks. Necessary and sufficient conditions guaranteeing concurrent asynchronous convergence are established in terms of contracting operators. Lyapunov exponents are computed formally to characterize the underlying nonlinear dynamics. Simulation results are presented to illustrate network convergence to the correct results, even in the presence of large delays.

  14. Mechanics from Newton's laws to deterministic chaos

    CERN Document Server

    Scheck, Florian

    2018-01-01

    This book covers all topics in mechanics from elementary Newtonian mechanics, the principles of canonical mechanics and rigid body mechanics to relativistic mechanics and nonlinear dynamics. It was among the first textbooks to include dynamical systems and deterministic chaos in due detail. As compared to the previous editions the present 6th edition is updated and revised with more explanations, additional examples and problems with solutions, together with new sections on applications in science.   Symmetries and invariance principles, the basic geometric aspects of mechanics as well as elements of continuum mechanics also play an important role. The book will enable the reader to develop general principles from which equations of motion follow, to understand the importance of canonical mechanics and of symmetries as a basis for quantum mechanics, and to get practice in using general theoretical concepts and tools that are essential for all branches of physics.   The book contains more than 150 problems ...

  15. Implementation of LT codes based on chaos

    International Nuclear Information System (INIS)

    Zhou Qian; Li Liang; Chen Zengqiang; Zhao Jiaxiang

    2008-01-01

    Fountain codes provide an efficient way to transfer information over erasure channels like the Internet. LT codes are the first codes fully realizing the digital fountain concept. They are asymptotically optimal rateless erasure codes with highly efficient encoding and decoding algorithms. In theory, for each encoding symbol of LT codes, its degree is randomly chosen according to a predetermined degree distribution, and its neighbours used to generate that encoding symbol are chosen uniformly at random. Practical implementation of LT codes usually realizes the randomness through pseudo-randomness number generator like linear congruential method. This paper applies the pseudo-randomness of chaotic sequence in the implementation of LT codes. Two Kent chaotic maps are used to determine the degree and neighbour(s) of each encoding symbol. It is shown that the implemented LT codes based on chaos perform better than the LT codes implemented by the traditional pseudo-randomness number generator. (general)

  16. Study of chaos in chaotic satellite systems

    Science.gov (United States)

    Khan, Ayub; Kumar, Sanjay

    2018-01-01

    In this paper, we study the qualitative behaviour of satellite systems using bifurcation diagrams, Poincaré section, Lyapunov exponents, dissipation, equilibrium points, Kaplan-Yorke dimension etc. Bifurcation diagrams with respect to the known parameters of satellite systems are analysed. Poincaré sections with different sowing axes of the satellite are drawn. Eigenvalues of Jacobian matrices for the satellite system at different equilibrium points are calculated to justify the unstable regions. Lyapunov exponents are estimated. From these studies, chaos in satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the considered system.

  17. On Nonextensive Statistics, Chaos and Fractal Strings

    CERN Document Server

    Castro, C

    2004-01-01

    Motivated by the growing evidence of universality and chaos in QFT and string theory, we study the Tsallis non-extensive statistics ( with a non-additive $ q$-entropy ) of an ensemble of fractal strings and branes of different dimensionalities. Non-equilibrium systems with complex dynamics in stationary states may exhibit large fluctuations of intensive quantities which are described in terms of generalized statistics. Tsallis statistics is a particular representative of such class. The non-extensive entropy and probability distribution of a canonical ensemble of fractal strings and branes is studied in terms of their dimensional spectrum which leads to a natural upper cutoff in energy and establishes a direct correlation among dimensions, energy and temperature. The absolute zero temperature ( Kelvin ) corresponds to zero dimensions (energy ) and an infinite temperature corresponds to infinite dimensions. In the concluding remarks some applications of fractal statistics, quasi-particles, knot theory, quantum...

  18. Generalized multistability and chaos in quantum optics

    Energy Technology Data Exchange (ETDEWEB)

    Arecchi, F T

    1984-12-18

    Three experimental situations for CO2 lasers (a laser with modulated losses, a ring laser with competition between forward and backward waves, and a laser with injected signal) are analysed as examples of the onset of chaos in systems with a homogeneous gain line and with a particular timescale imposed by the values of the relaxation constants. The coexistence of several basins of attraction (generalized multistability) and their coupling by external noise is stressed. This coupling induces a low-frequency branch in the power spectrum. Comparison is made between the spectra of noise-induced jumps over independent attractors and the spectrum of deterministic diffusion within subregions of the same attractor. At the borderline between the two classes of phenomena a scaling law holds, relating the control parameter and the external noise in their effect on the mean escape time from a given stability region. 10 references.

  19. Chaos synchronization based on intermittent state observer

    Institute of Scientific and Technical Information of China (English)

    Li Guo-Hui; Zhou Shi-Ping; Xu De-Ming

    2004-01-01

    This paper describes the method of synchronizing slave to the master trajectory using an intermittent state observer by constructing a synchronizer which drives the response system globally tracing the driving system asymptotically. It has been shown from the theory of synchronization error-analysis that a satisfactory result of chaos synchronization is expected under an appropriate intermittent period and state observer. Compared with continuous control method,the proposed intermittent method can target the desired orbit more efficiently. The application of the method is demonstrated on the hyperchaotic Rossler systems. Numerical simulations show that the length of the synchronization interval rs is of crucial importance for our scheme, and the method is robust with respect to parameter mismatch.

  20. Deterministic Chaos in Radon Time Variation

    International Nuclear Information System (INIS)

    Planinic, J.; Vukovic, B.; Radolic, V.; Faj, Z.; Stanic, D.

    2003-01-01

    Radon concentrations were continuously measured outdoors, in living room and basement in 10-minute intervals for a month. The radon time series were analyzed by comparing algorithms to extract phase-space dynamical information. The application of fractal methods enabled to explore the chaotic nature of radon in the atmosphere. The computed fractal dimensions, such as Hurst exponent (H) from the rescaled range analysis, Lyapunov exponent (λ ) and attractor dimension, provided estimates of the degree of chaotic behavior. The obtained low values of the Hurst exponent (0< H<0.5) indicated anti-persistent behavior (non random changes) of the time series, but the positive values of the λ pointed out the grate sensitivity on initial conditions and appearing deterministic chaos by radon time variations. The calculated fractal dimensions of attractors indicated more influencing (meteorological) parameters on radon in the atmosphere. (author)